Generalized pairwise comparisons for censored data: An overview.

The method of generalized pairwise comparisons (GPC) is an extension of the well-known nonparametric Wilcoxon-Mann-Whitney test for comparing two groups of observations. Multiple generalizations of Wilcoxon-Mann-Whitney test and other GPC methods have been proposed over the years to handle censored data. These methods apply different approaches to handling loss of information due to censoring: ignoring noninformative pairwise comparisons due to censoring (Gehan, Harrell, and Buyse); imputation using estimates of the survival distribution (Efron, Péron, and Latta); or inverse probability of censoring weighting (IPCW, Datta and Dong). Based on the GPC statistic, a measure of treatment effect, the "net benefit," can be defined. It quantifies the difference between the probabilities that a randomly selected individual from one group is doing better than an individual from the other group. This paper aims at evaluating GPC methods for censored data, both in the context of hypothesis testing and estimation, and providing recommendations related to their choice in various situations. The methods that ignore uninformative pairs have comparable power to more complex and computationally demanding methods in situations of low censoring, and are slightly superior for high proportions (>40%) of censoring. If one is interested in estimation of the net benefit, Harrell's c index is an unbiased estimator if the proportional hazards assumption holds. Otherwise, the imputation (Efron or Peron) or IPCW (Datta, Dong) methods provide unbiased estimators in case of proportions of drop-out censoring up to 60%.

Missing data strategies for time-varying confounders in comparative effectiveness studies of non-missing time-varying exposures and right-censored outcomes.

The treatment of missing data in comparative effectiveness studies with right-censored outcomes and time-varying covariates is challenging because of the multilevel structure of the data. In particular, the performance of an accessible method like multiple imputation (MI) under an imputation model that ignores the multilevel structure is unknown and has not been compared to complete-case (CC) and single imputation methods that are most commonly applied in this context. Through an extensive simulation study, we compared statistical properties among CC analysis, last value carried forward, mean imputation, the use of missing indicators, and MI-based approaches with and without auxiliary variables under an extended Cox model when the interest lies in characterizing relationships between non-missing time-varying exposures and right-censored outcomes. MI demonstrated favorable properties under a moderate missing-at-random condition (absolute bias <0.1) and outperformed CC and single imputation methods, even when the MI method did not account for correlated observations in the imputation model. The performance of MI decreased with increasing complexity such as when the missing data mechanism involved the exposure of interest, but was still preferred over other methods considered and performed well in the presence of strong auxiliary variables. We recommend considering MI that ignores the multilevel structure in the imputation model when data are missing in a time-varying confounder, incorporating variables associated with missingness in the MI models as well as conducting sensitivity analyses across plausible assumptions.

Quantile regression for survival data in modern cancer research: expanding statistical tools for precision medicine.

Quantile regression links the whole distribution of an outcome to the covariates of interest and has become an important alternative to commonly used regression models. However, the presence of censored data such as survival time, often the main endpoint in cancer studies, has hampered the use of quantile regression techniques because of the incompleteness of data. With the advent of the precision medicine era and availability of high throughput data, quantile regression with high-dimensional predictors has attracted much attention and provided added insight compared to traditional regression approaches. This paper provides a practical guide for using quantile regression for right censored outcome data with covariates of low- or high-dimensionality. We frame our discussion using a dataset from the Boston Lung Cancer Survivor Cohort, a hospital-based prospective cohort study, with the goals of broadening the scope of cancer research, maximizing the utility of collected data, and offering useful statistical alternatives. We use quantile regression to identify clinical and molecular predictors, for example CpG methylation sites, associated with high-risk lung cancer patients, for example those with short survival.