Start with data in exploratory.io at Mystery Caller/ortho/~March_Ortho analysis_3
| npi | name | N |
|---|---|---|
| NA | NA | NA |
| —: | :—- | –: |
| npi | name | Reason for exclusions | insurance | business_days_until_appointment |
|---|---|---|---|---|
| NA | NA | NA | NA | NA |
| —: | :—- | :——————— | :——— | ——————————-: |
| x |
|---|
| 4 |
| 5 |
| 28 |
| 80 |
| 130 |
| 166 |
| 205 |
| 272 |
| 297 |
| 320 |
| 343 |
| 345 |
| 396 |
| 412 |
| 495 |
| 521 |
| 550 |
| 586 |
| 603 |
| 668 |
| 691 |
| 815 |
| 915 |
| 942 |
| npi | calls_count |
|---|---|
| NA | NA |
| —: | ———–: |
A total of 371 unique orthopedic surgeons were identified in the dataset and were successfully contacted (i.e., with a recorded wait time for an appointment) in 47 states including the District of Columbia. The excluded states include North Dakota, West Virginia, Wyoming and District of Columbia.
| median_wait_time | Q1 | Q3 |
|---|---|---|
| 13 | 6 | 31 |
The median wait time across all subspecialties and insurance types was 13 business days, with an interquartile range (IQR) of 6 to 31.
Each physician received 2, phone calls with identical clinical scenarios. In this process, 3 ” physicians were excluded after two unsuccessful attempts to reach them. Out of the 978 phone calls made, 35 calls 3.5787321%) were on hold for more than five minutes, 75 7.6687117 %) went to voicemail, 133 13.599182%) physicians did not accept Medicaid insurance, 55 5.6237219%) required a referral before the appointment, and 8 0.8179959%) resulted in contacting a personal phone number of the physician.
Graph each variable
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”.
Creation of df3 dataset
| Orthopedists who Accept Medicaid and Blue Cross/Blue Shield (N=218) | Orthopedists who do not accept Medicaid (N=130) | Total (N=348) | p value | |
|---|---|---|---|---|
| Age category | 0.07 | |||
| - Less than 50 years old | 35 (17.9%) | 16 (13.1%) | 51 (16.0%) | |
| - 50 to 59.9 years old | 82 (41.8%) | 39 (32.0%) | 121 (38.1%) | |
| - 60 to 69.9 years old | 68 (34.7%) | 55 (45.1%) | 123 (38.7%) | |
| - Greater than or equal to 70 years old | 11 (5.6%) | 12 (9.8%) | 23 (7.2%) | |
| Gender | 0.24 | |||
| - Male | 203 (93.1%) | 125 (96.2%) | 328 (94.3%) | |
| - Female | 15 (6.9%) | 5 (3.8%) | 20 (5.7%) | |
| Orthopedics Specialty | < 0.01 | |||
| - Adult Reconstructive Orthopaedic Surgery | 40 (18.3%) | 18 (13.8%) | 58 (16.7%) | |
| - Foot & Ankle Orthopaedic Surgery | 30 (13.8%) | 18 (13.8%) | 48 (13.8%) | |
| - General Orthopaedic Surgery | 47 (21.6%) | 18 (13.8%) | 65 (18.7%) | |
| - Orthopaedic Surgery of the Spine | 24 (11.0%) | 29 (22.3%) | 53 (15.2%) | |
| - Pediatric Orthopaedic Surgery | 21 (9.6%) | 1 (0.8%) | 22 (6.3%) | |
| - Sports Medicine Orthopaedics | 29 (13.3%) | 28 (21.5%) | 57 (16.4%) | |
| - Surgery of the Hand | 27 (12.4%) | 18 (13.8%) | 45 (12.9%) | |
| Medical School Training | 0.93 | |||
| - US Senior | 188 (89.5%) | 106 (89.8%) | 294 (89.6%) | |
| - International Medical Graduate | 22 (10.5%) | 12 (10.2%) | 34 (10.4%) | |
| Medical School Location | 0.21 | |||
| - Allopathic training | 207 (95.0%) | 127 (97.7%) | 334 (96.0%) | |
| - Osteopathic training | 11 (5.0%) | 3 (2.3%) | 14 (4.0%) | |
| Medical School Graduation Year | 0.02 | |||
| - 1970 - 1979 | 9 (4.1%) | 11 (8.5%) | 20 (5.7%) | |
| - 1980 - 1989 | 61 (28.0%) | 51 (39.2%) | 112 (32.2%) | |
| - 1990 - 1999 | 90 (41.3%) | 41 (31.5%) | 131 (37.6%) | |
| - 2000 - 2009 | 53 (24.3%) | 27 (20.8%) | 80 (23.0%) | |
| - 2010 to Present | 5 (2.3%) | 0 (0.0%) | 5 (1.4%) | |
