Objective: This study aimed to investigate the impact of insurance status on wait times for otolaryngology care, comparing Medicaid-insured patients to commercially insured patients.
Study Design: The study utilized an audit methodology, known as a “mystery caller” study, to assess appointment availability and patient experiences regarding access to care in otolaryngology.
Setting: The study included physicians representing various otolaryngology subspecialties across the United States, excluding military medical practices.
Methods: Physicians were selected from patient-facing directories and stratified by region. Mystery callers, posing as patients with either Medicaid or commercial insurance, made two separate calls to each physician’s office to obtain the earliest possible appointment time. The calls were standardized and completed within one week. Data on appointment availability, earliest appointment dates, and additional information were collected using a secure electronic data capture tool.
Results: Out of 612 physicians contacted, 301 physicians accepting new patients were included in the analysis. The median wait time across all subspecialties and insurance types was 34.3 business days. The study found a statistically significant difference in wait times based on insurance type, with Medicaid-insured patients experiencing a 13.8% longer wait time than commercially insured patients. The model-estimated average wait times were 32.4 days for the commercially insured group and 36.8 days for the Medicaid group.
Conclusions: The study revealed that Medicaid-insured patients in otolaryngology care faced longer wait times compared to commercially insured patients. These findings contribute to the existing literature on access to care and highlight the need to address potential disparities in wait times to promote equitable access to otolaryngology services.
## # A tibble: 6 × 52
## `Reason for exclusions` No_Medicaid Physician Informatio…¹
## <chr> <fct> <chr>
## 1 Greater than 5 minutes on hold Yes the ph… Facial Plastic and Re…
## 2 Greater than 5 minutes on hold Yes the ph… Facial Plastic and Re…
## 3 Able to contact Yes the ph… Facial Plastic and Re…
## 4 Able to contact Yes the ph… Facial Plastic and Re…
## 5 Number contacted did not correspond to exp… Yes the ph… Facial Plastic and Re…
## 6 Number contacted did not correspond to exp… Yes the ph… Facial Plastic and Re…
## # ℹ abbreviated name:
## # ¹`Physician Information (see subspecialty, physician name, telephone number, and insurance variable combination) TEXT or e-mail Michaele with questions: 626-646-9087 Call Dr. Muffly with questions: 720-810-9863`
## # ℹ 49 more variables: business_days_until_appointment <dbl>,
## # `contacted_>_0_business_days_to_appt` <fct>, contacted <dbl>,
## # call_date <date>, call_date_wday <ord>,
## # central_number_e_g_appointment_center <chr>, Appointment_Date <date>,
## # `Number of Transfers (phone call transferred from one person or answering service to the next)` <fct>, …| npi | name | N |
|---|---|---|
| npi | name | Reason for exclusions | insurance | business_days_until_appointment |
|---|---|---|---|---|
A total of 352 unique otolaryngology head and neck surgeons were identified in the dataset and were successfully contacted (i.e., with a recorded wait time for an appointment) in 48 states including the District of Columbia. The excluded states include Alaska, Hawaii and Wyoming.
## $proportion
## [1] "14.8%"
##
## $tabyl_result
## # A tibble: 7 × 3
## specialty n percent
## <fct> <int> <dbl>
## 1 Facial Plastic and Reconstructive Surgery 172 0.147
## 2 General Otolaryngology 169 0.144
## 3 Head and Neck Surgery 167 0.142
## 4 Laryngology 163 0.139
## 5 Neurotology 174 0.148
## 6 Pediatric Otolaryngology 174 0.148
## 7 Rhinology 155 0.132The median age of the dataset was 52(IQR 25th percentile 44 to 75th percentile 61). The most common gender in the dataset was male (78.5%). The most common specialty was Neurotology (14.8%). The most common training was MD (97.3%). The academic affiliation status most frequently occurring was private practice (54.6%).
The median wait time across all subspecialties and insurance types was 29 business days, with an interquartile range (IQR) of 15 to 47.
Each physician received 2, phone calls with identical clinical scenarios. In this process, 0 ” physicians were excluded after two unsuccessful attempts to reach them. Out of the 1174 phone calls made, 146 calls 12.4361158%) were on hold for more than five minutes, 105 8.9437819 %) went to voicemail, 88 7.4957411%) physicians did not accept Medicaid insurance, 77 6.5587734%) required a referral before the appointment, and 11 0.9369676%) resulted in contacting a personal phone number of the physician.
Graph each variable
Here we conduct statistical tests to see if the profile differs for those who accept Medicaid and those who don’t. This analysis is only valid for variables that don’t change with insurance type.
We seem to have many physicians who don’t accept MEDICAID. Should them enter the analysis? It seems that these physicians would not be part of the eligible sample if the goal is to see if individuals who accept both leaves you waiting longer if you are on Medicaid. The research question would be: ** Do providers make patients to wait longer if they are on Medicaid, as compared to Blue Cross? I understand that here the provider must accept both. **
If we include all physicians, then the research question is more like: ** If I have Medicaid, do I wait longer when I try to book an appointment? **
Here we add a variable to the dataset that flag providers who have at least one occurrence of “Physician does not accept MEDICAID”.
df3 datasetThere are 1,174 providers in the dataset. Many of these providers could not be contacted. In the paper we probably want to report characteristics of contacted providers who have at least one waiting time and are therefore included in the analysis.
Total column is at the provider level. Not meaningful with insurance specific variables, like day of the week.
Insurance Type columns are at the Insurance Type level. Not meaningful with provider level variables.
MEDICAID Acceptance columns are at the provider level. Not meaningful with insurance specific variables.
In the Analysis columns are at the provider level. Not meaningful with insurance specific variables. Here, In the Analysis means those providers that have data for number of days until appointment, and therefore will be used in the analysis. A comparison between “In the Analsyis” and “Not in the Analysis” may give an idea of bias in the data, that is, what kind of providers were easier to reach and because of that are more represented in the sample than they should.
The total number of excluded people is 621.
| Reason for exclusions | n | Percent |
|---|---|---|
| Greater than 5 minutes on hold | 146 | 23.5% |
| Went to voicemail | 105 | 16.9% |
| Physician does not accept MEDICAID | 88 | 14.2% |
| Physician referral required before scheduling appointment | 77 | 12.4% |
| Not accepting new patients | 73 | 11.8% |
| Number contacted did not correspond to expected office/specialty | 54 | 8.7% |
| Phone not answered or busy signal on repeat calls | 45 | 7.2% |
| Closed medical system (e.g. Kaiser or military hospital) | 15 | 2.4% |
| Physician’s personal phone | 11 | 1.8% |
| Must see midlevel before seeing physician | 7 | 1.1% |
Demographics of all physicians called
| Blue Cross/Blue Shield (N=353) | Medicaid (N=243) | Total (N=596) | p value | |
|---|---|---|---|---|
| Age (years) | 0.27 | |||
| - n | 353 | 243 | 596 | |
| - Median (Q1, Q3) | 52.0 (43.0, 61.0) | 54.0 (45.5, 61.0) | 52.5 (44.0, 61.0) | |
| Gender | 0.75 | |||
| - Male | 275 (77.9%) | 192 (79.0%) | 467 (78.4%) | |
| - Female | 78 (22.1%) | 51 (21.0%) | 129 (21.6%) | |
| Medical School Training | 0.35 | |||
| - US Senior | 237 (82.3%) | 165 (85.5%) | 402 (83.6%) | |
| - International Medical Graduate | 51 (17.7%) | 28 (14.5%) | 79 (16.4%) | |
| Medical School Location | 0.19 | |||
| - Allopathic training | 341 (96.6%) | 239 (98.4%) | 580 (97.3%) | |
| - Osteopathic training | 12 (3.4%) | 4 (1.6%) | 16 (2.7%) | |
| Medical School Graduation Year | 0.21 | |||
| - Less than year 2000 | 185 (52.4%) | 131 (53.9%) | 316 (53.0%) | |
| - 2000 to 2004 | 43 (12.2%) | 40 (16.5%) | 83 (13.9%) | |
| - 2005 to 2009 | 67 (19.0%) | 43 (17.7%) | 110 (18.5%) | |
