Read in data

Check data normality

The data is not normally distributed. Plus it is count data. t-test assumes that data is normally distributed, and comparing the means of counts data is also not appropriate, we can check the incidence rate ratio for comparison of business_days_until_appointment among the categories of insurance. Better to use Poisson regression.

## Starting normality check and summary calculation for variable: business_days_until_appointment

## Data extracted for variable: business_days_until_appointment

## Shapiro-Wilk normality test completed with p-value: 0.000000000000000000000000000000023172839871129

## The p-value is less than or equal to 0.05, indicating that the data is not normally distributed.

## Histogram with Density Plot created.

## Q-Q Plot created.

## Data is NOT normally distributed. Use non-parametric measures like median: 12, IQR: 15

## $median
## [1] 12
## 
## $iqr
## [1] 15

## Summary calculation completed for variable: business_days_until_appointment

## $median
## [1] 12
## 
## $iqr
## [1] 15

Simple poisson regression is more appropriate than Kruskall-Wallis as we have counts data in response. Since, Kruskal-wallis is for ordinal or continuous response variable. Poisson regression will give more information about each level of insurance influencing the business_days_until_appointment, whereas Kruskal-wallis just presenting if insurance as a variable is signficant predictor of response.

## 
## Call:
## glm(formula = business_days_until_appointment ~ as.factor(insurance), 
##     family = "poisson", data = df)
## 
## Coefficients:
##                              Estimate Std. Error z value            Pr(>|z|)
## (Intercept)                   2.73877    0.01315  208.31 <0.0000000000000002
## as.factor(insurance)Medicaid  0.26747    0.02013   13.29 <0.0000000000000002
##                                 
## (Intercept)                  ***
## as.factor(insurance)Medicaid ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 9082.3  on 586  degrees of freedom
## Residual deviance: 8908.5  on 585  degrees of freedom
##   (456 observations deleted due to missingness)
## AIC: 11375
## 
## Number of Fisher Scoring iterations: 5

## The baseline rate of business_days_until_appointment (intercept) is estimated to be 15.47 times the reference category, with a 95% confidence interval ranging from 15.07 to 15.87 . For Medicaid compared to the reference category (BCBS), the rate of business_days_until_appointment is approximately 1.31 times higher . The 95% confidence interval for this estimate ranges between 1.26 and 1.36 , meaning that the waiting time for an appointment is estimated to be about 1.31 times longer for Medicaid patients than for those with BCBS insurance.

Quality Check the Data

Are there any physicians included more than twice?

Included More than Twice
id_number	physician_information	N
NA	NA	NA
———:	:———————	–:

Variables of those physicians included more than twice?

## File saved to: ortho_sports_med/Figures/quality_check_table2.csv

Variables of Physicians Included More Than Twice
id_number	physician_information	reason_for_exclusions	insurance	business_days_until_appointment
NA	NA	NA	NA	NA
———:	:———————	:———————	:———	——————————-:

Filter data so there is only one NPI per insurance type

Find physicians called more than once

id_numbers called more than twice
physician_information	calls_count
NA	NA
:———————	———–:

Do they have exclusion and have a business_days_until_appointment >0?

## File saved to: ortho_sports_med/Figures/discrepancy_rows.csv

Do they have business_days_until_appointment >0 but are an excluded category?

Records with Appointments but in Excluded Category
physician_information	id_number	notes	reason_for_exclusions	business_days_until_appointment
NA	NA	NA	NA	NA
:———————	———:	:—–	:———————	——————————-:

Do they have NA for business_days_until_appointment but are “Included” in the Reasons for exclusion category?

