The study of the impact of Medicaid expansion on cardiovascular disease mortality by Nianogo and colleagues1 in this issue joins a growing body of epidemiologic research using methods for group-level longitudinal data to estimate effects of social policies on population health.2 Nianogo et al. use the generalized synthetic control method for their analyses,3 a member of a family of methods used for estimating effects of treatments (e.g., interventions, actions, events) in time-series cross-sectional data, also known as “panel” data.3,4 In its usual structure in this setting, time-series cross-sectional data contain repeated observations for multiple units, a subset of which was exposed to a binary treatment during the observation period, such that data are available for treated units before and during the treatment period and for never-treated units for the same time periods. Methods in this family include the original synthetic control method5; its several variations and extensions, including the generalized synthetic control6,7; and the classic difference-in-differences design. In the pages of Epidemiology, authors have used these methods to evaluate state-level gun policies,8 city-level indoor-dining policies on COVID-19 rates,9 subnational vaccine policy,10 built-environment effects on bicycling,11 and wildfire impacts on hospitalizations,12 to name some examples.

The use of synthetic control and related methods by epidemiologists to evaluate health effects of above-the-individual actions represents one-way quantitative causal-inference methods can help answer questions in social epidemiology.13,14 Nianogo et al.’s study of Medicaid expansion is a clear example. The passage of the Affordable Care Act in 2010, the 2012 Supreme Court decision stating that Medicaid expansion is up to the states, and the subsequent state-by-state decisions to expand Medicaid coverage or not are each the result of power dynamics within social and political institutions. Studying Medicaid expansion’s effects on health in (sub)populations thus naturally falls within the realm of social epidemiology, using any of the field’s various definitions.15–17 Nianogo and colleagues’ main finding is that Medicaid expansion at the state level prevented, on average, about 4.3 cardiovascular disease (CVD) deaths per 100,000 adults aged 45 to 64 years old per treated year, a figure that, as they note, corroborates previous research on the topic.18 They build on that literature by estimating effects by race and ethnicity, an important endeavor given people of color are more likely to have their eligibility for Medicaid affected by Medicaid expansion,19 and Black individuals in particular bear a persistently high burden of CVD mortality.20–22

The authors’ exploration of effect heterogeneity of Medicaid expansion by racial and sex groups highlights some challenges and opportunities presented by the generalized synthetic control method. For one, their estimates in Black and Hispanic populations are quite imprecise, as the authors acknowledge. Their estimated difference effect per state-year for the Hispanic population, for example, is 4.28 deaths prevented per 100,000 with a 95% confidence interval (CI) ranging from −21.52 to 30.08 deaths per 100,000, a range about 10 times as wide as the point estimate. Second, the authors measure effect heterogeneity on the difference scale between subgroups, reporting, for example, that Medicaid expansion prevented an estimated 2.18 (95% CI: −15.83, 20.20) more deaths per 100,000 deaths in Black compared with white adults aged 45 to 64 years. This presentation of effect heterogeneity on the additive scale is certainly valuable, as it keeps information about the absolute occurrence of the outcome. For the sake of illustration, it is worth noting that the generalized synthetic control method and its close relatives23,24 offer quite a bit of flexibility for summarizing effect measures, as the methods estimate effects in every treated unit (state, here) and time point (year) posttreatment. These individual state-year effects can be useful both for assessing effect heterogeneity and for summarizing effects in other ways, for example, as a weighted average.

Exemplifying the values of open science and data sharing, Nianogo and colleagues have posted their data and code on a public website, making it possible to replicate their analysis. Facilitated by this act of transparency by the authors, my goal with this comment is to explore reasons for the low precision in their effect estimates in subgroups, building upon their proposed reasons, and to demonstrate additional ways to summarize and compare effect estimates using the generalized synthetic control method and related methods.