| - 2010 and Greater | 58 (16.4%) | 29 (11.9%) | 87 (14.6%) | |
| Specialty | 0.04 | |||
| - Facial Plastic and Reconstructive Surgery | 52 (14.7%) | 36 (14.8%) | 88 (14.8%) | |
| - General Otolaryngology | 63 (17.8%) | 23 (9.5%) | 86 (14.4%) | |
| - Head and Neck Surgery | 43 (12.2%) | 42 (17.3%) | 85 (14.3%) | |
| - Laryngology | 48 (13.6%) | 35 (14.4%) | 83 (13.9%) | |
| - Neurotology | 44 (12.5%) | 43 (17.7%) | 87 (14.6%) | |
| - Pediatric Otolaryngology | 53 (15.0%) | 36 (14.8%) | 89 (14.9%) | |
| - Rhinology | 50 (14.2%) | 28 (11.5%) | 78 (13.1%) | |
| Academic Affiliation | 0.16 | |||
| - Private Practice | 202 (57.2%) | 125 (51.4%) | 327 (54.9%) | |
| - Academic Practice | 151 (42.8%) | 118 (48.6%) | 269 (45.1%) | |
| American Academy of Otolaryngology Regions | < 0.01 | |||
| - Region 1 (Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, Vermont) | 18 (5.1%) | 44 (18.1%) | 62 (10.4%) | |
| - Region 2 (New Jersey, New York) | 56 (15.9%) | 6 (2.5%) | 62 (10.4%) | |
| - Region 3 (Delaware, District of Columbia, Maryland, Pennsylvania, Virginia, West Virginia) | 45 (12.7%) | 18 (7.4%) | 63 (10.6%) | |
| - Region 4 (Alabama, Florida, Georgia, Kentucky, Mississippi, North Carolina, South Carolina, Tennessee) | 41 (11.6%) | 19 (7.8%) | 60 (10.1%) | |
| - Region 5 (Illinois, Indiana, Michigan, Minnesota, Ohio, Wisconsin) | 45 (12.7%) | 12 (4.9%) | 57 (9.6%) | |
| - Region 6 (Arkansas, Louisiana, New Mexico, Oklahoma, Texas) | 36 (10.2%) | 26 (10.7%) | 62 (10.4%) | |
| - Region 7 (Iowa, Kansas, Missouri, Nebraska) | 29 (8.2%) | 28 (11.5%) | 57 (9.6%) | |
| - Region 8 (Colorado, Montana, North Dakota, South Dakota, Utah, Wyoming) | 26 (7.4%) | 23 (9.5%) | 49 (8.2%) | |
| - Region 9 (Alaska, Oregon, Washington) | 10 (2.8%) | 51 (21.0%) | 61 (10.2%) | |
| - Region 10 (Arizona, California, Hawaii, Nevada) | 47 (13.3%) | 16 (6.6%) | 63 (10.6%) | |
| Rurality | 0.79 | |||
| - Metropolitan area | 343 (97.2%) | 237 (97.5%) | 580 (97.3%) | |
| - Rural area | 10 (2.8%) | 6 (2.5%) | 16 (2.7%) | |
| Centeral Scheduling | 0.87 | |||
| - Yes, central scheduling number | 217 (61.5%) | 151 (62.1%) | 368 (61.7%) | |
| - No | 136 (38.5%) | 92 (37.9%) | 228 (38.3%) | |
| Number of Phone Transfers | 0.09 | |||
| - No transfers | 148 (41.9%) | 91 (37.4%) | 239 (40.1%) | |
| - One transfer | 158 (44.8%) | 111 (45.7%) | 269 (45.1%) | |
| - Two transfers | 28 (7.9%) | 33 (13.6%) | 61 (10.2%) | |
| - More than two transfers | 19 (5.4%) | 8 (3.3%) | 27 (4.5%) |
Subspecialty |
Insurance Type |
MEDICAID Acceptance |
In the Analysis |
|||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Total (N=1174) |
Facial Plastic and Reconstructive Surgery (N=172) |
General Otolaryngology (N=169) |
Head and Neck Surgery (N=167) |
Laryngology (N=163) |
Neurotology (N=174) |
Pediatric Otolaryngology (N=174) |
Rhinology (N=155) |
Blue Cross/Blue Shield (N=589) |
Medicaid (N=585) |
Yes the physician accepts Medicaid (N=1086) |
No the physician does NOT accept Medicaid (N=88) |
0 (N=344) |
1 (N=241) |
|
| Physician Gender | ||||||||||||||
| Female | 252 (21.5%) | 26 (15.1%) | 45 (26.6%) | 18 (10.8%) | 53 (32.5%) | 20 (11.5%) | 64 (36.8%) | 26 (16.8%) | 126 (21.4%) | 126 (21.5%) | 233 (21.5%) | 19 (21.6%) | 75 (21.8%) | 51 (21.2%) |
| Male | 922 (78.5%) | 146 (84.9%) | 124 (73.4%) | 149 (89.2%) | 110 (67.5%) | 154 (88.5%) | 110 (63.2%) | 129 (83.2%) | 463 (78.6%) | 459 (78.5%) | 853 (78.5%) | 69 (78.4%) | 269 (78.2%) | 190 (78.8%) |
| Physician Age in Years | ||||||||||||||
| Mean (SD) | 52.7 (11.5) | 55.3 (10.4) | 51.6 (13.7) | 55.4 (11.5) | 49.2 (9.59) | 54.5 (11.1) | 51.2 (10.5) | 51.1 (12.3) | 52.6 (11.6) | 52.7 (11.5) | 52.5 (11.6) | 54.7 (11.0) | 53.7 (12.2) | 51.2 (10.4) |
| Median [Min, Max] | 52.0 [29.0, 86.0] | 55.0 [32.0, 80.0] | 51.0 [32.0, 86.0] | 58.0 [33.0, 79.0] | 48.0 [34.0, 74.0] | 55.0 [32.0, 78.0] | 51.0 [29.0, 81.0] | 49.0 [29.0, 80.0] | 52.0 [29.0, 86.0] | 52.0 [29.0, 86.0] | 52.0 [29.0, 86.0] | 54.0 [35.0, 82.0] | 53.5 [29.0, 86.0] | 51.0 [29.0, 82.0] |
| Provider Credential Text | ||||||||||||||
| MD | 1142 (97.3%) | 160 (93.0%) | 159 (94.1%) | 165 (98.8%) | 159 (97.5%) | 172 (98.9%) | 174 (100%) | 153 (98.7%) | 573 (97.3%) | 569 (97.3%) | 1055 (97.1%) | 87 (98.9%) | 339 (98.5%) | 230 (95.4%) |
| DO | 32 (2.7%) | 12 (7.0%) | 10 (5.9%) | 2 (1.2%) | 4 (2.5%) | 2 (1.1%) | 0 (0%) | 2 (1.3%) | 16 (2.7%) | 16 (2.7%) | 31 (2.9%) | 1 (1.1%) | 5 (1.5%) | 11 (4.6%) |
| Graduation Year | ||||||||||||||
| Mean (SD) | 2000 (10.9) | 1990 (8.00) | 2000 (12.8) | 2000 (11.2) | 2000 (10.1) | 2000 (10.6) | 2000 (10.9) | 2000 (10.4) | 2000 (10.9) | 2000 (10.8) | 2000 (10.8) | 1990 (11.0) | 2000 (11.4) | 2000 (9.81) |
| Median [Min, Max] | 2000 [1970, 2020] | 1990 [1980, 2020] | 2000 [1970, 2020] | 2000 [1980, 2020] | 2000 [1980, 2020] | 2000 [1970, 2020] | 2000 [1970, 2020] | 2000 [1970, 2020] | 2000 [1970, 2020] | 2000 [1970, 2020] | 2000 [1970, 2020] | 1990 [1970, 2020] | 2000 [1970, 2020] | 2000 [1970, 2020] |
| Central Number | ||||||||||||||
| No | 447 (38.1%) | 69 (40.1%) | 101 (59.8%) | 49 (29.3%) | 56 (34.4%) | 51 (29.3%) | 77 (44.3%) | 44 (28.4%) | 219 (37.2%) | 228 (39.0%) | 401 (36.9%) | 46 (52.3%) | 138 (40.1%) | 90 (37.3%) |
| Yes | 727 (61.9%) | 103 (59.9%) | 68 (40.2%) | 118 (70.7%) | 107 (65.6%) | 123 (70.7%) | 97 (55.7%) | 111 (71.6%) | 370 (62.8%) | 357 (61.0%) | 685 (63.1%) | 42 (47.7%) | 206 (59.9%) | 151 (62.7%) |
| Number of Transfers | ||||||||||||||
| No transfers | 488 (41.6%) | 80 (46.5%) | 87 (51.5%) | 66 (39.5%) | 41 (25.2%) | 57 (32.8%) | 84 (48.3%) | 73 (47.1%) | 236 (40.1%) | 252 (43.1%) | 440 (40.5%) | 48 (54.5%) | 167 (48.5%) | 85 (35.3%) |
| One transfer | 518 (44.1%) | 77 (44.8%) | 64 (37.9%) | 74 (44.3%) | 91 (55.8%) | 96 (55.2%) | 56 (32.2%) | 60 (38.7%) | 266 (45.2%) | 252 (43.1%) | 485 (44.7%) | 33 (37.5%) | 137 (39.8%) | 115 (47.7%) |
| Two transfers | 120 (10.2%) | 15 (8.7%) | 12 (7.1%) | 22 (13.2%) | 24 (14.7%) | 15 (8.6%) | 17 (9.8%) | 15 (9.7%) | 62 (10.5%) | 58 (9.9%) | 115 (10.6%) | 5 (5.7%) | 30 (8.7%) | 28 (11.6%) |
| More than two transfers | 48 (4.1%) | 0 (0%) | 6 (3.6%) | 5 (3.0%) | 7 (4.3%) | 6 (3.4%) | 17 (9.8%) | 7 (4.5%) | 25 (4.2%) | 23 (3.9%) | 46 (4.2%) | 2 (2.3%) | 10 (2.9%) | 13 (5.4%) |
| Day of the Week | ||||||||||||||
| Monday | 316 (26.9%) | 46 (26.7%) | 37 (21.9%) | 34 (20.4%) | 58 (35.6%) | 32 (18.4%) | 51 (29.3%) | 58 (37.4%) | 206 (35.0%) | 110 (18.8%) | 303 (27.9%) | 13 (14.8%) | 61 (17.7%) | 49 (20.3%) |
| Tuesday | 207 (17.6%) | 14 (8.1%) | 73 (43.2%) | 17 (10.2%) | 20 (12.3%) | 44 (25.3%) | 29 (16.7%) | 10 (6.5%) | 113 (19.2%) | 94 (16.1%) | 191 (17.6%) | 16 (18.2%) | 61 (17.7%) | 33 (13.7%) |
| Wednesday | 181 (15.4%) | 58 (33.7%) | 10 (5.9%) | 35 (21.0%) | 16 (9.8%) | 23 (13.2%) | 25 (14.4%) | 14 (9.0%) | 74 (12.6%) | 107 (18.3%) | 165 (15.2%) | 16 (18.2%) | 69 (20.1%) | 38 (15.8%) |
| Thursday | 301 (25.6%) | 31 (18.0%) | 34 (20.1%) | 49 (29.3%) | 49 (30.1%) | 50 (28.7%) | 46 (26.4%) | 42 (27.1%) | 93 (15.8%) | 208 (35.6%) | 270 (24.9%) | 31 (35.2%) | 120 (34.9%) | 88 (36.5%) |
| Friday | 156 (13.3%) | 16 (9.3%) | 15 (8.9%) | 29 (17.4%) | 18 (11.0%) | 25 (14.4%) | 23 (13.2%) | 30 (19.4%) | 97 (16.5%) | 59 (10.1%) | 146 (13.4%) | 10 (11.4%) | 31 (9.0%) | 28 (11.6%) |
| Saturday | 13 (1.1%) | 7 (4.1%) | 0 (0%) | 3 (1.8%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 1 (0.6%) | 6 (1.0%) | 7 (1.2%) | 11 (1.0%) | 2 (2.3%) | 2 (0.6%) | 5 (2.1%) |
| Sunday | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) |
| Reason for Exclusions | ||||||||||||||
| Able to contact | 553 (47.1%) | 78 (45.3%) | 79 (46.7%) | 68 (40.7%) | 79 (48.5%) | 78 (44.8%) | 90 (51.7%) | 81 (52.3%) | 312 (53.0%) | 241 (41.2%) | 553 (50.9%) | 0 (0%) | 0 (0%) | 241 (100%) |
| Closed medical system (e.g. Kaiser or military hospital) | 15 (1.3%) | 2 (1.2%) | 1 (0.6%) | 4 (2.4%) | 2 (1.2%) | 2 (1.1%) | 2 (1.1%) | 2 (1.3%) | 8 (1.4%) | 7 (1.2%) | 15 (1.4%) | 0 (0%) | 7 (2.0%) | 0 (0%) |
| Greater than 5 minutes on hold | 146 (12.4%) | 23 (13.4%) | 16 (9.5%) | 21 (12.6%) | 26 (16.0%) | 15 (8.6%) | 24 (13.8%) | 21 (13.5%) | 83 (14.1%) | 63 (10.8%) | 146 (13.4%) | 0 (0%) | 63 (18.3%) | 0 (0%) |
| Must see midlevel before seeing physician | 7 (0.6%) | 0 (0%) | 1 (0.6%) | 0 (0%) | 0 (0%) | 4 (2.3%) | 0 (0%) | 2 (1.3%) | 4 (0.7%) | 3 (0.5%) | 7 (0.6%) | 0 (0%) | 3 (0.9%) | 0 (0%) |
| Not accepting new patients | 73 (6.2%) | 11 (6.4%) | 20 (11.8%) | 15 (9.0%) | 8 (4.9%) | 11 (6.3%) | 8 (4.6%) | 0 (0%) | 40 (6.8%) | 33 (5.6%) | 73 (6.7%) | 0 (0%) | 33 (9.6%) | 0 (0%) |