| Academic Affiliation | < 0.01 | |||
| - Not Academic | 186 (85.3%) | 124 (95.4%) | 310 (89.1%) | |
| - Academic | 32 (14.7%) | 6 (4.6%) | 38 (10.9%) | |
| US Census Bureau Subdivision | < 0.01 | |||
| - East North Central | 31 (14.2%) | 7 (5.4%) | 38 (10.9%) | |
| - East South Central | 24 (11.0%) | 11 (8.5%) | 35 (10.1%) | |
| - Middle Atlantic | 23 (10.6%) | 23 (17.7%) | 46 (13.2%) | |
| - Mountain | 23 (10.6%) | 10 (7.7%) | 33 (9.5%) | |
| - New England | 30 (13.8%) | 13 (10.0%) | 43 (12.4%) | |
| - Pacific | 21 (9.6%) | 18 (13.8%) | 39 (11.2%) | |
| - South Atlantic | 25 (11.5%) | 14 (10.8%) | 39 (11.2%) | |
| - West North Central | 24 (11.0%) | 5 (3.8%) | 29 (8.3%) | |
| - West South Central | 17 (7.8%) | 29 (22.3%) | 46 (13.2%) | |
| Rurality | < 0.01 | |||
| - Metropolitan area | 182 (83.5%) | 126 (96.9%) | 308 (88.5%) | |
| - Rural area | 36 (16.5%) | 4 (3.1%) | 40 (11.5%) | |
| Centeral Scheduling | 0.99 | |||
| - No | 124 (56.9%) | 74 (56.9%) | 198 (56.9%) | |
| - Yes, central scheduling number | 94 (43.1%) | 56 (43.1%) | 150 (43.1%) | |
| Number of Phone Transfers | 0.62 | |||
| - More than two transfers | 5 (2.3%) | 2 (1.5%) | 7 (2.0%) | |
| - No transfers | 135 (61.9%) | 87 (66.9%) | 222 (63.8%) | |
| - One transfer | 61 (28.0%) | 29 (22.3%) | 90 (25.9%) | |
| - Two transfers | 17 (7.8%) | 12 (9.2%) | 29 (8.3%) |
| Orthopedists who Accept Medicaid and Blue Cross/Blue Shield (N=218) | Orthopedists who do not accept Medicaid (N=130) | Total (N=348) | p value | |
|---|---|---|---|---|
| Age category | 0.07 | |||
| Less than 50 years old | 35 (17.9%) | 16 (13.1%) | 51 (16.0%) | |
| 50 to 59.9 years old | 82 (41.8%) | 39 (32.0%) | 121 (38.1%) | |
| 60 to 69.9 years old | 68 (34.7%) | 55 (45.1%) | 123 (38.7%) | |
| Greater than or equal to 70 years old | 11 (5.6%) | 12 (9.8%) | 23 (7.2%) | |
| Gender | 0.24 | |||
| Male | 203 (93.1%) | 125 (96.2%) | 328 (94.3%) | |
| Female | 15 (6.9%) | 5 (3.8%) | 20 (5.7%) | |
| Orthopedics Specialty | < 0.01 | |||
| Adult Reconstructive Orthopaedic Surgery | 40 (18.3%) | 18 (13.8%) | 58 (16.7%) | |
| Foot & Ankle Orthopaedic Surgery | 30 (13.8%) | 18 (13.8%) | 48 (13.8%) | |
| General Orthopaedic Surgery | 47 (21.6%) | 18 (13.8%) | 65 (18.7%) | |
| Orthopaedic Surgery of the Spine | 24 (11.0%) | 29 (22.3%) | 53 (15.2%) | |
| Pediatric Orthopaedic Surgery | 21 (9.6%) | 1 (0.8%) | 22 (6.3%) | |
| Sports Medicine Orthopaedics | 29 (13.3%) | 28 (21.5%) | 57 (16.4%) | |
| Surgery of the Hand | 27 (12.4%) | 18 (13.8%) | 45 (12.9%) | |
| Medical School Training | 0.93 | |||
| US Senior | 188 (89.5%) | 106 (89.8%) | 294 (89.6%) | |
| International Medical Graduate | 22 (10.5%) | 12 (10.2%) | 34 (10.4%) | |
| Medical School Location | 0.21 | |||
| Allopathic training | 207 (95.0%) | 127 (97.7%) | 334 (96.0%) | |
| Osteopathic training | 11 (5.0%) | 3 (2.3%) | 14 (4.0%) | |
| Medical School Graduation Year | 0.02 | |||
| 1970 - 1979 | 9 (4.1%) | 11 (8.5%) | 20 (5.7%) | |
| 1980 - 1989 | 61 (28.0%) | 51 (39.2%) | 112 (32.2%) | |
| 1990 - 1999 | 90 (41.3%) | 41 (31.5%) | 131 (37.6%) | |
| 2000 - 2009 | 53 (24.3%) | 27 (20.8%) | 80 (23.0%) | |
| 2010 to Present | 5 (2.3%) | 0 (0.0%) | 5 (1.4%) | |
| Academic Affiliation | < 0.01 | |||
| Not Academic | 186 (85.3%) | 124 (95.4%) | 310 (89.1%) | |
| Academic | 32 (14.7%) | 6 (4.6%) | 38 (10.9%) | |
| US Census Bureau Subdivision | < 0.01 | |||
| East North Central | 31 (14.2%) | 7 (5.4%) | 38 (10.9%) | |
| East South Central | 24 (11.0%) | 11 (8.5%) | 35 (10.1%) | |
| Middle Atlantic | 23 (10.6%) | 23 (17.7%) | 46 (13.2%) | |
