Objective Examining covariate balance is the prescribed method for determining when propensity score methods are successful at reducing bias. This study assessed the performance of various balance measures, including a proposed balance measure based on the prognostic score (also known as the disease-risk score), to determine which balance measures best correlate with bias in the treatment effect estimate. Study Design and Setting The correlations of multiple common balance measures with bias in the treatment effect estimate produced by weighting by the odds, subclassification on the propensity score, and full matching on the propensity score were calculated. Simulated data were used, based on realistic data settings. Settings included both continuous and binary covariates and continuous covariates only. Results The standardized mean difference in prognostic scores, the mean standardized mean difference, and the mean t-statistic all had high correlations with bias in the effect estimate. Overall, prognostic scores displayed the highest correlations of all the balance measures considered. Prognostic score measure performance was generally not affected by model misspecification and performed well under a variety of scenarios. Conclusion Researchers should consider using prognostic score–based balance measures for assessing the performance of propensity score methods for reducing bias in non-experimental studies.

The major genetic determinants of cutaneous melanoma risk in the general population are disruptive variants (R alleles) in the melanocortin 1 receptor (MC1R) gene. These alleles are also linked to red hair, freckling, and sun sensitivity, all of which are known melanoma phenotypic risk factors. Here we report that in melanomas and for somatic C>T mutations, a signature linked to sun exposure, the expected single-nucleotide variant count associated with the presence of an R allele is estimated to be 42% (95% CI, 15–76%) higher than that among persons without an R allele. This figure is comparable to the expected mutational burden associated with an additional 21 years of age. We also find significant and similar enrichment of non-C>T mutation classes supporting a role for additional mutagenic processes in melanoma development in individuals carrying R alleles.

Summary Propensity and prognostic score methods seek to improve the quality of causal inference in non-randomized or observational studies by replicating the conditions found in a controlled experiment, at least with respect to observed characteristics. Propensity scores model receipt of the treatment of interest; prognostic scores model the potential outcome under a single treatment condition. While the popularity of propensity score methods continues to grow, prognostic score methods and methods combining propensity and prognostic scores have thus far received little attention. To this end, we performed a simulation study that compared subclassification and full matching on a single estimated propensity or prognostic score with three approaches combining estimated propensity and prognostic scores: full matching on a Mahalanobis distance combining the estimated propensity and prognostic scores (FULL-MAHAL); full matching on the estimated prognostic propensity score within propensity score calipers (FULL-PGPPTY); and subclassification on an estimated propensity and prognostic score grid with 5 × 5 subclasses (SUBCLASS(5*5)). We considered settings in which one, both or neither score model was misspecified. The data generating mechanisms varied in the degree of linearity and additivity in the true treatment assignment and outcome models. FULL-MAHAL and FULL-PGPPTY exhibited strong to superior performance in root mean square error terms across all simulation settings and scenarios. Methods combining propensity and prognostic scores were no less robust to model misspecification than single-score methods even when both score models were incorrectly specified. Our findings support the joint use of propensity and prognostic scores in estimation of the average treatment effect on the treated.

The not‐at‐random fully conditional specification (NARFCS) procedure provides a flexible means for the imputation of multivariable missing data under missing‐not‐at‐random conditions. Recent work has outlined difficulties with eliciting the sensitivity parameters of the procedure from expert opinion due to their conditional nature. Failure to adequately account for this conditioning will generate imputations that are inconsistent with the assumptions of the user.In this paper, we clarify the importance of correct conditioning of NARFCS sensitivity parameters and develop procedures to calibrate these sensitivity parameters by relating them to more easily elicited quantities, in particular, the sensitivity parameters from simpler pattern mixture models. Additionally, we consider how to include the missingness indicators as part of the imputation models of NARFCS, recommending including all of them in each model as default practice.Algorithms are developed to perform the calibration procedure and demonstrated on data from the Avon Longitudinal Study of Parents and Children, as well as with simulation studies.