| Number contacted did not correspond to expected office/specialty | 54 (4.6%) | 13 (7.6%) | 11 (6.5%) | 11 (6.6%) | 1 (0.6%) | 5 (2.9%) | 6 (3.4%) | 7 (4.5%) | 30 (5.1%) | 24 (4.1%) | 54 (5.0%) | 0 (0%) | 24 (7.0%) | 0 (0%) |
| Phone not answered or busy signal on repeat calls | 45 (3.8%) | 6 (3.5%) | 10 (5.9%) | 3 (1.8%) | 10 (6.1%) | 6 (3.4%) | 9 (5.2%) | 1 (0.6%) | 22 (3.7%) | 23 (3.9%) | 45 (4.1%) | 0 (0%) | 23 (6.7%) | 0 (0%) |
| Physician does not accept MEDICAID | 88 (7.5%) | 21 (12.2%) | 13 (7.7%) | 14 (8.4%) | 6 (3.7%) | 13 (7.5%) | 8 (4.6%) | 13 (8.4%) | 0 (0%) | 88 (15.0%) | 0 (0%) | 88 (100%) | 88 (25.6%) | 0 (0%) |
| Physician referral required before scheduling appointment | 77 (6.6%) | 3 (1.7%) | 2 (1.2%) | 18 (10.8%) | 20 (12.3%) | 21 (12.1%) | 7 (4.0%) | 6 (3.9%) | 32 (5.4%) | 45 (7.7%) | 77 (7.1%) | 0 (0%) | 45 (13.1%) | 0 (0%) |
| Physician's personal phone | 11 (0.9%) | 0 (0%) | 3 (1.8%) | 2 (1.2%) | 0 (0%) | 3 (1.7%) | 3 (1.7%) | 0 (0%) | 6 (1.0%) | 5 (0.9%) | 11 (1.0%) | 0 (0%) | 5 (1.5%) | 0 (0%) |
| Went to voicemail | 105 (8.9%) | 15 (8.7%) | 13 (7.7%) | 11 (6.6%) | 11 (6.7%) | 16 (9.2%) | 17 (9.8%) | 22 (14.2%) | 52 (8.8%) | 53 (9.1%) | 105 (9.7%) | 0 (0%) | 53 (15.4%) | 0 (0%) |
| Business Days until Appointment | ||||||||||||||
| Mean (SD) | 34.4 (26.8) | 27.9 (20.9) | 29.8 (26.9) | 28.9 (30.5) | 33.9 (24.0) | 41.9 (25.5) | 51.9 (30.1) | 23.9 (16.0) | 32.4 (27.8) | 37.0 (25.3) | 34.4 (26.8) | NA (NA) | NA (NA) | 37.0 (25.3) |
| Median [Min, Max] | 29.0 [1.00, 192] | 20.5 [1.00, 92.0] | 23.0 [1.00, 142] | 19.5 [1.00, 192] | 27.0 [1.00, 93.0] | 37.5 [1.00, 114] | 47.5 [2.00, 140] | 23.0 [1.00, 107] | 25.0 [1.00, 192] | 33.0 [1.00, 142] | 29.0 [1.00, 192] | NA [NA, NA] | NA [NA, NA] | 33.0 [1.00, 142] |
| Missing | 621 (52.9%) | 94 (54.7%) | 90 (53.3%) | 99 (59.3%) | 84 (51.5%) | 96 (55.2%) | 84 (48.3%) | 74 (47.7%) | 277 (47.0%) | 344 (58.8%) | 533 (49.1%) | 88 (100%) | 344 (100%) | 0 (0%) |
| District | ||||||||||||||
| Region 1 | 123 (10.5%) | 18 (10.5%) | 18 (10.7%) | 16 (9.6%) | 17 (10.4%) | 18 (10.3%) | 18 (10.3%) | 18 (11.6%) | 61 (10.4%) | 62 (10.6%) | 119 (11.0%) | 4 (4.5%) | 33 (9.6%) | 29 (12.0%) |
| Region 2 | 123 (10.5%) | 18 (10.5%) | 18 (10.7%) | 17 (10.2%) | 18 (11.0%) | 18 (10.3%) | 18 (10.3%) | 16 (10.3%) | 61 (10.4%) | 62 (10.6%) | 91 (8.4%) | 32 (36.4%) | 52 (15.1%) | 10 (4.1%) |
| Region 3 | 125 (10.6%) | 18 (10.5%) | 17 (10.1%) | 18 (10.8%) | 18 (11.0%) | 18 (10.3%) | 18 (10.3%) | 18 (11.6%) | 63 (10.7%) | 62 (10.6%) | 119 (11.0%) | 6 (6.8%) | 34 (9.9%) | 28 (11.6%) |
| Region 4 | 120 (10.2%) | 18 (10.5%) | 12 (7.1%) | 18 (10.8%) | 18 (11.0%) | 18 (10.3%) | 18 (10.3%) | 18 (11.6%) | 60 (10.2%) | 60 (10.3%) | 115 (10.6%) | 5 (5.7%) | 39 (11.3%) | 21 (8.7%) |
| Region 5 | 111 (9.5%) | 13 (7.6%) | 16 (9.5%) | 12 (7.2%) | 17 (10.4%) | 18 (10.3%) | 17 (9.8%) | 18 (11.6%) | 57 (9.7%) | 54 (9.2%) | 107 (9.9%) | 4 (4.5%) | 25 (7.3%) | 29 (12.0%) |
| Region 6 | 123 (10.5%) | 18 (10.5%) | 17 (10.1%) | 18 (10.8%) | 16 (9.8%) | 18 (10.3%) | 18 (10.3%) | 18 (11.6%) | 62 (10.5%) | 61 (10.4%) | 111 (10.2%) | 12 (13.6%) | 35 (10.2%) | 26 (10.8%) |
| Region 7 | 109 (9.3%) | 15 (8.7%) | 18 (10.7%) | 18 (10.8%) | 14 (8.6%) | 14 (8.0%) | 16 (9.2%) | 14 (9.0%) | 53 (9.0%) | 56 (9.6%) | 106 (9.8%) | 3 (3.4%) | 25 (7.3%) | 31 (12.9%) |
| Region 8 | 97 (8.3%) | 18 (10.5%) | 18 (10.7%) | 15 (9.0%) | 10 (6.1%) | 16 (9.2%) | 16 (9.2%) | 4 (2.6%) | 49 (8.3%) | 48 (8.2%) | 90 (8.3%) | 7 (8.0%) | 27 (7.8%) | 21 (8.7%) |
| Region 9 | 122 (10.4%) | 18 (10.5%) | 18 (10.7%) | 18 (10.8%) | 18 (11.0%) | 18 (10.3%) | 18 (10.3%) | 14 (9.0%) | 61 (10.4%) | 61 (10.4%) | 119 (11.0%) | 3 (3.4%) | 29 (8.4%) | 32 (13.3%) |
| Region 10 | 121 (10.3%) | 18 (10.5%) | 17 (10.1%) | 17 (10.2%) | 17 (10.4%) | 18 (10.3%) | 17 (9.8%) | 17 (11.0%) | 62 (10.5%) | 59 (10.1%) | 109 (10.0%) | 12 (13.6%) | 45 (13.1%) | 14 (5.8%) |
| State | ||||||||||||||
| Alabama | 10 (0.9%) | 2 (1.2%) | 0 (0%) | 2 (1.2%) | 2 (1.2%) | 2 (1.1%) | 2 (1.1%) | 0 (0%) | 5 (0.8%) | 5 (0.9%) | 10 (0.9%) | 0 (0%) | 3 (0.9%) | 2 (0.8%) |
| Alaska | 2 (0.2%) | 0 (0%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (0.2%) | 1 (0.2%) | 2 (0.2%) | 0 (0%) | 1 (0.3%) | 0 (0%) |
| Arizona | 11 (0.9%) | 2 (1.2%) | 0 (0%) | 2 (1.2%) | 0 (0%) | 4 (2.3%) | 2 (1.1%) | 1 (0.6%) | 6 (1.0%) | 5 (0.9%) | 10 (0.9%) | 1 (1.1%) | 4 (1.2%) | 1 (0.4%) |
| Arkansas | 12 (1.0%) | 2 (1.2%) | 4 (2.4%) | 0 (0%) | 4 (2.5%) | 2 (1.1%) | 0 (0%) | 0 (0%) | 6 (1.0%) | 6 (1.0%) | 12 (1.1%) | 0 (0%) | 2 (0.6%) | 4 (1.7%) |
| California | 105 (8.9%) | 16 (9.3%) | 15 (8.9%) | 15 (9.0%) | 17 (10.4%) | 14 (8.0%) | 14 (8.0%) | 14 (9.0%) | 54 (9.2%) | 51 (8.7%) | 94 (8.7%) | 11 (12.5%) | 39 (11.3%) | 12 (5.0%) |
| Colorado | 69 (5.9%) | 12 (7.0%) | 14 (8.3%) | 13 (7.8%) | 6 (3.7%) | 10 (5.7%) | 12 (6.9%) | 2 (1.3%) | 35 (5.9%) | 34 (5.8%) | 63 (5.8%) | 6 (6.8%) | 20 (5.8%) | 14 (5.8%) |
| Connecticut | 26 (2.2%) | 4 (2.3%) | 6 (3.6%) | 0 (0%) | 6 (3.7%) | 2 (1.1%) | 4 (2.3%) | 4 (2.6%) | 13 (2.2%) | 13 (2.2%) | 25 (2.3%) | 1 (1.1%) | 6 (1.7%) | 7 (2.9%) |
| Delaware | 4 (0.3%) | 0 (0%) | 0 (0%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 2 (1.1%) | 0 (0%) | 2 (0.3%) | 2 (0.3%) | 4 (0.4%) | 0 (0%) | 1 (0.3%) | 1 (0.4%) |
| District of Columbia | 12 (1.0%) | 0 (0%) | 0 (0%) | 4 (2.4%) | 2 (1.2%) | 4 (2.3%) | 2 (1.1%) | 0 (0%) | 6 (1.0%) | 6 (1.0%) | 12 (1.1%) | 0 (0%) | 3 (0.9%) | 3 (1.2%) |
| Florida | 38 (3.2%) | 0 (0%) | 4 (2.4%) | 6 (3.6%) | 6 (3.7%) | 6 (3.4%) | 10 (5.7%) | 6 (3.9%) | 19 (3.2%) | 19 (3.2%) | 36 (3.3%) | 2 (2.3%) | 12 (3.5%) | 7 (2.9%) |
| Georgia | 16 (1.4%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 6 (3.7%) | 2 (1.1%) | 0 (0%) | 6 (3.9%) | 8 (1.4%) | 8 (1.4%) | 16 (1.5%) | 0 (0%) | 6 (1.7%) | 2 (0.8%) |
| Idaho | 2 (0.2%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (0.2%) | 1 (0.2%) | 2 (0.2%) | 0 (0%) | 0 (0%) | 1 (0.4%) |
| Illinois | 31 (2.6%) | 2 (1.2%) | 4 (2.4%) | 6 (3.6%) | 6 (3.7%) | 4 (2.3%) | 3 (1.7%) | 6 (3.9%) | 16 (2.7%) | 15 (2.6%) | 29 (2.7%) | 2 (2.3%) | 8 (2.3%) | 7 (2.9%) |
| Indiana | 11 (0.9%) | 3 (1.7%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 2 (1.1%) | 2 (1.1%) | 2 (1.3%) | 6 (1.0%) | 5 (0.9%) | 11 (1.0%) | 0 (0%) | 1 (0.3%) | 4 (1.7%) |
| Iowa | 16 (1.4%) | 0 (0%) | 4 (2.4%) | 2 (1.2%) | 0 (0%) | 4 (2.3%) | 4 (2.3%) | 2 (1.3%) | 8 (1.4%) | 8 (1.4%) | 16 (1.5%) | 0 (0%) | 3 (0.9%) | 5 (2.1%) |
| Kansas | 28 (2.4%) | 7 (4.1%) | 6 (3.6%) | 2 (1.2%) | 4 (2.5%) | 0 (0%) | 3 (1.7%) | 6 (3.9%) | 13 (2.2%) | 15 (2.6%) | 26 (2.4%) | 2 (2.3%) | 8 (2.3%) | 7 (2.9%) |
| Kentucky | 10 (0.9%) | 2 (1.2%) | 4 (2.4%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (1.3%) | 5 (0.8%) | 5 (0.9%) | 9 (0.8%) | 1 (1.1%) | 3 (0.9%) | 2 (0.8%) |
| Louisiana | 24 (2.0%) | 2 (1.2%) | 0 (0%) | 8 (4.8%) | 6 (3.7%) | 0 (0%) | 4 (2.3%) | 4 (2.6%) | 12 (2.0%) | 12 (2.1%) | 22 (2.0%) | 2 (2.3%) | 8 (2.3%) | 4 (1.7%) |
| Maine | 4 (0.3%) | 0 (0%) | 4 (2.4%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (0.3%) | 2 (0.3%) | 4 (0.4%) | 0 (0%) | 1 (0.3%) | 1 (0.4%) |
| Maryland | 20 (1.7%) | 2 (1.2%) | 4 (2.4%) | 2 (1.2%) | 4 (2.5%) | 2 (1.1%) | 0 (0%) | 6 (3.9%) | 10 (1.7%) | 10 (1.7%) | 19 (1.7%) | 1 (1.1%) | 7 (2.0%) | 3 (1.2%) |
| Massachusetts | 77 (6.6%) | 12 (7.0%) | 6 (3.6%) | 14 (8.4%) | 11 (6.7%) | 12 (6.9%) | 8 (4.6%) | 14 (9.0%) | 38 (6.5%) | 39 (6.7%) | 75 (6.9%) | 2 (2.3%) | 22 (6.4%) | 17 (7.1%) |
| Michigan | 16 (1.4%) | 2 (1.2%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 10 (5.7%) | 2 (1.1%) | 0 (0%) | 8 (1.4%) | 8 (1.4%) | 15 (1.4%) | 1 (1.1%) | 2 (0.6%) | 6 (2.5%) |
| Minnesota | 9 (0.8%) | 2 (1.2%) | 0 (0%) | 2 (1.2%) | 1 (0.6%) | 0 (0%) | 0 (0%) | 4 (2.6%) | 5 (0.8%) | 4 (0.7%) | 9 (0.8%) | 0 (0%) | 1 (0.3%) | 3 (1.2%) |
| Mississippi | 6 (0.5%) | 4 (2.3%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 3 (0.5%) | 3 (0.5%) | 6 (0.6%) | 0 (0%) | 2 (0.6%) | 1 (0.4%) |
| Missouri | 45 (3.8%) | 6 (3.5%) | 4 (2.4%) | 8 (4.8%) | 8 (4.9%) | 8 (4.6%) | 9 (5.2%) | 2 (1.3%) | 22 (3.7%) | 23 (3.9%) | 44 (4.1%) | 1 (1.1%) | 8 (2.3%) | 15 (6.2%) |
| Montana | 4 (0.3%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (1.1%) | 0 (0%) | 0 (0%) | 2 (0.3%) | 2 (0.3%) | 3 (0.3%) | 1 (1.1%) | 1 (0.3%) | 1 (0.4%) |
| Nebraska | 20 (1.7%) | 2 (1.2%) | 4 (2.4%) | 6 (3.6%) | 2 (1.2%) | 2 (1.1%) | 0 (0%) | 4 (2.6%) | 10 (1.7%) | 10 (1.7%) | 20 (1.8%) | 0 (0%) | 6 (1.7%) | 4 (1.7%) |