| Mountain | 23 (10.6%) | 10 (7.7%) | 33 (9.5%) | |
| New England | 30 (13.8%) | 13 (10.0%) | 43 (12.4%) | |
| Pacific | 21 (9.6%) | 18 (13.8%) | 39 (11.2%) | |
| South Atlantic | 25 (11.5%) | 14 (10.8%) | 39 (11.2%) | |
| West North Central | 24 (11.0%) | 5 (3.8%) | 29 (8.3%) | |
| West South Central | 17 (7.8%) | 29 (22.3%) | 46 (13.2%) | |
| Rurality | < 0.01 | |||
| Metropolitan area | 182 (83.5%) | 126 (96.9%) | 308 (88.5%) | |
| Rural area | 36 (16.5%) | 4 (3.1%) | 40 (11.5%) | |
| Centeral Scheduling | 0.99 | |||
| No | 124 (56.9%) | 74 (56.9%) | 198 (56.9%) | |
| Yes, central scheduling number | 94 (43.1%) | 56 (43.1%) | 150 (43.1%) | |
| Number of Phone Transfers | 0.62 | |||
| More than two transfers | 5 (2.3%) | 2 (1.5%) | 7 (2.0%) | |
| No transfers | 135 (61.9%) | 87 (66.9%) | 222 (63.8%) | |
| One transfer | 61 (28.0%) | 29 (22.3%) | 90 (25.9%) | |
| Two transfers | 17 (7.8%) | 12 (9.2%) | 29 (8.3%) |
| Variable | Orthopedists who Accept Medicaid and Blue Cross/Blue Shield, N = 2181 | Orthopedists who do not accept Medicaid, N = 1301 | p-value2 |
|---|---|---|---|
| Age category | 0.074 | ||
| Less than 50 years old | 35 (18%) | 16 (13%) | |
| 50 to 59.9 years old | 82 (42%) | 39 (32%) | |
| 60 to 69.9 years old | 68 (35%) | 55 (45%) | |
| Greater than or equal to 70 years old | 11 (5.6%) | 12 (9.8%) | |
| Gender | 0.2 | ||
| Male | 203 (93%) | 125 (96%) | |
| Female | 15 (6.9%) | 5 (3.8%) | |
| Orthopedics Specialty | <0.001 | ||
| Adult Reconstructive Orthopaedic Surgery | 40 (18%) | 18 (14%) | |
| Foot & Ankle Orthopaedic Surgery | 30 (14%) | 18 (14%) | |
| General Orthopaedic Surgery | 47 (22%) | 18 (14%) | |
| Orthopaedic Surgery of the Spine | 24 (11%) | 29 (22%) | |
| Pediatric Orthopaedic Surgery | 21 (9.6%) | 1 (0.8%) | |
| Sports Medicine Orthopaedics | 29 (13%) | 28 (22%) | |
| Surgery of the Hand | 27 (12%) | 18 (14%) | |
| Medical School Training | >0.9 | ||
| US Senior | 188 (90%) | 106 (90%) | |
| International Medical Graduate | 22 (10%) | 12 (10%) | |
| Medical School Location | 0.2 | ||
| Allopathic training | 207 (95%) | 127 (98%) | |
| Osteopathic training | 11 (5.0%) | 3 (2.3%) | |
| Medical School Graduation Year | 0.023 | ||
| 1970 - 1979 | 9 (4.1%) | 11 (8.5%) | |
| 1980 - 1989 | 61 (28%) | 51 (39%) | |
| 1990 - 1999 | 90 (41%) | 41 (32%) | |
| 2000 - 2009 | 53 (24%) | 27 (21%) | |
| 2010 to Present | 5 (2.3%) | 0 (0%) | |
| Academic Affiliation | 0.004 | ||
| Not Academic | 186 (85%) | 124 (95%) | |
| Academic | 32 (15%) | 6 (4.6%) | |
| US Census Bureau Subdivision | <0.001 | ||
| East North Central | 31 (14%) | 7 (5.4%) | |
| East South Central | 24 (11%) | 11 (8.5%) | |
| Middle Atlantic | 23 (11%) | 23 (18%) | |
| Mountain | 23 (11%) | 10 (7.7%) | |
| New England | 30 (14%) | 13 (10%) | |
| Pacific | 21 (9.6%) | 18 (14%) | |
| South Atlantic | 25 (11%) | 14 (11%) | |
| West North Central | 24 (11%) | 5 (3.8%) | |
| West South Central | 17 (7.8%) | 29 (22%) | |
| Rurality | <0.001 | ||
| Metropolitan area | 182 (83%) | 126 (97%) | |
| Rural area | 36 (17%) | 4 (3.1%) | |
| Centeral Scheduling | >0.9 | ||
| No | 124 (57%) | 74 (57%) | |
| Yes, central scheduling number | 94 (43%) | 56 (43%) | |
| Number of Phone Transfers | 0.6 | ||
| More than two transfers | 5 (2.3%) | 2 (1.5%) | |
| No transfers | 135 (62%) | 87 (67%) | |
| One transfer | 61 (28%) | 29 (22%) | |
| Two transfers | 17 (7.8%) | 12 (9.2%) | |
| 1 n (%) | |||
| 2 Pearson’s Chi-squared test; Fisher’s exact test | |||
This does not work when knitting for some reason. It works with the R code.