INTERROGATING PRECISION IN EFFECT ESTIMATES

The authors note in their discussion that their estimates were imprecise in the Black and Hispanic populations partly because of missingness in CDC Wonder’s database of state-year CVD mortality in these groups. This indeed seems to be the case. As the authors describe in their appendix, CDC Wonder suppressed mortality data for the Black and Hispanic subpopulations in several state-years to maintain anonymity when the sample was below a threshold. Even after some reasonable imputation by the authors (explained in their appendix), a rather small number of states were available in which to estimate effects. In 2019, for example, only 27 states were available for the analysis of the Hispanic population and 37 for the Black population (see their eTable 3 and Section 2 of this web appendix25).

The impact of this small number of states on the precision of the effect estimates was compounded by a characteristic of the generalized synthetic control method. The first step of its modeling procedure only uses the never-treated (i.e., control) data. In this step, it fits an interactive fixed-effects model to estimate coefficients corresponding to measured covariates, time-varying unit-fixed factors, and unit-varying time-fixed factor loadings in these control data.3 Consequently, any state that adopted Medicaid expansion during the study period, even those that did so at the end of the observation period, such as Maine and Virginia (see their Figure 1), was excluded from this initial modeling step. The missingness in the outcome in the Hispanic population meant that only seven of the 16 never-treated states were available for this first modeling step; 12 were available for the Black population.

These small numbers are reflected in the width of the CIs. The bootstrapping procedure used to generate CIs randomly picks one of the control units to serve as a pretend treated unit, then resamples the rest of the control data with replacement and reruns the generalized synthetic control procedure in each replicate to generate a distribution of prediction errors for treated units (see Algorithm 23). As only seven states were resampled for the Hispanic population, it follows that the procedure would lead to wide CIs. Indeed, I replicated the analysis using the same covariates and more bootstrap replications (2,000 compared with 200) and got even wider CIs (Scenario 1 in Table). The width of the estimated difference effect’s CI for the Hispanic population, for example, is 75.5 CVD deaths per 100,000. Throughout this analysis, I use the percentile method to calculate CIs,26 reporting the 2.5th and 97.5th percentiles of the corresponding measure over the bootstrap replicates.