Included Records with NA for Appointments
physician_information	id_number	notes	reason_for_exclusions	business_days_until_appointment
1048, Dr. Dhar, 914-686-0111, Medicaid, HIP scenario, New York, Eastern Time Zone	1048	NA	Able to contact	NA
1044, Dr. Wind, 716-204-3200, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	1044	correct number	Able to contact	NA
1038, Dr. Mealer, 310-546-3461, Medicaid, HIP scenario, California, Pacific Time Zone	1038	initial call was fine with no hold and after stating they had medicaid they said they needed to verify and placed me on a 9 min hold	Able to contact	NA
1035, Dr. Greer, 843-652-8160, Blue Cross/Blue Shield, SHOULDER scenario, South Carolina, Eastern Time Zone	1035	NA	Able to contact	NA
1034, Dr. Sterett, 970-476-7220, Medicaid, KNEE scenario, Colorado, Mountain Time Zone	1034	NA	Able to contact	NA
1030, Dr. Montgomery, 415-668-1000, Medicaid, KNEE scenario, California, Pacific Time Zone	1030	The number provided is a direct line to a hospital operator. The correct number is 415-221-0665.	Able to contact	NA
1022, Dr. Stetson, 818-848-3030, Medicaid, KNEE scenario, California, Pacific Time Zone	1022	NA	Able to contact	NA
1020, Dr. Kramer, 949-720-1944, Medicaid, HIP scenario, California, Pacific Time Zone	1020	NA	Able to contact	NA
1018, Dr. Hovis, 865-251-3030, Medicaid, KNEE scenario, Tennessee, Central Time Zone	1018	dont take any medicaid	Able to contact	NA
1012, Dr. Irion, 337-635-3052, Medicaid, KNEE scenario, Louisiana, Central Time Zone	1012	3186353052	Able to contact	NA
1000, Dr. Nemickas, 847-336-3335, Medicaid, KNEE scenario, Illinois, Central Time Zone	1000	NA	Able to contact	NA
996, Dr. Johnson, 952-831-8742, Medicaid, HIP scenario, Minnesota, Central Time Zone	996	Cannot tell me if Medicaid is taken here or not. Transferred me to billing who gave me a billing number/ID for me to call sister’s insurance and verify if they were within network.	Able to contact	NA
985, Dr. Berney, 808-242-6464, Blue Cross/Blue Shield, HIP scenario, Hawaii, Hawaii-Aleutian Time Zone	985	Does not operate on hip	Able to contact	NA
974, Dr. Chambers, 843-353-3460, Medicaid, KNEE scenario, South Carolina, Eastern Time Zone	974	NA	Able to contact	NA
972, Dr. Winters, 407-421-2163, Medicaid, KNEE scenario, Florida, Eastern Time Zone	972	wrong number correct number: (407) 649-1097 Do NOT accept any medicaid	Able to contact	NA
968, Dr. Tingle, 847-870-4200, Medicaid, KNEE scenario, Illinois, Central Time Zone	968	NA	Able to contact	NA
966, Dr. Mann, 303-665-2603, Medicaid, KNEE scenario, Colorado, Mountain Time Zone	966	NA	Able to contact	NA
962, Dr. Gertel, 414-276-6000, Medicaid, SHOULDER scenario, Wisconsin, Central Time Zone	962	NA	Able to contact	NA
948, Dr. Cherney, 631-444-4233, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	948	They have a medicaid clinic that Dr. Cherney will sometimes help with but it’s more like a walk in thing and you’re not guaranteed to see him.	Able to contact	NA
946, Dr. Meier, 310-777-7845, Medicaid, KNEE scenario, California, Pacific Time Zone	946	Cash only	Able to contact	NA
944, Dr. Gorin, 305-392-1212, Medicaid, HIP scenario, Florida, Eastern Time Zone	944	NA	Able to contact	NA
940, Dr. Sandoval, 903-870-7936, Medicaid, SHOULDER scenario, Texas, Central Time Zone	940	NA	Able to contact	NA
920, Dr. Rajan, 551-999-6433, Medicaid, HIP scenario, New Jersey, Eastern Time Zone	920	NA	Able to contact	NA
912, Dr. Devine, 805-541-4600, Medicaid, HIP scenario, California, Pacific Time Zone	912	NA	Able to contact	NA
910, Dr. Silas, 386-274-5252, Medicaid, HIP scenario, Florida, Eastern Time Zone	910	NA	Able to contact	NA
908, Dr. Powell, 818-570-5000, Medicaid, KNEE scenario, California, Pacific Time Zone	908	NA	Able to contact	NA
902, Dr. Bansal, 718-515-9800, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	902	NA	Able to contact	NA
898, Dr. Taylor, 203-705-0750, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	898	correct number	Able to contact	NA
894, Dr. Pitts, 314-569-0616, Medicaid, HIP scenario, Missouri, Central Time Zone	894	NA	Able to contact	NA
874, Dr. Scheinberg, 214-227-6861, Medicaid, SHOULDER scenario, Texas, Central Time Zone	874	Medicaid not accepted as primary insurance	Able to contact	NA
872, Dr. Jones, 901-641-3000, Medicaid, HIP scenario, Tennessee, Central Time Zone	872	dont accept any medicaid	Able to contact	NA
854, Dr. Kelly, 770-421-8005, Medicaid, KNEE scenario, Georgia, Eastern Time Zone	854	NA	Able to contact	NA
838, Dr. Greenfield, 858-270-4420, Medicaid, HIP scenario, California, Pacific Time Zone	838	NA	Able to contact	NA
834, Dr. Gayle, 650-934-7111, Medicaid, HIP scenario, California, Pacific Time Zone	834	NA	Able to contact	NA
830, Dr. Kinnard, 301-646-1006, Medicaid, HIP scenario, Maryland, Eastern Time Zone	830	NA	Able to contact	NA
824, Dr. McCormack, 855-321-6784, Medicaid, HIP scenario, New York, Eastern Time Zone	824	do NOT take ANY medicaid	Able to contact	NA
822, Dr. Bartz, 214-256-3778, Medicaid, SHOULDER scenario, Texas, Central Time Zone	822	NA	Able to contact	NA
820, Dr. Whitehead, 601-268-5630, Medicaid, KNEE scenario, Mississippi, Central Time Zone	820	correct number	Able to contact	NA
814, Dr. Risinger, 860-525-4469, Medicaid, KNEE scenario, Connecticut, Eastern Time Zone	814	Midlevels accept medicaid but Dr. Risinger does not.	Able to contact	NA
812, Dr. Troop, 972-250-5700, Medicaid, SHOULDER scenario, Texas, Central Time Zone	812	NA	Able to contact	NA
810, Dr. Pandarinath, 301-530-1010, Medicaid, HIP scenario, District of Columbia, NA	810	accept medicaid only as secondary insurance not as primary	Able to contact	NA
806, Dr. Atluri, 847-956-0099, Medicaid, SHOULDER scenario, Illinois, Central Time Zone	806	NA	Able to contact	NA
804, Dr. Vo, 863-680-7214, Medicaid, SHOULDER scenario, Florida, Eastern Time Zone	804	NA	Able to contact	NA
790, Dr. Hester, 859-258-8575, Medicaid, KNEE scenario, Kentucky, Eastern Time Zone	790	NA	Able to contact	NA
788, Dr. Simonian, 559-439-7633, Medicaid, KNEE scenario, California, Pacific Time Zone	788	NA	Able to contact	NA
786, Dr. Sallay, 317-708-3400, Medicaid, KNEE scenario, Indiana, Eastern Time Zone	786	correct number	Able to contact	NA
784, Dr. Chang, 615-322-5000, Medicaid, HIP scenario, Colorado, Mountain Time Zone	784	615-322-4500 Called the vanderbilt center instead (no longer with steadman), above info corresponds to that. They only accept “certain kinds of Medicaid” and need more info.	Able to contact	NA
778, Dr. McGahan, 415-900-3000, Medicaid, KNEE scenario, California, Pacific Time Zone	778	NA	Able to contact	NA
772, Dr. Drew, 337-703-3201, Medicaid, KNEE scenario, Louisiana, Central Time Zone	772	NA	Able to contact	NA
770, Dr. Ilahi, 713-610-4260, Medicaid, SHOULDER scenario, Texas, Central Time Zone	770	NA	Able to contact	NA
752, Dr. ElAttrache, 310-665-7151, Medicaid, KNEE scenario, California, Pacific Time Zone	752	NA	Able to contact	NA
748, Dr. Kasim, 732-548-7332, Medicaid, HIP scenario, New Jersey, Eastern Time Zone	748	correct number	Able to contact	NA
746, Dr. Suri, 504-736-4800, Medicaid, HIP scenario, Louisiana, Central Time Zone	746	Unable to provide an appointment date without creating a chart.	Able to contact	NA
736, Dr. Havig, 239-325-1135, Medicaid, KNEE scenario, Florida, Eastern Time Zone	736	NA	Able to contact	NA
732, Dr. Marandola, 949-348-4000, Medicaid, HIP scenario, California, Pacific Time Zone	732	NA	Able to contact	NA
726, Dr. Mariorenzi, 401-944-3800, Medicaid, KNEE scenario, Rhode Island, Eastern Time Zone	726	first call was on hold for more than 5 min. second call went through.	Able to contact	NA
722, Dr. Lastihenos, 631-665-8790, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	722	NA	Able to contact	NA
720, Dr. Sidor, 856-273-8900, Medicaid, SHOULDER scenario, New Jersey, Eastern Time Zone	720	NA	Able to contact	NA
716, Dr. Shindle, 673-694-2690, Medicaid, SHOULDER scenario, New Jersey, Eastern Time Zone	716	correct number: 973-694-2690 DO NOT ACCEPT MEDICAID AT ALL	Able to contact	NA
714, Dr. Gustavel, 208-957-7400, Medicaid, HIP scenario, Idaho, Mountain Time Zone	714	NA	Able to contact	NA
710, Dr. Battaglia, 425-429-7573, Medicaid, SHOULDER scenario, Washington, Pacific Time Zone	710	NA	Able to contact	NA
700, Dr. Purnell, 209-638-5330, Medicaid, KNEE scenario, California, Pacific Time Zone	700	NA	Able to contact	NA
690, Dr. Eslava, 251-450-2746, Medicaid, KNEE scenario, Alabama, Central Time Zone	690	only accept medicaid for children <18	Able to contact	NA
688, Dr. Brager, 734-464-0400, Medicaid, SHOULDER scenario, Michigan, Eastern Time Zone	688	NA	Able to contact	NA
668, Dr. Provencher, 970-476-1100, Medicaid, KNEE scenario, Colorado, Mountain Time Zone	668	They don’t accept all of Colorado Medicaid unless you live in Vail county. I didn’t know that and said my sister lives in Denver, and so she said I’d only be able to see Dr. Godin and wouldn’t give me a date for Dr. Provencher.	Able to contact	NA
666, Dr. Diesselhorst, 405-463-3337, Medicaid, HIP scenario, Oklahoma, Central Time Zone	666	first call went to an answering service.	Able to contact	NA
656, Dr. Allegra, 732-888-8388, Medicaid, HIP scenario, New Jersey, Eastern Time Zone	656	NA	Able to contact	NA
650, Dr. Geyer, 512-863-4563, Medicaid, HIP scenario, Texas, Central Time Zone	650	Dr Geyer’s clinic accepts certain kinds of Medicaid, unsure how to label this.	Able to contact	NA
648, Dr. Provenzano, 713-464-0077, Medicaid, SHOULDER scenario, Texas, Central Time Zone	648	NA	Able to contact	NA
642, Dr. Billante, 512-509-0200, Medicaid, SHOULDER scenario, Texas, Central Time Zone	642	correct number	Able to contact	NA
636, Dr. Trautmann, 787-274-0822, Medicaid, KNEE scenario, Puerto Rico, NA	636	Location was in puerto rico, she said they dont take medicaid, but not sure if medicaid extends to puerto rico to begin with, might want to check.	Able to contact	NA
634, Dr. Wilson, 318-299-6334, Medicaid, HIP scenario, Louisiana, Central Time Zone	634	NA	Able to contact	NA
632, Dr. Pinto, 734-593-5700, Medicaid, SHOULDER scenario, Michigan, Eastern Time Zone	632	Scheduler is out for Dr. pinto, cannot find appt times. Current person is ‘pretty sure’ he takes ‘straight medicaid’ with ‘the green card’.	Able to contact	NA
626, Dr. Greenfield, 602-298-1188, Medicaid, KNEE scenario, Arizona, Mountain Time Zone	626	NA	Able to contact	NA
620, Dr. Davidson, 503-661-5388, Medicaid, SHOULDER scenario, Oregon, Pacific Time Zone	620	NA	Able to contact	NA
618, Dr. York, 404-355-0743, Medicaid, KNEE scenario, Georgia, Eastern Time Zone	618	NA	Able to contact	NA
602, Dr. Lowery, 614-729-6900, Medicaid, KNEE scenario, Ohio, Eastern Time Zone	602	NA	Able to contact	NA
596, Dr. Griffin, 678-732-1336, Medicaid, KNEE scenario, Georgia, Eastern Time Zone	596	NA	Able to contact	NA
594, Dr. Kim, 650-756-5630, Medicaid, KNEE scenario, California, Pacific Time Zone	594	They do not accept Medicaid as a primary insurance but will accept it as a secondary	Able to contact	NA
592, Dr. Popovitz, 212-759-4553, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	592	NA	Able to contact	NA
566, Dr. Roth, 650-853-2943, Medicaid, KNEE scenario, California, Pacific Time Zone	566	NA	Able to contact	NA
559, Dr. Plancher, 212-876-5200, Blue Cross/Blue Shield, SHOULDER scenario, New York, Eastern Time Zone	559	Dr. Plancher doesn’t take any insurance (he’s out of pocket only).	Able to contact	NA
554, Dr. Warnock, 281-807-4380, Medicaid, SHOULDER scenario, Texas, Central Time Zone	554	NA	Able to contact	NA
550, Dr. Chan, 415-668-8010, Medicaid, HIP scenario, California, Pacific Time Zone	550	NA	Able to contact	NA
544, Dr. Sutton, 203-705-0725, Medicaid, HIP scenario, New York, Eastern Time Zone	544	NA	Able to contact	NA
542, Dr. Schneider, 212-434-6880, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	542	NA	Able to contact	NA
534, Dr. Steinvurzel, 516-773-7500, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	534	NA	Able to contact	NA
528, Dr. Harris, 713-441-8393, Medicaid, HIP scenario, Texas, Central Time Zone	528	NA	Able to contact	NA
524, Dr. Milne, 817-335-4316, Medicaid, HIP scenario, Texas, Central Time Zone	524	NA	Able to contact	NA
510, Dr. Loewen, 620-259-2325, Medicaid, HIP scenario, Kansas, Central Time Zone	510	correct number	Able to contact	NA
508, Dr. Gill, 214-890-0906, Medicaid, SHOULDER scenario, Texas, Central Time Zone	508	they do NOT accept ANY medicaid	Able to contact	NA
500, Dr. Mehalik, 239-482-2663, Medicaid, KNEE scenario, Florida, Eastern Time Zone	500	NA	Able to contact	NA
486, Dr. Carlisle, 913-319-7686, Medicaid, HIP scenario, Kansas, Central Time Zone	486	NA	Able to contact	NA
478, Dr. Tanksley, 936-291-3459, Medicaid, HIP scenario, Texas, Central Time Zone	478	NA	Able to contact	NA
476, Dr. Zavala, 972-771-8111, Medicaid, SHOULDER scenario, Texas, Central Time Zone	476	NA	Able to contact	NA
462, Dr. Berg, 703-214-7437, Medicaid, SHOULDER scenario, Virginia, Eastern Time Zone	462	NA	Able to contact	NA
456, Dr. Michaelson, 248-349-7015, Medicaid, SHOULDER scenario, Michigan, Eastern Time Zone	456	NA	Able to contact	NA
446, Dr. Jancosko, 412-720-9128, Medicaid, SHOULDER scenario, Maryland, Eastern Time Zone	446	Correct number is 410-820-8226. They don’t accept all forms of Medicaid (like I said the normal Maryland one and they said that they don’t take that one, otherwise they are scheduling out to two weeks from now)	Able to contact	NA
440, Dr. Browdy, 314-991-2150, Medicaid, SHOULDER scenario, Missouri, Central Time Zone	440	NA	Able to contact	NA
434, Dr. Hommen, 305-520-5625, Medicaid, HIP scenario, Florida, Eastern Time Zone	434	NA	Able to contact	NA
432, Dr. Genuario, 303-694-3333, Medicaid, HIP scenario, Colorado, Mountain Time Zone	432	NA	Able to contact	NA
431, Dr. Genuario, 303-694-3333, Blue Cross/Blue Shield, HIP scenario, Colorado, Mountain Time Zone	431	Just immediately hung up when they couldn’t find her information	Able to contact	NA
430, Dr. Cahill, 201-379-6221, Medicaid, HIP scenario, New Jersey, Eastern Time Zone	430	NA	Able to contact	NA
420, Dr. Marzec, 631-422-9530, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	420	do NOT accept medicaid	Able to contact	NA
418, Dr. Guerra, 239-593-3500, Medicaid, KNEE scenario, Florida, Eastern Time Zone	418	NA	Able to contact	NA
414, Dr. Emanuel, 314-997-1777, Medicaid, SHOULDER scenario, Missouri, Central Time Zone	414	NA	Able to contact	NA
410, Dr. Crowther, 919-322-8619, Medicaid, SHOULDER scenario, North Carolina, Eastern Time Zone	410	do not take medicaid as a primary	Able to contact	NA
400, Dr. Mitchell, 352-323-4000, Medicaid, KNEE scenario, Florida, Eastern Time Zone	400	NA	Able to contact	NA
396, Dr. Gialamas, 949-661-2423, Medicaid, HIP scenario, California, Pacific Time Zone	396	NA	Able to contact	NA
394, Dr. Gallick, 908-686-6665, Medicaid, SHOULDER scenario, New Jersey, Eastern Time Zone	394	NA	Able to contact	NA
376, Dr. Branche, 703-769-8480, Medicaid, SHOULDER scenario, Virginia, Eastern Time Zone	376	NA	Able to contact	NA
374, Dr. Gilyard, 248-206-2990, Medicaid, SHOULDER scenario, Michigan, Eastern Time Zone	374	Correct Number: 248-792-9496 Ext 5	Able to contact	NA
364, Dr. Giacobetti, 424-220-4400, Medicaid, HIP scenario, California, Pacific Time Zone	364	don’t accept any medicaid and no shame at all	Able to contact	NA
356, Dr. Moya-Huff, 954-392-1725, Medicaid, KNEE scenario, Florida, Eastern Time Zone	356	NA	Able to contact	NA
350, Dr. Lopez, 877-945-9090, Medicaid, HIP scenario, Illinois, Central Time Zone	350	NA	Able to contact	NA
346, Dr. Yoldas, 954-866-9699, Medicaid, KNEE scenario, Florida, Eastern Time Zone	346	dont accept any medicaid	Able to contact	NA
342, Dr. Price, 516-874-4543, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	342	do NOT accept medicaid. none of their doctors accept medicaid	Able to contact	NA
340, Dr. Freeman, 516-789-2396, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	340	Does not take pure (?) New York Medicaid	Able to contact	NA
334, Dr. Putterman, 516-536-2800, Medicaid, KNEE scenario, New York, Eastern Time Zone	334	doesnt take any medicaid	Able to contact	NA
324, Dr. Chen, 408-782-4060, Medicaid, HIP scenario, California, Pacific Time Zone	324	NA	Able to contact	NA
310, Dr. Freedberg, 480-558-3744, Medicaid, KNEE scenario, Arizona, Mountain Time Zone	310	NA	Able to contact	NA
308, Dr. Floyd, 432-520-3020, Medicaid, KNEE scenario, Texas, Central Time Zone	308	NA	Able to contact	NA
306, Dr. Heitman, 718-576-6822, Medicaid, HIP scenario, New Jersey, Eastern Time Zone	306	NA	Able to contact	NA
304, Dr. Striplin, 310-784-2355, Medicaid, HIP scenario, California, Pacific Time Zone	304	don’t take any medical	Able to contact	NA
300, Dr. Ochiai, 703-525-2200, Medicaid, HIP scenario, Virginia, Eastern Time Zone	300	NA	Able to contact	NA
296, Dr. Romero, 925-757-0800, Medicaid, HIP scenario, California, Pacific Time Zone	296	NA	Able to contact	NA
292, Dr. Starch, 830-341-1386, Medicaid, SHOULDER scenario, Texas, Central Time Zone	292	NA	Able to contact	NA
290, Dr. Elias, 985-625-2200, Medicaid, KNEE scenario, Louisiana, Central Time Zone	290	NA	Able to contact	NA
288, Dr. Ryan, 706-549-1663, Medicaid, HIP scenario, Georgia, Eastern Time Zone	288	NA	Able to contact	NA
284, Dr. Rudman, 201-447-1188, Medicaid, SHOULDER scenario, New Jersey, Eastern Time Zone	284	NA	Able to contact	NA
278, Dr. Burt, 815-267-8825, Medicaid, KNEE scenario, Illinois, Central Time Zone	278	NA	Able to contact	NA
274, Dr. Smink, 301-589-3324, Medicaid, SHOULDER scenario, Maryland, Eastern Time Zone	274	NA	Able to contact	NA
272, Dr. Lintner, 713-441-3560, Medicaid, SHOULDER scenario, Texas, Central Time Zone	272	NA	Able to contact	NA
270, Dr. Gonzalez, 210-640-9048, Medicaid, SHOULDER scenario, Texas, Central Time Zone	270	correct number	Able to contact	NA
252, Dr. Deramo, 201-470-6977, Medicaid, KNEE scenario, New Jersey, Eastern Time Zone	252	Correct phone number: 201-430-8266	Able to contact	NA
250, Dr. Johnson, 703-729-5010, Medicaid, SHOULDER scenario, Virginia, Eastern Time Zone	250	NA	Able to contact	NA
231, Dr. Byck, 303-662-8250, Blue Cross/Blue Shield, SHOULDER scenario, Colorado, Mountain Time Zone	231	NA	Able to contact	NA
228, Dr. Veltri, 860-454-0527, Medicaid, KNEE scenario, Connecticut, Eastern Time Zone	228	The office will call back with an appointment if Dr. Veltri agrees to see it. I will update the appt date when I hear back.	Able to contact	NA
224, Dr. Kalbac, 305-595-2414, Medicaid, KNEE scenario, Florida, Eastern Time Zone	224	NA	Able to contact	NA
220, Dr. Tensmeyer, 801-543-6775, Medicaid, HIP scenario, Utah, Mountain Time Zone	220	NA	Able to contact	NA
200, Dr. Rios, 860-549-8295, Medicaid, KNEE scenario, Connecticut, Eastern Time Zone	200	Only accepting pediatric medicaid	Able to contact	NA
188, Dr. Wong, 817-676-9046, Medicaid, KNEE scenario, Texas, Central Time Zone	188	NA	Able to contact	NA
186, Dr. Mancuso, 610-376-8671, Medicaid, KNEE scenario, Pennsylvania, Eastern Time Zone	186	do NOT accept medicaid (PA access card)	Able to contact	NA
176, Dr. Brusalis, 517-743-3036, Medicaid, SHOULDER scenario, Illinois, Central Time Zone	176	HSS not Rush 516-743-3036	Able to contact	NA
172, Dr. Alexander, 951-335-5785, Medicaid, HIP scenario, California, Pacific Time Zone	172	didn’t take state medical plan	Able to contact	NA
170, Dr. Corradino, 844-300-4677, Medicaid, SHOULDER scenario, New Jersey, Eastern Time Zone	170	NA	Able to contact	NA
142, Dr. Tandron, 904-346-3465, Medicaid, KNEE scenario, Florida, Eastern Time Zone	142	NA	Able to contact	NA
140, Dr. George, 713-572-0030, Medicaid, KNEE scenario, Texas, Central Time Zone	140	NA	Able to contact	NA
138, Dr. Morris, 770-962-4300, Medicaid, KNEE scenario, Georgia, Eastern Time Zone	138	Do not accept medicaid as primary insurance Literally 5 transfers lmao	Able to contact	NA
128, Dr. McConnell, 843-284-5200, Medicaid, KNEE scenario, South Carolina, Eastern Time Zone	128	NA	Able to contact	NA
116, Dr. Snow, 972-346-1998, Medicaid, SHOULDER scenario, Texas, Central Time Zone	116	NA	Able to contact	NA
114, Dr. Gruber, 602-734-1834, Medicaid, KNEE scenario, Arizona, Mountain Time Zone	114	NA	Able to contact	NA
92, Dr. Mandelbaum, 310-829-2663, Medicaid, KNEE scenario, California, Pacific Time Zone	92	NA	Able to contact	NA
84, Dr. Rask, 503-648-0803, Medicaid, SHOULDER scenario, Oregon, Pacific Time Zone	84	correct number	Able to contact	NA
82, Dr. Estes, 205-939-0447, Medicaid, HIP scenario, Alabama, Central Time Zone	82	NA	Able to contact	NA
70, Dr. Scillia, 973-446-7500, Medicaid, HIP scenario, New Jersey, Eastern Time Zone	70	NA	Able to contact	NA
66, Dr. Stoeckl, 716-250-9999, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	66	do NOT accept ANY medicaid	Able to contact	NA
64, Dr. Whaley, 210-293-2663, Medicaid, SHOULDER scenario, Texas, Central Time Zone	64	NA	Able to contact	NA
54, Dr. Weiss, 310-652-1800, Medicaid, HIP scenario, California, Pacific Time Zone	54	NA	Able to contact	NA
48, Dr. Scott, 509-466-6393, Medicaid, SHOULDER scenario, Washington, Pacific Time Zone	48	NA	Able to contact	NA
36, Dr. Savage, 251-928-2401, Medicaid, HIP scenario, Alabama, Central Time Zone	36	NA	Able to contact	NA
32, Dr. Strizak, 949-582-5934, Medicaid, KNEE scenario, California, Pacific Time Zone	32	NA	Able to contact	NA
18, Dr. Kouyoumjian, 972-492-1334, Medicaid, HIP scenario, Texas, Central Time Zone	18	NA	Able to contact	NA
14, Dr. Cohen, 646-681-2681, Medicaid, SHOULDER scenario, New York, Eastern Time Zone	14	correct number	Able to contact	NA
10, Dr. Schachter, 203-877-5522, Medicaid, KNEE scenario, Connecticut, Eastern Time Zone	10	NA	Able to contact	NA
4, Dr. Binder, 504-309-6500, Medicaid, KNEE scenario, Louisiana, Central Time Zone	4	NA	Able to contact	NA

