This article proposes different tests for treatment effect heterogeneity when the outcome of interest, typically a duration variable, may be right-censored. The proposed tests study whether a policy 1) has zero distributional (average) effect for all subpopulations defined by covariate values, and 2) has homogeneous average effect across different subpopulations. The proposed tests are based on two-step Kaplan-Meier integrals and do not rely on parametric distributional assumptions, shape restrictions, or on restricting the potential treatment effect heterogeneity across different subpopulations. Our framework is suitable not only to exogenous treatment allocation but can also account for treatment noncompliance - an important feature in many applications. The proposed tests are consistent against fixed alternatives, and can detect nonparametric alternatives converging to the null at the parametric $n^{-1/2}$-rate, $n$ being the sample size. Critical values are computed with the assistance of a multiplier bootstrap. The finite sample properties of the proposed tests are examined by means of a Monte Carlo study and an application about the effect of labor market programs on unemployment duration. Open-source software is available for implementing all proposed tests.
We consider the problem of testing for treatment effect heterogeneity in observational studies, and propose a nonparametric test based on multisample U-statistics. To account for potential confounders, we use reweighted data where the weights are determined by estimated propensity scores. The proposed method does not require any parametric assumptions on the outcomes and bypasses the need for modeling the treatment effect for each study subgroup. We establish the asymptotic normality for the test statistic, and demonstrate its superior numerical performance over several competing approaches vi…
This paper analyzes the effect of a discrete treatment Z on a duration T. The treatment is not randomly assigned. The confounding issue is treated using a discrete instrumental variable explaining the treatment and independent of the error term of the model. Our framework is nonparametric and allows for random right censoring. This specification generates a nonlinear inverse problem and the average treatment effect is derived from its solution. We provide local and global identification properties that rely on a nonlinear system of equations. We propose an estimation procedure to solve this sy…
Recently, conditional average treatment effect (CATE) estimation has been attracting much attention due to its importance in various fields such as statistics, social and biomedical sciences. This study proposes a partially linear nonparametric Bayes model for the heterogeneous treatment effect estimation. A partially linear model is a semiparametric model that consists of linear and nonparametric components in an additive form. A nonparametric Bayes model that uses a Gaussian process to model the nonparametric component has already been studied. However, this model cannot handle the heterogen…
Identifying heterogeneity in a population's response to a health or policy intervention is crucial for evaluating and informing policy decisions. We propose a novel heterogeneous treatment effect estimator in the difference-in-differences design with repeated cross sectional data, where we observe different samples of a population at two time periods separated by the onset of a policy intervention, as well as samples of a population that serves as the control. Our estimator has orthogonality properties that enable fast rates on learning the treatment effect while allowing slower rates for esti…
This paper discusses endogenous treatment models with duration outcomes, competing risks and random right censoring. The endogeneity issue is solved using a discrete instrumental variable. We show that the competing risks model generates a non-parametric quantile instrumental regression problem. The cause-specific cumulative incidence, the cause-specific hazard and the subdistribution hazard can be recovered from the regression function. A distinguishing feature of the model is that censoring and competing risks prevent identification at some quantiles. We characterize the set of quantiles for…
Estimating treatment effects conditional on observed covariates can improve the ability to tailor treatments to particular individuals. Doing so effectively requires dealing with potential confounding, and also enough data to adequately estimate effect moderation. A recent influx of work has looked into estimating treatment effect heterogeneity using data from multiple randomized controlled trials and/or observational datasets. With many new methods available for assessing treatment effect heterogeneity using multiple studies, it is important to understand which methods are best used in which …
The pervasive use of prevalent cohort studies on disease duration, increasingly calls for appropriate methodologies to account for the biases that invariably accompany samples formed by such data. It is well-known, for example, that subjects with shorter lifetime are less likely to be present in such studies. Moreover, certain covariate values could be preferentially selected into the sample, being linked to the long-term survivors. The existing methodology for estimation of the propensity score using data collected on prevalent cases requires the correct conditional survival/hazard function g…
We propose a novel nonparametric Bayesian IRT model in this paper by introducing the clustering effect at question level and further assume heterogeneity at examinee level under each question cluster, characterized by the mixture of Binomial distributions. The main contribution of this work is threefold: (1) We demonstrate that the model is identifiable. (2) The clustering effect can be captured asymptotically and the parameters of interest that measure the proficiency of examinees in solving certain questions can be estimated at a root n rate (up to a log term). (3) We present a tractable sam…
This paper considers identification and estimation of the causal effect of the time Z until a subject is treated on a survival outcome T. The treatment is not randomly assigned, T is randomly right censored by a random variable C and the time to treatment Z is right censored by min(T,C). The endogeneity issue is treated using an instrumental variable explaining Z and independent of the error term of the model. We study identification in a fully nonparametric framework. We show that our specification generates an integral equation, of which the regression function of interest is a solution. We …
