arXiv subjects

Ronghui Xu

Publications and source records attributed to Ronghui Xu.

31 records · Page 2Linked to original sources

arXiv2023

On Defense of the Hazard Ratio

In this short communication, we describe the recent debate on whether the hazard function should be used for causal inference in time-to-event studies and consider three different potential outcomes frameworks (by Rubin, Robins, and Pearl, respectively) as well as use the single-world intervention graph to show mathematically that the hazard function has causal interpretations under all three frameworks. In addition, we argue that the hazard ratio over time can provide a useful interpretation in practical settings.

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arXiv2023

Doubly Robust Estimation under Covariate-Induced Dependent Left Truncation

In prevalent cohort studies with follow-up, the time-to-event outcome is subject to left truncation leading to selection bias. For estimation of the distribution of time-to-event, conventional methods adjusting for left truncation tend to rely on the (quasi-)independence assumption that the truncation time and the event time are "independent" on the observed region. This assumption is violated when there is dependence between the truncation time and the event time possibly induced by measured covariates. Inverse probability of truncation weighting leveraging covariate information can be used in this case, but it is sensitive to misspecification of the truncation model. In this work, we apply the semiparametric theory to find the efficient influence curve of an expected (arbitrarily transformed) survival time in the presence of covariate-induced dependent left truncation. We then use it to construct estimators that are shown to enjoy double-robustness properties. Our work represents the first attempt to construct doubly robust estimators in the presence of left truncation, which does not fall under the established framework of coarsened data where doubly robust approaches are developed. We provide technical conditions for the asymptotic properties that appear to not have been carefully examined in the literature for time-to-event data, and study the estimators via extensive simulation. We apply the estimators to two data sets from practice, with different right-censoring patterns.

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arXiv2022

Causal Effects of Prenatal Drug Exposure on Birth Defects with Missing by Terathanasia

A recent cohort study revealed a positive correlate between major structural birth defects in infants and a certain medication taken by pregnant women. To draw valid causal inference, an outstanding problem to overcome was the missing birth defect outcomes among pregnancy losses resulting from spontaneous abortion. This led to missing not at random since, according to the theory of "terathanasia", a defected fetus is more likely to be spontaneously aborted. Other complications in the data included left truncation, right censoring, observational nature, and rare events. In addition, the previous analysis stratified on live birth against spontaneous abortion, which was itself a post-exposure variable and hence did not lead to a causal interpretation of the stratified results. In this paper we aim to estimate and provide inference for the causal parameters of scientific interest, including the principal effects, making use of the missing data mechanism informed by "terathanasia". The rare events with missing outcomes led to multiple sensitivity analyses where the causal parameters can be estimated with better confidence in each setting. Our findings should shed light on how studies on causal effects of medication or other exposures during pregnancy may be analyzed using state-of-the-art methodologies.

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arXiv2022

Doubly Robust Inference for Hazard Ratio under Informative Censoring with Machine Learning

Randomized clinical trials with time-to-event outcomes have traditionally used the log-rank test followed by the Cox proportional hazards (PH) model to estimate the hazard ratio between the treatment groups. These are valid under the assumption that the right-censoring mechanism is non-informative, i.e. independent of the time-to-event of interest within each treatment group. More generally, the censoring time might depend on additional covariates, and inverse probability of censoring weighting (IPCW) can be used to correct for the bias resulting from the informative censoring. IPCW requires a correctly specified censoring time model conditional on the treatment and the covariates. Doubly robust inference in this setting has not been plausible previously due to the non-collapsibility of the Cox model. However, with the recent development of data-adaptive machine learning methods we derive an augmented IPCW (AIPCW) estimator that has the following doubly robust (DR) properties: it is model doubly robust, in that it is consistent and asymptotic normal (CAN), as long as one of the two models, one for the failure time and one for the censoring time, is correctly specified; it is also rate doubly robust, in that it is CAN as long as the product of the estimation error rates under these two models is faster than root-$n$. We investigate the AIPCW estimator using extensive simulation in finite samples.