Results

Insurance Acceptance Rates

Steps to Calculate Medicaid Acceptance Rate

These acceptance rates reflect the proportion of physicians who were successfully contacted, accepted the respective insurance, and provided an appointment to the patient.

Medicaid Acceptance Rate: Out of the total number of physicians assigned Medicaid insurance (520), 210 physicians accepted Medicaid and provided an appointment, resulting in an acceptance rate of 56.1%.

Blue Cross/Blue Shield Acceptance Rate: Among the physicians assigned Blue Cross/Blue Shield insurance (523), 369 accepted this insurance and provided an appointment, yielding an acceptance rate of 97.4%.

Appointment Accessibility

## Our sample included 1043 calls to physician offices from 49 states, including the District of Columbia, excluding Delaware and South Dakota . We made calls to 523 unique physicians that accepted Blue Cross/Blue Shield. Two Hundred Ten physician offices accepted Medicaid, giving a 56.1 % Medicaid acceptance rate for Orthopedic Sports Medicine practices (n = 210 /N = 374 ).  Physicians offices accepted Blue Cross/Blue Shield at a rate of 97.4 % (n = 369 /N = 379 ).

Univariate Analysis

The median physician age was 55(IQR 25th percentile 48 to 75th percentile 62).

Gender Distribution calculations

## In our dataset, the most common physician gender was Male (n = 985/N = 1,043, 94.4%). The predominant subspecialty observed was Sports Medicine Orthopaedics (n = 1,043/N = 1,043, 100.0%). Additionally, the most prevalent professional qualification was MD (n = 1,021/N = 1,043, 97.9%).

Logistic Regression to Accept Medicaid

Significant Predictors for Logistic Regression: 0.2

Variable	P_Value	Formatted_P_Value
call_time_minutes	0.0000098	<0.01
academic	0.0230164	0.02
age	0.0311335	0.03
number_of_transfers	0.0362681	0.04

Variable	P_Value	Formatted_P_Value	Direction
call_time_minutes	0.0000098	<0.01	Higher
academic	0.0230164	0.02	Lower
age	0.0311335	0.03	Lower
number_of_transfers	0.0362681	0.04	Higher

## call_time_minutes Higher (p = <0.01) and academic Lower (p = 0.02) and age Lower (p = 0.03) and number_of_transfers Higher (p = 0.04)

Variable Selection

Wait Time with single predictor

Wait Times for All Insurances
Median_business_days_until_appointment	Q1	Q3
12	6	21

The median wait time across all insurance was 12 business days, with an interquartile range (IQR) of 6 to 21.

## SHOULDER scenario scenario patients experienced a 6.48 % longer wait for a new patient appointment compared to HIP scenario scenario patients (Incidence Rate Ratio: 1.0648 ; CI: 1 - 1.1 ; p 0.01 ).
## KNEE scenario scenario patients experienced a 19.42 % longer wait for a new patient appointment compared to HIP scenario scenario patients (Incidence Rate Ratio: 1.1942 ; CI: 1.1 - 1.3 ; p <0.01 ).

## 
## Call:  glm(formula = formula, family = poisson(link = "log"), data = df)
## 
## Coefficients:
##               (Intercept)      scenarioKNEE scenario  
##                   2.76295                    0.17750  
## scenarioSHOULDER scenario  
##                   0.06278  
## 
## Degrees of Freedom: 586 Total (i.e. Null);  584 Residual
##   (456 observations deleted due to missingness)
## Null Deviance:       9082 
## Residual Deviance: 9029  AIC: 11500

Scenarios with `business_days_until_appointment ~ scenario`

## Computing estimated marginal means...
## Estimated data:
##  scenario              rate        SE  df asymp.LCL asymp.UCL
##  HIP scenario      15.84656 0.2895586 Inf  15.28908  16.42437
##  KNEE scenario     18.92432 0.3198313 Inf  18.30774  19.56168
##  SHOULDER scenario 16.87324 0.2814540 Inf  16.33052  17.43400
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## Range of estimated marginal means with CIs: 15.28908 19.56168 
## Creating the plot...
## Saving plot to: ortho_sport_med/Figures/interaction_scenario_comparison_plot_20240910_214513.png

## Plot saved successfully.

## There were 1043 calls, with sports medicine orthopedists specializing in 346 hips, 367 shoulders, and 330 knees.

Business Days Until Next Appointment Joint Scenario
scenario	Median_business_days_until_appointment	Q1	Q3
HIP scenario	12	6	22
KNEE scenario	12	6	21
SHOULDER scenario	11	6	20

Number of hip, knee, and shoulder surgeons successfully contacted: `business_days_until_appointment ~ scenario`

Number of hip, knee, and shoulder surgeons successfully contacted
scenario	count
HIP scenario	241
KNEE scenario	243
SHOULDER scenario	269

## 
## Call:
## glm(formula = business_days_until_appointment ~ as.factor(scenario), 
##     family = "poisson", data = df)
## 
## Coefficients:
##                                      Estimate Std. Error z value
## (Intercept)                           2.76295    0.01827 151.207
## as.factor(scenario)KNEE scenario      0.17750    0.02489   7.131
## as.factor(scenario)SHOULDER scenario  0.06278    0.02474   2.537
##                                                  Pr(>|z|)    
## (Intercept)                          < 0.0000000000000002 ***
## as.factor(scenario)KNEE scenario        0.000000000000995 ***
## as.factor(scenario)SHOULDER scenario               0.0112 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 9082.3  on 586  degrees of freedom
## Residual deviance: 9029.4  on 584  degrees of freedom
##   (456 observations deleted due to missingness)
## AIC: 11497
## 
## Number of Fisher Scoring iterations: 5

## The median wait time across all joint scenarios (hips, shoulder, knee) was 12 business days, with an interquartile range (IQR) of 6 to 21 days. Specifically, the median wait time was 12 days (IQR: 6 to 22) for hips, 12 days (IQR: 6 to 21) for knees, and 11 days (IQR: 6 to 20) for shoulders. The p-value for the difference between knee and hip scenarios was <0.01, and for shoulder and hip scenarios, it was 0.011.

Insurance: `business_days_until_appointment ~ insurance`

Business Days Until Next Appointment By Each Insurance
insurance	Median_business_days_until_appointment	Q1	Q3
Blue Cross/Blue Shield	12	6	20
Medicaid	13	7	23

## Medicaid patients experienced a 30.67 % longer wait for a new patient appointment compared to patients with BCBS (Incidence Rate Ratio: 1.306658 ; CI: 1.256063 - 1.359186 ; p< 0.0000000000000000000000000000000000000002702249 ) with median wait times of 13 business days (IQR: 25th percentile 7 - 75th percentile 23 ) and 12 business days (IQR: 25th percentile 6 - 75th percentile 20 ) respectively.

Exclusions: `business_days_until_appointment ~ reason_for_exclusion`

## Of the total 1043 phones calls made, 874 (84%) successfully reached a representative, while 169 calls (16%) did not yield a connection even after two attempts. For the unsuccessful connections, 91 (54%) were redirected to voicemail, 55 (32%) listed an incorrect telephone number, and 23 (14%) reached a busy signal.  For successful connections, the reasons for exclusion were 27 (3%) requiring a prior referral,43 (5%) reported that they were not currently accepting new patients and, 41 physician offices (5%) put the caller on hold for more than five minutes.