## [1] "The number of physicians who gave a date for the next appointment N= 356 AND who accepted BOTH Medicaid and Blue Cross/Blue Shield is N= 218. (61.2)%. Therefore 38.8% or N= 138 met exclusion criteria and were excluded."| Exclusion Criteria for Orthopedists who Accept Medicaid AND Blue Cross/Blue Shield | |
| Reason for exclusions | n |
|---|---|
| Went to voicemail | 33 |
| Number contacted did not correspond to expected office/specialty | 28 |
| Physician referral required before scheduling appointment | 26 |
| Greater than 5 minutes on hold | 18 |
| Not accepting new patients | 13 |
| Phone not answered or busy signal on repeat calls | 9 |
| Must see midlevel before seeing physician | 5 |
| Physician's personal phone | 4 |
| Closed medical system (e.g. Kaiser or military hospital) | 2 |
## # A tibble: 1 × 1
## count_appointment_date
## <int>
## 1 218
## # A tibble: 1 × 1
## count_excluded
## <int>
## 1 138
## # A tibble: 9 × 2
## `Reason for exclusions` n
## <chr> <int>
## 1 Went to voicemail 33
## 2 Number contacted did not correspond to expected office/specialty 28
## 3 Physician referral required before scheduling appointment 26
## 4 Greater than 5 minutes on hold 18
## 5 Not accepting new patients 13
## 6 Phone not answered or busy signal on repeat calls 9
## 7 Must see midlevel before seeing physician 5
## 8 Physician's personal phone 4
## 9 Closed medical system (e.g. Kaiser or military hospital) 2–of the 359 physicians who GAVE A DATE… -wait time for Medicaid vs. BCBS -wait times for Medicaid vs. BCBS within each specialty -comparison of wait times between specialties for BCBS and Medicaid
## # A tibble: 2 × 2
## Insurance Mean_Wait
## <chr> <dbl>
## 1 Blue Cross/Blue Shield 23.0
## 2 Medicaid 25.2## # A tibble: 7 × 3
## # Groups: Orthopedics Specialty [7]
## `Orthopedics Specialty` `Blue Cross/Blue Shield` Medicaid
## <chr> <dbl> <dbl>
## 1 Adult Reconstructive Orthopaedic Surgery 33.8 24.7
## 2 Foot & Ankle Orthopaedic Surgery 17.1 13.5
## 3 General Orthopaedic Surgery 16.6 29.4
## 4 Orthopaedic Surgery of the Spine 24.6 32.9
## 5 Pediatric Orthopaedic Surgery 21.1 17.2
## 6 Sports Medicine Orthopaedics 18.3 22.7
## 7 Surgery of the Hand 29.6 37.2There are 486 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 194.
| Reason for exclusions | n | Percent |
|---|---|---|
| Went to voicemail on two repeated attempts | 74 | 38.1% |
| Number contacted did not correspond to expected office/specialty | 43 | 22.2% |
| Physician referral required before scheduling appointment | 36 | 18.6% |
| Greater than 5 minutes on hold | 27 | 13.9% |
| Not accepting new patients | 20 | 10.3% |
| Must see midlevel before seeing physician | 10 | 5.2% |
| Closed medical system (e.g. Kaiser or military hospital) | 5 | 2.6% |
| Physician’s personal phone | 4 | 2.1% |
Demographics of all physicians called
| Overall (N=489) | |
|---|---|
| Gender | |
| - Male | 454 (92.8%) |
| - Female | 35 (7.2%) |
| Age category | |
| - Less than 50 years old | 76 (17.1%) |
| - 50 to 59.9 years old | 173 (38.9%) |
| - 60 to 69.9 year old | 160 (36.0%) |
| - Greater than or equal to 70 years old | 36 (8.1%) |
| Medical School Training | |
| - US Senior | 399 (88.7%) |
| - International Medical Graduate | 51 (11.3%) |
| Medical School Location | |
| - Allopathic training | 468 (95.7%) |
| - Osteopathic training | 21 (4.3%) |
| Medical School Graduation Year | |
| - 1970 - 1979 | 29 (5.9%) |
| - 1980 - 1989 | 142 (29.0%) |
| - 1990 - 1999 | 196 (40.1%) |
| - 2000 - 2009 | 115 (23.5%) |
| - 2010 to Present | 7 (1.4%) |
| Academic Affiliation | |
| - Not Academic | 416 (85.1%) |
| - Academic | 73 (14.9%) |
| American College of Obstetricians and Gynecologists Districts | |
| - East North Central | 58 (11.9%) |
| - East South Central | 46 (9.4%) |
| - Middle Atlantic | 62 (12.7%) |
| - Mountain | 50 (10.2%) |
| - New England | 60 (12.3%) |
| - Pacific | 56 (11.5%) |
| - South Atlantic | 54 (11.0%) |
| - West North Central | 42 (8.6%) |
| - West South Central | 61 (12.5%) |
| Rurality | |
| - Metropolitan area | 435 (89.1%) |
| - Rural area | 53 (10.9%) |
| Centeral Scheduling | |
| - No | 293 (59.9%) |
| - Yes, central scheduling number | 196 (40.1%) |
| Number of Phone Transfers | |
| - No transfers | 298 (60.9%) |
| - One transfer | 141 (28.8%) |
| - Two transfers | 38 (7.8%) |
| - More than two transfers | 12 (2.5%) |
| Insurance | |
| - Blue Cross/Blue Shield | 245 (50.1%) |
| - Medicaid | 244 (49.9%) |
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.
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 wait time value.
Since the lines connect points with the same npi, if they are horizontal, it suggests similar waiting times for the same npi across both insurance types. If the lines have a slope, it indicates a difference in waiting times.
