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A treatment regime is a deterministic function that dictates personalized treatment based on patients’ individual prognostic information. There is increasing interest in finding optimal treatment regimes, which determine treatment at one or more treatment decision points to maximize expected long-term clinical outcomes, where larger outcomes are preferred. For chronic diseases such as cancer or human immunodeficiency virus infection, survival time is often the outcome of interest, and the goal is to select treatment to maximize survival probability. We propose two non-parametric estimators for the survival function of patients following a given treatment regime involving one or more decisions, i.e. the so-called value. On the basis of data from a clinical or observational study, we estimate an optimal regime by maximizing these estimators for the value over a prespecified class of regimes. Because the value function is very jagged, we introduce kernel smoothing within the estimator to improve performance. Asymptotic properties of the proposed estimators of value functions are established under suitable regularity conditions, and simulation studies evaluate the finite sample performance of the regime estimators. The methods are illustrated by application to data from an acquired immune deficiency syndrome clinical trial.

We propose inverse probability weighted estimators for the local average treatment effect (LATE) and the local average treatment effect for the treated (LATT) under instrumental variable assumptions with covariates. We show that these estimators are asymptotically normal and efficient. When the (binary) instrument satisfies one-sided noncompliance, we propose a Durbin-Wu-Hausman-type test of whether treatment assignment is unconfounded conditional on some observables. The test is based on the fact that under one-sided noncompliance LATT coincides with the average treatment effect for the treated (ATT). We conduct Monte Carlo simulations to demonstrate, among other things, that part of the theoretical efficiency gain afforded by unconfoundedness in estimating ATT survives pretesting. We illustrate the implementation of the test on data from training programs administered under the Job Training Partnership Act in the United States. This article has online supplementary material.

We consider a functional parameter called the conditional average treatment effect (CATE), designed to capture the heterogeneity of a treatment effect across subpopulations when the unconfoundedness assumption applies. In contrast to quantile regressions, the subpopulations of interest are defined in terms of the possible values of a set of continuous covariates rather than the quantiles of the potential outcome distributions. We show that the CATE parameter is nonparametrically identified under unconfoundedness and propose inverse probability weighted estimators for it. Under regularity conditions, some of which are standard and some are new in the literature, we show (pointwise) consistency and asymptotic normality of a fully nonparametric and a semiparametric estimator. We apply our methods to estimate the average effect of a first-time mother's smoking during pregnancy on the baby's birth weight as a function of the mother's age. A robust qualitative finding is that the expected effect becomes stronger (more negative) for older mothers.

We consider estimation, from longitudinal observational data, of the parameters of marginal structural mean models for unconstrained outcomes. Current proposals include inverse probability of treatment weighted and double robust (DR) estimators. A difficulty with DR estimation is that it requires postulating a sequence of models, one for the each mean of the counterfactual outcome given covariate and treatment history up to each exposure time point. Most natural models for such means are often incompatible. Robins et al., (2000b) proposed a parameterization of the likelihood which implies compatible parametric models for such means. Their parameterization has not been exploited to construct DR estimators and one goal of this article is to fill this gap. More importantly, exploiting this parameterization we propose a multiple robust (MR) estimator that confers even more protection against model misspecification than DR estimators. Our methods are easy to implement as they are based on the iterative fit of a sequence of weighted regressions.

Under the case-cohort design introduced by Prentice (Biometrica 73:1–11, 1986 ), the covariate histories are ascertained only for the subjects who experience the event of interest (i.e., the cases) during the follow-up period and for a relatively small random sample from the original cohort (i.e., the subcohort). The case-cohort design has been widely used in clinical and epidemiological studies to assess the effects of covariates on failure times. Most statistical methods developed for the case-cohort design use the proportional hazards model, and few methods allow for time-varying regression coefficients. In addition, most methods disregard data from subjects outside of the subcohort, which can result in inefficient inference. Addressing these issues, this paper proposes an estimation procedure for the semiparametric additive hazards model with case-cohort/two-phase sampling data, allowing the covariates of interest to be missing for cases as well as for non-cases. A more flexible form of the additive model is considered that allows the effects of some covariates to be time varying while specifying the effects of others to be constant. An augmented inverse probability weighted estimation procedure is proposed. The proposed method allows utilizing the auxiliary information that correlates with the phase-two covariates to improve efficiency. The asymptotic properties of the proposed estimators are established. An extensive simulation study shows that the augmented inverse probability weighted estimation is more efficient than the widely adopted inverse probability weighted complete-case estimation method. The method is applied to analyze data from a preventive HIV vaccine efficacy trial.

In this paper, a penalized weighted least squares approach is proposed for small area estimation under the unit level model. The new method not only unifies the traditional empirical best linear unbiased prediction that does not take sampling design into account and the pseudo-empirical best linear unbiased prediction that incorporates sampling weights but also has the desirable robustness property to model misspecification compared with existing methods. The empirical small area estimator is given, and the corresponding second-order approximation to mean squared error estimator is derived. Numerical comparisons based on synthetic and real data sets show superior performance of the proposed method to currently available estimators in the literature.

Methodology of sufficient dimension reduction (SDR) has offered an effective means to facilitate regression analysis of high-dimensional data. When the response is censored, however, most existing SDR estimators cannot be applied, or require some restrictive conditions. In this article, we propose a new class of inverse censoring probability weighted SDR estimators for censored regressions. Moreover, regularization is introduced to achieve simultaneous variable selection and dimension reduction. Asymptotic properties and empirical performance of the proposed methods are examined.

We propose a new causal parameter, which is a natural extension of existing approaches to causal inference such as marginal structural models. Modelling approaches are proposed for the difference between a treatment-specific counterfactual population distribution and the actual population distribution of an outcome in the target population of interest. Relevant parameters describe the effect of a hypothetical intervention on such a population and therefore we refer to these models as population intervention models. We focus on intervention models estimating the effect of an intervention in terms of a difference and ratio of means, called risk difference and relative risk if the outcome is binary. We provide a class of inverse-probability-of-treatment-weighted and doubly-robust estimators of the causal parameters in these models. The finite-sample performance of these new estimators is explored in a simulation study.

This paper analyzes whether the two major labor market reforms implemented in Spain in the 1990s to reduce the share of temporary employment succeed in promoting flows into permanent employment. The 1994 reform severely restricted temporary contracts and the 1997 reform introduced a new permanent contract figure with lower payroll taxes and dismissal costs than the ordinary. To evaluate these non-targeted treatments I present an estimation procedure that uses pre-treatment outcomes to predict the one thatwould have been otherwise observed in the post-treatment period in the absence of the treatment and I derive its large sample properties. Using data from the Spanish Labor Force Survey I find that both reforms failed at reducing the share of temporary employment because they had no impact on contract conversions, which account for most new permanent contracts. The 1997 reform succeed in increasing permanent hirings for some groups of workers. My findings suggest that Spanish employers took advantage of wage and dismissal cost reductions to substitute permanent contracts for otherwise temporary ones.

We present a method for estimating the survival curve of a continuous failure time random variable from right‐censored data. Our method allows adjustment for informative censoring due to measured prognostic factors for time‐to‐event and censoring while simultaneously quantifying the sensitivity of the inference to residual dependence between failure and censoring due to unmeasured factors. We present the results of a simulation study and illustrate our approach using data from the AIDS Clinical Trial Group 175 study.