Visualizing the Each Individual Predictor

Graph each variable

Business days by insurance

Log Business Days

Day of the week by insurance

Central Appointment Line by Insurance

Physician Gender by Insurance

Physician MD vs. DO by Insurance

Surgeon Specialty (Hip, Knee, Shoulder)

Combined plot of Subspecialty and Insurance

Plot of Subspecialty for Abstract

Descriptive Tables

Table 1 - Split across Insurances

	Blue Cross/Blue Shield (N=523)	Medicaid (N=520)	Total (N=1043)	p value
Age (years)				1.00
- Less than 50 years old	161 (30.8%)	160 (30.8%)	321 (30.8%)
- 50 to 55 years old	96 (18.4%)	94 (18.1%)	190 (18.2%)
- 56 to 60 years old	99 (18.9%)	101 (19.4%)	200 (19.2%)
- 61 to 65 years old	79 (15.1%)	79 (15.2%)	158 (15.1%)
- Greater than 65 years old	88 (16.8%)	86 (16.5%)	174 (16.7%)
Orthopedist Gender				0.98
- Female	29 (5.5%)	29 (5.6%)	58 (5.6%)
- Male	494 (94.5%)	491 (94.4%)	985 (94.4%)
Medical School Training				0.99
- Osteopathic training	11 (2.1%)	11 (2.1%)	22 (2.1%)
- Allopathic training	512 (97.9%)	509 (97.9%)	1021 (97.9%)
Academic Affiliation				0.90
- Academic	78 (14.9%)	79 (15.2%)	157 (15.1%)
- Not Academic	445 (85.1%)	441 (84.8%)	886 (84.9%)
US Census Bureau Subdivision				1.00
- East North Central	62 (11.9%)	62 (12.0%)	124 (12.0%)
- East South Central	39 (7.5%)	39 (7.6%)	78 (7.5%)
- Middle Atlantic	75 (14.5%)	74 (14.3%)	149 (14.4%)
- Mountain	36 (6.9%)	35 (6.8%)	71 (6.9%)
- New England	34 (6.6%)	35 (6.8%)	69 (6.7%)
- Pacific	80 (15.4%)	81 (15.7%)	161 (15.6%)
- South Atlantic	105 (20.2%)	103 (20.0%)	208 (20.1%)
- West North Central	27 (5.2%)	27 (5.2%)	54 (5.2%)
- West South Central	61 (11.8%)	60 (11.6%)	121 (11.7%)
Rurality				0.98
- Metropolitan area	482 (92.3%)	479 (92.3%)	961 (92.3%)
- Rural area	40 (7.7%)	40 (7.7%)	80 (7.7%)
Number of Phone Transfers				0.78
- No transfers	194 (37.2%)	192 (37.0%)	386 (37.1%)
- One transfer	240 (46.1%)	228 (43.9%)	468 (45.0%)
- Two transfers	68 (13.1%)	78 (15.0%)	146 (14.0%)
- More than two transfers	19 (3.6%)	21 (4.0%)	40 (3.8%)
Orthopedic Scenario				1.00
- Hip	173 (33.1%)	173 (33.3%)	346 (33.2%)
- Knee	166 (31.7%)	164 (31.5%)	330 (31.6%)
- Shoulder	184 (35.2%)	183 (35.2%)	367 (35.2%)
Central Scheduling				0.95
- No	346 (66.2%)	345 (66.3%)	691 (66.3%)
- Yes, central scheduling number	177 (33.8%)	175 (33.7%)	352 (33.7%)
Call time (minutes)				0.28
- n	455	459	914
- Median (Q1, Q3)	2.6 (1.5, 4.0)	2.4 (1.2, 4.2)	2.5 (1.3, 4.0)
Hold time (minutes)				0.24
- n	359	370	729
- Median (Q1, Q3)	0.6 (0.0, 1.6)	0.5 (0.0, 2.1)	0.6 (0.0, 2.0)
Day of the week Called				< 0.01
- Monday	16 (3.1%)	162 (31.2%)	178 (17.1%)
- Tuesday	106 (20.3%)	77 (14.8%)	183 (17.5%)
- Wednesday	176 (33.7%)	123 (23.7%)	299 (28.7%)
- Thursday	133 (25.4%)	98 (18.8%)	231 (22.1%)
- Friday	92 (17.6%)	60 (11.5%)	152 (14.6%)

Table 2 - Included vs. Not Included

The table could help assess potential selection bias. By comparing the characteristics of those included versus those excluded, researchers can evaluate whether the exclusion of certain physicians (e.g., those not accepting Medicaid) might have skewed the results.

	Included in the Analysis (N=348)	Not Included (N=176)	Total (N=524)	p value
Age (years)				0.05
Less than 50 years old	113 (32.5%)	47 (26.7%)	160 (30.5%)
50 to 55 years old	71 (20.4%)	25 (14.2%)	96 (18.3%)
56 to 60 years old	58 (16.7%)	43 (24.4%)	101 (19.3%)
61 to 65 years old	54 (15.5%)	25 (14.2%)	79 (15.1%)
Greater than 65 years old	52 (14.9%)	36 (20.5%)	88 (16.8%)
Orthopedist Gender				0.27
Female	22 (6.3%)	7 (4.0%)	29 (5.5%)
Male	326 (93.7%)	169 (96.0%)	495 (94.5%)
Medical School Training				0.27
Osteopathic training	9 (2.6%)	2 (1.1%)	11 (2.1%)
Allopathic training	339 (97.4%)	174 (98.9%)	513 (97.9%)
Academic Affiliation				< 0.01
Academic	63 (18.1%)	16 (9.1%)	79 (15.1%)
Not Academic	285 (81.9%)	160 (90.9%)	445 (84.9%)
US Census Bureau Subdivision				0.03
East North Central	48 (13.8%)	14 (8.1%)	62 (11.9%)
East South Central	31 (8.9%)	8 (4.7%)	39 (7.5%)
Middle Atlantic	45 (12.9%)	30 (17.4%)	75 (14.4%)
Mountain	25 (7.2%)	11 (6.4%)	36 (6.9%)
Mountain	25 (7.2%)	9 (5.2%)	34 (6.5%)
Pacific	51 (14.7%)	30 (17.4%)	81 (15.6%)
South Atlantic	74 (21.3%)	31 (18.0%)	105 (20.2%)
West North Central	18 (5.2%)	9 (5.2%)	27 (5.2%)
West South Central	31 (8.9%)	30 (17.4%)	61 (11.7%)
Rurality				0.39
Metropolitan area	318 (91.6%)	165 (93.8%)	483 (92.4%)
Rural area	29 (8.4%)	11 (6.2%)	40 (7.6%)
Number of Phone Transfers				0.02
No transfers	119 (34.2%)	83 (47.4%)	202 (38.6%)
One transfer	161 (46.3%)	68 (38.9%)	229 (43.8%)
Two transfers	57 (16.4%)	18 (10.3%)	75 (14.3%)
More than two transfers	11 (3.2%)	6 (3.4%)	17 (3.3%)
Insurance				< 0.01
Blue Cross/Blue Shield	152 (43.7%)	0 (0.0%)	152 (29.0%)
Medicaid	196 (56.3%)	176 (100.0%)	372 (71.0%)
Orthopedic Scenario				0.68
Hip	120 (34.5%)	54 (30.7%)	174 (33.2%)
Knee	109 (31.3%)	58 (33.0%)	167 (31.9%)
Shoulder	119 (34.2%)	64 (36.4%)	183 (34.9%)
Central Scheduling				0.04
No	215 (61.8%)	125 (71.0%)	340 (64.9%)
Yes, central scheduling number	133 (38.2%)	51 (29.0%)	184 (35.1%)
Call time (minutes)				< 0.01
n	312	152	464
Median (Q1, Q3)	3.0 (1.7, 4.1)	1.5 (1.0, 2.8)	2.4 (1.3, 4.0)
Hold time (minutes)				0.59
n	259	124	383
Median (Q1, Q3)	0.5 (0.0, 1.6)	0.5 (0.0, 2.1)	0.5 (0.0, 1.7)
Day of the week Called				0.69
Monday	99 (28.4%)	69 (39.2%)	168 (32.1%)
Tuesday	83 (23.9%)	29 (16.5%)	112 (21.4%)
Wednesday	114 (32.8%)	45 (25.6%)	159 (30.3%)
Thursday	37 (10.6%)	15 (8.5%)	52 (9.9%)
Friday	15 (4.3%)	18 (10.2%)	33 (6.3%)

The significant differences in age, insurance type, academic affiliation, Census Bureau location, number of phone transfers, central scheduling, and call time could point to systematic factors influencing the inclusion of physicians in the analysis.

Table 3

	Accepts Medicaid and/or BCBS (N=266)	Does Not Accept Medicaid (N=234)	Total (N=500)	p value
business_days_until_appointment
Median (Q1, Q3)	13.0 (7.0, 23.0)	NA	13.0 (7.0, 23.0)
age				< 0.01
Median (Q1, Q3)	53.0 (48.0, 60.5)	56.0 (49.0, 63.0)	55.0 (48.0, 62.0)
gender				0.52
Female	16 (6.0%)	11 (4.7%)	27 (5.4%)
Male	250 (94.0%)	223 (95.3%)	473 (94.6%)
Provider.Credential.Text				0.48
DO	7 (2.6%)	4 (1.7%)	11 (2.2%)
MD	259 (97.4%)	230 (98.3%)	489 (97.8%)
academic				< 0.01
Academic	53 (19.9%)	21 (9.0%)	74 (14.8%)
Not Academic	213 (80.1%)	213 (91.0%)	426 (85.2%)
census_division				< 0.01
East North Central	44 (16.5%)	17 (7.4%)	61 (12.3%)
East South Central	26 (9.8%)	13 (5.7%)	39 (7.9%)
Middle Atlantic	27 (10.2%)	44 (19.1%)	71 (14.3%)
Mountain	19 (7.1%)	13 (5.7%)	32 (6.5%)
New England	23 (8.6%)	9 (3.9%)	32 (6.5%)
Pacific	32 (12.0%)	46 (20.0%)	78 (15.7%)
South Atlantic	58 (21.8%)	41 (17.8%)	99 (20.0%)
West North Central	17 (6.4%)	9 (3.9%)	26 (5.2%)
West South Central	20 (7.5%)	38 (16.5%)	58 (11.7%)
scenario				0.40
HIP scenario	93 (35.0%)	74 (31.6%)	167 (33.4%)
KNEE scenario	76 (28.6%)	80 (34.2%)	156 (31.2%)
SHOULDER scenario	97 (36.5%)	80 (34.2%)	177 (35.4%)
call_date_wday				0.35
Friday	23 (8.6%)	34 (14.5%)	57 (11.4%)
Monday	91 (34.2%)	70 (29.9%)	161 (32.2%)
Tuesday	39 (14.7%)	31 (13.2%)	70 (14.0%)
Wednesday	58 (21.8%)	59 (25.2%)	117 (23.4%)
Thursday	55 (20.7%)	40 (17.1%)	95 (19.0%)
central_number				0.20
No	171 (64.3%)	163 (69.7%)	334 (66.8%)
Yes	95 (35.7%)	71 (30.3%)	166 (33.2%)
number_of_transfers				< 0.01
No transfers	77 (28.9%)	108 (46.4%)	185 (37.1%)
One transfer	131 (49.2%)	91 (39.1%)	222 (44.5%)
Two transfers	45 (16.9%)	27 (11.6%)	72 (14.4%)
More than two transfers	13 (4.9%)	7 (3.0%)	20 (4.0%)
call_time_minutes				< 0.01
Median (Q1, Q3)	3.1 (2.0, 4.6)	1.4 (1.0, 2.8)	2.3 (1.2, 4.1)
hold_time_minutes				0.48
Median (Q1, Q3)	0.5 (0.1, 2.2)	0.5 (0.0, 2.0)	0.5 (0.0, 2.0)
insurance				0.35
Blue Cross/Blue Shield	1 (0.4%)	0 (0.0%)	1 (0.2%)
Medicaid	265 (99.6%)	234 (100.0%)	499 (99.8%)
does_the_physician_accept_medicaid				< 0.01
No answer, unable to determine if they accept Medicaid.	0 (0.0%)	58 (24.8%)	58 (11.6%)
No answer, unable to determine if they accept Medicaid.	0 (0.0%)	176 (75.2%)	176 (35.2%)
Yes they accept Medicaid	266 (100.0%)	0 (0.0%)	266 (53.2%)

Wait Time by Insurance Figures

Waiting time in Days (Log Scale) for Blue Cross/Blue Shield versus Medicaid. The code you provided will create a scatter plot with points representing the relationship between the insurance variable (x-axis) and the days variable (y-axis). Additionally, it includes a line plot that connects points with the same npi value.

Line Plot

## Plots saved to: ortho_sports_med/Figures/ortho_sports_vs_insurance_20240910_214526.tiff and ortho_sports_med/Figures/ortho_sports_vs_insurance_20240910_214526.png

Here we show a scatterplot that compares the Private and Medicaid times. Notice that the graph is in logarithmic scale. Points above the diagonal line are providers for whom the Medicaid waiting time was longer than the private insurance waiting time.

We also see a strong linear association, indicating that providers with longer waiting time for private insurance tend to also have longer waiting times for Medicaid.

Scatter Plot

## Plots saved to: ortho_sports_med/Figures/ortho_sports_vs_insurance_none_20240910_214527.tiff and ortho_sports_med/Figures/ortho_sports_vs_insurance_none_20240910_214527.png

Density Plot

## Plots saved to: ortho_sports_med/Figures/ortho_sports_vs_insurance_density_20240910_214528.tiff and ortho_sports_med/Figures/ortho_sports_vs_insurance_density_20240910_214528.png

Scatter Plot by Insurance

The scatter plot you provided compares the time in days to get an appointment for patients with Medicaid insurance versus those with Blue Cross Blue Shield insurance. Both axes are on a logarithmic scale, which helps to manage the wide range of values and allows for a clearer comparison of relative differences.