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.
From this information, the scatterplot likely explores the relationship between the time to appointment for patients with Medicaid versus those with Blue Cross/Blue Shield. The use of a logarithmic scale suggests a wide range of days to appointment, and the linear regression line (best fitting line) helps understand if there’s a linear relationship between these two variables on the log scale. The scatterplot might be used to analyze if there’s a systematic difference in waiting times for appointments between the two types of insurance.
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 output from the code indicates that the best-fitting line (linear regression line) intersects with the 45-degree line at 33.6 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 (>33.6 days) Medicaid patients start to experience longer waiting times compared to Blue Cross/Blue Shield patients for the same period.
The models need to be able to deal with NA in the days
outcome variable (413) and also non-parametric data.
poissonGiven 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.
$$
\[\begin{align*}\\ P(\text{{Days until New Patient Appointment}} = x) = \frac{{e^{-\lambda} \cdot \lambda^x}}{{x!}}\\ \\where\\ \log(\lambda) = & \beta_0 + \beta_1 \cdot \text{{Patient Insurance}} \\ & + \beta_2 \cdot \text{{Physician Age}}\\ & + \beta_3 \cdot \text{{Physician Academic Affiliation}} \\ & + \beta_4 \cdot \text{{US Census Bureau Divisions}}\\ & + \beta_5 \cdot \text{{Physician Medical Training}} \\ & + \beta_6 \cdot \text{{Physician Gender}} \\ & + \beta_7 \cdot \text{{Central Appointment Phone Number}} \end{align*}\]
$$
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.
## GVIF Df GVIF^(1/(2*Df))
## insurance 1.147395 1 1.071165
## gender 1.173654 1 1.083353
## Call_time_minutes 1.146364 1 1.070684
## ACOG_District 1.833029 8 1.038599
## title 1.163310 1 1.078568
## central 1.083690 1 1.041004
## Grd_yr 1.563310 4 1.057440
## Med_sch 1.134416 1 1.065090
## ntransf 1.178679 3 1.027778
## specialty 1.624522 6 1.041263
## cbsatype10 1.130996 1 1.063483
## academic_affiliation 1.146201 1 1.070608
## Generalized linear mixed model fit by maximum likelihood (Adaptive
## Gauss-Hermite Quadrature, nAGQ = 0) [glmerMod]
## Family: poisson ( log )
## Formula: days ~ insurance + gender + Call_time_minutes + ACOG_District +
## title + central + Grd_yr + Med_sch + ntransf + specialty +
## cbsatype10 + academic_affiliation + (1 | name)
## Data: df3
##
## AIC BIC logLik deviance df.resid
## 3273.0 3395.1 -1605.5 3211.0 348
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.7739 -0.5589 -0.0460 0.2350 5.2316