| Nevada | 5 (0.4%) | 0 (0%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (0.6%) | 2 (1.3%) | 2 (0.3%) | 3 (0.5%) | 5 (0.5%) | 0 (0%) | 2 (0.6%) | 1 (0.4%) |
| New Hampshire | 8 (0.7%) | 0 (0%) | 2 (1.2%) | 2 (1.2%) | 0 (0%) | 2 (1.1%) | 2 (1.1%) | 0 (0%) | 4 (0.7%) | 4 (0.7%) | 8 (0.7%) | 0 (0%) | 2 (0.6%) | 2 (0.8%) |
| New Jersey | 10 (0.9%) | 8 (4.7%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (1.1%) | 0 (0%) | 5 (0.8%) | 5 (0.9%) | 6 (0.6%) | 4 (4.5%) | 4 (1.2%) | 1 (0.4%) |
| New Mexico | 4 (0.3%) | 0 (0%) | 0 (0%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (1.3%) | 2 (0.3%) | 2 (0.3%) | 4 (0.4%) | 0 (0%) | 1 (0.3%) | 1 (0.4%) |
| New York | 109 (9.3%) | 10 (5.8%) | 18 (10.7%) | 15 (9.0%) | 16 (9.8%) | 18 (10.3%) | 16 (9.2%) | 16 (10.3%) | 54 (9.2%) | 55 (9.4%) | 82 (7.6%) | 27 (30.7%) | 46 (13.4%) | 9 (3.7%) |
| North Carolina | 16 (1.4%) | 4 (2.3%) | 0 (0%) | 2 (1.2%) | 0 (0%) | 4 (2.3%) | 4 (2.3%) | 2 (1.3%) | 8 (1.4%) | 8 (1.4%) | 15 (1.4%) | 1 (1.1%) | 5 (1.5%) | 3 (1.2%) |
| North Dakota | 4 (0.3%) | 0 (0%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 2 (1.1%) | 0 (0%) | 0 (0%) | 2 (0.3%) | 2 (0.3%) | 4 (0.4%) | 0 (0%) | 0 (0%) | 2 (0.8%) |
| Ohio | 32 (2.7%) | 0 (0%) | 6 (3.6%) | 0 (0%) | 10 (6.1%) | 2 (1.1%) | 8 (4.6%) | 6 (3.9%) | 16 (2.7%) | 16 (2.7%) | 32 (2.9%) | 0 (0%) | 8 (2.3%) | 8 (3.3%) |
| Oklahoma | 4 (0.3%) | 2 (1.2%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (0.3%) | 2 (0.3%) | 3 (0.3%) | 1 (1.1%) | 1 (0.3%) | 1 (0.4%) |
| Oregon | 42 (3.6%) | 6 (3.5%) | 8 (4.7%) | 10 (6.0%) | 2 (1.2%) | 2 (1.1%) | 6 (3.4%) | 8 (5.2%) | 21 (3.6%) | 21 (3.6%) | 42 (3.9%) | 0 (0%) | 6 (1.7%) | 15 (6.2%) |
| Pennsylvania | 58 (4.9%) | 8 (4.7%) | 8 (4.7%) | 10 (6.0%) | 8 (4.9%) | 4 (2.3%) | 8 (4.6%) | 12 (7.7%) | 29 (4.9%) | 29 (5.0%) | 54 (5.0%) | 4 (4.5%) | 16 (4.7%) | 13 (5.4%) |
| Puerto Rico | 4 (0.3%) | 0 (0%) | 0 (0%) | 2 (1.2%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (0.3%) | 2 (0.3%) | 3 (0.3%) | 1 (1.1%) | 2 (0.6%) | 0 (0%) |
| Rhode Island | 6 (0.5%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (1.1%) | 2 (1.1%) | 0 (0%) | 3 (0.5%) | 3 (0.5%) | 5 (0.5%) | 1 (1.1%) | 2 (0.6%) | 1 (0.4%) |
| South Carolina | 10 (0.9%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 4 (2.5%) | 4 (2.3%) | 0 (0%) | 0 (0%) | 5 (0.8%) | 5 (0.9%) | 10 (0.9%) | 0 (0%) | 4 (1.2%) | 1 (0.4%) |
| South Dakota | 4 (0.3%) | 2 (1.2%) | 0 (0%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (0.3%) | 2 (0.3%) | 4 (0.4%) | 0 (0%) | 0 (0%) | 2 (0.8%) |
| Tennessee | 14 (1.2%) | 2 (1.2%) | 2 (1.2%) | 6 (3.6%) | 0 (0%) | 0 (0%) | 2 (1.1%) | 2 (1.3%) | 7 (1.2%) | 7 (1.2%) | 13 (1.2%) | 1 (1.1%) | 4 (1.2%) | 3 (1.2%) |
| Texas | 79 (6.7%) | 12 (7.0%) | 11 (6.5%) | 8 (4.8%) | 6 (3.7%) | 16 (9.2%) | 14 (8.0%) | 12 (7.7%) | 40 (6.8%) | 39 (6.7%) | 70 (6.4%) | 9 (10.2%) | 23 (6.7%) | 16 (6.6%) |
| Utah | 16 (1.4%) | 2 (1.2%) | 2 (1.2%) | 0 (0%) | 4 (2.5%) | 2 (1.1%) | 4 (2.3%) | 2 (1.3%) | 8 (1.4%) | 8 (1.4%) | 16 (1.5%) | 0 (0%) | 6 (1.7%) | 2 (0.8%) |
| Vermont | 2 (0.2%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 2 (1.1%) | 0 (0%) | 1 (0.2%) | 1 (0.2%) | 2 (0.2%) | 0 (0%) | 0 (0%) | 1 (0.4%) |
| Virginia | 21 (1.8%) | 4 (2.3%) | 3 (1.8%) | 0 (0%) | 4 (2.5%) | 6 (3.4%) | 4 (2.3%) | 0 (0%) | 11 (1.9%) | 10 (1.7%) | 20 (1.8%) | 1 (1.1%) | 5 (1.5%) | 5 (2.1%) |
| Washington | 76 (6.5%) | 10 (5.8%) | 8 (4.7%) | 8 (4.8%) | 16 (9.8%) | 16 (9.2%) | 12 (6.9%) | 6 (3.9%) | 38 (6.5%) | 38 (6.5%) | 73 (6.7%) | 3 (3.4%) | 22 (6.4%) | 16 (6.6%) |
| West Virginia | 10 (0.9%) | 4 (2.3%) | 2 (1.2%) | 0 (0%) | 0 (0%) | 2 (1.1%) | 2 (1.1%) | 0 (0%) | 5 (0.8%) | 5 (0.9%) | 10 (0.9%) | 0 (0%) | 2 (0.6%) | 3 (1.2%) |
| Wisconsin | 12 (1.0%) | 4 (2.3%) | 2 (1.2%) | 4 (2.4%) | 0 (0%) | 0 (0%) | 2 (1.1%) | 0 (0%) | 6 (1.0%) | 6 (1.0%) | 11 (1.0%) | 1 (1.1%) | 5 (1.5%) | 1 (0.4%) |
Here we compare the providers in the analysis because they have some data available and the ones that are excluded from the analysis. Assuming that the “Total” column is representative, we can have an idea if the analyzed providers are skewed.
Caution - Some variables like “Day of the Week” varies with Insurance type and should not be looked at. For this table we selected only the Insurance Type Medicaid.
Analysis Status |
|||
|---|---|---|---|
| Total (N=585) |
0 (N=321) |
1 (N=264) |
|
| Physician Gender | |||
| Female | 126 (21.5%) | 67 (20.9%) | 59 (22.3%) |
| Male | 459 (78.5%) | 254 (79.1%) | 205 (77.7%) |
| Physician Age in Years | |||
| Mean (SD) | 52.7 (11.5) | 52.7 (11.8) | 52.6 (11.2) |
| Median [Min, Max] | 52.0 [29.0, 86.0] | 52.0 [29.0, 86.0] | 52.0 [29.0, 82.0] |
| specialty | |||
| Facial Plastic and Reconstructive Surgery | 86 (14.7%) | 49 (15.3%) | 37 (14.0%) |
| General Otolaryngology | 83 (14.2%) | 42 (13.1%) | 41 (15.5%) |
| Head and Neck Surgery | 83 (14.2%) | 45 (14.0%) | 38 (14.4%) |
| Laryngology | 81 (13.8%) | 44 (13.7%) | 37 (14.0%) |
| Neurotology | 87 (14.9%) | 56 (17.4%) | 31 (11.7%) |
| Pediatric Otolaryngology | 88 (15.0%) | 47 (14.6%) | 41 (15.5%) |
| Rhinology | 77 (13.2%) | 38 (11.8%) | 39 (14.8%) |
| Professional Title | |||
| MD | 569 (97.3%) | 311 (96.9%) | 258 (97.7%) |
| DO | 16 (2.7%) | 10 (3.1%) | 6 (2.3%) |
| Central Number | NA | NA | NA |
| Number of Transfers | |||
| No transfers | 252 (43.1%) | 144 (44.9%) | 108 (40.9%) |
| One transfer | 252 (43.1%) | 128 (39.9%) | 124 (47.0%) |
| Two transfers | 58 (9.9%) | 37 (11.5%) | 21 (8.0%) |
| More than two transfers | 23 (3.9%) | 12 (3.7%) | 11 (4.2%) |
| Day of the Week | |||
| Friday | 66 (11.3%) | 35 (10.9%) | 31 (11.7%) |
| Monday | 110 (18.8%) | 61 (19.0%) | 49 (18.6%) |
| Tuesday | 94 (16.1%) | 58 (18.1%) | 36 (13.6%) |
| Wednesday | 107 (18.3%) | 59 (18.4%) | 48 (18.2%) |
| Thursday | 208 (35.6%) | 108 (33.6%) | 100 (37.9%) |
| Reason for Exclusions | |||
| Able to contact | 241 (41.2%) | 121 (37.7%) | 120 (45.5%) |
| Closed medical system (e.g. Kaiser or military hospital) | 7 (1.2%) | 3 (0.9%) | 4 (1.5%) |
| Greater than 5 minutes on hold | 63 (10.8%) | 39 (12.1%) | 24 (9.1%) |
| Must see midlevel before seeing physician | 3 (0.5%) | 1 (0.3%) | 2 (0.8%) |
| Not accepting new patients | 33 (5.6%) | 19 (5.9%) | 14 (5.3%) |
| Number contacted did not correspond to expected office/specialty | 24 (4.1%) | 16 (5.0%) | 8 (3.0%) |
| Phone not answered or busy signal on repeat calls | 23 (3.9%) | 13 (4.0%) | 10 (3.8%) |
| Physician does not accept MEDICAID | 88 (15.0%) | 42 (13.1%) | 46 (17.4%) |
| Physician referral required before scheduling appointment | 45 (7.7%) | 30 (9.3%) | 15 (5.7%) |
| Physician's personal phone | 5 (0.9%) | 3 (0.9%) | 2 (0.8%) |
| Went to voicemail | 53 (9.1%) | 34 (10.6%) | 19 (7.2%) |
| Business Days until Appointment | |||
| Mean (SD) | 37.0 (25.3) | 38.5 (25.9) | 35.6 (24.7) |
| Median [Min, Max] | 33.0 [1.00, 142] | 34.0 [4.00, 142] | 30.0 [1.00, 108] |
| Missing | 344 (58.8%) | 200 (62.3%) | 144 (54.5%) |
| MEDICAID Acceptance | |||
| Yes the physician accepts Medicaid | 497 (85.0%) | 279 (86.9%) | 218 (82.6%) |
| No the physician does NOT accept Medicaid | 88 (15.0%) | 42 (13.1%) | 46 (17.4%) |
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.
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.
The models need to be able to deal with NA in the days
outcome variable (621) and also non-parametric data.
## [1] 1174 51## [1] 621## [1] 0## [1] 402 51## [1] 402## [1] 51poissonGiven that the “days” 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.
$$
\[\begin{align*}\\ P(\text{{Days until New Patient Appointment}} = x) = \frac{{e^{-\lambda} \cdot \lambda^x}}{{x!}}\\ \\where\\ \log(\lambda) = & \beta_0 + \beta_1 \cdot \text{{Patient Insurance}} \\ & + \beta_2 \cdot \text{{Physician Age}}\\ & + \beta_3 \cdot \text{{Physician Academic Affiliation}} \\ & + \beta_4 \cdot \text{{American Academy of Otolaryngology Board of Governor Regions}}\\ & + \beta_5 \cdot \text{{Physician Medical Training}} \\ & + \beta_6 \cdot \text{{Physician Gender}} \\ & + \beta_7 \cdot \text{{Central Appointment Phone Number}} \\ & + \beta_8 \cdot \text{{Physician Specialty}} \end{align*}\]
$$
Summary of the Poisson model called poisson. According
to the model, Medicaid is associated with 6% longer waiting time in
terms of number of business days. The ICC is quite high (93%) indicating
that waiting times are correlated (similar) within providers.