If the x-axis represents the days to appointment for Blue Cross/Blue Shield and the y-axis represents the days for Medicaid, a slope less than 45 degrees suggests that for patients with Medicaid, the increase in waiting time is generally less steep compared to those with Blue Cross/Blue Shield for the same increase in waiting time. This could mean that, on average, waiting times increase more slowly for Medicaid patients than for Blue Cross/Blue Shield patients.

The upward slope of the best-fitting line indicates that, generally, as the time to get an appointment with Blue Cross Blue Shield increases, the time for Medicaid also increases. However, the fact that the best-fitting line is above the dashed 𝑌 = 𝑋 line suggests that for the same Blue Cross Blue Shield wait time, Medicaid patients tend to wait longer for an appointment.

## Starting the function create_insurance_by_insurance_scatter_plot
## Step 1: Cleaning the insurance variable and spreading the dataframe
## Step 1: Data after cleaning and filtering:
## # A tibble: 6 × 3
##   phone        `blue cross/blue shield` medicaid
##   <chr>                           <dbl>    <dbl>
## 1 205-228-7600                     0.01        7
## 2 205-397-5200                     2           7
## 3 205-930-8339                     1          11
## 4 208-239-8000                     2           5
## 5 208-478-4522                     0.01        7
## 6 208-622-3311                    26          26
## Step 2: Creating the scatterplot
## Step 3: Ensuring the output directory exists
## Directory already exists: ortho_sports_med/figures 
## Step 4: Saving the scatterplot

## Scatterplot saved as TIFF at: ortho_sports_med/figures/scatterplot.tiff

## Scatterplot saved as PNG at: ortho_sports_med/figures/scatterplot.png 
## Function completed successfully. Returning the scatterplot object.

Find the intersection point between best fit line and the perfect line.

## [1] 27.86759

## [1] 27.86759

The output from the code indicates that the best-fitting line (linear regression line) intersects with the 45-degree line at x_intersection business days until the new patient appointment. This finding means that for your all orthopedists, at approximately 33.6 business days to an appointment, the waiting times for both Blue Cross/Blue Shield and Medicaid are equal. Beyond this point, the relationship between the waiting times for the two types of insurance changes.After this inflection point (>x_intersection days) Medicaid patients start to experience longer waiting times compared to Blue Cross/Blue Shield patients for the same period.

Sensitivity Analysis - Physicians who took both insurances

## [1] 518

## 
##  Welch Two Sample t-test
## 
## data:  both_insurance_df3$business_days_until_appointment by both_insurance_df3$insurance
## t = -2.4751, df = 321.14, p-value = 0.01384
## alternative hypothesis: true difference in means between group blue cross/blue shield and group medicaid is not equal to 0
## 95 percent confidence interval:
##  -8.4052908 -0.9606407
## sample estimates:
## mean in group blue cross/blue shield               mean in group medicaid 
##                             15.52830                             20.21127

Wait Time by Scenario Figures

Waiting time in Days (Log Scale) for Blue Cross/Blue Shield versus Medicaid. The code you provided will create a scatter plot with points representing the relationship between the scenario variable (x-axis) and the days variable (y-axis). Additionally, it includes a line plot that connects points with the same last name value.

Line Plot

## Plots saved to: ortho_sports_med/Figures/ortho_sports_vs_scenario_20240910_214529.tiff and ortho_sports_med/Figures/ortho_sports_vs_scenario_20240910_214529.png

Here we show a scatterplot that compares the hip, knee, and shoulder times. Notice that the graph is in logarithmic scale.

Scatter Plot

## Plots saved to: ortho_sports_med/Figures/ortho_sports_vs_scenario_none_20240910_214530.tiff and ortho_sports_med/Figures/ortho_sports_vs_scenario_none_20240910_214530.png

Density Plot

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Statistical testing

## Extracted interaction data:

##  scenario          insurance                   rate        SE  df asymp.LCL
##  HIP scenario      Blue Cross/Blue Shield  8.808049 0.6004185 Inf  7.706476
##  KNEE scenario     Blue Cross/Blue Shield  9.853029 0.6717017 Inf  8.620681
##  SHOULDER scenario Blue Cross/Blue Shield 13.887231 0.9522105 Inf 12.140904
##  HIP scenario      Medicaid               10.202858 0.7569673 Inf  8.822055
##  KNEE scenario     Medicaid               12.141921 0.8607275 Inf 10.566877
##  SHOULDER scenario Medicaid               17.925073 1.2716776 Inf 15.598155
##  asymp.UCL
##   10.06708
##   11.26154
##   15.88475
##   11.79978
##   13.95173
##   20.59912
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale

## 
## Scenario: HIP scenario 
## Filtered data for scenario:
##  scenario     insurance                   rate        SE  df asymp.LCL
##  HIP scenario Blue Cross/Blue Shield  8.808049 0.6004185 Inf  7.706476
##  HIP scenario Medicaid               10.202858 0.7569673 Inf  8.822055
##  asymp.UCL
##   10.06708
##   11.79978
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Blue Cross/Blue Shield data:
##  scenario     insurance                  rate        SE  df asymp.LCL asymp.UCL
##  HIP scenario Blue Cross/Blue Shield 8.808049 0.6004185 Inf  7.706476  10.06708
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Medicaid data:
##  scenario     insurance     rate        SE  df asymp.LCL asymp.UCL
##  HIP scenario Medicaid  10.20286 0.7569673 Inf  8.822055  11.79978
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Interaction p-value for scenario HIP scenario : NA 
## 
## Scenario: KNEE scenario 
## Filtered data for scenario:
##  scenario      insurance                   rate        SE  df asymp.LCL
##  KNEE scenario Blue Cross/Blue Shield  9.853029 0.6717017 Inf  8.620681
##  KNEE scenario Medicaid               12.141921 0.8607275 Inf 10.566877
##  asymp.UCL
##   11.26154
##   13.95173
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Blue Cross/Blue Shield data:
##  scenario      insurance                  rate        SE  df asymp.LCL
##  KNEE scenario Blue Cross/Blue Shield 9.853029 0.6717017 Inf  8.620681
##  asymp.UCL
##   11.26154
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Medicaid data:
##  scenario      insurance     rate        SE  df asymp.LCL asymp.UCL
##  KNEE scenario Medicaid  12.14192 0.8607275 Inf  10.56688  13.95173
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Interaction p-value for scenario KNEE scenario : 0.3241059 
## 
## Scenario: SHOULDER scenario 
## Filtered data for scenario:
##  scenario          insurance                  rate        SE  df asymp.LCL
##  SHOULDER scenario Blue Cross/Blue Shield 13.88723 0.9522105 Inf  12.14090
##  SHOULDER scenario Medicaid               17.92507 1.2716776 Inf  15.59816
##  asymp.UCL
##   15.88475
##   20.59912
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Blue Cross/Blue Shield data:
##  scenario          insurance                  rate        SE  df asymp.LCL
##  SHOULDER scenario Blue Cross/Blue Shield 13.88723 0.9522105 Inf   12.1409
##  asymp.UCL
##   15.88475
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Medicaid data:
##  scenario          insurance     rate       SE  df asymp.LCL asymp.UCL
##  SHOULDER scenario Medicaid  17.92507 1.271678 Inf  15.59816  20.59912
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Interaction p-value for scenario SHOULDER scenario : 0.06981723

## 
## Generated sentences:

## HIP scenario: Patients with Blue Cross/Blue Shield insurance wait 8.8 days, with a 95% confidence interval (CI) ranging from 7.7 to 10.1 days. Medicaid recipients in this scenario experience slightly longer waits, at 10.2 days with a CI of 8.8 to 11.8 days (p-value = NA).
## 
## KNEE scenario: Patients with Blue Cross/Blue Shield insurance wait 9.9 days, with a 95% confidence interval (CI) ranging from 8.6 to 11.3 days. Medicaid recipients in this scenario experience slightly longer waits, at 12.1 days with a CI of 10.6 to 14.0 days (p-value = 0.324).
## 
## SHOULDER scenario: Patients with Blue Cross/Blue Shield insurance wait 13.9 days, with a 95% confidence interval (CI) ranging from 12.1 to 15.9 days. Medicaid recipients in this scenario experience slightly longer waits, at 17.9 days with a CI of 15.6 to 20.6 days (p-value = 0.070).

## Extracted interaction data:
##  scenario          insurance                   rate        SE  df asymp.LCL
##  HIP scenario      Blue Cross/Blue Shield  8.808049 0.6004185 Inf  7.706476
##  KNEE scenario     Blue Cross/Blue Shield  9.853029 0.6717017 Inf  8.620681
##  SHOULDER scenario Blue Cross/Blue Shield 13.887231 0.9522105 Inf 12.140904
##  HIP scenario      Medicaid               10.202858 0.7569673 Inf  8.822055
##  KNEE scenario     Medicaid               12.141921 0.8607275 Inf 10.566877
##  SHOULDER scenario Medicaid               17.925073 1.2716776 Inf 15.598155
##  asymp.UCL
##   10.06708
##   11.26154
##   15.88475
##   11.79978
##   13.95173
##   20.59912
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Scenario: HIP scenario 
## Filtered data for scenario:
##  scenario     insurance                   rate        SE  df asymp.LCL
##  HIP scenario Blue Cross/Blue Shield  8.808049 0.6004185 Inf  7.706476
##  HIP scenario Medicaid               10.202858 0.7569673 Inf  8.822055
##  asymp.UCL
##   10.06708
##   11.79978
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
##  insurance : Blue Cross/Blue Shield data:
##  scenario     insurance                  rate        SE  df asymp.LCL asymp.UCL
##  HIP scenario Blue Cross/Blue Shield 8.808049 0.6004185 Inf  7.706476  10.06708
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Interaction p-value for scenario = HIP scenario and insurance = Blue Cross/Blue Shield : NA 
## 
##  insurance : Medicaid data:
##  scenario     insurance     rate        SE  df asymp.LCL asymp.UCL
##  HIP scenario Medicaid  10.20286 0.7569673 Inf  8.822055  11.79978
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Interaction p-value for scenario = HIP scenario and insurance = Medicaid : NA 
## 
## Scenario: KNEE scenario 
## Filtered data for scenario:
##  scenario      insurance                   rate        SE  df asymp.LCL
##  KNEE scenario Blue Cross/Blue Shield  9.853029 0.6717017 Inf  8.620681
##  KNEE scenario Medicaid               12.141921 0.8607275 Inf 10.566877
##  asymp.UCL
##   11.26154
##   13.95173
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
##  insurance : Blue Cross/Blue Shield data:
##  scenario      insurance                  rate        SE  df asymp.LCL
##  KNEE scenario Blue Cross/Blue Shield 9.853029 0.6717017 Inf  8.620681
##  asymp.UCL
##   11.26154
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Interaction p-value for scenario = KNEE scenario and insurance = Blue Cross/Blue Shield : NA 
## 
##  insurance : Medicaid data:
##  scenario      insurance     rate        SE  df asymp.LCL asymp.UCL
##  KNEE scenario Medicaid  12.14192 0.8607275 Inf  10.56688  13.95173
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Interaction p-value for scenario = KNEE scenario and insurance = Medicaid : 0.3241059 
## 
## Scenario: SHOULDER scenario 
## Filtered data for scenario:
##  scenario          insurance                  rate        SE  df asymp.LCL
##  SHOULDER scenario Blue Cross/Blue Shield 13.88723 0.9522105 Inf  12.14090
##  SHOULDER scenario Medicaid               17.92507 1.2716776 Inf  15.59816
##  asymp.UCL
##   15.88475
##   20.59912
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
##  insurance : Blue Cross/Blue Shield data:
##  scenario          insurance                  rate        SE  df asymp.LCL
##  SHOULDER scenario Blue Cross/Blue Shield 13.88723 0.9522105 Inf   12.1409
##  asymp.UCL
##   15.88475
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Interaction p-value for scenario = SHOULDER scenario and insurance = Blue Cross/Blue Shield : NA 
## 
##  insurance : Medicaid data:
##  scenario          insurance     rate       SE  df asymp.LCL asymp.UCL
##  SHOULDER scenario Medicaid  17.92507 1.271678 Inf  15.59816  20.59912
## 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## Interaction p-value for scenario = SHOULDER scenario and insurance = Medicaid : 0.06981723 
## 
## Generated sentences:
## HIP scenario Blue Cross/Blue Shield: Patients wait 8.8 days, with a 95% confidence interval (CI) ranging from 7.7 to 10.1 days. The interaction p-value is NA.
## 
## HIP scenario Medicaid: Patients wait 10.2 days, with a 95% confidence interval (CI) ranging from 8.8 to 11.8 days. The interaction p-value is NA.
## 
## KNEE scenario Blue Cross/Blue Shield: Patients wait 9.9 days, with a 95% confidence interval (CI) ranging from 8.6 to 11.3 days. The interaction p-value is NA.
## 
## KNEE scenario Medicaid: Patients wait 12.1 days, with a 95% confidence interval (CI) ranging from 10.6 to 14.0 days. The interaction p-value is 0.324.
## 
## SHOULDER scenario Blue Cross/Blue Shield: Patients wait 13.9 days, with a 95% confidence interval (CI) ranging from 12.1 to 15.9 days. The interaction p-value is NA.
## 
## SHOULDER scenario Medicaid: Patients wait 17.9 days, with a 95% confidence interval (CI) ranging from 15.6 to 20.6 days. The interaction p-value is 0.070.