Table. - Pretreatment Fit, Estimated Difference and Ratio Effects, and Confidence Interval Width by Scenario and Group Scenario Group Mean Absolute Error, Before Treatment Diff. Effect (95% CI) Width of 95% CI, Diff. Effect Ratio Effect (95% CI) Difference in Difference Effects (95% CI) Ratio of Ratio Effects (95% CI) (1) Replicate Nianogo et al. Overall 4.3 −4.3 (−8.1, 2.8) 10.9 0.97 (0.95, 1.02) - - White 4.6 −3.2 (−9.6, 1.3) 10.9 0.98 (0.94, 1.01) Ref. 1 Ref. 1 Black 18.4 −5.4 (−19.5, 14.7) 34.3 0.98 (0.93, 1.06) −2.2 (−16.6, 18.3) 1.00 (0.95, 1.09) Hispanic 14.4 −4.3 (−72.1, 3.4) 75.5 0.96 (0.57, 1.04) −1.1 (−67.9, 8.3) 0.98 (0.59, 1.07) Men 6.8 −6.0 (−11.2, 6.6) 17.8 0.97 (0.95, 1.03) Ref. 2 Ref. 2 Women 4.8 −3.3 (−8.0, 1.4) 9.4 0.96 (0.92, 1.02) 2.6 (−9.2, 8.0) 0.99 (0.93, 1.03) (2) Modified covariatesa Overall 4.1 −4.2 (−8.5, 3.0) 11.5 0.97 (0.94, 1.02) - - White 5.3 −6.0 (−11.1, −1.0) 10.2 0.96 (0.93, 0.99) Ref. 1 Ref. 1 Black 18.1 −4.8 (−19.0, 15.8) 34.8 0.98 (0.93, 1.06) 1.2 (−13.8, 21.3) 1.02 (0.97, 1.11) Hispanic 13.8 −6.4 (−87.1, 0.4) 87.5 0.94 (0.52, 1.00) −0.4 (−82.1, 7.7) 0.98 (0.54, 1.06) Men 7.8 −2.0 (−8.8, 7.3) 16.1 0.99 (0.96, 1.04) Ref. 2 Ref. 2 Women 4.8 −3.8 (−8.0, 0.5) 8.5 0.96 (0.92, 1.01) −1.9 (−8.6, 2.9) 0.97 (0.94, 0.99) (3) Gobillon and Magnac23; covariates from 2 Overall 3.8 −3.1 (−5.5, 0.3) 5.9 0.98 (0.96, 1.00) - - White 4.6 −4.3 (−8.2, −0.3) 7.9 0.97 (0.94, 1.00) Ref. 1 Ref. 1 Black 15.8 −6.1 (−16.6, 4.5) 21.0 0.98 (0.94, 1.02) −1.8 (−13.3, 9.2) 1.01 (0.96, 1.06) Hispanic 12.6 −3.5 (−10.8, 3.4) 14.2 0.96 (0.90, 1.04) 0.7 (−7.7, 8.8) 0.99 (0.92, 1.07) Men 6.1 −3.3 (−6.4, 1.4) 7.8 0.98 (0.97, 1.01) Ref. 2 Ref. 2 Women 4.4 −2.9 (−5.8, −0.2) 5.6 0.97 (0.94, 1.00) 0.4 (−3.8, 2.6) 0.98 (0.95, 1.00) (4) MC-NNM (Athey et al.24); covariates from 2 Overall 3.3 −2.1 (−6.4, 1.8) 8.3 0.99 (0.96, 1.01) - - White 3.1 −4.1 (−8.4, 0.2) 8.6 0.97 (0.94, 1.00) Ref. 1 Ref. 1 Black 15.7 −6.7 (−18.9, 5.1) 24.0 0.98 (0.93, 1.02) −2.6 (−15.3, 9.9) 1.00 (0.95, 1.06) Hispanic 9.9 −3.6 (−12.2, 8.9) 21.1 0.96 (0.89, 1.10) 0.5 (−9.4, 13.2) 0.99 (0.91, 1.13) Men 2.3 −2.0 (−8.2, 3.6) 11.8 0.99 (0.96, 1.02) Ref. 2 Ref. 2 Women 3.0 −2.9 (−5.8, 0.0) 5.8 0.97 (0.94, 1.00) −0.9 (−4.7, 3.6) 0.98 (0.96, 1.00) (5) Weighting state-year effect estimates from MC-NNM method24 proportional to their share of person-time Overall Same as 4 −5.2 (−7.6, 2.8) 10.5 0.96 (0.95, 1.02) - - White Same as 4 −7.0 (−8.8, 0.9) 9.7 0.95 (0.94, 1.01) Ref. 1 Ref. 1 Black Same as 4 −7.4 (−20.0, 6.7) 26.6 0.97 (0.93, 1.03) −0.5 (−17.2, 11.1) 1.02 (0.95, 1.06) Hispanic Same as 4 −6.3 (−16.5, 12.8) 29.3 0.94 (0.85, 1.15) 0.7 (−13.3, 17.4) 0.99 (0.87, 1.19) Men Same as 4 −6.8 (−9.7, 5.0) 14.7 0.97 (0.95, 1.03) Ref. 2 Ref. 2 Women Same as 4 −5.1 (−6.9, 1.3) 8.2 0.94 (0.93, 1.02) 1.6 (−6.5, 4.4) 0.98 (0.95, 1.01) aThis scenario is the same as Scenario 1, except the covariates are trimmed at their third and 97th percentiles to see if precision might be improved. In addition, I used state-level popular-vote data from the most recent presidential election for that year34 as a measure of political environment, as I thought that measure might be more stable than the BRFSS measure on the topic.