## Generalized linear mixed model fit by maximum likelihood (Adaptive
## Gauss-Hermite Quadrature, nAGQ = 0) [glmerMod]
## Family: poisson ( log )
## Formula: days ~ insurance + Age + academic_affiliation + AAO_regions +
## title + gender + central + specialty + (1 | name)
## Data: df3
##
## AIC BIC logLik deviance df.resid
## 5139.9 5239.1 -2546.9 5093.9 530
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -8.6858 -0.3268 -0.0485 0.2202 8.4932
##
## Random effects:
## Groups Name Variance Std.Dev.
## name (Intercept) 0.5416 0.736
## Number of obs: 553, groups: name, 352
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 3.015533 0.284355 10.605
## insuranceMedicaid 0.057309 0.016418 3.491
## Age 0.001275 0.004107 0.310
## academic_affiliationUniversity 0.316874 0.097599 3.247
## AAO_regionsRegion 2 -0.555242 0.198829 -2.793
## AAO_regionsRegion 3 -0.389432 0.184143 -2.115
## AAO_regionsRegion 4 -0.211254 0.186665 -1.132
## AAO_regionsRegion 5 -0.074786 0.185574 -0.403
## AAO_regionsRegion 6 -0.433545 0.188610 -2.299
## AAO_regionsRegion 7 -0.148452 0.180822 -0.821
## AAO_regionsRegion 8 -0.229150 0.197853 -1.158
## AAO_regionsRegion 9 -0.023481 0.182088 -0.129
## AAO_regionsRegion 10 0.075549 0.194875 0.388
## titleDO 0.422752 0.230211 1.836
## genderMale -0.110520 0.106967 -1.033
## centralYes 0.163706 0.036433 4.493
## specialtyGeneral Otolaryngology 0.026267 0.154674 0.170
## specialtyHead and Neck Surgery -0.066436 0.157449 -0.422
## specialtyLaryngology 0.147474 0.156193 0.944
## specialtyNeurotology 0.413882 0.155498 2.662
## specialtyPediatric Otolaryngology 0.603786 0.158086 3.819
## specialtyRhinology -0.115600 0.159114 -0.727
## Pr(>|z|)
## (Intercept) < 0.0000000000000002 ***
## insuranceMedicaid 0.000482 ***
## Age 0.756208
## academic_affiliationUniversity 0.001168 **
## AAO_regionsRegion 2 0.005229 **
## AAO_regionsRegion 3 0.034444 *
## AAO_regionsRegion 4 0.257749
## AAO_regionsRegion 5 0.686948
## AAO_regionsRegion 6 0.021526 *
## AAO_regionsRegion 7 0.411657
## AAO_regionsRegion 8 0.246791
## AAO_regionsRegion 9 0.897395
## AAO_regionsRegion 10 0.698253
## titleDO 0.066303 .
## genderMale 0.301502
## centralYes 0.00000701 ***
## specialtyGeneral Otolaryngology 0.865150
## specialtyHead and Neck Surgery 0.673061
## specialtyLaryngology 0.345078
## specialtyNeurotology 0.007776 **
## specialtyPediatric Otolaryngology 0.000134 ***
## specialtyRhinology 0.467516
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1| days | |||
|---|---|---|---|
| Predictors | Incidence Rate Ratios | CI | p |
| (Intercept) | 20.40 | 11.68 – 35.62 | <0.001 |
| insurance [Medicaid] | 1.06 | 1.03 – 1.09 | <0.001 |
| Age | 1.00 | 0.99 – 1.01 | 0.756 |
|
academic affiliation [University] |
1.37 | 1.13 – 1.66 | 0.001 |
| AAO regions [Region 2] | 0.57 | 0.39 – 0.85 | 0.005 |
| AAO regions [Region 3] | 0.68 | 0.47 – 0.97 | 0.034 |
| AAO regions [Region 4] | 0.81 | 0.56 – 1.17 | 0.258 |
| AAO regions [Region 5] | 0.93 | 0.65 – 1.34 | 0.687 |
| AAO regions [Region 6] | 0.65 | 0.45 – 0.94 | 0.022 |
| AAO regions [Region 7] | 0.86 | 0.60 – 1.23 | 0.412 |
| AAO regions [Region 8] | 0.80 | 0.54 – 1.17 | 0.247 |
| AAO regions [Region 9] | 0.98 | 0.68 – 1.40 | 0.897 |
| AAO regions [Region 10] | 1.08 | 0.74 – 1.58 | 0.698 |
| title [DO] | 1.53 | 0.97 – 2.40 | 0.066 |
| gender [Male] | 0.90 | 0.73 – 1.10 | 0.302 |
| central [Yes] | 1.18 | 1.10 – 1.27 | <0.001 |
|
specialty [General Otolaryngology] |
1.03 | 0.76 – 1.39 | 0.865 |
|
specialty [Head and Neck Surgery] |
0.94 | 0.69 – 1.27 | 0.673 |
| specialty [Laryngology] | 1.16 | 0.85 – 1.57 | 0.345 |
| specialty [Neurotology] | 1.51 | 1.12 – 2.05 | 0.008 |
|
specialty [Pediatric Otolaryngology] |
1.83 | 1.34 – 2.49 | <0.001 |
| specialty [Rhinology] | 0.89 | 0.65 – 1.22 | 0.468 |
| Random Effects | |||
| σ2 | 0.04 | ||
| τ00 name | 0.54 | ||
| ICC | 0.93 | ||
| N name | 352 | ||
| Observations | 553 | ||
| Marginal R2 / Conditional R2 | 0.220 / 0.947 | ||
## # Indices of model performance
##
## AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma | Score_log | Score_spherical
## --------------------------------------------------------------------------------------------------------------
## 5139.868 | 5141.955 | 5239.121 | 0.947 | 0.220 | 0.932 | 8.017 | 1.000 | -3.342 | 0.037Checking the binned residuals but because the data is non-parametric the residuals will not be normally distributed. Collinearity was tested.
Here we see that the Normal model is quite reasonable for this data, as the residuals looks normally distributed.
## Warning: Probably bad model fit. Only about 71% of the residuals are inside the error bounds.## GVIF Df GVIF^(1/(2*Df))
## insurance 1.003839 1 1.001917
## Age 1.181465 1 1.086952
## academic_affiliation 1.388681 1 1.178423
## AAO_regions 1.434957 9 1.020266
## title 1.086238 1 1.042227
## gender 1.137024 1 1.066313
## central 1.039516 1 1.019567
## specialty 1.441629 6 1.030950## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance
## insurance 1.00 [1.00, 4.64e+06] 1.00 1.00
## Age 1.18 [1.10, 1.33] 1.09 0.85
## academic_affiliation 1.39 [1.27, 1.56] 1.18 0.72
## AAO_regions 1.43 [1.31, 1.61] 1.20 0.70
## title 1.09 [1.03, 1.25] 1.04 0.92
## gender 1.14 [1.07, 1.29] 1.07 0.88
## central 1.04 [1.00, 1.35] 1.02 0.96
## specialty 1.44 [1.31, 1.62] 1.20 0.69
## Tolerance 95% CI
## [0.00, 1.00]
## [0.75, 0.91]
## [0.64, 0.79]
## [0.62, 0.76]
## [0.80, 0.97]
## [0.78, 0.94]
## [0.74, 1.00]
## [0.62, 0.76]## OK: No outliers detected.
## - Based on the following method and threshold: cook (0.7).
## - For variable: (Whole model)In order to have an idea if there is over-dispersion we divide the Pearson Chi-square by the degree of freedom of the residuals. This ratio should be around 1, with values larger then 1 indicating over-dispersion and lower than 1 indicating under-dispersion. In our case we get the value 1.488 which indicates some over-dispersion. However, if we have overdispersion, our p-value is going to be too small than it should be, so that a significant p-value will be less significant under over-dispersion.
## # Overdispersion test
##
## dispersion ratio = 1.488
## Pearson's Chi-Squared = 788.471
## p-value = < 0.001## chisq ratio rdf
## 788.471296951755107330 1.487681692361802144 530.000000000000000000
## p
## 0.000000000001905755## Warning: Autocorrelated residuals detected (p < .001).## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance
## insurance 1.00 [1.00, 4.64e+06] 1.00 1.00
## Age 1.18 [1.10, 1.33] 1.09 0.85
## academic_affiliation 1.39 [1.27, 1.56] 1.18 0.72
## AAO_regions 1.43 [1.31, 1.61] 1.20 0.70
## title 1.09 [1.03, 1.25] 1.04 0.92
## gender 1.14 [1.07, 1.29] 1.07 0.88
## central 1.04 [1.00, 1.35] 1.02 0.96
## specialty 1.44 [1.31, 1.62] 1.20 0.69
## Tolerance 95% CI
## [0.00, 1.00]
## [0.75, 0.91]
## [0.64, 0.79]
## [0.62, 0.76]
## [0.80, 0.97]
## [0.78, 0.94]
## [0.74, 1.00]
## [0.62, 0.76]## [1] FALSETesting 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.' 4.425602 (df=23)This command will create a residuals plot that can help you check the assumptions of your Poisson regression model. If the plot shows a random scatter, then the assumptions are likely met. If the plot shows a clear pattern or trend, then the assumptions might not be met, and you might need to consider a different modeling approach.
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.
We will need to check interaction of insurance with the
other significant variables. “significant variables in the model
estimates” refer to predictors that have a significant effect on the
response variable individually, while the “ANOVA” assesses the overall
significance of the model and the joint significance of all
predictors.
| x |
|---|
| insurance |
| academic_affiliation |
| AAO_regions |
| central |
| specialty |
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, AAO_regions, central, specialty), 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 insurance, 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.
There is a statistically significant different with the interaction
between insurance and academic affiliation. The interaction term
insuranceMedicaid:academic_affiliationUniversity is
statistically significant (p < 0.005), which suggests that the effect
of having Medicaid insurance on the number of days until a new patient
appointment (the outcome variable) depends on whether the affiliation is
with a university or not.
The estimated coefficient for this interaction term is -0.095328. When we exponentiate -0.095328, we get approximately 0.91. So, for university-affiliated providers, having Medicaid insurance is associated with about a 9% decrease in the expected count of days until a new patient appointment, compared to not having Medicaid insurance. This is a relative comparison and it’s conditional on the other variables in the model.
We can show the effect in a graph. Notice that these are model adjusted means, that is, it is not just average waiting time, but the average waiting time controlled for the other variable in the model.
Usually the graph above should be good enough, but people always want to conduct statistical tests.
## $emmeans
## academic_affiliation = Private Practice:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 26.2 3.22 Inf 20.6 33.3
## Medicaid 27.7 3.41 Inf 21.8 35.3
##
## academic_affiliation = University:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 35.9 5.06 Inf 27.3 47.3
## Medicaid 38.0 5.35 Inf 28.9 50.1
##
## Results are averaged over the levels of: AAO_regions, title, gender, central, specialty
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale
##
## $contrasts
## academic_affiliation = Private Practice:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## academic_affiliation = University:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## Results are averaged over the levels of: AAO_regions, title, gender, central, specialty
## Tests are performed on the log scaleThe interaction term allows us to understand how the effect of one predictor variable (here, insuranceMedicaid) on the response variable (days) changes at different levels of another predictor variable (AAO_regions).
insuranceMedicaid:AAO_regionsRegion 2: The interaction term is negative and significant (p = 0.000734), suggesting that the effect of having Medicaid insurance on the number of days until appointment is less in AAO region 2 compared to the reference region (Region 1).
insuranceMedicaid:AAO_regionsRegion 7: The interaction term is negative and significant (p = 0.001404), implying that the effect of having Medicaid insurance on the number of days until appointment is less in AAO region 7 compared to the reference region.
insuranceMedicaid:AAO_regionsRegion 10: The interaction term is positive and significant (p = 0.003653), suggesting that the effect of having Medicaid insurance on the number of days until appointment is greater in AAO region 10 compared to the reference region.
Usually the graph above should be good enough, but people always want to conduct statistical tests.
