This paper studies theCox model with time-varying coefficients for cause-specific hazard
functions when the causes of failure are subject to missingness. Inverse probability
weighted and augmented inverse probability weighted estimators are investigated. The
latter is considered as a two-stage estimator by directly utilizing the inverse probability
weighted estimator and through modeling available auxiliary variables to improve efficiency.
The asymptotic properties of the two estimators are investigated. Hypothesis
testing procedures are developed to test the null hypotheses that the covariate effects
are zero and that the covariate effects are constant. We conduct simulation studies to
examine the finite sample properties of the proposed estimation and hypothesis testing
procedures under various settings of the auxiliary variables and the percentages
of the failure causes that are missing. These simulation results demonstrate that the
augmented inverse probability weighted estimators are more efficient than the inverse
probability weighted estimators and that the proposed testing procedures have the
expected satisfactory results in sizes and powers. The proposed methods are illustrated
using the Mashi clinical trial data for investigating the effect of randomization
to formula-feeding versus breastfeeding plus extended infant zidovudine prophylaxis
on death due to mother-to-child HIV transmission in Botswana.
more »
« less
GEAR: On optimal decision making with auxiliary data
Personalized optimal decision making, finding the optimal decision rule (ODR) based on individual characteristics, has attracted increasing attention recently in many fields, such as education, economics, and medicine. Current ODR methods usually require the primary outcome of interest in samples for assessing treatment effects, namely, the experimental sample. However, in many studies, treatments may have a long‐term effect, and as such, the primary outcome of interest cannot be observed in the experimental sample due to the limited duration of experiments, which makes the estimation of ODR impossible. This paper is inspired to address this challenge by making use of an auxiliary sample to facilitate the estimation of ODR in the experimental sample. We propose an auGmented inverse propensity weighted Experimental and Auxiliary sample‐based decision Rule (GEAR) by maximizing the augmented inverse propensity weighted value estimator over a class of decision rules using the experimental sample, with the primary outcome being imputed based on the auxiliary sample. The asymptotic properties of the proposed GEAR estimators and their associated value estimators are established. Simulation studies are conducted to demonstrate its empirical validity with a real AIDS application.
more » « less- PAR ID:
- 10445988
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Stat
- Volume:
- 10
- Issue:
- 1
- ISSN:
- 2049-1573
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Data driven individualized decision making problems have received a lot of attentions in recent years. In particular, decision makers aim to determine the optimal Individualized Treatment Rule (ITR) so that the expected speci ed outcome averaging over heterogeneous patient-speci c characteristics is maximized. Many existing methods deal with binary or a moderate number of treatment arms and may not take potential treatment e ect structure into account. However, the e ectiveness of these methods may deteriorate when the number of treatment arms becomes large. In this article, we propose GRoup Outcome Weighted Learning (GROWL) to estimate the latent structure in the treatment space and the op- timal group-structured ITRs through a single optimization. In particular, for estimating group-structured ITRs, we utilize the Reinforced Angle based Multicategory Support Vec- tor Machines (RAMSVM) to learn group-based decision rules under the weighted angle based multi-class classi cation framework. Fisher consistency, the excess risk bound, and the convergence rate of the value function are established to provide a theoretical guaran- tee for GROWL. Extensive empirical results in simulation studies and real data analysis demonstrate that GROWL enjoys better performance than several other existing methods.more » « less
-
Adaptive experimental designs can dramatically improve efficiency in randomized trials. But with adaptively collected data, common estimators based on sample means and inverse propensity-weighted means can be biased or heavy-tailed. This poses statistical challenges, in particular when the experimenter would like to test hypotheses about parameters that were not targeted by the data-collection mechanism. In this paper, we present a class of test statistics that can handle these challenges. Our approach is to adaptively reweight the terms of an augmented inverse propensity-weighting estimator to control the contribution of each term to the estimator’s variance. This scheme reduces overall variance and yields an asymptotically normal test statistic. We validate the accuracy of the resulting estimates and their CIs in numerical experiments and show that our methods compare favorably to existing alternatives in terms of mean squared error, coverage, and CI size.more » « less
-
more » « less
Summary Comparative effectiveness research often involves evaluating the differences in the risks of an event of interest between two or more treatments using observational data. Often, the post‐treatment outcome of interest is whether the event happens within a pre‐specified time window, which leads to a binary outcome. One source of bias for estimating the causal treatment effect is the presence of confounders, which are usually controlled using propensity score‐based methods. An additional source of bias is right‐censoring, which occurs when the information on the outcome of interest is not completely available due to dropout, study termination, or treatment switch before the event of interest. We propose an inverse probability weighted regression‐based estimator that can simultaneously handle both confounding and right‐censoring, calling the method CIPWR, with the letter C highlighting the censoring component. CIPWR estimates the average treatment effects by averaging the predicted outcomes obtained from a logistic regression model that is fitted using a weighted score function. The CIPWR estimator has a double robustness property such that estimation consistency can be achieved when either the model for the outcome or the models for both treatment and censoring are correctly specified. We establish the asymptotic properties of the CIPWR estimator for conducting inference, and compare its finite sample performance with that of several alternatives through simulation studies. The methods under comparison are applied to a cohort of prostate cancer patients from an insurance claims database for comparing the adverse effects of four candidate drugs for advanced stage prostate cancer.
-
more » « less
Abstract We propose a new procedure for inference on optimal treatment regimes in the model‐free setting, which does not require to specify an outcome regression model. Existing model‐free estimators for optimal treatment regimes are usually not suitable for the purpose of inference, because they either have nonstandard asymptotic distributions or do not necessarily guarantee consistent estimation of the parameter indexing the Bayes rule due to the use of surrogate loss. We first study a smoothed robust estimator that directly targets the parameter corresponding to the Bayes decision rule for optimal treatment regimes estimation. This estimator is shown to have an asymptotic normal distribution. Furthermore, we verify that a resampling procedure provides asymptotically accurate inference for both the parameter indexing the optimal treatment regime and the optimal value function. A new algorithm is developed to calculate the proposed estimator with substantially improved speed and stability. Numerical results demonstrate the satisfactory performance of the new methods.
