Two Birds with One Stone: Outcome of Medication Adherence
Medication adherence measures are some of the most important measures in Medicare Advantage’s Star Ratings system. Not only are they heavily weighted measures, but they are also lead measures for other clinical outcome measures.
Improving Diabetes Medication Adherence Leads to a Better Blood Sugar Control score.
In Star Ratings, Diabetes Medication Adherence (DMA) represents the percent of diabetic members who adhere to their prescribed diabetes drugs, and Blood Sugar Control (BSC) indicates the percent of diabetic members who showed their average blood sugar is under control.
Many clinical studies have shown that drug adherence is strongly associated with metabolic control — a 10% increase in drug adherence results in 0.16% decrease in A1c level [1,2]. Would this relationship hold in Star Rating measures? Let’s find out.
Individual-level Correlation ≠ Population-level Correlation
Some people may think that improving a plan’s DMA score would of course lead to a higher BSC score. Well, if you are familiar with statistics, you may have heard of ecological fallacy or Simpson’s paradox: individual- and population-level correlations are not necessarily in the same direction. Furthermore, if you take a look at Medicare Advantage Star Ratings datasets, you may find that these two measures are not so much correlated.
Surprised to see almost randomly scattered points? The chart above shows the relationship between the changes of DMA and BSC measures. In fact, the results from a linear regression model between these two variables show that the correlation between these two variables is inconclusive (p-value of 0.166).
Call:
lm(formula = d.BSC ~ d.DMA, data = data)Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.04747 0.23960 4.372 1.32e-05 ***
d.DMA 0.12399 0.08947 1.386 0.166
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 8.102 on 1415 degrees of freedom
Multiple R-squared: 0.001355, Adjusted R-squared: 0.0006495
F-statistic: 1.92 on 1 and 1415 DF, p-value: 0.166- d.DMA: Change of DMA from the previous to the current year
- d.BSC: Change of BSC from the previous to the current year
Understanding How Data is Generated
Don’t give up hope yet. It takes time to find a meaningful relationship at the population level. While I was examining the Star Ratings dataset, I began to realize some nuances of the data:
- Both DMA and BSC measures are percent measures from a heterogeneous population. In other words, diverse groups of members contribute to these measures.
- There always exists a group of members who would never adhere to their drugs. Therefore, as an MA plan improves its DMA score, it becomes more difficult to improve its DMA score than when it was lower. Mathematically speaking, Change of DMA is a function of DMA.
- Similarly, there exists a group of members whose blood sugar levels cannot be well-controlled by medication adherence. As an MA plan improves its BSC score, it becomes more challenging to improve further. Likewise, Change of BSC is a function of BSC.
These findings suggest that a multivariate regression model is better suited than a univariate regression model. Let’s include two more variables, DMA and BSC, and run a multivariate regression analysis:
Call:
lm(formula = d.BSC ~ d.DMA + log(DMA) + log(BSC), data = data)Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 32.46350 9.83436 3.301 0.000987 ***
d.DMA 0.19476 0.07732 2.519 0.011879 *
log(DMA) 17.29883 2.52703 6.846 1.13e-11 ***
log(BSC) -24.70053 0.90975 -27.151 < 2e-16 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 6.52 on 1413 degrees of freedom
Multiple R-squared: 0.3542, Adjusted R-squared: 0.3528
F-statistic: 258.3 on 3 and 1413 DF, p-value: < 2.2e-16- DMA: DMA value in the previous measurement year
- BSC: BSC value in the previous measurement year
- d.DMA: change of DMA values from the previous to the current year
- d.BSC: change of BSC values from the previous to the current year
Do you see what I see? The correlation between the changes of DMA and BSC is “statistically significant” (p-value of 0.011879).
A +1% increase in the Diabetes Medication Adherence measure results in +0.2% increase in the Blood Sugar Control measure.
Look at the R-squared value: 0.3542. Although simple, this model is very powerful; it explains 35% of variance in the change of BSC.
Indeed, focusing on Medication Adherence can positively affect other Star Rating measures. Although we only showed one such example in this post, other outcome measures can be analyzed in a similar way. You will easily find that many outcome measures are directly/indirectly associated with the Medication Adherence measures.
References
[1] J. M. Schectman et al. The Association Between Diabetes Metabolic Control and Drug Adherence in an Indigent Population http://care.diabetesjournals.org/content/25/6/1015
[2] M. T. Brown and J. K. Bussell. Medication Adherence: WHO Cares http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3068890/