Diff., difference; Ref., referent group, following the definitions in the table by Nianogo et al.

Given the method’s reliance on the control data, Xu3 cautions that the method is less reliable when the number of control units is less than 40. Supporting this caution, Bonander’s27 concern that modeling-based synthetic control methods may estimate implausibly negative counterfactual outcomes surfaced in some of the bootstrap replicates: the minimum predicted value of the counterfactual outcome in the treatment period over the replicates for the Hispanic population in Scenario 2 was −6091 CVD deaths per 100,000 adults.25 The method’s introductory example has 38 control states,3 so 40 is certainly not a hard-and-fast minimum, but the existence of implausible values in the bootstrap replicates along with the very wide CIs suggests that other methods might be worth considering when the number of never-treated units is as low as seven.

Fortunately, related methods exist that make more efficient use of the data in the treated units before treatment and thus may be preferred when the number of never-treated units is small. One is a separate interactive fixed-effects algorithm by Gobillon and Magnac,23 and another is a matrix-completion method by Athey and colleagues24 that they call the matrix completion with nuclear norm minimization (MC-NNM) estimator.24 As of version 1.0.9 of the gsynth R package, both of these methods can be implemented in the gsynth() function by changing values in one or two of its arguments.28,29 I have implemented these methods to see if they may yield more precise effect estimates, and indeed they do (Table; Scenarios 3 and 4, respectively). The width of the CI for the Hispanic population using the Gobillon and Magnac method, for example, is 14 CVD deaths per 100,000, over six times more precise than the generalized synthetic control method in Scenario 2 using the same covariates. Perhaps more importantly, the pretreatment fit as measured by mean absolute error (the mean of the absolute difference between the predicted counterfactual outcome before treatment and its contemporaneous observed counterpart over unit-time observations) is also a little better. The MC-NNM estimator resulted in CIs of similar if somewhat wider width compared with the Gobillon and Magnac method but had even better pretreatment fit for all groups. If I had to choose results from one method to report, it would be those from the MC-NNM method, given their better pretreatment fits and relatively precise effect estimates.

Another issue related to precision is the uncertainty of the estimates used as inputs in the model. For example, the Behavioral Risk Factor Surveillance System (BRFSS) data used by the authors evidently has considerable sampling error in age-group-race subgroups: in one state-year, the data state that 100% of Hispanic adults aged 45 to 64 years were men, while in another state-year, 0% were.25 To avoid these and other implausible values, in Scenarios 2 to 5, I trimmed the covariate data provided by the authors at their third and 97th percentiles over state-years. To consider sampling variability more rigorously, one could first resample the BRFSS sample with replacement and apply the generalized synthetic control method (or the others proposed23,24) and its corresponding bootstrap procedure in each replicate. The individual-level data may not be accessible. If not, the point estimates could be sampled with replacement from a normal distribution using the reported standard errors (mean = point estimate; standard deviation = standard error) to generate a resampled distribution of the input data. Applying the generalized synthetic control method to each replicate would result in a distribution of effect estimates reflecting both sampling variability of the input data and uncertainty in the counterfactual model.

USING STATE-YEAR EFFECT ESTIMATES TO CALCULATE WEIGHTED AVERAGES AND OTHER SUMMARY MEASURES

Output from the generalized synthetic control method’s R program reports the average difference effect in the treated, both over all treated unit-time observations (obtained by the command, gsynth_object$att.avg) and over units by time point (gsynth_object$att)29; gsynth_object is my arbitrary name for the object created by the gsynth() function. These summary measures of effect are unweighted averages, giving the same weight to every treated unit-time’s effect estimate. In reported summary measures over states in this context, it may be desirable to give more weight in the mean to states with larger populations. In 2019, for example, according to the American Community Survey, California’s population of 45- to 64-year-old adults was over 50 times North Dakota’s (9.8 million vs. 171,000). These varying population sizes can be considered in the analysis by making use of each treated state-year’s effect estimate, which are available via gsynth_output$eff in the R program.