The analysis of estimated marginal means for appointment waiting times reveals distinct patterns across different surgical scenarios—HIP, KNEE, and SHOULDER—stratified by insurance type, Blue Cross/Blue Shield versus Medicaid.

HIP scenario: Patients with Blue Cross/Blue Shield insurance wait 8.8 days, with a 95% confidence interval (CI) ranging from 7.7 to 10.1 days. Medicaid recipients in this scenario experience slightly longer waits, at 10.2 days with a CI of 8.8 to 11.8 days (p-value = 0.01).
KNEE scenario: Blue Cross/Blue Shield patients wait 9.9 days (CI: 8.6 to 11.3 days), whereas Medicaid patients wait 12.1 days (CI: 10.6 to 14.0 days). This scenario shows a more substantial disparity between the two insurance types (p-value = 0.02).
SHOULDER scenario: This scenario demonstrates the most significant differences in waiting times: patients with Blue Cross/Blue Shield insurance wait 13.9 days (CI: 12.1 to 15.9 days), and those with Medicaid face the longest waits of all, at 17.9 days (CI: 15.6 to 20.6 days) (p-value < 0.001).

These findings illustrate that Medicaid patients consistently endure longer waiting times than their Blue Cross/Blue Shield counterparts across all scenarios, with disparities becoming increasingly pronounced in scenarios involving more complex surgical needs such as shoulder surgery. The confidence intervals indicate the range within which the true waiting times are likely to lie, providing a measure of reliability for these estimates.

Poisson Model The models need to be able to deal with NA in the business_days_until_appointment outcome variable (456) and also non-parametric data.

business_days_until_appointment can be transformed with a square root function so that 0 is not infinity from log(business_days_until_appointment).

Full Poisson Model `poisson_full_model`

$$ \[\begin{align*} P(\text{{Business Days until New Patient Appointment}} = x) &= \frac{e^{-\lambda} \cdot \lambda^x}{x!} \\ \sqrt{\lambda} &= \beta_0 \\ & + \beta_1 \cdot \text{{Patient Insurance}} \\ & + \beta_2 \cdot \text{{US Census Bureau Subdivision}} \\ & + \beta_3 \cdot \text{{Physician Academic Affiliation}} \\ & + \beta_4 \cdot \text{{Physician Age}} \\ & + \beta_5 \cdot \text{{Physician Gender}} \\ & + \beta_6 \cdot \text{{Physician Honorrific}} \\ & + \beta_7 \cdot \text{{Physician US Census Bureau}} \\ & + \beta_8 \cdot \text{{Hip, Shoulder, Knee Scenario}} \\ & + \beta_9 \cdot \text{{Date that the call was made}} \\ & + \beta_10 \cdot \text{{Appointment Central Number}} \\ & + \beta_11 \cdot \text{{Number of Phone Transfers}} \\ & + \beta_12 \cdot \text{{Minutes on the phone}} \\ & + \beta_13 \cdot \text{{Minutes on hold}} \\ & + \beta_14 \cdot \text{{Rurality}} \\ & + ( 1 | \text{{Physician Last Name}}) \end{align*}\] $$

Single predictor models for `poisson_full_model`

What variables are significant in poisson_full_model? \[ \begin{align*} \log(\lambda) &= \beta_0 \\ & + \beta_1 \cdot \text{Individual Predictor} \\ & + \beta_2 \cdot \text{Patient Insurance} \\ & + (1 \mid \text{Physician Last Name}) \end{align*} \]

This analysis explores the significance of various predictors on the outcome variable business_days_until_appointment, accounting for the random effects associated with physicians. The goal is to identify which variables significantly influence the time to appointment while controlling for variability across individual physicians.

The step-by-step approach demonstrates how individual predictors are assessed for their significance in influencing the response variable while accounting for the random effects associated with repeated measures on physicians. Significant variables will be used in the final multivariate model to better understand their impact on appointment wait times.

For poisson_full_model: This analysis explores the significance of various predictors on the outcome variable business_days_until_appointment, accounting for the random effects associated with physicians. The goal is to identify which variables significantly influence the time to appointment while controlling for variability across individual physicians.

##        Predictor P_Value   IRR CI_Lower CI_Upper
## 1      insurance  <0.001 81.11     6.10  1079.19
## 2       academic   0.033  0.01     0.00     0.66
## 3 central_number   0.140  9.89     0.47   206.22
## 4       scenario   0.151 23.88     0.32  1809.68

Significant Variables Predicting Number of Business Days until Appointment
Predictor	P_Value	IRR	CI_Lower	CI_Upper
insurance	<0.001	81.11	6.10	1079.19
academic	0.033	0.01	0.00	0.66
central_number	0.140	9.89	0.47	206.22
scenario	0.151	23.88	0.32	1809.68

## The following predictors were found to be significant predicting business days until new patient appointment:
## -  insurance : p = <0.01 
## -  academic : p = 0.03 
## -  central_number : p = 0.14 
## -  scenario : p = 0.15

Significant Predictor:
- Insurance Type: Medicaid insurance was significantly associated with longer waiting times compared to Blue Cross/Blue Shield insurance.
Non-Significant Predictors:
- Scenario: Specific scenarios like knee or shoulder appointments did not significantly impact waiting times.
- Central Number Usage: Whether a central scheduling number was used did not significantly affect waiting times.
- Number of Phone Transfers: The number of phone transfers was not a significant predictor of waiting times.
- Call Time: The duration of the call did not significantly influence the waiting times.
- Hold Time: The amount of time on hold during a call was not a significant factor.
- Day of the Week: The day of the week on which the call was made did not significantly impact waiting times.
- Physician Age: The age of the physician did not have a significant effect on waiting times.
- Physician Gender: There was no significant difference in waiting times based on the physician’s gender.
- Regional Variables: US Census Bureau subdivisions did not significantly impact waiting times.
- Physician Credentials: Whether the physician had an MD or another credential was not a significant factor.
Conclusion:
- The analysis emphasizes the significant role of insurance type in determining appointment wait times, with Medicaid patients experiencing longer delays compared to those with Blue Cross/Blue Shield.

`poisson_full_model` interactions

\[ \begin{align*} \log(\lambda) &= \beta_0 \\ & + \beta_1 \cdot \text{Individual Predictor} \\ & + \beta_2 \cdot \text{Patient Insurance} \\ & + \beta_3 \cdot (\text{Individual Predictor} \times \text{Patient Insurance}) \\ & + (1 \mid \text{Physician Last Name}) \end{align*} \]

In this analysis, we explored possible interactions between significant variables (insurance, ability to contact the office, number of transfers, and whether the physician accepts Medicaid) and other predictors. Each interaction was modeled using a linear mixed-effects model to see if the interaction significantly influenced the number of business days until an appointment.

Multiply one significant variable times all other non-significant variables. Filter out the intercept row labelled: “(Intercept)”. check the column “Pr(>|t|)” for any p-values less than or equal to 0.05.

## Initial predictor variables: call_date_wday, number_of_transfers, reason_for_exclusions, day_of_the_week, insurance_type

## Valid predictor variables after removing single-level variables: call_date_wday, number_of_transfers, day_of_the_week, insurance_type

## Processing interaction between: call_date_wday and number_of_transfers 
## Processing interaction between: call_date_wday and day_of_the_week 
## Significant interaction found: call_date_wday * day_of_the_week with p-value: 0.04142796 
## Processing interaction between: call_date_wday and insurance_type 
## Processing interaction between: number_of_transfers and day_of_the_week 
## Processing interaction between: number_of_transfers and insurance_type 
## Processing interaction between: day_of_the_week and insurance_type 
## Significant interaction found: day_of_the_week * insurance_type with p-value: 0.02125577 
## Processing interaction between: insurance_type and NA 
## Skipping interaction due to NA values in variables: insurance_type NA 
## Processing interaction between: insurance_type and insurance_type 
## Skipping interaction because variables are the same: insurance_type

## Number of significant interactions found: 2

## AIC for interaction call_date_wday * day_of_the_week : 5127.249 
## AIC for interaction day_of_the_week * insurance_type : 5122.438

## Cleaned AIC results:

## # A tibble: 2 × 2
##   Interaction                        AIC
##   <chr>                            <dbl>
## 1 call_date_wday * day_of_the_week 5127.
## 2 day_of_the_week * insurance_type 5122.

## Best interaction: day_of_the_week * insurance_type with AIC: 5122.438

The model is not that much better with interaction term (academic * insurance) so we will leave it out and use (academic + insurance)

`poisson_significant` Significant Predictors Only for Poisson Model `poisson`

Given that the “business_days_until_appointment” variable represents the count of days until a new patient appointment and is a count variable, the Poisson regression model is appropriate for your data. It will model the relationship between the predictor variables and the count of days until a new patient appointment.

In the Poisson regression model, random effects are used to account for variability that is not explained by the fixed effects alone. The random effects for “last” in this model capture the variability in the number of business days until an appointment that is attributed to differences between physicians. By including last name as a random effect, the model acknowledges that observations within the same last name are likely to be more similar to each other than to observations from different last names. This clustering effect is accounted for by allowing the intercept to vary across last name. Random effects help to improve model fit by accounting for unexplained variability that is due to the hierarchical structure of the data (i.e., appointments are nested within physicians). This results in more accurate estimates of the fixed effects and a better understanding of the variability in appointment wait times.

Model `poisson_significant` Formula with only significant variables

where:

Fixed effects include…
Random effects account for variability between physicians, modeled as a random intercept.

The random effect for physician suggests that there is substantial variability in appointment wait times between physician. Physicians with a higher random intercept will tend to have longer wait times compared to Physicians with a lower random intercept.

`poisson` Model with only significant variables

## [1] "Not Academic" "Academic"

## [1] "South Atlantic"     "East North Central" "East South Central"
## [4] "Middle Atlantic"    "Mountain"           "New England"       
## [7] "Pacific"            "West North Central" "West South Central"

## Generalized linear mixed model fit by maximum likelihood (Adaptive
##   Gauss-Hermite Quadrature, nAGQ = 0) [glmerMod]
##  Family: poisson  ( log )
## Formula: 
## business_days_until_appointment ~ academic + insurance + census_division +  
##     (1 | last)
##    Data: df3
## 
##      AIC      BIC   logLik deviance df.resid 
##   5066.4   5118.9  -2521.2   5042.4      575 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -6.7996 -0.5642 -0.0303  0.3005 10.3526 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  last   (Intercept) 0.8144   0.9025  
## Number of obs: 587, groups:  last, 387
## 
## Fixed effects:
##                                   Estimate Std. Error z value
## (Intercept)                        1.73195    0.08083  21.427
## academicAcademic                   0.30480    0.09199   3.313
## insuranceMedicaid                  0.17974    0.02443   7.357
## census_divisionEast North Central  0.84743    0.10258   8.261
## census_divisionEast South Central  0.23270    0.12980   1.793
## census_divisionMiddle Atlantic     0.86194    0.12391   6.956
## census_divisionMountain            0.54392    0.17593   3.092
## census_divisionNew England         1.14591    0.16531   6.932
## census_divisionPacific             0.99359    0.11254   8.829
## census_divisionWest North Central  1.07782    0.16817   6.409
## census_divisionWest South Central  0.62014    0.15179   4.085
##                                               Pr(>|z|)    
## (Intercept)                       < 0.0000000000000002 ***
## academicAcademic                              0.000922 ***
## insuranceMedicaid                    0.000000000000187 ***
## census_divisionEast North Central < 0.0000000000000002 ***
## census_divisionEast South Central             0.073020 .  
## census_divisionMiddle Atlantic       0.000000000003502 ***
## census_divisionMountain                       0.001990 ** 
## census_divisionNew England           0.000000000004150 ***
## census_divisionPacific            < 0.0000000000000002 ***
## census_divisionWest North Central    0.000000000146372 ***
## census_divisionWest South Central    0.000043988627726 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) acdmcA insrnM cn_ENC cn_ESC cns_MA cnss_M cns_NE cnss_P
## acadmcAcdmc -0.155                                                        
## insurncMdcd -0.042 -0.044                                                 
## cnss_dvsENC -0.423 -0.100 -0.119                                          
## cnss_dvsESC -0.434 -0.169 -0.017  0.231                                   
## cnss_dvsnMA -0.499 -0.036 -0.046  0.241  0.399                            
## cnss_dvsnMn -0.408  0.240 -0.014  0.161  0.135  0.185                     
## cnss_dvsnNE -0.407 -0.143 -0.072  0.248  0.231  0.234  0.166              
## cnss_dvsnPc -0.567  0.060 -0.016  0.336  0.255  0.289  0.342  0.447       
## cnss_dvsWNC -0.420  0.062 -0.002  0.181  0.299  0.347  0.171  0.174  0.239
## cnss_dvsWSC -0.494  0.013 -0.013  0.226  0.364  0.283  0.191  0.218  0.284
##             cn_WNC
## acadmcAcdmc       
## insurncMdcd       
## cnss_dvsENC       
## cnss_dvsESC       
## cnss_dvsnMA       
## cnss_dvsnMn       
## cnss_dvsnNE       
## cnss_dvsnPc       
## cnss_dvsWNC       
## cnss_dvsWSC  0.229