## $emmeans
## AAO_regions = Region 1:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 37.4 6.55 Inf 26.5 52.7
## Medicaid 39.6 6.93 Inf 28.1 55.8
##
## AAO_regions = Region 2:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 21.5 4.01 Inf 14.9 30.9
## Medicaid 22.7 4.25 Inf 15.8 32.8
##
## AAO_regions = Region 3:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 25.3 4.39 Inf 18.0 35.6
## Medicaid 26.8 4.65 Inf 19.1 37.7
##
## AAO_regions = Region 4:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 30.3 5.38 Inf 21.4 42.9
## Medicaid 32.1 5.70 Inf 22.6 45.4
##
## AAO_regions = Region 5:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 34.7 5.70 Inf 25.2 47.9
## Medicaid 36.8 6.03 Inf 26.7 50.7
##
## AAO_regions = Region 6:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 24.2 4.34 Inf 17.1 34.4
## Medicaid 25.7 4.59 Inf 18.1 36.5
##
## AAO_regions = Region 7:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 32.2 5.20 Inf 23.5 44.2
## Medicaid 34.1 5.50 Inf 24.9 46.8
##
## AAO_regions = Region 8:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 29.7 5.41 Inf 20.8 42.5
## Medicaid 31.5 5.73 Inf 22.0 45.0
##
## AAO_regions = Region 9:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 36.5 6.35 Inf 26.0 51.4
## Medicaid 38.7 6.72 Inf 27.5 54.4
##
## AAO_regions = Region 10:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 40.3 7.28 Inf 28.3 57.5
## Medicaid 42.7 7.72 Inf 30.0 60.9
##
## Results are averaged over the levels of: academic_affiliation, title, gender, central, specialty
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale
##
## $contrasts
## AAO_regions = Region 1:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## AAO_regions = Region 2:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## AAO_regions = Region 3:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## AAO_regions = Region 4:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## AAO_regions = Region 5:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## AAO_regions = Region 6:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## AAO_regions = Region 7:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## AAO_regions = Region 8:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## AAO_regions = Region 9:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## AAO_regions = Region 10:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## Results are averaged over the levels of: academic_affiliation, title, gender, central, specialty
## Tests are performed on the log scaleThe interaction term insuranceMedicaid:centralYes is negative and statistically significant (p < 0.0001). This implies that the effect of having Medicaid insurance on the number of days until appointment is less when there is a central appointment phone number (centralYes) compared to when there isn’t a central appointment phone number.
In other words, the presence of a central appointment phone number appears to mitigate the impact of having Medicaid insurance on the number of days until appointment. However, this interpretation assumes that all other variables in the model are held constant.
As with any statistical analysis, it’s important to remember that correlation does not imply causation. While we can identify relationships between variables, these relationships don’t necessarily mean that one variable is causing the other to change. Further research might be needed to explore these relationships in more detail.
Usually the graph above should be good enough, but people always want to conduct statistical tests.
## $emmeans
## central = No:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 28.2 3.55 Inf 22.1 36.1
## Medicaid 29.9 3.75 Inf 23.4 38.3
##
## central = Yes:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 33.3 4.09 Inf 26.2 42.3
## Medicaid 35.2 4.33 Inf 27.7 44.8
##
## Results are averaged over the levels of: academic_affiliation, AAO_regions, title, gender, specialty
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale
##
## $contrasts
## central = No:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## central = Yes:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## Results are averaged over the levels of: academic_affiliation, AAO_regions, title, gender, specialty
## Tests are performed on the log scaleThis model contains multiple interaction terms between the
insuranceMedicaid and each level of the
specialty variable. Each interaction term allows us to
understand how the effect of having Medicaid insurance on the response
variable (days) changes at different levels of the
specialty variable.
insuranceMedicaid:specialtyGeneral Otolaryngology:
This interaction term is not statistically significant (p = 0.471061),
which suggests that there is no significant difference in the number of
days until appointment for Medicaid patients in the General
Otolaryngology specialty compared to those not in this specialty,
assuming all other variables in the model are held constant.
insuranceMedicaid:specialtyHead and Neck Surgery:
This interaction term is statistically significant (p = 0.006185) and
negative. This suggests that for patients in the Head and Neck Surgery
specialty, having Medicaid insurance is associated with fewer days until
appointment, compared to those not in this specialty, assuming all other
variables in the model are held constant.
Remember that these interpretations are based on the statistical model and the data used, and they don’t necessarily imply causation. They should be used as part of a larger investigation into these relationships.
Usually the graph above should be good enough, but people always want to conduct statistical tests. So in this case, the code is computing the estimated marginal means of the insurance factor within each level of the specialty factor, and then back-transforming the results to the original scale of the data (i.e., count data in the case of a Poisson model). It is also computing pairwise comparisons of the levels of the insurance factor within each level of the specialty factor. This can be useful for understanding the differences in the expected counts between different levels of the insurance factor within each specialty
## $emmeans
## specialty = Facial Plastic and Reconstructive Surgery:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 26.5 4.16 Inf 19.5 36.1
## Medicaid 28.1 4.40 Inf 20.7 38.2
##
## specialty = General Otolaryngology:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 27.2 4.22 Inf 20.1 36.9
## Medicaid 28.9 4.47 Inf 21.3 39.1
##
## specialty = Head and Neck Surgery:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 24.8 4.15 Inf 17.9 34.5
## Medicaid 26.3 4.39 Inf 19.0 36.5
##
## specialty = Laryngology:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 30.8 4.90 Inf 22.5 42.0
## Medicaid 32.6 5.18 Inf 23.8 44.5
##
## specialty = Neurotology:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 40.1 6.66 Inf 29.0 55.6
## Medicaid 42.5 7.05 Inf 30.7 58.8
##
## specialty = Pediatric Otolaryngology:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 48.5 7.50 Inf 35.9 65.7
## Medicaid 51.4 7.94 Inf 38.0 69.6
##
## specialty = Rhinology:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/Blue Shield 23.6 3.86 Inf 17.2 32.6
## Medicaid 25.0 4.09 Inf 18.2 34.5
##
## Results are averaged over the levels of: academic_affiliation, AAO_regions, title, gender, central
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale
##
## $contrasts
## specialty = Facial Plastic and Reconstructive Surgery:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## specialty = General Otolaryngology:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## specialty = Head and Neck Surgery:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## specialty = Laryngology:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## specialty = Neurotology:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## specialty = Pediatric Otolaryngology:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## specialty = Rhinology:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/Blue Shield) / Medicaid 0.944 0.0155 Inf 1 -3.491 0.0005
##
## Results are averaged over the levels of: academic_affiliation, AAO_regions, title, gender, central
## Tests are performed on the log scalegamma_model| days | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 17.60 | 10.04 – 30.85 | <0.001 |
| insurance [Medicaid] | 1.15 | 1.06 – 1.24 | 0.001 |
| Age | 1.00 | 0.99 – 1.01 | 0.729 |
|
academic affiliation [University] |
1.39 | 1.15 – 1.69 | 0.001 |
| AAO regions [Region 2] | 0.57 | 0.39 – 0.83 | 0.004 |
| AAO regions [Region 3] | 0.69 | 0.48 – 0.98 | 0.040 |
| AAO regions [Region 4] | 0.83 | 0.58 – 1.20 | 0.323 |
| AAO regions [Region 5] | 0.95 | 0.66 – 1.37 | 0.778 |
| AAO regions [Region 6] | 0.64 | 0.45 – 0.93 | 0.019 |
| AAO regions [Region 7] | 0.89 | 0.62 – 1.26 | 0.496 |
| AAO regions [Region 8] | 0.84 | 0.57 – 1.24 | 0.375 |
| AAO regions [Region 9] | 1.01 | 0.71 – 1.44 | 0.945 |
| AAO regions [Region 10] | 1.15 | 0.78 – 1.69 | 0.486 |
| title [DO] | 1.56 | 1.00 – 2.44 | 0.052 |
| gender [Male] | 0.90 | 0.73 – 1.11 | 0.342 |
| central [Yes] | 1.22 | 1.06 – 1.41 | 0.007 |
|
specialty [General Otolaryngology] |
1.06 | 0.78 – 1.43 | 0.718 |
|
specialty [Head and Neck Surgery] |
0.94 | 0.70 – 1.28 | 0.711 |
| specialty [Laryngology] | 1.18 | 0.87 – 1.59 | 0.296 |
| specialty [Neurotology] | 1.54 | 1.14 – 2.09 | 0.005 |
|
specialty [Pediatric Otolaryngology] |
1.89 | 1.39 – 2.58 | <0.001 |
| specialty [Rhinology] | 0.91 | 0.67 – 1.24 | 0.542 |
| Random Effects | |||
| σ2 | 0.18 | ||
| τ00 name | 0.45 | ||
| ICC | 0.72 | ||
| N name | 352 | ||
| Observations | 553 | ||
| Marginal R2 / Conditional R2 | 0.229 / 0.783 | ||
## # Indices of model performance
##
## AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma
## ---------------------------------------------------------------------------------
## 4557.195 | 4559.467 | 4660.763 | 0.783 | 0.229 | 0.719 | 10.186 | 0.419## Warning: Autocorrelated residuals detected (p < .001).## [1] FALSE## Warning: Probably bad model fit. Only about 46% of the residuals are inside the error bounds.## # Distribution of Model Family
##
## Predicted Distribution of Residuals
##
## Distribution Probability
## cauchy 50%
## normal 28%
## beta 9%
##
## Predicted Distribution of Response
##
## Distribution Probability
## neg. binomial (zero-infl.) 78%
## gamma 9%
## beta-binomial 6%## [[1]]## days ~ insurance + Age + academic_affiliation + AAO_regions +
## title + gender + central + specialty + (1 | name)mixed.lmer\[ \begin{align*} \textit{Business Days Until a New Patient Visit} = &\beta_0 + \beta_1 \, \text{Physician Age} \\ & + \beta_2 \, \text{Physician Gender} + \beta_3 \, \text{Physician Subspecialty} \\ & + \beta_4 \, \text{Physician Medical School Training} + \beta_5 \, \text{Physician Academic Affiliation} \\ & + \beta_6 \, \text{Physician American Academy of Otolaryngology Head and Neck Surgery Region}\\ & + \beta_7 \, \text{Number of Phone Transfers} + \beta_8 \,\text{Patient Insurance } + (1|\text{ Physician Name})\\ & + u_{0i} + \epsilon_{ij}\\ \end{align*} \] mixed.lmer <- lmerTest::lmer(formula = days ~ insurance + Age + academic_affiliation + AAO_regions + title + gender + central + specialty + (1 | name), data = df3, verbose = 0L)
The parameter \(\beta_0\) represents the intercept term in the linear regression equation. It denotes the expected value of the response variable (in this case, the log of the (\(Business\ Days\ Until\ a\ New\ Patient\ Visit)\) when all other predictor variables in the model are set to zero or their reference levels. In other words, \(\beta_0\) represents the average or baseline value of the response variable when all predictors are absent or have no effect. \(\beta_1\), \(\beta_2\), \(\beta_3\), \(\beta_4\), \(\beta_5\), \(\beta_6\), \(\beta_7\), and \(\beta_8\) are the regression coefficients associated with the respective predictor variables.
The term (\(1|Physician\ Name)\) represents the random effect component in the linear mixed model. It indicates that there is random variation in the intercept (or baseline level) of the response variable across different levels of the “Physician Name” variable. This random effect allows for individual-level variability and accounts for potential heterogeneity among individuals in terms of their baseline values. In other words, it acknowledges that individuals with different years of leadership position experience may have different intercepts or starting points for the response variable. The notation “(\(1|Physician\ Name)\)” specifies that the random effect is associated with the grouping variable ( \(Physician\ Name)\).
\(u_{0i}\) represents the random effect, capturing the individual-level variability and accounting for potential heterogeneity among individuals in terms of the intercept.
\(\epsilon_{ij}\) is the error term, representing the random variation not accounted for by the fixed and random effects.