Causal inference is widely used in various fields, such as biology, psychology and economics, etc. In observational studies, we need to balance the covariates before estimating causal effect. This study extends the one-dimensional entropy balancing method to multiple dimensions to balance the covariates. Both parametric and nonparametric methods are proposed to estimate the causal effect of multivariate continuous treatments and theoretical properties of the two estimations are provided. Furthermore, the simulation results show that the proposed method is better than other methods in various c…
The COVID-19 pandemic has led to a vast amount of growth for statistical models and methods which characterize features of disease outbreaks. One class of models that came to light in this regard has been the use of self-exciting point processes, wherein infections occur both "at random" and also more systematically from person-to-person transmission. Beyond the modeling of the overall COVID-19 outbreak, the pandemic has also motivated research assessing various policy decisions and event outcomes. One such area of study, addressed here, relates to the formulation of methods which measure the …
In many biomedical problems, data are often heterogeneous, with samples spanning multiple patient subgroups, where different subgroups may have different disease subtypes, stages, or other medical contexts. These subgroups may be related, but they are also expected to have differences with respect to the underlying biology. The heterogeneous data presents a precious opportunity to explore the heterogeneities and commonalities between related subgroups. Unfortunately, effective statistical analysis methods are still lacking. Recently, several novel methods based on integrative analysis have bee…
We study nonparametric methods for the setting where multiple distinct networks are observed on the same set of nodes. Such samples may arise in the form of replicated networks drawn from a common distribution, or in the form of heterogeneous networks, with the network generating process varying from one network to another, e.g.~dynamic and cross-sectional networks. Nonparametric methods for undirected networks have focused on estimation of the graphon model. While the graphon model accounts for nodal heterogeneity, it does not account for network heterogeneity, a feature specific to applicati…
There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi-Markovianity, which has been developed mainly in the parametric frequentist setting, to allow construction of highly interp…
In survey analysis, the estimation of the cumulative distribution function (cdf) is of great interest: it allows for instance to derive quantiles estimators or other non linear parameters derived from the cdf. We consider the case where the response variable is a right censored duration variable. In this framework, the classical estimator of the cdf is the Kaplan-Meier estimator. As an alternative, we propose a nonparametric model-based estimator of the cdf in a finite population. The new estimator uses auxiliary information brought by a continuous covariate and is based on nonparametric media…
Modeling Nonlinear Ability Trajectories and Learner Heterogeneity in Online Learning: A Bayesian Nonparametric Dynamic IRT Framework
Shenzhen University（深圳大学）；University of California, Los Angeles（加州大学洛杉矶分校）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Michigan State University（密歇根州立大学）
The stratified proportional hazards model represents a simple solution to account for heterogeneity within the data while keeping the multiplicative effect on the hazard function. Strata are typically defined a priori by resorting to the values taken by a categorical covariate. A general framework is proposed, which allows for the stratification of a generic accelerated life time model, including as a special case the Weibull proportional hazard model. The stratification is determined a posteriori by taking into account that strata might be characterized by different baseline survivals as well…
This research attempts to model the stochastic process of trades in a limit order book market as a marked point process. We propose a semi-parametric model for the conditional distribution given the past, attempting to capture the effect of the recent past in a nonparametric way and the effect of the more distant past using a parametric time series model. Our framework provides more flexibility than the most commonly used family of models, known as Autoregressive Conditional Duration (ACD), in terms of the shape of the density of durations and in the form of dependence across time. We also pro…
An important problem in contemporary immunology studies based on single-cell protein expression data is to determine whether cellular expressions are remodeled post infection by a pathogen. One natural approach for detecting such changes is to use non-parametric two-sample statistical tests. However, in single-cell studies, direct application of these tests is often inadequate because single-cell level expression data from uninfected populations often contains attributes of several latent sub-populations with highly heterogeneous characteristics. As a result, viruses often infect these differe…
Although combination antiretroviral therapy (ART) is highly effective in suppressing viral load for people with HIV (PWH), many ART agents may exacerbate central nervous system (CNS)-related adverse effects including depression. Therefore, understanding the effects of ART drugs on the CNS function, especially mental health, can help clinicians personalize medicine with less adverse effects for PWH and prevent them from discontinuing their ART to avoid undesirable health outcomes and increased likelihood of HIV transmission. The emergence of electronic health records offers researchers unpreced…
Longitudinal study designs are indispensable for studying disease progression. Inferring covariate effects from longitudinal data, however, requires interpretable methods that can model complicated covariance structures and detect nonlinear effects of both categorical and continuous covariates, as well as their interactions. Detecting disease effects is hindered by the fact that they often occur rapidly near the disease initiation time, and this time point cannot be exactly observed. An additional challenge is that the effect magnitude can be heterogeneous over the subjects. We present lgpr, a…
Precision medicine is an emerging field that takes into account individual heterogeneity to inform better clinical practice. In clinical trials, the evaluation of treatment effect heterogeneity is an important component, and recently, many statistical methods have been proposed for stratifying patients into different subgroups based on such heterogeneity. However, the majority of existing methods developed for this purpose focus on the case with a dichotomous treatment and are not directly applicable to multi-arm trials. In this paper, we consider the problem of patient stratification in multi…