##
## Random effects:
## Groups Name Variance Std.Dev.
## name (Intercept) 0.8864 0.9415
## Number of obs: 379, groups: name, 251
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 1.829938 0.405500 4.513
## insuranceMedicaid 0.084865 0.028297 2.999
## genderFemale -0.009242 0.247119 -0.037
## Call_time_minutes 0.088333 0.017068 5.175
## ACOG_DistrictEast South Central 0.087372 0.253683 0.344
## ACOG_DistrictMiddle Atlantic 0.099713 0.253593 0.393
## ACOG_DistrictMountain 0.324385 0.254090 1.277
## ACOG_DistrictNew England -1.005776 0.742554 -1.354
## ACOG_DistrictPacific 0.657082 0.250808 2.620
## ACOG_DistrictSouth Atlantic 0.167263 0.241946 0.691
## ACOG_DistrictWest North Central 0.484703 0.282408 1.716
## ACOG_DistrictWest South Central -0.001755 0.233461 -0.008
## titleDO -0.131915 0.283699 -0.465
## centralYes 0.098193 0.041602 2.360
## Grd_yr1980 - 1989 0.148390 0.330457 0.449
## Grd_yr1990 - 1999 0.198590 0.327955 0.606
## Grd_yr2000 - 2009 0.278981 0.343898 0.811
## Grd_yr2010 to Present -0.361452 0.685760 -0.527
## Med_schUS Senior Medical Student -0.104906 0.202104 -0.519
## ntransfOne transfer -0.148349 0.041564 -3.569
## ntransfTwo transfers 0.071141 0.078057 0.911
## ntransfMore than two transfers -0.047344 0.164562 -0.288
## specialtyFoot & Ankle Orthopaedic Surgery -0.077104 0.273759 -0.282
## specialtyGeneral Orthopaedic Surgery 0.114956 0.251474 0.457
## specialtyOrthopaedic Surgery of the Spine 0.315155 0.277886 1.134
## specialtyPediatric Orthopaedic Surgery -0.058999 0.349341 -0.169
## specialtySports Medicine Orthopaedics 0.009865 0.270773 0.036
## specialtySurgery of the Hand 0.456144 0.271160 1.682
## cbsatype10Micro -0.152323 0.204791 -0.744
## academic_affiliationAcademic 0.453439 0.222169 2.041
## Pr(>|z|)
## (Intercept) 0.000006398 ***
## insuranceMedicaid 0.002707 **
## genderFemale 0.970167
## Call_time_minutes 0.000000228 ***
## ACOG_DistrictEast South Central 0.730536
## ACOG_DistrictMiddle Atlantic 0.694170
## ACOG_DistrictMountain 0.201725
## ACOG_DistrictNew England 0.175583
## ACOG_DistrictPacific 0.008796 **
## ACOG_DistrictSouth Atlantic 0.489363
## ACOG_DistrictWest North Central 0.086103 .
## ACOG_DistrictWest South Central 0.994002
## titleDO 0.641944
## centralYes 0.018261 *
## Grd_yr1980 - 1989 0.653400
## Grd_yr1990 - 1999 0.544821
## Grd_yr2000 - 2009 0.417232
## Grd_yr2010 to Present 0.598136
## Med_schUS Senior Medical Student 0.603714
## ntransfOne transfer 0.000358 ***
## ntransfTwo transfers 0.362084
## ntransfMore than two transfers 0.773580
## specialtyFoot & Ankle Orthopaedic Surgery 0.778212
## specialtyGeneral Orthopaedic Surgery 0.647579
## specialtyOrthopaedic Surgery of the Spine 0.256745
## specialtyPediatric Orthopaedic Surgery 0.865885
## specialtySports Medicine Orthopaedics 0.970937
## specialtySurgery of the Hand 0.092531 .
## cbsatype10Micro 0.456998
## academic_affiliationAcademic 0.041254 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1| days | |||
|---|---|---|---|
| Predictors | Incidence Rate Ratios | CI | p |
| (Intercept) | 6.23 | 2.82 – 13.80 | <0.001 |
| insurance [Medicaid] | 1.09 | 1.03 – 1.15 | 0.003 |
| genderFemale | 0.99 | 0.61 – 1.61 | 0.970 |
| Call time minutes | 1.09 | 1.06 – 1.13 | <0.001 |
|
ACOG District [East South Central] |
1.09 | 0.66 – 1.79 | 0.731 |
|
ACOG District [Middle Atlantic] |
1.10 | 0.67 – 1.82 | 0.694 |
| ACOG District [Mountain] | 1.38 | 0.84 – 2.28 | 0.202 |
|
ACOG District [New England] |
0.37 | 0.09 – 1.57 | 0.176 |
| ACOG District [Pacific] | 1.93 | 1.18 – 3.15 | 0.009 |
|
ACOG District [South Atlantic] |
1.18 | 0.74 – 1.90 | 0.489 |
|
ACOG District [West North Central] |
1.62 | 0.93 – 2.82 | 0.086 |
|
ACOG District [West South Central] |
1.00 | 0.63 – 1.58 | 0.994 |
| title [DO] | 0.88 | 0.50 – 1.53 | 0.642 |
| central [Yes] | 1.10 | 1.02 – 1.20 | 0.018 |
| Grd yr [1980 - 1989] | 1.16 | 0.61 – 2.22 | 0.653 |
| Grd yr [1990 - 1999] | 1.22 | 0.64 – 2.32 | 0.545 |
| Grd yr [2000 - 2009] | 1.32 | 0.67 – 2.59 | 0.417 |
| Grd yr [2010 to Present] | 0.70 | 0.18 – 2.67 | 0.598 |
|
Med sch [US Senior Medical Student] |
0.90 | 0.61 – 1.34 | 0.604 |
| ntransf [One transfer] | 0.86 | 0.79 – 0.94 | <0.001 |
| ntransf [Two transfers] | 1.07 | 0.92 – 1.25 | 0.362 |
|
ntransf [More than two transfers] |
0.95 | 0.69 – 1.32 | 0.774 |
|
specialty [Foot & Ankle Orthopaedic Surgery] |
0.93 | 0.54 – 1.58 | 0.778 |
|
specialty [General Orthopaedic Surgery] |
1.12 | 0.69 – 1.84 | 0.648 |
|
specialty [Orthopaedic Surgery of the Spine] |
1.37 | 0.79 – 2.36 | 0.257 |
|
specialty [Pediatric Orthopaedic Surgery] |
0.94 | 0.48 – 1.87 | 0.866 |
|
specialty [Sports Medicine Orthopaedics] |
1.01 | 0.59 – 1.72 | 0.971 |
|
specialty [Surgery of the Hand] |
1.58 | 0.93 – 2.68 | 0.093 |
| cbsatype10 [Micro] | 0.86 | 0.57 – 1.28 | 0.457 |
|
academic affiliation [Academic] |
1.57 | 1.02 – 2.43 | 0.041 |
| Random Effects | |||
| σ2 | 0.07 | ||
| τ00 name | 0.89 | ||
| ICC | 0.93 | ||
| N name | 251 | ||
| Observations | 379 | ||
| Marginal R2 / Conditional R2 | 0.133 / 0.936 | ||
Checking 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.
## GVIF Df GVIF^(1/(2*Df))
## insurance 1.147395 1 1.071165
## gender 1.173654 1 1.083353
## Call_time_minutes 1.146364 1 1.070684
## ACOG_District 1.833029 8 1.038599
## title 1.163310 1 1.078568
## central 1.083690 1 1.041004
## Grd_yr 1.563310 4 1.057440
## Med_sch 1.134416 1 1.065090
## ntransf 1.178679 3 1.027778
## specialty 1.624522 6 1.041263
## cbsatype10 1.130996 1 1.063483
## academic_affiliation 1.146201 1 1.070608## 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 = 1.600
## Pearson's Chi-Squared = 556.824
## p-value = < 0.001
## chisq ratio rdf
## 556.823967290310292810 1.600068871523880221 348.000000000000000000
## p
## 0.000000000007349562## Warning: Autocorrelated residuals detected (p < .001).## [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.' 3.405133 (df=31)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 |
| Call_time_minutes |
| central |
| ntransf |
| academic_affiliation |
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 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.
