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Impact of Regression to the Mean on the Synthetic Control Method: Bias and Sensitivity Analysis.

ABSTRACT: To make informed policy recommendations from observational panel data, researchers must consider the effects of confounding and temporal variability in outcome variables. Difference-in-difference methods allow for estimation of treatment effects under the parallel trends assumption. To justify this assumption, methods for matching based on covariates, outcome levels, and outcome trends-such as the synthetic control approach-have been proposed. While these tools can reduce bias and variability in some settings, we show that certain applications can introduce regression to the mean (RTM) bias into estimates of the treatment effect. Through simulations, we show RTM bias can lead to inflated type I error rates and bias toward the null in typical policy evaluation settings. We develop a novel correction for RTM bias that allows for valid inference and show how this correction can be used in a sensitivity analysis. We apply our proposed sensitivity analysis to reanalyze data concerning the effects of California's Proposition 99, a large-scale tobacco control program, on statewide smoking rates.

SUBMITTER: Illenberger NA

PROVIDER: S-EPMC7541515 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Regression toward the mean--a detection method for unknown population mean based on Mee and Chua's algorithm.

Project description:BACKGROUND: Regression to the mean (RTM) occurs in situations of repeated measurements when extreme values are followed by measurements in the same subjects that are closer to the mean of the basic population. In uncontrolled studies such changes are likely to be interpreted as a real treatment effect. METHODS: Several statistical approaches have been developed to analyse such situations, including the algorithm of Mee and Chua which assumes a known population mean mu. We extend this approach to a situation where mu is unknown and suggest to vary it systematically over a range of reasonable values. Using differential calculus we provide formulas to estimate the range of mu where treatment effects are likely to occur when RTM is present. RESULTS: We successfully applied our method to three real world examples denoting situations when (a) no treatment effect can be confirmed regardless which mu is true, (b) when a treatment effect must be assumed independent from the true mu and (c) in the appraisal of results of uncontrolled studies. CONCLUSION: Our method can be used to separate the wheat from the chaff in situations, when one has to interpret the results of uncontrolled studies. In meta-analysis, health-technology reports or systematic reviews this approach may be helpful to clarify the evidence given from uncontrolled observational studies.

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Project description:We propose sensitivity analyses for publication bias in meta-analyses. We consider a publication process such that 'statistically significant' results are more likely to be published than negative or "non-significant" results by an unknown ratio, η. Our proposed methods also accommodate some plausible forms of selection based on a study's standard error. Using inverse probability weighting and robust estimation that accommodates non-normal population effects, small meta-analyses, and clustering, we develop sensitivity analyses that enable statements such as 'For publication bias to shift the observed point estimate to the null, "significant" results would need to be at least 30 fold more likely to be published than negative or "non-significant" results'. Comparable statements can be made regarding shifting to a chosen non-null value or shifting the confidence interval. To aid interpretation, we describe empirical benchmarks for plausible values of η across disciplines. We show that a worst-case meta-analytic point estimate for maximal publication bias under the selection model can be obtained simply by conducting a standard meta-analysis of only the negative and 'non-significant' studies; this method sometimes indicates that no amount of such publication bias could 'explain away' the results. We illustrate the proposed methods by using real meta-analyses and provide an R package: PublicationBias.

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