An Aggregation Scheme for Increased Power

An Aggregation Scheme for Increased Power

Tuesday January 10, 2023

4:00 p.m. - 5:45 p.m. MST

Tuesday January 10, 2023

4:00 p.m. - 5:45 p.m. MST


International Conference on Health Policy Statistics 2023


Tim Lycurgus, PhD

Postdoctoral Fellow, d3center


Outcome analysis with repeated measurements often involves fitting regression models with a variable denoting treatment assignment; its coefficient estimates the treatment effect. Yet estimating the average difference in potential outcomes may not be as simple. To illustrate, outcome analysis of a repeated-measurements observational study may call for separate average treatment effect estimates of the causal effect during each occasion of follow-up. How then should those separate estimates be combined to determine whether the treatment was beneficial in sum? Treatments occurring at different times and with different intensities further complicates this question.

Randomized trials and observational studies often possess some formal or informal theory of how effects will accumulate, i.e. why should the desired improvement in outcomes occur and on whom should those benefits concentrate? In scenarios with repeated measurements and treatments that occur at different times, subgroups may be more or less likely to manifest a treatment effect; the theory of the intervention provides guidance as to which subgroups are best situated to demonstrate a benefit. Our method, power-maximizing weighting for repeated-measurements with delayed-effects (PWRD aggregation) converts that theory of how effects accumulate into a test statistic with greater relative Pitman efficiency and thus, greater statistical power than extant alternatives when the theory holds. PWRD aggregation is compatible with standard methods for effect estimation and clustered errors when it is possible to measure effects on separate subgroups and occasions of follow-up along with their mutual correlations.

We illustrate the benefit of PWRD aggregation both through a simulation study, which finds stark benefits in terms of power for the method, and its application on county-level data examining changes in healthcare amenable mortality due to Medicaid expansion through the Affordable Care Act (ACA). Starting in 2014, states had the option to expand Medicaid eligibility to all working-age adults with incomes beneath 138% of the federal poverty limit. Over the ensuing 7 years, many states (although not all) chose to expand Medicaid and provide health insurance to many of their low-income residents.

Since states opted into Medicaid expansion at different points, states belong to separate “cohorts” where each cohort has a different length of exposure to the treatment. In addition, more or fewer residents stood to benefit from Medicaid expansion in each state depending on income distributions and pre-ACA Medicaid eligibility requirements. For example, the Massachusetts Healthcare Reform of 2006, on which the ACA was modeled, largely covered this population already and as such, Massachusetts residents were less likely to benefit from Medicaid expansion despite belonging to the treatment group. Montana, on the other hand, had strict pre-ACA Medicaid eligibility requirements so many more residents were newly eligible for healthcare. Thus the data exhibit different levels of exposure, both in terms of the proportion of residents potentially now eligible for health insurance and in terms of the number of years residents had to benefit from the expansion.

Rather than treating each county and year-of-follow-up as equivalent, PWRD aggregation deduces the counties and occasions of follow-up best situated to demonstrate the benefit of Medicaid expansion using one simple rule: those residents newly eligible for health insurance are most likely to benefit from the expansion and thus, the size of the benefit in each county should be proportional to the share of that county that is newly eligible. Using our method on mortality data from 2014-2018, we find there was a significant decrease in healthcare amenable mortality due to this expansion.

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