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arXiv2021

Doubly Robust Estimation of the Hazard Difference for Competing Risks Data

We consider the conditional treatment effect for competing risks data in observational studies. While it is described as a constant difference between the hazard functions given the covariates, we do not assume specific functional forms for the covariates. We derive the efficient score for the treatment effect using modern semiparametric theory, as well as two doubly robust scores with respect to 1) the assumed propensity score for treatment and the censoring model, and 2) the outcome models for the competing risks. An important asymptotic result regarding the estimators is rate double robustness, in addition to the classical model double robustness. Rate double robustness enables the use of machine learning and nonparametric methods in order to estimate the nuisance parameters, while preserving the root-$n$ asymptotic normality of the estimators for inferential purposes. We study the performance of the estimators using simulation. The estimators are applied to the data from a cohort of Japanese men in Hawaii followed since 1960s in order to study the effect of mid-life drinking behavior on late life cognitive outcomes.

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arXiv2020

Explained Variation under the Additive Hazards Model

We study explained variation under the additive hazards regression model for right-censored data. We consider different approaches for developing such a measure, and focus on one that estimates the proportion of variation in the failure time explained by the covariates. We study the properties of the measure both analytically, and through extensive simulations. We apply the measure to a well-known survival data set as well as the linked Surveillance, Epidemiology and End Results (SEER)-Medicare database for prediction of mortality in early-stage prostate cancer patients using high dimensional claims codes.

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arXiv2019

Sensitivity Analysis of Treatment Effect to Unmeasured Confounding in Observational Studies with Survival and Competing Risks Outcomes

No unmeasured confounding is often assumed in estimating treatment effects in observational data when using approaches such as propensity scores and inverse probability weighting. However, in many such studies due to the limitation of the databases, collected confounders are not exhaustive, and it is crucial to examine the extent to which the resulting estimate is sensitive to the unmeasured confounders. We consider this problem for survival and competing risks data. Due to the complexity of models for such data, we adapt the simulated potential confounders approach of Carnegie et al. (2016), which provides a general tool for sensitivity analysis due to unmeasured confounding. More specifically, we specify one sensitivity parameter to quantify the association between an unmeasured confounder and the treatment assignment, and another set of parameters to quantify the association between the confounder and the time-to-event outcomes. By varying the magnitudes of the sensitivity parameters, we estimate the treatment effect of interest using the stochastic EM and the EM algorithms. We demonstrate the performance of our methods on simulated data, and apply them to a comparative effectiveness study in inflammatory bowel disease (IBD).

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arXiv2019

Fine-Gray competing risks model with high-dimensional covariates: estimation and Inference

The purpose of this paper is to construct confidence intervals for the regression coefficients in the Fine-Gray model for competing risks data with random censoring, where the number of covariates can be larger than the sample size. Despite strong motivation from biomedical applications, a high-dimensional Fine-Gray model has attracted relatively little attention among the methodological or theoretical literature. We fill in this gap by developing confidence intervals based on a one-step bias-correction for a regularized estimation. We develop a theoretical framework for the partial likelihood, which does not have independent and identically distributed entries and therefore presents many technical challenges. We also study the approximation error from the weighting scheme under random censoring for competing risks and establish new concentration results for time-dependent processes. In addition to the theoretical results and algorithms, we present extensive numerical experiments and an application to a study of non-cancer mortality among prostate cancer patients using the linked Medicare-SEER data.

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arXiv2018

Two-Stage Residual Inclusion under the Additive Hazards Model - An Instrumental Variable Approach with Application to SEER-Medicare Linked Data

Instrumental variable is an essential tool for addressing unmeasured confounding in observational studies. Two stage predictor substitution (2SPS) estimator and two stage residual inclusion(2SRI) are two commonly used approaches in applying instrumental variables. Recently 2SPS was studied under the additive hazards model in the presence of competing risks of time-to-events data, where linearity was assumed for the relationship between the treatment and the instrument variable. This assumption may not be the most appropriate when we have binary treatments. In this paper, we consider the 2SRI estimator under the additive hazards model for general survival data and in the presence of competing risks, which allows generalized linear models for the relation between the treatment and the instrumental variable. We derive the asymptotic properties including a closed-form asymptotic variance estimate for the 2SRI estimator. We carry out numerical studies in finite samples, and apply our methodology to the linked Surveillance, Epidemiology and End Results (SEER) - Medicare database comparing radical prostatectomy versus conservative treatment in early-stage prostate cancer patients.