## Warning: Non-normality of residuals detected (p < .001).## Warning: Heteroscedasticity (non-constant error variance) detected (p < .001).## Warning: Autocorrelated residuals detected (p < .001).## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
## insurance 1.01 [1.00, 7.46] 1.01 0.99 [0.13, 1.00]
## Age 1.18 [1.10, 1.33] 1.09 0.85 [0.75, 0.91]
## academic_affiliation 1.42 [1.29, 1.59] 1.19 0.71 [0.63, 0.77]
## AAO_regions 1.54 [1.40, 1.74] 1.24 0.65 [0.58, 0.71]
## title 1.09 [1.03, 1.26] 1.05 0.91 [0.80, 0.97]
## gender 1.14 [1.06, 1.29] 1.07 0.88 [0.78, 0.94]
## central 1.16 [1.08, 1.30] 1.08 0.87 [0.77, 0.93]
## specialty 1.46 [1.33, 1.65] 1.21 0.68 [0.61, 0.75]## [1] FALSE## # Indices of model performance
##
## AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma
## ---------------------------------------------------------------------------------
## 4896.947 | 4899.220 | 5000.516 | 0.769 | 0.206 | 0.709 | 9.240 | 13.146## Analysis of Deviance Table (Type II Wald chisquare tests)
##
## Response: days
## Chisq Df Pr(>Chisq)
## insurance 2.6920 1 0.100856
## Age 0.0086 1 0.926069
## academic_affiliation 8.2028 1 0.004182 **
## AAO_regions 16.3170 9 0.060549 .
## title 1.7170 1 0.190074
## gender 1.8209 1 0.177203
## central 5.7873 1 0.016143 *
## specialty 43.0185 6 0.0000001157 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [1] "academic_affiliation" "central" "specialty"We can show the effect in a graph. Notice that these are model adjusted means, that is, it is not just average waiting time, but the average waiting time controlled for the other variable in the model.
## insurance emmean SE df lower.CL upper.CL
## Blue Cross/Blue Shield 38.22310 3.822004 333.56 30.70484 45.74137
## Medicaid 40.28832 3.821665 335.41 32.77087 47.80577
##
## Results are averaged over the levels of: academic_affiliation, AAO_regions, title, gender, central, specialty
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95The estimated marginal means (average response) for the insurance variable are as follows:
Blue Cross/Blue Shield: The estimated average waiting time (rate) is 38.22 days. The standard error (SE) associated with this estimate is 3.82. The degrees of freedom (df) are infinite. The 95% confidence interval for the average waiting time ranges from 30.7 to 45.74 days.
Medicaid: The estimated average waiting time (rate) is 40.29 days. The standard error (SE) associated with this estimate is 3.82. The degrees of freedom (df) are infinite. The 95% confidence interval for the average waiting time ranges from 32.77 to 47.81 days.
Look at each set of statistically significant variables.
## Analysis of Deviance Table (Type II Wald chisquare tests)
##
## Response: days
## Chisq Df Pr(>Chisq)
## insurance 2.6920 1 0.100856
## Age 0.0086 1 0.926069
## academic_affiliation 8.2028 1 0.004182 **
## AAO_regions 16.3170 9 0.060549 .
## title 1.7170 1 0.190074
## gender 1.8209 1 0.177203
## central 5.7873 1 0.016143 *
## specialty 43.0185 6 0.0000001157 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## academic_affiliation emmean SE df lower.CL upper.CL
## Private Practice 34.94179 3.752374 313.50 27.55877 42.32481
## University 43.56963 4.344862 325.42 35.02207 52.11720
##
## Results are averaged over the levels of: insurance, AAO_regions, title, gender, central, specialty
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95## AAO_regions emmean SE df lower.CL upper.CL
## Region 1 47.06905 5.374782 315.27 36.49408 57.64403
## Region 2 33.08380 5.760264 349.37 21.75465 44.41296
## Region 3 32.94172 5.318999 320.98 22.47722 43.40623
## Region 4 36.56160 5.509696 334.33 25.72356 47.39964
## Region 5 45.65301 5.005133 316.84 35.80551 55.50051
## Region 6 34.91020 5.413114 322.45 24.26072 45.55968
## Region 7 40.34934 4.929196 317.69 30.65135 50.04733
## Region 8 35.07326 5.520348 313.10 24.21159 45.93493
## Region 9 40.71568 5.328724 322.09 30.23218 51.19918
## Region 10 46.19946 5.601506 343.26 35.18186 57.21705
##
## Results are averaged over the levels of: insurance, academic_affiliation, title, gender, central, specialty
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95## specialty emmean SE df lower.CL
## Facial Plastic and Reconstructive Surgery 35.58671 4.780385 327.44 26.18257
## General Otolaryngology 37.15389 4.708783 316.49 27.88942
## Head and Neck Surgery 35.02958 5.109204 328.06 24.97864
## Laryngology 37.29721 4.904670 327.67 27.64860
## Neurotology 46.81708 5.113254 325.48 36.75788
## Pediatric Otolaryngology 55.06258 4.735815 316.36 45.74491
## Rhinology 27.84293 4.988039 320.27 18.02947
## upper.CL
## 44.99086
## 46.41836
## 45.08051
## 46.94583
## 56.87628
## 64.38025
## 37.65639
##
## Results are averaged over the levels of: insurance, academic_affiliation, AAO_regions, title, gender, central
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95## insurance emmean SE df lower.CL upper.CL
## Blue Cross/Blue Shield 38.22310 3.822004 333.56 30.70484 45.74137
## Medicaid 40.28832 3.821665 335.41 32.77087 47.80577
##
## Results are averaged over the levels of: academic_affiliation, AAO_regions, title, gender, central, specialty
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95## central emmean SE df lower.CL upper.CL
## No 36.51713 4.101914 364.49 28.45074 44.58351
## Yes 41.99430 3.769014 318.42 34.57898 49.40962
##
## Results are averaged over the levels of: insurance, academic_affiliation, AAO_regions, title, gender, specialty
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95Subspecialty is significant as we see in the ANOVA table. Estimates with confidence interval of the number of days of waiting time. We also look at pairwise differences. Here we use Bonferroni adjustment for multiple
| days | |||
|---|---|---|---|
| Predictors | Incidence Rate Ratios | CI | p |
| (Intercept) | 19.97 | 11.42 – 34.91 | <0.001 |
| insurance [Medicaid] | 1.06 | 1.03 – 1.09 | <0.001 |
| Age | 1.00 | 0.99 – 1.01 | 0.758 |
|
academic affiliation [University] |
1.38 | 1.14 – 1.67 | 0.001 |
| AAO regions [Region 2] | 0.57 | 0.38 – 0.84 | 0.004 |
| AAO regions [Region 3] | 0.68 | 0.47 – 0.97 | 0.034 |
| AAO regions [Region 4] | 0.81 | 0.56 – 1.17 | 0.255 |
| AAO regions [Region 5] | 0.93 | 0.64 – 1.33 | 0.681 |
| AAO regions [Region 6] | 0.64 | 0.44 – 0.93 | 0.019 |
| AAO regions [Region 7] | 0.86 | 0.60 – 1.23 | 0.409 |
| AAO regions [Region 8] | 0.79 | 0.54 – 1.17 | 0.247 |
| AAO regions [Region 9] | 0.98 | 0.69 – 1.40 | 0.910 |
| AAO regions [Region 10] | 1.08 | 0.74 – 1.58 | 0.697 |
| title [DO] | 1.55 | 0.98 – 2.43 | 0.059 |
| gender [Male] | 0.89 | 0.72 – 1.10 | 0.295 |
| central [Yes] | 1.18 | 1.10 – 1.27 | <0.001 |
|
specialty [General Otolaryngology] |
1.03 | 0.76 – 1.39 | 0.858 |
|
specialty [Head and Neck Surgery] |
0.93 | 0.69 – 1.27 | 0.669 |
| specialty [Laryngology] | 1.17 | 0.86 – 1.58 | 0.328 |
| specialty [Neurotology] | 1.53 | 1.12 – 2.07 | 0.007 |
|
specialty [Pediatric Otolaryngology] |
1.85 | 1.36 – 2.52 | <0.001 |
| specialty [Rhinology] | 0.89 | 0.65 – 1.22 | 0.480 |
| Random Effects | |||
| σ2 | 0.04 | ||
| τ00 name | 0.54 | ||
| ICC | 0.93 | ||
| N name | 352 | ||
| Observations | 553 | ||
| Marginal R2 / Conditional R2 | 0.225 / 0.947 | ||
## # Indices of model performance
##
## AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma | Score_log | Score_spherical
## --------------------------------------------------------------------------------------------------------------
## 2359.627 | 2361.714 | 2458.880 | 0.947 | 0.225 | 0.931 | 8.017 | 1.000 | -3.341 | 0.037## Warning: Probably bad model fit. Only about 71% of the residuals are inside the error bounds.## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance
## insurance 1.00 [1.00, 3.53e+06] 1.00 1.00
## Age 1.18 [1.10, 1.33] 1.09 0.85
## academic_affiliation 1.39 [1.27, 1.56] 1.18 0.72
## AAO_regions 1.43 [1.31, 1.61] 1.20 0.70
## title 1.09 [1.03, 1.25] 1.04 0.92
## gender 1.14 [1.07, 1.29] 1.07 0.88
## central 1.04 [1.00, 1.35] 1.02 0.96
## specialty 1.44 [1.31, 1.62] 1.20 0.69
## Tolerance 95% CI
## [0.00, 1.00]
## [0.75, 0.91]
## [0.64, 0.79]
## [0.62, 0.76]
## [0.80, 0.97]
## [0.78, 0.94]
## [0.74, 1.00]
## [0.62, 0.76]## # Overdispersion test
##
## dispersion ratio = 1.487
## Pearson's Chi-Squared = 788.016
## p-value = < 0.001## Warning: Autocorrelated residuals detected (p < .001).## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance
## insurance 1.00 [1.00, 3.53e+06] 1.00 1.00
## Age 1.18 [1.10, 1.33] 1.09 0.85
## academic_affiliation 1.39 [1.27, 1.56] 1.18 0.72
## AAO_regions 1.43 [1.31, 1.61] 1.20 0.70
## title 1.09 [1.03, 1.25] 1.04 0.92
## gender 1.14 [1.07, 1.29] 1.07 0.88
## central 1.04 [1.00, 1.35] 1.02 0.96
## specialty 1.44 [1.31, 1.62] 1.20 0.69
## Tolerance 95% CI
## [0.00, 1.00]
## [0.75, 0.91]
## [0.64, 0.79]
## [0.62, 0.76]
## [0.80, 0.97]
## [0.78, 0.94]
## [0.74, 1.00]
## [0.62, 0.76]## [1] FALSEHere we will look at all providers for whom waiting time data is available AND who also accepts Medicaid. These are 354 such providers, adding up to 562 data points.
glmm_model Moderation effectDoes subspecialty affect the difference in waiting times between private and Medicaid? The ANOVA tabler below shows that yes, we have evidence for the interaction.
Some variables are significant as we see in the ANOVA table. We will
need to check interaction of insurance with the other
significant variables.
## chisq ratio rdf
## 788.015627393444560767 1.486821938478197325 530.000000000000000000
## p
## 0.000000000002056946## Generalized linear mixed model fit by maximum likelihood (Adaptive
## Gauss-Hermite Quadrature, nAGQ = 0) [glmerMod]
## Family: poisson ( log )
## Formula: days ~ insurance + Age + academic_affiliation + AAO_regions +
## title + gender + central + specialty + (1 | name)
## Data: df3
##
## AIC BIC logLik deviance df.resid
## 5139.9 5239.1 -2546.9 5093.9 530
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -8.6858 -0.3268 -0.0485 0.2202 8.4932
