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Effect modification plays a central role in stratified medicine, of which the goal is often to find biomarker profiles that identify individuals who benefit from a treatment of interest. We consider the problem of causal inference regarding the effect modifying role of a biomarker, which is only available for some individuals in an observational study. We develop inverse probability weighted mean score estimating functions with one weight to account for confounding and a second weight for the missing data process. An iterative approach is described for solving the equations in the spirit of the expectation-maximization algorithm, and large sample properties of the resulting estimator are developed. Simulation studies are conducted to compare the proposed method with a doubly weighted complete case analysis and a propensity score weighted multiple imputation approach. An application to a study of the effect of a biologic therapy on inflammation in a rheumatology cohort is given for illustration. [ABSTRACT FROM AUTHOR]

Estimating a patient's mortality risk is important in making treatment decisions. Survival trees are a useful tool and employ recursive partitioning to separate patients into different risk groups. Existing 'loss based' recursive partitioning procedures that would be used in the absence of censoring have previously been extended to the setting of right censored outcomes using inverse probability censoring weighted estimators of loss functions. In this paper, we propose new 'doubly robust' extensions of these loss estimators motivated by semiparametric efficiency theory for missing data that better utilize available data. Simulations and a data analysis demonstrate strong performance of the doubly robust survival trees compared with previously used methods. Copyright © 2016 John Wiley & Sons, Ltd.

Inference regarding exposure effects within subgroups of individuals and regarding the effect‐modifying role of some covariates plays a central role in research on stratified medicine. Large administrative databases offer an appealing basis for investigating these questions but causal inference can be challenging due to confounding and missing data. We consider the setting where subgroups are defined by the value of an incompletely observed potential effect modifier. We first formulate simple doubly inverse probability‐weighted estimating equations involving one weight to facilitate causal inference with complete data and another weight to adjust for the fact that the effect modifier is only partially observed. We then develop a nested doubly robust (NDR) estimating function which is shown to yield more efficient and robust estimators. In simulation studies, both approaches are shown to yield valid inference in finite samples, but the advantages of the NDR estimators are evident when one or more of the auxiliary models are misspecified. An application to a study of the effect of biological therapy on inflammation in a rheumatology cohort is given for illustration. [ABSTRACT FROM AUTHOR]

Interval‐censored data arise when a failure process is under intermittent observation and failure status is only known at assessment times. We consider the development of predictive algorithms when training samples involve interval censoring. Using censoring unbiased transformations and pseudo‐observations, we define observed data loss functions, which are unbiased estimates of the corresponding complete data loss functions. We show that regression trees based on these loss functions can recover the tree structure and yield good predictive accuracy. An application is given to a study involving individuals with psoriatic arthritis where the aim is to identify genetic markers useful for the prediction of axial disease within 10 years of a baseline assessment. [ABSTRACT FROM AUTHOR]

This article proposes a novel paradigm for building regression trees and ensemble learning in survival analysis. Generalizations of the classification and regression trees (CART) and random forests (RF) algorithms for general loss functions, and in the latter case more general bootstrap procedures, are both introduced. These results, in combination with an extension of the theory of censoring unbiased transformations (CUTs) applicable to loss functions, underpin the development of two new classes of algorithms for constructing survival trees and survival forests: censoring unbiased regression trees and censoring unbiased regression ensembles. For a certain "doubly robust" CUT of squared error loss, we further show how these new algorithms can be implemented using existing software (e.g., CART, RF). Comparisons of these methods to existing ensemble procedures for predicting survival probabilities are provided in both simulated settings and through applications to four datasets. It is shown that these new methods either improve upon, or remain competitive with, existing implementations of random survival forests, conditional inference forests, and recursively imputed survival trees. [ABSTRACT FROM AUTHOR]

A copula-based model is described which enables joint analysis of multiple progressive multistate processes. Unlike intensity-based or frailty-based approaches to joint modeling, the copula formulation proposed herein ensures that a wide range of marginal multistate processes can be specified and the joint model will retain these marginal features. The copula formulation also facilitates a variety of approaches to estimation and inference including composite likelihood and two-stage estimation procedures. We consider processes with Markov margins in detail, which are often suitable when chronic diseases are progressive in nature. We give special attention to the setting in which individuals are examined intermittently and transition times are consequently interval-censored. Simulation studies give empirical insight into the different methods of analysis and an application involving progression in joint damage in psoriatic arthritis provides further illustration. [ABSTRACT FROM AUTHOR]