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Despite the growing popularity of propensity score (PS) methods in epidemiology, relatively little has been written in the epidemiologic literature about the problem of variable selection for PS models. The authors present the results of two simulation studies designed to help epidemiologists gain insight into the variable selection problem in a PS analysis. The simulation studies illustrate how the choice of variables that are included in a PS model can affect the bias, variance, and mean squared error of an estimated exposure effect. The results suggest that variables that are unrelated to the exposure but related to the outcome should always be included in a PS model. The inclusion of these variables will decrease the variance of an estimated exposure effect without increasing bias. In contrast, including variables that are related to the exposure but not to the outcome will increase the variance of the estimated exposure effect without decreasing bias. In very small studies, the inclusion of variables that are strongly related to the exposure but only weakly related to the outcome can be detrimental to an estimate in a mean squared error sense. The addition of these variables removes only a small amount of bias but can increase the variance of the estimated exposure effect. These simulation studies and other analytical results suggest that standard model-building tools designed to create good predictive models of the exposure will not always lead to optimal PS models, particularly in small studies.

Concepts of cause and causal inference are largely self-taught from early learning experiences. A model of causation that describes causes in terms of sufficient causes and their component causes illuminates important principles such as multi-causality, the dependence of the strength of component causes on the prevalence of complementary component causes, and interaction between component causes. Philosophers agree that causal propositions cannot be proved, and find flaws or practical limitations in all philosophies of causal inference. Hence, the role of logic, belief, and observation in evaluating causal propositions is not settled. Causal inference in epidemiology is better viewed as an exercise in measurement of an effect rather than as a criterion-guided process for deciding whether an effect is present or not.

Body mass index (BMI) has various deficiencies as a measure of obesity, especially when the BMI measure is based on self-reported height and weight. BMI is an indirect measure of body fat compared with more direct approaches such as bioelectrical impedance. Moreover, BMI does not necessarily reflect the changes that occur with age. The proportion of body fat increases with age, whereas muscle mass decreases, but corresponding changes in height, weight and BMI may not reflect changes in body fat and muscle mass. Both the sensitivity and specificity of BMI have been shown to be poor. Additionally, the relation between BMI and percentage of body fat is not linear and differs for men and women. The consequences of the errors in the measurement of obesity with BMI depend on whether they are differential or nondifferential. Differential misclassification, a potentially greater problem in case-control and cross-sectional studies than in prospective cohort studies, can produce a bias toward or away from the null. Nondifferential misclassification produces a bias toward the null for a dichotomous exposure; for measures of exposure that are not dichotomous, the bias may be away from the null. In short, the use of BMI as a measure of obesity can introduce misclassification problems that may result in important bias in estimating the effects related to obesity.

Publication of results based on propensity score methods has increased dramatically, but there is little evidence that these methods yield substantially different estimates compared with conventional multivariable methods.

Calculating the ROR in spontaneous report databases offers advantages over the PRR. It allows for estimation of the relative risk, and focuses attention on which people or reports should be included or excluded from the control series, permitting more deliberate elimination of biases. It also highlights the inherent weaknesses in spontaneous report data, which become more evident in light of the usual principles of control selection in case-control studies.

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.

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