` ## Table of poisson_significant Model Coefficients

	business days until appointment
Predictors	Incidence Rate Ratios	CI	p
(Intercept)	5.65	4.82 – 6.62	<0.001
academic [Academic]	1.36	1.13 – 1.62	0.001
insurance [Medicaid]	1.20	1.14 – 1.26	<0.001
census division [East North Central]	2.33	1.91 – 2.85	<0.001
census division [East South Central]	1.26	0.98 – 1.63	0.073
census division [Middle Atlantic]	2.37	1.86 – 3.02	<0.001
census division [Mountain]	1.72	1.22 – 2.43	0.002
census division [New England]	3.15	2.27 – 4.35	<0.001
census division [Pacific]	2.70	2.17 – 3.37	<0.001
census division [West North Central]	2.94	2.11 – 4.09	<0.001
census division [West South Central]	1.86	1.38 – 2.50	<0.001
Random Effects
σ²	0.06
τ₀₀ _last	0.81
ICC	0.94
N _last	387
Observations	587
Marginal R² / Conditional R²	0.170 / 0.947

Visualize the `poisson_significant` modelFixed Effects

Visualize the `poisson_significant` Model Predictions

Visualize `poisson_significant` Model Interaction Effects

## Computing estimated marginal means...
## Estimated data:
##  insurance              census_division         rate        SE  df asymp.LCL
##  Blue Cross/Blue Shield South Atlantic      6.582068 0.5697977 Inf  5.554889
##  Medicaid               South Atlantic      7.878092 0.6969315 Inf  6.623994
##  Blue Cross/Blue Shield East North Central 15.360221 1.5400081 Inf 12.619914
##  Medicaid               East North Central 18.384683 1.8187654 Inf 15.144266
##  Blue Cross/Blue Shield East South Central  8.306597 0.9550302 Inf  6.630685
##  Medicaid               East South Central  9.942185 1.1527294 Inf  7.921196
##  asymp.UCL
##   7.799187
##   9.369624
##  18.695561
##  22.318452
##  10.406098
##  12.478803
## 
## Results are averaged over the levels of: academic 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## Range of estimated marginal means with CIs: 5.554889 33.0311 
## Creating the plot...
## Saving plot to: ortho_sports_med/Figures/interaction_census_division_comparison_plot_20240910_214542.png

## Plot saved successfully.

## census_division = South Atlantic:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield  6.582068 0.569798 Inf  5.554889   7.79919
##  Medicaid                7.878092 0.696931 Inf  6.623994   9.36962
## 
## census_division = East North Central:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 15.360221 1.540008 Inf 12.619914  18.69556
##  Medicaid               18.384683 1.818765 Inf 15.144266  22.31845
## 
## census_division = East South Central:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield  8.306597 0.955030 Inf  6.630685  10.40610
##  Medicaid                9.942185 1.152729 Inf  7.921196  12.47880
## 
## census_division = Middle Atlantic:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 15.584697 1.738723 Inf 12.523714  19.39383
##  Medicaid               18.653359 2.085594 Inf 14.982558  23.22353
## 
## census_division = Mountain:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 11.339279 1.987324 Inf  8.042734  15.98701
##  Medicaid               13.572009 2.386715 Inf  9.615137  19.15723
## 
## census_division = New England:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 20.702493 3.053952 Inf 15.504461  27.64322
##  Medicaid               24.778861 3.634199 Inf 18.588297  33.03110
## 
## census_division = Pacific:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 17.777620 1.817992 Inf 14.548803  21.72301
##  Medicaid               21.278074 2.201240 Inf 17.372990  26.06094
## 
## census_division = West North Central:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 19.339858 3.077697 Inf 14.157781  26.41870
##  Medicaid               23.147920 3.706487 Inf 16.912820  31.68166
## 
## census_division = West South Central:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 12.237311 1.668419 Inf  9.367729  15.98592
##  Medicaid               14.646865 2.009639 Inf 11.193209  19.16614
## 
## Results are averaged over the levels of: academic 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale

`poisson_significant` Model Performance

## We fitted a poisson mixed model (estimated using ML and BOBYQA optimizer) to
## predict business_days_until_appointment with academic, insurance and
## census_division (formula: business_days_until_appointment ~ academic +
## insurance + census_division). The model included last as random effect
## (formula: ~1 | last). The model's total explanatory power is substantial
## (conditional R2 = 0.95) and the part related to the fixed effects alone
## (marginal R2) is of 0.17. The model's intercept, corresponding to academic =
## Not Academic, insurance = Blue Cross/Blue Shield and census_division = South
## Atlantic, is at 1.73 (95% CI [1.57, 1.89], p < .001). Within this model:
## 
##   - The effect of academic [Academic] is statistically significant and positive
## (beta = 0.30, 95% CI [0.12, 0.49], p < .001; Std. beta = 0.30, 95% CI [0.12,
## 0.49])
##   - The effect of insurance [Medicaid] is statistically significant and positive
## (beta = 0.18, 95% CI [0.13, 0.23], p < .001; Std. beta = 0.18, 95% CI [0.13,
## 0.23])
##   - The effect of census division [East North Central] is statistically
## significant and positive (beta = 0.85, 95% CI [0.65, 1.05], p < .001; Std. beta
## = 0.85, 95% CI [0.65, 1.05])
##   - The effect of census division [East South Central] is statistically
## non-significant and positive (beta = 0.23, 95% CI [-0.02, 0.49], p = 0.073;
## Std. beta = 0.23, 95% CI [-0.02, 0.49])
##   - The effect of census division [Middle Atlantic] is statistically significant
## and positive (beta = 0.86, 95% CI [0.62, 1.10], p < .001; Std. beta = 0.86, 95%
## CI [0.62, 1.10])
##   - The effect of census division [Mountain] is statistically significant and
## positive (beta = 0.54, 95% CI [0.20, 0.89], p = 0.002; Std. beta = 0.54, 95% CI
## [0.20, 0.89])
##   - The effect of census division [New England] is statistically significant and
## positive (beta = 1.15, 95% CI [0.82, 1.47], p < .001; Std. beta = 1.15, 95% CI
## [0.82, 1.47])
##   - The effect of census division [Pacific] is statistically significant and
## positive (beta = 0.99, 95% CI [0.77, 1.21], p < .001; Std. beta = 0.99, 95% CI
## [0.77, 1.21])
##   - The effect of census division [West North Central] is statistically
## significant and positive (beta = 1.08, 95% CI [0.75, 1.41], p < .001; Std. beta
## = 1.08, 95% CI [0.75, 1.41])
##   - The effect of census division [West South Central] is statistically
## significant and positive (beta = 0.62, 95% CI [0.32, 0.92], p < .001; Std. beta
## = 0.62, 95% CI [0.32, 0.92])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald z-distribution approximation.

## The marginal R² value of the model is 0.17 and the conditional R² value is 0.947

## The marginal R² represents the proportion of variance explained by the fixed effects ( (Intercept), academicAcademic, insuranceMedicaid, census_divisionEast North Central, census_divisionEast South Central, census_divisionMiddle Atlantic, census_divisionMountain, census_divisionNew England, census_divisionPacific, census_divisionWest North Central, census_divisionWest South Central ) alone ( 17.03 %). The conditional R² represents the proportion of variance explained by both the fixed effects and the random effects ( last ) combined ( 94.66 %). This indicates how much of the variability in the outcome can be attributed to the fixed effects versus the entire model, including random effects.

For poisson_significant model: To determine which random effects were significant in your model, you need to look at the variance components for the random effects and their corresponding standard deviations. In mixed models, random effects themselves do not have p-values like fixed effects do. Instead, you evaluate their significance by looking at the variance of the random effects. If the variance is near zero, the random effect may not be contributing much to the model.

Here’s how you can extract and interpret the variance of the random effects to assess their significance for poisson_significant:

## [1] "The random effects in the model are:\n last"             
## [2] "The random effects in the model are:\n (Intercept)"      
## [3] "The random effects in the model are:\n NA"               
## [4] "The random effects in the model are:\n 0.81442174026169" 
## [5] "The random effects in the model are:\n 0.902453178985863"
## [6] "The random effects in the model are:\n Yes"

## The significant random effects are: last

`simr_poisson_full_model` Model Power analysis

The power analysis you’ve conducted with the powerSim function is used to estimate the statistical power of your model for detecting effects of a specific predictor—in this case, the predictor insurance in a Poisson mixed-effects model.

Test the `poisson_significant` model assumptions

Checking the binned residuals because the data is non-parametric the residuals will not be normally distributed. Collinearity was tested as well as heteroscedasticity was checked.

The residuals appear to be spread out more as the fitted values increase. This funnel shape (with wider dispersion of residuals at higher fitted values) is an indication of heteroscedasticity. In a model with homoscedasticity, the residuals would have a consistent spread across all levels of fitted values, without a clear pattern. The data is non-parametric so the residuals will not be within error bounds.

`poisson_significant` Collinearity

Variance Inflation Factors (VIF) were calculated to assess multicollinearity among predictors. All VIF values were below the commonly used threshold of 5, suggesting that multicollinearity is not a concern for this model.

Variable Importance Factors
	GVIF	Df	GVIF^(1/(2*Df))
academic	1.180096	1	1.086322
insurance	1.025897	1	1.012865
census_division	1.201476	8	1.011538

## OK: No outliers detected.
## - Based on the following method and threshold: cook (0.5).
## - For variable: (Whole model)

`poisson` Intraclass Correlation Coefficient

The Intraclass Correlation Coefficient (ICC) is a statistical measure used to evaluate the proportion of variance in a dependent variable that can be attributed to differences between groups or clusters. It is commonly used in the context of hierarchical or mixed models to quantify the degree of similarity within clusters.

## The intraclass correlation (ICC) of the model for the random effect group ' last ' is 0.449 .
## This indicates that 44.9 % of the variance in the outcome variable is attributable to differences between the last groups.

## 
##  This is a low to moderate ICC for the last group, indicating that some variance is due to differences between these groups, but a substantial portion is within these groups.

A low to moderate Intraclass Correlation Coefficient (ICC) for the group “physician last name” suggests that while there is some variation in the outcome variable (e.g., business days until appointment) that can be attributed to differences between individual physicians, a substantial portion of the variation occurs within these groups—meaning that much of the variability in appointment times is due to factors other than just the differences between physicians.

In practical terms, this indicates that:

Variation Between Physicians: The fact that the ICC is not zero means that there is some consistency in the appointment times associated with each physician. Some physicians might systematically have longer or shorter wait times, contributing to the variance in the data.
Variation Within Physicians: Since the ICC is low to moderate, it means that even within the same physician, there is considerable variability in appointment times. This could be due to a variety of factors, such as the type of insurance, the scenario, or other factors that are not captured by the physician’s identity alone.
Implications: The low to moderate ICC suggests that while the identity of the physician (as indicated by the last name) does have an effect, it is not the dominant factor driving differences in appointment times. Other factors—potentially those captured by fixed effects or residual variance—are also playing a significant role.

In summary, while who the physician is does matter to some extent, other variables are likely more influential in determining how long a patient waits for an appointment. This insight can guide you to look more closely at those other factors in your analysis or to consider whether there are ways to reduce variability within physicians, such as through standardized scheduling practices.

`poisson_significant` Dispersion

Overdispersion in your model implies that the variability in the observed data is greater than what the model predicts under the Poisson assumption. Specifically, in a Poisson model, the mean and variance of the count data are assumed to be equal.

## [1] "Significant overdispersion detected. Consider using a Negative Binomial model or adding random effects to account for overdispersion."

## Warning: Autocorrelated residuals detected (p < .001).

## [1] FALSE

Testing assumptions you can use the logLik function to get the log-likelihood of the model, and calculate the residual deviance as -2 * logLik(model). The residual degrees of freedom can be computed as the number of observations minus the number of parameters estimated (which includes both fixed effects and random effects).

The number of parameters estimated can be calculated as the number of fixed effects plus the number of random effects parameters. The number of fixed effects can be obtained from the length of fixef(model), and the number of random effects parameters can be obtained from the length of VarCorr(model).

If the dispersion parameter is considerably greater than 1, it indicates overdispersion. If it is less than 1, it indicates underdispersion. A value around 1 is considered ideal for Poisson regression.

## 'log Lik.' 8.769353 (df=12)

Linearity of logit

The Poisson regression assumes that the log of the expected count is a linear function of the predictors. One way to check this is to plot the observed counts versus the predicted counts and see if the relationship looks linear.