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arXiv2017

Semiparametric Sieve Maximum Likelihood Estimation Under Cure Model with Partly Interval Censored and Left Truncated Data for Application to Spontaneous Abortion Data

This work was motivated by observational studies in pregnancy with spontaneous abortion (SAB) as outcome. Clearly some women experience the SAB event but the rest do not. In addition, the data are left truncated due to the way pregnant women are recruited into these studies. For those women who do experience SAB, their exact event times are sometimes unknown. Finally, a small percentage of the women are lost to follow-up during their pregnancy. All these give rise to data that are left truncated, partly interval and right-censored, and with a clearly defined cured portion. We consider the non-mixture Cox regression cure rate model and adopt the semiparametric spline-based sieve maximum likelihood approach to analyze such data. Using modern empirical process theory we show that both the parametric and the nonparametric parts of the sieve estimator are consistent, and we establish the asymptotic normality for both parts. Simulation studies are conducted to establish the finite sample performance. Finally, we apply our method to a database of observational studies on spontaneous abortion.

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arXiv2017

High-Dimensional Variable Selection and Prediction under Competing Risks with Application to SEER-Medicare Linked Data

Competing risk analysis considers event times due to multiple causes, or of more than one event types. Commonly used regression models for such data include 1) cause-specific hazards model, which focuses on modeling one type of event while acknowledging other event types simultaneously; and 2) subdistribution hazards model, which links the covariate effects directly to the cumulative incidence function. Their use and in particular statistical properties in the presence of high-dimensional predictors are largely unexplored. Motivated by an analysis using the linked SEER-Medicare database for the purposes of predicting cancer versus non-cancer mortality for patients with prostate cancer, we study the accuracy of prediction and variable selection of existing statistical learning methods under both models using extensive simulation experiments, including different approaches to choosing penalty parameters in each method. We then apply the optimal approaches to the analysis of the SEER-Medicare data.

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arXiv2017

The Impact of Confounder Selection in Propensity Scores for Rare Events Data - with Applications to Birth Defects

Our work was motivated by a recent study on birth defects of infants born to pregnant women exposed to a certain medication for treating chronic diseases. Outcomes such as birth defects are rare events in the general population, which often translate to very small numbers of events in the unexposed group. As drug safety studies in pregnancy are typically observational in nature, we control for confounding in this rare events setting using propensity scores (PS). Using our empirical data, we noticed that the estimated odds ratio for birth defects due to exposure varied drastically depending on the specific approach used. The commonly used approaches with PS are matching, stratification, inverse probability weighting (IPW) and regression adjustment. The extremely rare events setting renders the matching or stratification infeasible. In addition, the PS itself may be formed via different approaches to select confounders from a relatively long list of potential confounders. We carried out simulation experiments to compare different combinations of approaches: IPW or regression adjustment, with 1) including all potential confounders without selection, 2) selection based on univariate association between the candidate variable and the outcome, 3) selection based on change in effects (CIE). The simulation showed that IPW without selection leads to extremely large variances in the estimated odds ratio, which help to explain the empirical data analysis results that we had observed. The simulation also showed that IPW with selection based on univariate association with the outcome is preferred over IPW with CIE. Regression adjustment has small variances of the estimated odds ratio regardless of the selection methods used.

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arXiv2016

A Nonparametric Maximum Likelihood Approach for Partially Observed Cured Data with Left Truncation and Right-Censoring

Partially observed cured data occur in the analysis of spontaneous abortion (SAB) in observational studies in pregnancy. In contrast to the traditional cured data, such data has an observable `cured' portion as women who do not abort spontaneously. The data is also subject to left truncate in addition to right-censoring because women may enter or withdraw from a study any time during their pregnancy. Left truncation in particular causes unique bias in the presence of a cured portion. In this paper, we study a cure rate model and develop a conditional nonparametric maximum likelihood approach. To tackle the computational challenge we adopt an EM algorithm making use of "ghost copies" of the data, and a closed form variance estimator is derived. Under suitable assumptions, we prove the consistency of the resulting estimator involving an unbounded cumulative baseline hazard function, as well as the asymptotic normality. Simulation results are carried out to evaluate the finite sample performance. We present the analysis of the motivating SAB study to illustrate the power of our model addressing both occurrence and timing of SAB, as compared to existing approaches in practice.

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