## Generalized linear mixed model fit by maximum likelihood (Adaptive
## Gauss-Hermite Quadrature, nAGQ = 0) [glmerMod]
## Family: poisson ( log )
## Formula: days ~ insurance + gender + Call_time_minutes + ACOG_District +
## title + central + Grd_yr + Med_sch + ntransf + specialty +
## cbsatype10 + academic_affiliation + (1 | name)
## Data: df3
##
## AIC BIC logLik deviance df.resid
## 3273.0 3395.1 -1605.5 3211.0 348
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.7739 -0.5589 -0.0460 0.2350 5.2316
##
## Random effects:
## Groups Name Variance Std.Dev.
## name (Intercept) 0.8864 0.9415
## Number of obs: 379, groups: name, 251
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 1.829938 0.405500 4.513
## insuranceMedicaid 0.084865 0.028297 2.999
## genderFemale -0.009242 0.247119 -0.037
## Call_time_minutes 0.088333 0.017068 5.175
## ACOG_DistrictEast South Central 0.087372 0.253683 0.344
## ACOG_DistrictMiddle Atlantic 0.099713 0.253593 0.393
## ACOG_DistrictMountain 0.324385 0.254090 1.277
## ACOG_DistrictNew England -1.005776 0.742554 -1.354
## ACOG_DistrictPacific 0.657082 0.250808 2.620
## ACOG_DistrictSouth Atlantic 0.167263 0.241946 0.691
## ACOG_DistrictWest North Central 0.484703 0.282408 1.716
## ACOG_DistrictWest South Central -0.001755 0.233461 -0.008
## titleDO -0.131915 0.283699 -0.465
## centralYes 0.098193 0.041602 2.360
## Grd_yr1980 - 1989 0.148390 0.330457 0.449
## Grd_yr1990 - 1999 0.198590 0.327955 0.606
## Grd_yr2000 - 2009 0.278981 0.343898 0.811
## Grd_yr2010 to Present -0.361452 0.685760 -0.527
## Med_schUS Senior Medical Student -0.104906 0.202104 -0.519
## ntransfOne transfer -0.148349 0.041564 -3.569
## ntransfTwo transfers 0.071141 0.078057 0.911
## ntransfMore than two transfers -0.047344 0.164562 -0.288
## specialtyFoot & Ankle Orthopaedic Surgery -0.077104 0.273759 -0.282
## specialtyGeneral Orthopaedic Surgery 0.114956 0.251474 0.457
## specialtyOrthopaedic Surgery of the Spine 0.315155 0.277886 1.134
## specialtyPediatric Orthopaedic Surgery -0.058999 0.349341 -0.169
## specialtySports Medicine Orthopaedics 0.009865 0.270773 0.036
## specialtySurgery of the Hand 0.456144 0.271160 1.682
## cbsatype10Micro -0.152323 0.204791 -0.744
## academic_affiliationAcademic 0.453439 0.222169 2.041
## Pr(>|z|)
## (Intercept) 0.000006398 ***
## insuranceMedicaid 0.002707 **
## genderFemale 0.970167
## Call_time_minutes 0.000000228 ***
## ACOG_DistrictEast South Central 0.730536
## ACOG_DistrictMiddle Atlantic 0.694170
## ACOG_DistrictMountain 0.201725
## ACOG_DistrictNew England 0.175583
## ACOG_DistrictPacific 0.008796 **
## ACOG_DistrictSouth Atlantic 0.489363
## ACOG_DistrictWest North Central 0.086103 .
## ACOG_DistrictWest South Central 0.994002
## titleDO 0.641944
## centralYes 0.018261 *
## Grd_yr1980 - 1989 0.653400
## Grd_yr1990 - 1999 0.544821
## Grd_yr2000 - 2009 0.417232
## Grd_yr2010 to Present 0.598136
## Med_schUS Senior Medical Student 0.603714
## ntransfOne transfer 0.000358 ***
## ntransfTwo transfers 0.362084
## ntransfMore than two transfers 0.773580
## specialtyFoot & Ankle Orthopaedic Surgery 0.778212
## specialtyGeneral Orthopaedic Surgery 0.647579
## specialtyOrthopaedic Surgery of the Spine 0.256745
## specialtyPediatric Orthopaedic Surgery 0.865885
## specialtySports Medicine Orthopaedics 0.970937
## specialtySurgery of the Hand 0.092531 .
## cbsatype10Micro 0.456998
## academic_affiliationAcademic 0.041254 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## $data
## ntransf = No transfers:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 16.36658 1.341873 Inf 13.93700 19.21971
## Medicaid 18.11542 1.502420 Inf 15.39760 21.31295
##
## ntransf = One transfer:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 14.72457 1.272135 Inf 12.43090 17.44145
## Medicaid 16.29795 1.421332 Inf 13.73726 19.33595
##
## ntransf = Two transfers:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 16.32577 1.668230 Inf 13.36271 19.94586
## Medicaid 18.07024 1.803732 Inf 14.85932 21.97500
##
## ntransf = More than two transfers:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 17.26735 2.414334 Inf 13.12835 22.71126
## Medicaid 19.11243 2.719718 Inf 14.46070 25.26055
##
## Results are averaged over the levels of: central, academic_affiliation
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale
##
## $plot## $emmeans
## ntransf = No transfers:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 16.4 1.34 Inf 13.9 19.2
## Medicaid 18.1 1.50 Inf 15.4 21.3
##
## ntransf = One transfer:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 14.7 1.27 Inf 12.4 17.4
## Medicaid 16.3 1.42 Inf 13.7 19.3
##
## ntransf = Two transfers:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 16.3 1.67 Inf 13.4 19.9
## Medicaid 18.1 1.80 Inf 14.9 22.0
##
## ntransf = More than two transfers:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 17.3 2.41 Inf 13.1 22.7
## Medicaid 19.1 2.72 Inf 14.5 25.3
##
## Results are averaged over the levels of: central, academic_affiliation
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale
