Post-doctoral Researcher McGill University, Department of Epidemiology, Biostatistics, and Occupational Health McGill University Montreal, Canada
Background: External validity is an essential consideration in pharmacoepidemiologic research. External validity bias can be reduced by weighting to account for different distributions of effect measure modifiers (EMMs) between trial and target populations. For internal validity, control of non-confounders can improve variance. For external validity, however, it is unclear how adjustment for non-EMMs affects variance.
Objectives: To assess how accounting for various types of variables when transporting estimates using inverse odds weights (IOW) affected variance of the transported risk difference (RD) and whether including non-EMMs amplified residual external validity bias in the same way that adjusting for instruments amplifies residual confounding bias.
Methods: We simulated 1000 replicates of a 10,000-person randomized trial (S=1) of a binary treatment X and binary outcome Y and a 10,000-person target population (S=0). 6 binary, independent covariates Z1-Z6 were simulated in both. Z1-Z3 were distributed identically in both populations; Z1 had no direct effect on Y; Z2 caused Y, and was not an EMM; Z3 caused Y, and was an EMM; and Z4-Z6 differed in distribution between the trial and target but were otherwise identical to Z1-Z3 regarding associations with Y and whether they were EMMs. We included Z6 in a model to estimate inverse odds weights (a minimally sufficient set for external validity) and assessed the impact of including other covariates in that model on empirical standard errors (ESE). We then omitted Z6 from the model and evaluated whether including Z1, Z2, Z3, Z4, or Z5 amplified bias from omitting Z6.
Results: The true RD in the trial was 0.17 and the true RD in the target was 0.23. All models including Z6 were unbiased. The ESE when adjusting only for Z6 was 0.0174. ESEs did not change when including Z1, Z2, or Z3 (the identically distributed covariates). Including Z4 (ESE 0.0313) or Z5 (ESE 0.0317) substantially increased ESEs. When Z6 was omitted, we did not observe any bias amplification regardless of which covariates were included.
Conclusions: Non-EMM variables that nonetheless differ in distribution between study and target populations increase variance when included in statistical models regardless of the variables’ association with the outcome. Adjusting for all outcome-related variables when transporting treatment effect estimates can reduce precision but should not amplify bias from unmeasured EMMs provided sufficient sample size.
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