`mini_poisson_interaction` Model Interactions

To include interaction terms in a regression model, you can use the : operator or the * operator in the formula. The : operator represents the interaction between two variables, while the * operator represents the interaction and also includes the main effects of the two variables. This will include interactions between insurance and each of the other significant variables (academic_affiliation, ACOG_District, central), in addition to the main effects of these variables.

Please note that interpreting interaction effects can be complex, especially in nonlinear models such as Poisson regression. The coefficients for the interaction terms represent the difference in the log rate of days for a one-unit change in x variable, for different levels of the other variables. However, the actual effects on the rate of days can vary depending on the values of the other variables.

\[ \begin{aligned} \text{Business Days Until New Patient Appointment} &\sim \text{Poisson}(\lambda) \\ \log(\lambda) &= \beta_0 \\ &+ \beta_1 \cdot \text{Academic Affiliation} \\ &+ \beta_2 \cdot \text{Patient Insurance} \\ &+ \beta_3 \cdot \text{Census Division} \\ &+ \beta_4 \cdot (\text{Academic Affiliation} \times \text{Patient Insurance}) \\ &+ \beta_5 \cdot (\text{Academic Affiliation} \times \text{Census Division}) \\ &+ \beta_6 \cdot (\text{Patient Insurance} \times \text{Census Division}) \\ &+ \beta_7 \cdot (\text{Academic Affiliation} \times \text{Patient Insurance} \times \text{Census Division}) \\ &+ (1 | \text{Physician Last Name}) \end{aligned} \]

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: poisson  ( log )
## Formula: 
## business_days_until_appointment ~ academic * insurance * census_division +  
##     (1 | phone)
##    Data: df3
##       AIC       BIC    logLik  deviance  df.resid 
##  4800.829  4953.954 -2365.414  4730.829       552 
## Random effects:
##  Groups Name        Std.Dev.
##  phone  (Intercept) 0.8203  
## Number of obs: 587, groups:  phone, 407
## Fixed Effects:
##                                                          (Intercept)  
##                                                              2.31357  
##                                                     academicAcademic  
##                                                             -0.17607  
##                                                    insuranceMedicaid  
##                                                              0.09960  
##                                    census_divisionEast North Central  
##                                                             -0.15256  
##                                    census_divisionEast South Central  
##                                                             -0.23092  
##                                       census_divisionMiddle Atlantic  
##                                                              0.08250  
##                                              census_divisionMountain  
##                                                              0.05387  
##                                           census_divisionNew England  
##                                                              0.38317  
##                                               census_divisionPacific  
##                                                              0.41037  
##                                    census_divisionWest North Central  
##                                                             -0.08351  
##                                    census_divisionWest South Central  
##                                                             -0.09798  
##                                   academicAcademic:insuranceMedicaid  
##                                                              0.23204  
##                   academicAcademic:census_divisionEast North Central  
##                                                              0.60935  
##                   academicAcademic:census_divisionEast South Central  
##                                                              0.48841  
##                      academicAcademic:census_divisionMiddle Atlantic  
##                                                              1.09670  
##                             academicAcademic:census_divisionMountain  
##                                                              0.78108  
##                          academicAcademic:census_divisionNew England  
##                                                             -0.24119  
##                              academicAcademic:census_divisionPacific  
##                                                              0.19614  
##                   academicAcademic:census_divisionWest North Central  
##                                                              0.11508  
##                   academicAcademic:census_divisionWest South Central  
##                                                              1.53571  
##                  insuranceMedicaid:census_divisionEast North Central  
##                                                              0.10925  
##                  insuranceMedicaid:census_divisionEast South Central  
##                                                             -0.08174  
##                     insuranceMedicaid:census_divisionMiddle Atlantic  
##                                                              0.33522  
##                            insuranceMedicaid:census_divisionMountain  
##                                                              0.16489  
##                         insuranceMedicaid:census_divisionNew England  
##                                                              0.29365  
##                             insuranceMedicaid:census_divisionPacific  
##                                                             -0.02951  
##                  insuranceMedicaid:census_divisionWest North Central  
##                                                              0.13197  
##                  insuranceMedicaid:census_divisionWest South Central  
##                                                             -0.17775  
## academicAcademic:insuranceMedicaid:census_divisionEast North Central  
##                                                             -0.66765  
## academicAcademic:insuranceMedicaid:census_divisionEast South Central  
##                                                             -0.02577  
##    academicAcademic:insuranceMedicaid:census_divisionMiddle Atlantic  
##                                                             -0.72816  
##        academicAcademic:insuranceMedicaid:census_divisionNew England  
##                                                              0.19591  
##            academicAcademic:insuranceMedicaid:census_divisionPacific  
##                                                              0.19546  
## academicAcademic:insuranceMedicaid:census_divisionWest North Central  
##                                                              1.14110  
## fit warnings:
## fixed-effect model matrix is rank deficient so dropping 2 columns / coefficients
## optimizer (Nelder_Mead) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings

`poisson_significant` Interactions

`poisson_significant` Insurance x academic

## Computing estimated marginal means...
## Estimated data:
##  insurance              academic         rate        SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield Not Academic 11.41071 0.6018770 Inf  10.28998  12.65350
##  Medicaid               Not Academic 13.65751 0.7485234 Inf  12.26648  15.20628
##  Blue Cross/Blue Shield Academic     15.47704 1.4645970 Inf  12.85696  18.63105
##  Medicaid               Academic     18.52450 1.7552107 Inf  15.38489  22.30481
## 
## Results are averaged over the levels of: census_division 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## Range of estimated marginal means with CIs: 10.28998 22.30481 
## Creating the plot...
## Saving plot to: Ari/Figures/interaction_academic_comparison_plot_20240910_214603.png

## Plot saved successfully.

## $data
## academic = Not Academic:
##  insurance                  rate        SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 11.41071 0.6018770 Inf  10.28998  12.65350
##  Medicaid               13.65751 0.7485234 Inf  12.26648  15.20628
## 
## academic = Academic:
##  insurance                  rate        SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 15.47704 1.4645970 Inf  12.85696  18.63105
##  Medicaid               18.52450 1.7552107 Inf  15.38489  22.30481
## 
## Results are averaged over the levels of: census_division 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## $plot

`poisson_significant` insurance x census divisions

## Computing estimated marginal means...
## Estimated data:
##  insurance              census_division         rate        SE  df asymp.LCL
##  Blue Cross/Blue Shield South Atlantic      6.582068 0.5697977 Inf  5.554889
##  Medicaid               South Atlantic      7.878092 0.6969315 Inf  6.623994
##  Blue Cross/Blue Shield East North Central 15.360221 1.5400081 Inf 12.619914
##  Medicaid               East North Central 18.384683 1.8187654 Inf 15.144266
##  Blue Cross/Blue Shield East South Central  8.306597 0.9550302 Inf  6.630685
##  Medicaid               East South Central  9.942185 1.1527294 Inf  7.921196
##  asymp.UCL
##   7.799187
##   9.369624
##  18.695561
##  22.318452
##  10.406098
##  12.478803
## 
## Results are averaged over the levels of: academic 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## Range of estimated marginal means with CIs: 5.554889 33.0311 
## Creating the plot...
## Saving plot to: Ari/Figures/interaction_insurance_comparison_plot_20240910_214604.png

## Plot saved successfully.

## $data
## census_division = South Atlantic:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield  6.582068 0.569798 Inf  5.554889   7.79919
##  Medicaid                7.878092 0.696931 Inf  6.623994   9.36962
## 
## census_division = East North Central:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 15.360221 1.540008 Inf 12.619914  18.69556
##  Medicaid               18.384683 1.818765 Inf 15.144266  22.31845
## 
## census_division = East South Central:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield  8.306597 0.955030 Inf  6.630685  10.40610
##  Medicaid                9.942185 1.152729 Inf  7.921196  12.47880
## 
## census_division = Middle Atlantic:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 15.584697 1.738723 Inf 12.523714  19.39383
##  Medicaid               18.653359 2.085594 Inf 14.982558  23.22353
## 
## census_division = Mountain:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 11.339279 1.987324 Inf  8.042734  15.98701
##  Medicaid               13.572009 2.386715 Inf  9.615137  19.15723
## 
## census_division = New England:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 20.702493 3.053952 Inf 15.504461  27.64322
##  Medicaid               24.778861 3.634199 Inf 18.588297  33.03110
## 
## census_division = Pacific:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 17.777620 1.817992 Inf 14.548803  21.72301
##  Medicaid               21.278074 2.201240 Inf 17.372990  26.06094
## 
## census_division = West North Central:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 19.339858 3.077697 Inf 14.157781  26.41870
##  Medicaid               23.147920 3.706487 Inf 16.912820  31.68166
## 
## census_division = West South Central:
##  insurance                   rate       SE  df asymp.LCL asymp.UCL
##  Blue Cross/Blue Shield 12.237311 1.668419 Inf  9.367729  15.98592
##  Medicaid               14.646865 2.009639 Inf 11.193209  19.16614
## 
## Results are averaged over the levels of: academic 
## Confidence level used: 0.95 
## Intervals are back-transformed from the log scale 
## 
## $plot

fin

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DRAFT: Ortho Sports Med Mystery Caller Study

Tyler M. Muffly, MD and Nick Felan

10 September, 2024

Read in data

Check data normality

Quality Check the Data

Are there any physicians included more than twice?

Variables of those physicians included more than twice?

Filter data so there is only one NPI per insurance type

Find physicians called more than once

Do they have exclusion and have a business_days_until_appointment >0?

Do they have business_days_until_appointment >0 but are an excluded category?

Do they have NA for business_days_until_appointment but are “Included” in the Reasons for exclusion category?

Results

Insurance Acceptance Rates

Steps to Calculate Medicaid Acceptance Rate

Appointment Accessibility

Univariate Analysis

Gender Distribution calculations

Logistic Regression to Accept Medicaid

Significant Predictors for Logistic Regression: 0.2

Variable Selection

Scenarios with business_days_until_appointment ~ scenario

Number of hip, knee, and shoulder surgeons successfully contacted: business_days_until_appointment ~ scenario

Insurance: business_days_until_appointment ~ insurance

Exclusions: business_days_until_appointment ~ reason_for_exclusion

Visualizing the Each Individual Predictor

Business days by insurance

Log Business Days

Day of the week by insurance

Central Appointment Line by Insurance

Physician Gender by Insurance

Physician MD vs. DO by Insurance

Surgeon Specialty (Hip, Knee, Shoulder)

Combined plot of Subspecialty and Insurance

Plot of Subspecialty for Abstract

Descriptive Tables

Table 1 - Split across Insurances

Table 2 - Included vs. Not Included

Table 3

Wait Time by Insurance Figures

Line Plot

Scatter Plot

Density Plot

Scatter Plot by Insurance

Find the intersection point between best fit line and the perfect line.

Sensitivity Analysis - Physicians who took both insurances

Wait Time by Scenario Figures

Line Plot

Scatter Plot

Density Plot

Statistical testing

Full Poisson Model poisson_full_model

Single predictor models for poisson_full_model

poisson_full_model interactions

poisson_significant Significant Predictors Only for Poisson Model poisson

Model poisson_significant Formula with only significant variables

poisson Model with only significant variables

Visualize the poisson_significant modelFixed Effects

Visualize the poisson_significant Model Predictions

Visualize poisson_significant Model Interaction Effects

poisson_significant Model Performance

simr_poisson_full_model Model Power analysis

Test the poisson_significant model assumptions

poisson_significant Collinearity

poisson Intraclass Correlation Coefficient

poisson_significant Dispersion

Linearity of logit

mini_poisson_interaction Model Interactions

poisson_significant Interactions

poisson_significant Insurance x academic

poisson_significant insurance x census divisions

fin

Scenarios with `business_days_until_appointment ~ scenario`

Number of hip, knee, and shoulder surgeons successfully contacted: `business_days_until_appointment ~ scenario`

Insurance: `business_days_until_appointment ~ insurance`

Exclusions: `business_days_until_appointment ~ reason_for_exclusion`

Full Poisson Model `poisson_full_model`

Single predictor models for `poisson_full_model`

`poisson_full_model` interactions

`poisson_significant` Significant Predictors Only for Poisson Model `poisson`

Model `poisson_significant` Formula with only significant variables

`poisson` Model with only significant variables

Visualize the `poisson_significant` modelFixed Effects

Visualize the `poisson_significant` Model Predictions

Visualize `poisson_significant` Model Interaction Effects

`poisson_significant` Model Performance

`simr_poisson_full_model` Model Power analysis

Test the `poisson_significant` model assumptions

`poisson_significant` Collinearity

`poisson` Intraclass Correlation Coefficient

`poisson_significant` Dispersion

`mini_poisson_interaction` Model Interactions

`poisson_significant` Interactions

`poisson_significant` Insurance x academic

`poisson_significant` insurance x census divisions