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.

With incomplete data, the “missing at random” (MAR) assumption is widely understood to enable unbiased estimation with appropriate methods. While the need to assess the plausibility of MAR and to perform sensitivity analyses considering “missing not at random” (MNAR) scenarios has been emphasized, the practical difficulty of these tasks is rarely acknowledged. With multivariable missingness, what MAR means is difficult to grasp, and in many MNAR scenarios unbiased estimation is possible using methods commonly associated with MAR. Directed acyclic graphs (DAGs) have been proposed as an alternative framework for specifying practically accessible assumptions beyond the MAR-MNAR dichotomy. However, there is currently no general algorithm for deciding how to handle the missing data given a specific DAG. Here we construct “canonical” DAGs capturing typical missingness mechanisms in epidemiologic studies with incomplete data on exposure, outcome, and confounding factors. For each DAG, we determine whether common target parameters are “recoverable,” meaning that they can be expressed as functions of the available data distribution and thus estimated consistently, or whether sensitivity analyses are necessary. We investigate the performance of available-case and multiple-imputation procedures. Using data from waves 1–3 of the Longitudinal Study of Australian Children (2004–2008), we illustrate how our findings can guide the treatment of missing data in point-exposure studies.

Multiple imputation with delta adjustment provides a flexible and transparent means to impute univariate missing data under general missing-not-at-random mechanisms. This facilitates the conduct of analyses assessing sensitivity to the missing-at-random (MAR) assumption. We review the delta-adjustment procedure and demonstrate how it can be used to assess sensitivity to departures from MAR, both when estimating the prevalence of a partially observed outcome and when performing parametric causal mediation analyses with a partially observed mediator. We illustrate the approach using data from 34,446 respondents to a tuberculosis and human immunodeficiency virus (HIV) prevalence survey that was conducted as part of the Zambia–South Africa TB and AIDS Reduction Study (2006–2010). In this study, information on partially observed HIV serological values was supplemented by additional information on self-reported HIV status. We present results from 2 types of sensitivity analysis: The first assumed that the degree of departure from MAR was the same for all individuals with missing HIV serological values; the second assumed that the degree of departure from MAR varied according to an individual's self-reported HIV status. Our analyses demonstrate that multiple imputation offers a principled approach by which to incorporate auxiliary information on self-reported HIV status into analyses based on partially observed HIV serological values.

Carpenter et al. (2013) propose a multiple imputation (MI) approach for analyzing data from clinical trials with protocol deviations. Sensitivity analysis to departures from missing at random (MAR) is widely acknowledged as important, but is poorly handled in practice, so we welcome their detailed proposals. However, here we highlight two problems with their method: an implicit assumption of noninformative deviation, and failure of the Rubin's Rule (RR) variance estimator. THE METHOD OF CARPENTER ET AL. (2013)We start by summarizing the method of Carpenter et al. (2013), using their notation and additional notation μ T , μ T,O , μ T,M , T,OO , T,MO , Y * M , and Y * . The number of repeated outcomes per patient and number of patients are J and n, respectively. For each patient, D denotes the deviation time (i.e., time of last outcome before protocol deviation), T is the randomization group (r for reference, a for active), and Y O are the outcomes prior to deviation.denotes a vector of hypothetical outcomes after deviation. These may or may not be the same as the actual postdeviation outcomes Y M . Carpenter et al. specify separate normal distributions for Y * given T = r and for Y * given T = a, and denote the unknown means of these distributions by μ r = μ r,1 , . . . , μ r,J and μ a = μ a,1 , . . . , μ a,J , and the variances by r and a . Let μ T,O and μ T,M (T = r, a) denote μ T,1 , . . . , μ T,D T and μ T,D+1 , . . . , μ T,J T , respectively, and let the submatrices of

Objective Exposure to prenatal stress is a ubiquitous and non‐specific risk factor for adverse outcomes in adulthood. In this study, we examined associations between exposure to subjective maternal stress during pregnancy and subsequent diagnosis of psychiatric disorders in offspring. Method This study used the Helsinki Longitudinal Temperament Cohort, a prospective birth cohort of individuals born between 1 July 1975 and 30 June 1976 in Helsinki, Finland. The sample for this study comprised 3626 infants whose mothers had completed health and well‐being assessments during pregnancy which included a measure of self‐reported stress. We ran logistic regressions to assess potential associations between prenatal stress and offspring psychiatric disorder in adulthood, identified through the Finnish Hospital Discharge Register. Results Individuals whose mothers reported stress during pregnancy had significantly greater odds of developing a psychiatric disorder (OR = 1.41, 95% CI = 1.10–1.81) particularly a mood disorder (OR = 1.67, 95% CI = 1.10–2.54). These associations remained after adjusting for parental psychiatric history, and other prenatal factors. Conclusions Individuals exposed to prenatal stress had significantly increased risk of developing psychiatric disorders later in life. This finding highlights the importance of supporting the mental health and emotional well‐being of women during pregnancy.