Treatment effects in the presence of unmeasured confounding: dealing with observations in the tails of the propensity score distribution--a simulation study

Abstract

Frailty, a poorly measured confounder in older patients, can promote treatment in some situations and discourage it in others. This can create unmeasured confounding and lead to nonuniform treatment effects over the propensity score (PS). The authors compared bias and mean squared error for various PS implementations under PS trimming, thereby excluding persons treated contrary to prediction. Cohort studies were simulated with a binary treatment T as a function of 8 covariates X. Two of the covariates were assumed to be unmeasured strong risk factors for the outcome and present in persons treated contrary to prediction. The outcome Y was simulated as a Poisson function of T and all X's. In analyses based on measured covariates only, the range of PS's was trimmed asymmetrically according to the percentile of PS in treated patients at the lower end and in untreated patients at the upper end. PS trimming reduced bias due to unmeasured confounders and mean squared error in most scenarios assessed. Treatment effect estimates based on PS range restrictions do not correspond to a causal parameter but may be less biased by such unmeasured confounding. Increasing validity based on PS trimming may be a unique advantage of PS's over conventional outcome models.

Figure 1.

Conceptual diagram of a simulation study depicting treatment (T) and outcome (Y) as a function of measured covariates (X₁–X₆) and unmeasured covariates (X₇ and X₈). The solid lines represent causal associations, and the dashed lines represent noncausal associations used in the 2-step simulation process to mimic treatment contrary to prediction by measured covariates (X₁–X₆).

Figure 2.

Schematic of asymmetric range restriction. PS, propensity score.