##
## $contrasts
## ntransf = No transfers:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/\nBlue Shield) / Medicaid 0.903 0.021 Inf 1 -4.374 <.0001
##
## ntransf = One transfer:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/\nBlue Shield) / Medicaid 0.903 0.021 Inf 1 -4.374 <.0001
##
## ntransf = Two transfers:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/\nBlue Shield) / Medicaid 0.903 0.021 Inf 1 -4.374 <.0001
##
## ntransf = More than two transfers:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/\nBlue Shield) / Medicaid 0.903 0.021 Inf 1 -4.374 <.0001
##
## Results are averaged over the levels of: central, academic_affiliation
## Tests are performed on the log scale## $data
## Call_time_minutes = 2.809223:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 16.14451 1.394132 Inf 13.63079 19.12181
## Medicaid 17.86962 1.556476 Inf 15.06517 21.19612
##
## Results are averaged over the levels of: ntransf, central, academic_affiliation
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale
##
## $plot## $emmeans
## Call_time_minutes = 2.81:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 16.1 1.39 Inf 13.6 19.1
## Medicaid 17.9 1.56 Inf 15.1 21.2
##
## Results are averaged over the levels of: ntransf, central, academic_affiliation
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale
##
## $contrasts
## Call_time_minutes = 2.8092225241479:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/\nBlue Shield) / Medicaid 0.903 0.021 Inf 1 -4.374 <.0001
##
## Results are averaged over the levels of: ntransf, central, academic_affiliation
## Tests are performed on the log scale## [1] "insurance" "Call_time_minutes" "central"
## [4] "ntransf" "academic_affiliation"
## $data
## central = No:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 15.09737 1.329513 Inf 12.70405 17.94156
## Medicaid 16.71058 1.479933 Inf 14.04776 19.87816
##
## central = Yes:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 17.26429 1.521281 Inf 14.52590 20.51890
## Medicaid 19.10904 1.702312 Inf 16.04761 22.75451
##
## Results are averaged over the levels of: ntransf, academic_affiliation
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale
##
## $plot## $emmeans
## central = No:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 15.1 1.33 Inf 12.7 17.9
## Medicaid 16.7 1.48 Inf 14.0 19.9
##
## central = Yes:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 17.3 1.52 Inf 14.5 20.5
## Medicaid 19.1 1.70 Inf 16.0 22.8
##
## Results are averaged over the levels of: ntransf, academic_affiliation
## 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/\nBlue Shield) / Medicaid 0.903 0.021 Inf 1 -4.374 <.0001
##
## central = Yes:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/\nBlue Shield) / Medicaid 0.903 0.021 Inf 1 -4.374 <.0001
##
## Results are averaged over the levels of: ntransf, academic_affiliation
## Tests are performed on the log scale## [1] "insurance" "Call_time_minutes" "central"
## [4] "ntransf" "academic_affiliation"
## $data
## academic_affiliation = Not Academic:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 12.29590 0.835998 Inf 10.76186 14.04862
## Medicaid 13.60977 0.943823 Inf 11.88012 15.59124
##
## academic_affiliation = Academic:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 21.19773 3.241173 Inf 15.70866 28.60485
## Medicaid 23.46279 3.593102 Inf 17.37906 31.67620
##
## Results are averaged over the levels of: ntransf, central
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale
##
## $plot## $emmeans
## academic_affiliation = Not Academic:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 12.3 0.836 Inf 10.8 14.0
## Medicaid 13.6 0.944 Inf 11.9 15.6
##
## academic_affiliation = Academic:
## insurance rate SE df asymp.LCL asymp.UCL
## Blue Cross/\nBlue Shield 21.2 3.241 Inf 15.7 28.6
## Medicaid 23.5 3.593 Inf 17.4 31.7
##
## Results are averaged over the levels of: ntransf, central
## Confidence level used: 0.95
## Intervals are back-transformed from the log scale
##
## $contrasts
## academic_affiliation = Not Academic:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/\nBlue Shield) / Medicaid 0.903 0.021 Inf 1 -4.374 <.0001
##
## academic_affiliation = Academic:
## contrast ratio SE df null z.ratio p.value
## (Blue Cross/\nBlue Shield) / Medicaid 0.903 0.021 Inf 1 -4.374 <.0001
##
## Results are averaged over the levels of: ntransf, central
## Tests are performed on the log scale–>
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