Abstract:
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For ethical and cost-effective considerations, some observational studies adopt a "retrospective convenience sampling (RCS)". With the sample size in each arm pre-specified, RCS randomly select subjects from the treatment-inclined subpopulation into the treatment arm, and those from the control-inclined into the control arm. Samples in each arm are representative of the respective subpopulation, but the proportion of the two subpopulations is usually not preserved in the sample data. We show in this work that, under RCS, existing causal effect estimators actually estimate the treatment effect over the sample population instead of the underlying study population. We investigate how to correct existing methods for consistent estimation of the treatment effect over the underlying population. When the tendency to receive treatment is low in a study population, the corrected treatment effect estimators under RCS is more efficient than their parallels under random sampling. These properties are investigated theoretically and through numerical studies.
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