##
## Random effects:
## Groups Name Variance Std.Dev.
## name (Intercept) 0.5416 0.736
## Number of obs: 553, groups: name, 352
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 3.015533 0.284355 10.605
## insuranceMedicaid 0.057309 0.016418 3.491
## Age 0.001275 0.004107 0.310
## academic_affiliationUniversity 0.316874 0.097599 3.247
## AAO_regionsRegion 2 -0.555242 0.198829 -2.793
## AAO_regionsRegion 3 -0.389432 0.184143 -2.115
## AAO_regionsRegion 4 -0.211254 0.186665 -1.132
## AAO_regionsRegion 5 -0.074786 0.185574 -0.403
## AAO_regionsRegion 6 -0.433545 0.188610 -2.299
## AAO_regionsRegion 7 -0.148452 0.180822 -0.821
## AAO_regionsRegion 8 -0.229150 0.197853 -1.158
## AAO_regionsRegion 9 -0.023481 0.182088 -0.129
## AAO_regionsRegion 10 0.075549 0.194875 0.388
## titleDO 0.422752 0.230211 1.836
## genderMale -0.110520 0.106967 -1.033
## centralYes 0.163706 0.036433 4.493
## specialtyGeneral Otolaryngology 0.026267 0.154674 0.170
## specialtyHead and Neck Surgery -0.066436 0.157449 -0.422
## specialtyLaryngology 0.147474 0.156193 0.944
## specialtyNeurotology 0.413882 0.155498 2.662
## specialtyPediatric Otolaryngology 0.603786 0.158086 3.819
## specialtyRhinology -0.115600 0.159114 -0.727
## Pr(>|z|)
## (Intercept) < 0.0000000000000002 ***
## insuranceMedicaid 0.000482 ***
## Age 0.756208
## academic_affiliationUniversity 0.001168 **
## AAO_regionsRegion 2 0.005229 **
## AAO_regionsRegion 3 0.034444 *
## AAO_regionsRegion 4 0.257749
## AAO_regionsRegion 5 0.686948
## AAO_regionsRegion 6 0.021526 *
## AAO_regionsRegion 7 0.411657
## AAO_regionsRegion 8 0.246791
## AAO_regionsRegion 9 0.897395
## AAO_regionsRegion 10 0.698253
## titleDO 0.066303 .
## genderMale 0.301502
## centralYes 0.00000701 ***
## specialtyGeneral Otolaryngology 0.865150
## specialtyHead and Neck Surgery 0.673061
## specialtyLaryngology 0.345078
## specialtyNeurotology 0.007776 **
## specialtyPediatric Otolaryngology 0.000134 ***
## specialtyRhinology 0.467516
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Generalized linear mixed model fit by maximum likelihood (Adaptive
## Gauss-Hermite Quadrature, nAGQ = 0) [glmerMod]
## Family: Gamma ( log )
## Formula: days ~ age + academic_affiliation + grad + AAO_regions + specialty +
## insurance + gender + (1 | name)
## Data: df3
##
## AIC BIC logLik deviance df.resid
## 4561.6 4678.1 -2253.8 4507.6 526
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3443 -0.2872 0.0556 0.3538 3.2355
##
## Random effects:
## Groups Name Variance Std.Dev.
## name (Intercept) 0.4453 0.6673
## Residual 0.1751 0.4185
## Number of obs: 553, groups: name, 352
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.580370 0.319408 8.079
## age 0.010726 0.005222 2.054
## academic_affiliationUniversity 0.333411 0.095937 3.475
## grad.L 0.407535 0.147896 2.756
## grad.Q -0.172999 0.111560 -1.551
## grad.C 0.001661 0.101340 0.016
## grad^4 0.090853 0.095561 0.951
## grad^5 -0.045995 0.095822 -0.480
## AAO_regionsRegion 2 -0.590994 0.196249 -3.011
## AAO_regionsRegion 3 -0.397834 0.181519 -2.192
## AAO_regionsRegion 4 -0.243974 0.185807 -1.313
## AAO_regionsRegion 5 -0.170162 0.184098 -0.924
## AAO_regionsRegion 6 -0.580375 0.185414 -3.130
## AAO_regionsRegion 7 -0.196852 0.179144 -1.099
## AAO_regionsRegion 8 -0.302667 0.195395 -1.549
## AAO_regionsRegion 9 -0.106575 0.181147 -0.588
## AAO_regionsRegion 10 -0.014727 0.196071 -0.075
## specialtyGeneral Otolaryngology 0.018430 0.155475 0.119
## specialtyHead and Neck Surgery -0.051642 0.156822 -0.329
## specialtyLaryngology 0.153011 0.155722 0.983
## specialtyNeurotology 0.442692 0.154203 2.871
## specialtyPediatric Otolaryngology 0.615188 0.158106 3.891
## specialtyRhinology -0.114616 0.158309 -0.724
## insuranceMedicaid 0.137261 0.040094 3.423
## genderMale -0.061176 0.106230 -0.576
## Pr(>|z|)
## (Intercept) 0.000000000000000655 ***
## age 0.039996 *
## academic_affiliationUniversity 0.000510 ***
## grad.L 0.005859 **
## grad.Q 0.120968
## grad.C 0.986925
## grad^4 0.341736
## grad^5 0.631227
## AAO_regionsRegion 2 0.002600 **
## AAO_regionsRegion 3 0.028402 *
## AAO_regionsRegion 4 0.189166
## AAO_regionsRegion 5 0.355329
## AAO_regionsRegion 6 0.001747 **
## AAO_regionsRegion 7 0.271836
## AAO_regionsRegion 8 0.121381
## AAO_regionsRegion 9 0.556307
## AAO_regionsRegion 10 0.940125
## specialtyGeneral Otolaryngology 0.905641
## specialtyHead and Neck Surgery 0.741927
## specialtyLaryngology 0.325811
## specialtyNeurotology 0.004094 **
## specialtyPediatric Otolaryngology 0.000099842728419138 ***
## specialtyRhinology 0.469064
## insuranceMedicaid 0.000618 ***
## genderMale 0.564692
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: formula
## Data: df3
##
## REML criterion at convergence: 4848.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.9201 -0.2954 -0.0635 0.2351 7.6647
##
## Random effects:
## Groups Name Variance Std.Dev.
## name (Intercept) 422.1 20.54
## Residual 172.8 13.15
## Number of obs: 553, groups: name, 352
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 32.32980 8.80170 350.60100 3.673
## insuranceMedicaid 2.06521 1.25873 242.86541 1.641
## Age 0.01166 0.12564 345.00490 0.093
## academic_affiliationUniversity 8.62784 3.01245 344.68169 2.864
## AAO_regionsRegion 2 -13.98525 6.04600 343.57746 -2.313
## AAO_regionsRegion 3 -14.12733 5.58188 318.35340 -2.531
## AAO_regionsRegion 4 -10.50745 5.71541 330.21282 -1.838
## AAO_regionsRegion 5 -1.41604 5.70495 331.22093 -0.248
## AAO_regionsRegion 6 -12.15885 5.75111 331.21734 -2.114
## AAO_regionsRegion 7 -6.71971 5.51278 323.39823 -1.219
## AAO_regionsRegion 8 -11.99579 6.05468 327.64775 -1.981
## AAO_regionsRegion 9 -6.35337 5.57258 327.03612 -1.140
## AAO_regionsRegion 10 -0.86959 6.07936 352.27379 -0.143
## titleDO 9.19846 7.01979 319.86133 1.310
## genderMale -4.42948 3.28252 339.07331 -1.349
## centralYes 5.47717 2.27677 523.67223 2.406
## specialtyGeneral Otolaryngology 1.56718 4.69785 341.91343 0.334
## specialtyHead and Neck Surgery -0.55713 4.78931 346.46847 -0.116
## specialtyLaryngology 1.71050 4.77847 345.33525 0.358
## specialtyNeurotology 11.23037 4.76477 340.49827 2.357
## specialtyPediatric Otolaryngology 19.47587 4.84231 339.07244 4.022
## specialtyRhinology -7.74378 4.83753 341.12431 -1.601
## Pr(>|t|)
## (Intercept) 0.000277 ***
## insuranceMedicaid 0.102151
## Age 0.926122
## academic_affiliationUniversity 0.004439 **
## AAO_regionsRegion 2 0.021305 *
## AAO_regionsRegion 3 0.011857 *
## AAO_regionsRegion 4 0.066896 .
## AAO_regionsRegion 5 0.804124
## AAO_regionsRegion 6 0.035247 *
## AAO_regionsRegion 7 0.223758
## AAO_regionsRegion 8 0.048400 *
## AAO_regionsRegion 9 0.255073
## AAO_regionsRegion 10 0.886340
## titleDO 0.191014
## genderMale 0.178103
## centralYes 0.016488 *
## specialtyGeneral Otolaryngology 0.738890
## specialtyHead and Neck Surgery 0.907459
## specialtyLaryngology 0.720592
## specialtyNeurotology 0.018991 *
## specialtyPediatric Otolaryngology 0.0000712 ***
## specialtyRhinology 0.110353
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Generalized linear mixed model fit by maximum likelihood (Adaptive
## Gauss-Hermite Quadrature, nAGQ = 10) [glmerMod]
## Family: poisson ( log )
## Formula: days ~ insurance + Age + academic_affiliation + AAO_regions +
## title + gender + central + specialty + (1 | name)
## Data: df3
##
## AIC BIC logLik deviance df.resid
## 2359.6 2458.9 -1156.8 2313.6 530
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -8.6840 -0.3224 -0.0453 0.2248 8.4927
##
## Random effects:
## Groups Name Variance Std.Dev.
## name (Intercept) 0.5428 0.7368
## Number of obs: 553, groups: name, 352
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 2.994239 0.284931 10.509
## insuranceMedicaid 0.057576 0.016421 3.506
## Age 0.001267 0.004115 0.308
## academic_affiliationUniversity 0.323731 0.097799 3.310
## AAO_regionsRegion 2 -0.568312 0.199287 -2.852
## AAO_regionsRegion 3 -0.390629 0.184432 -2.118
## AAO_regionsRegion 4 -0.212858 0.186955 -1.139
## AAO_regionsRegion 5 -0.076366 0.185865 -0.411
## AAO_regionsRegion 6 -0.442171 0.188979 -2.340
## AAO_regionsRegion 7 -0.149608 0.181102 -0.826
## AAO_regionsRegion 8 -0.229454 0.198171 -1.158
## AAO_regionsRegion 9 -0.020663 0.182363 -0.113
## AAO_regionsRegion 10 0.075940 0.195185 0.389
## titleDO 0.435670 0.230585 1.889
## genderMale -0.112307 0.107149 -1.048
## centralYes 0.164330 0.036454 4.508
## specialtyGeneral Otolaryngology 0.027826 0.154999 0.180
## specialtyHead and Neck Surgery -0.067514 0.157790 -0.428
## specialtyLaryngology 0.153143 0.156511 0.978
## specialtyNeurotology 0.422245 0.155797 2.710
## specialtyPediatric Otolaryngology 0.614678 0.158408 3.880
## specialtyRhinology -0.112717 0.159462 -0.707
## Pr(>|z|)
## (Intercept) < 0.0000000000000002 ***
## insuranceMedicaid 0.000454 ***
## Age 0.758180
## academic_affiliationUniversity 0.000932 ***
## AAO_regionsRegion 2 0.004348 **
## AAO_regionsRegion 3 0.034174 *
## AAO_regionsRegion 4 0.254890
## AAO_regionsRegion 5 0.681170
## AAO_regionsRegion 6 0.019294 *
## AAO_regionsRegion 7 0.408751
## AAO_regionsRegion 8 0.246923
## AAO_regionsRegion 9 0.909786
## AAO_regionsRegion 10 0.697227
## titleDO 0.058837 .
## genderMale 0.294575
## centralYes 0.00000655 ***
## specialtyGeneral Otolaryngology 0.857527
## specialtyHead and Neck Surgery 0.668743
## specialtyLaryngology 0.327837
## specialtyNeurotology 0.006724 **
## specialtyPediatric Otolaryngology 0.000104 ***
## specialtyRhinology 0.479653
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.044146 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?## # Indices of model performance
##
## AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma | Score_log | Score_spherical
## --------------------------------------------------------------------------------------------------------------
## 5139.868 | 5141.955 | 5239.121 | 0.947 | 0.220 | 0.932 | 8.017 | 1.000 | -3.342 | 0.037## # Indices of model performance
##
## AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma
## ---------------------------------------------------------------------------------
## 4561.587 | 4564.467 | 4678.101 | 0.783 | 0.233 | 0.718 | 10.292 | 0.418## # Indices of model performance
##
## AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma
## ---------------------------------------------------------------------------------
## 4896.947 | 4899.220 | 5000.516 | 0.769 | 0.206 | 0.709 | 9.240 | 13.146## # Comparison of Model Performance Indices
##
## Name | Model | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma | AIC weights | AICc weights | BIC weights | Performance-Score
## --------------------------------------------------------------------------------------------------------------------------------------------
## Model 2 | glmerMod | 0.783 | 0.233 | 0.718 | 10.292 | 0.418 | 1.00 | 1.00 | 1.00 | 63.94%
## Model 1 | glmerMod | 0.947 | 0.220 | 0.932 | 8.017 | 1.000 | 2.68e-126 | 3.98e-126 | 1.50e-122 | 55.94%
## Model 3 | lmerModLmerTest | 0.769 | 0.206 | 0.709 | 9.240 | 13.146 | 4.24e-93 | 5.75e-93 | 2.75e-90 | 5.78%| Name | Model | R2_conditional | R2_marginal | ICC | RMSE | Sigma | Score_log | Score_spherical | AIC_wt | AICc_wt | BIC_wt | Performance_Score |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Model 2 | glmerMod | 0.7833688 | 0.2325286 | 0.7177338 | 10.292376 | 0.4184956 | NA | NA | 1 | 1 | 1 | 0.6394460 |
| Model 1 | glmerMod | 0.9469441 | 0.2200021 | 0.9319794 | 8.016976 | 1.0000000 | -3.342491 | 0.0371964 | 0 | 0 | 0 | 0.5593737 |
| Model 3 | lmerModLmerTest | 0.7694407 | 0.2063948 | 0.7094787 | 9.239855 | 13.1462457 | NA | NA | 0 | 0 | 0 | 0.0578207 |