Tuesday, January 3, 2017

Logistical Regression Models of Access to Specialists

Logistical Regression Models of Access to Specialists


Question:   Using logistical regression models evaluate the impact of insurance type, health status, and mental health status on whether patients are deemed to need to see a specialist. 

Estimate the logistical regression model for all income categories and estimate the model for a sample containing only households with income less than 200 percent of the Federal Poverty Line.   How do results from the model estimated over all households differ from results for the model estimated only over households with income less than 200% FPL?

Note:  I am running separate regressions for low-income groups because insurance market composition and doctor behavior varies with income.

Medicaid is generally only available for people with low-income.   There may be some exceptions under spend-down rules but in general your income has to be really low to qualify for Medicaid.   Also, tax incentives for people enrolled in state exchanges tend to favor lower-income households and people without access to employer-sponsored insurance possible because they are part-time workers at smaller firms.   These markets for many people are not substitutes. 

Doctors may treat low-income and high-income people differently and these differences may be confused with differences stemming from the type of insurance that a person has.  I strongly suspect that combining high and low-income people into one regression will impact regression coefficients.

This hypothesis can be verified or refuted simple by estimating separate models for different income categories.  

Discussion of Data:  The data for this exercise was obtained in the MEPS 2014 consolidated database.   The table below summarizes the information I am using in this study.

Overview of Data
Need Specialist
Yes
4211
No
8742
Total
12953
Income
<200 FPL
4485
>=200 FPL
8468
Total
12953
Poor or fair Health Self Reported
Yes
1848
No
11105
12953
Poor or Fair Mental Health Self Reported
Yes
1124
No
11829
Total
12953
Insurance Type
Medicaid
3,491
State Exchange
9043
Employer Sponsored
419
Total
12,953




The Logistical Regression Model Results:  The coefficients and the p-values for the coefficients of the logistical regression model for the two samples are presented below.


Logistical Regression Models of Need Specialist for Two Populations
All Households
Coefficient
p-value
medicaid
-0.2231102
0.02
exchange
-0.3921029
0.008
notgood_health
1.192095
0
notgood_mental
0.0541186
0.655
_cons
-0.773526
0
Income Less than 200% FPL
Coefficient
p-value
medicaid
0.2029451
0.009
exchange
0.2688624
0.147
notgood_health
1.141829
0
notgood_mental
0.2900854
0.003
_cons
-1.346823
0

Discussion of Logistical Regression Results:

The Logistical Regression model has dummy variables for people in Medicaid and people in state exchanges.    The excluded dummy variable is for people in employer-sponsored insurance.   A negative/positive value for the Medicaid and exchange variables indicates that members of these groups are less likely/more likely to require a specialist.

In the sample consisting of all households regardless of income, people on Medicaid and people in state exchanges are less likely to need a specialist than people with employer-based insurance.

In the lower-income household sample people in Medicaid are more likely to need to see a specialist.   The state exchange coefficient while positive is not significantly different from zero.

The not-good health variable is consistently positive and highly significant in both samples.

The not-good mental health variable is not significant for the entire population but is positive and significant for the lower-income household group.

Comment on why samples matter:  In my view, it makes little sense to estimate a regression model for the impact of Medicaid when the sample includes people with household income over 200% FPL because the Medicaid eligibility rules make it very hard to qualify for income if your household income is above 138% FPL.  Higher-income people tend to get access to specialists if needed and this difference impacts the Medicaid coefficient and the State-exchange coefficient.

The coefficient of health status variables may differ for different program.  It would be interesting to estimate separate logistical models for the three different insurance programs – employer-based, state exchange, and Medicaid.  

Concluding Remarks: This post looked at variable ASSPEC42 – whether a person was diagnosed as needing a specialist.    Some previous posts on my health care blog looked at variable ADSPEC421 -- a variable that measures whether it is hard or easy for a person to obtain an appointment with a specialist. 



Ideally, one would look at both of these variables in sequence perhaps using a multilevel or hierarchical regression model.

People interested in this work should look at the following books:

Multilevel Analysis:


Hierarchical Linear Models:



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