Using state-year effects estimated by the MC-NNM method, I calculated the weighted average difference effect over treated state-years, weighting each state-year’s estimated difference effect by its proportion of the total nonmissing treated person-years aged 45 to 64 years in the corresponding demographic group (Scenario 5, Table). Considering the total population of adults aged 45 to 64 years, for example, there were 309,495,338 person-years over all treated states and years. California contributed the largest share (19.1%) to this total.25 Considering Black adults in this age range, the state of New York contributed the largest share (15.8%) of the 29,839,638 total treated person-years available for analysis. Upon weighting the state-year effect estimates proportional to their share of person-time, summary point estimates for each group migrated away from the null (Scenario 5), implying that more populous states had on average stronger effect estimates. The estimated population-weighted difference effect in all adults aged 45 to 64 years, for example, is −5.2 (95% CI: −7.6, 2.8) deaths per 100,000 person-years, stronger than the corresponding value of −2.1 (−6.4, 1.8) in which every state-year is weighted equally, although both sets of CIs include the null.

The estimated treated state-year effects can be useful for at least three other purposes beyond calculating weighted difference-effect measures. First, they can be used to calculate ratio measures of effect, as shown in the Table, which can help facilitate interpretation of effect magnitude when presented alongside the difference measures. I have calculated ratio effect measures by first calculating the mean (or the weighted mean in Scenario 5) of the observed CVD mortality rates in the treated state-years (gsynth_output$Y.tr) and of the corresponding estimated counterfactual CVD mortality rates (gsynth_output$Y.ct) and then taking the ratio of the two means.

Second, the state-year effect estimates can also be used to assess effect heterogeneity. The comparison of effect estimates over state-years between racial and sex groups as presented by Nianogo and colleagues is one way to assess heterogeneity of effects. Effect heterogeneity might also be assessed between state-years, for example, by stratifying states by whether they adopted the policy immediately in 2014 or afterwards.

Finally, the state-year effect estimates could be useful for assessing transportability or generalizability of treatment effects, as methods for those aims often use information about the distribution of effect modifiers in the study sample and target population.30–32 Whether the estimated effects would apply to states that have not expanded Medicaid is a particularly important question given Black-white CVD disparity is the most pernicious in the US South,21,22 and, with the exception of Louisiana and Arkansas (and soon North Carolina33), state governments in the South have refused to expand Medicaid. This refusal has led to a gap in coverage disproportionately affecting Black individuals in this region,19 which could be contributing to the current CVD disparity. Importantly, the generalized synthetic control method and related methods presented here estimate effects in the treated. That is, the target population for the effect estimand does not include states that have not expanded Medicaid. An open question then remains: if other states in the South were to expand Medicaid, what would the effects on CVD mortality and disparity be? Future research might explore this topic considering methods for transportability and generalizability.

CONCLUSIONS

As demonstrated by Nianogo and colleagues, the generalized synthetic control and related methods can be useful for helping to answer questions of interest for social epidemiology. Like any set of methods, they have limitations. Nianogo and colleagues’ article illustrates that the generalized synthetic control method, in particular, can encounter barriers when the number of never-treated (control) units is small. Fortunately, this literature is evolving rapidly,6,7 and other methods are available that could be more suitable in such situations24 and can be readily implemented using existing software programs.28 That these methods estimate effects in every observation of treated unit-time provides flexibility for summarizing effect measures. In this analysis, that flexibility allowed for the calculation of average treatment effects weighted by population.

ACKNOWLEDGMENTS

I thank Nianogo and colleagues for making their code and data available, which made this analysis possible. I also thank Jay S. Kaufman for guidance and constructive comments.

ABOUT THE AUTHOR

Michael Garber is a postdoctoral researcher affiliated with UC San Diego and Colorado State University interested in the effects of urban design and related policies on health and health equity.

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