Nonparametric tests for transition probabilities in nonhomogeneous Markov processes

This paper proposes nonparametric two-sample tests for the direct comparison of the probabilities of a particular transition between states of a continuous time non-homogeneous Markov process with a finite state space. The proposed tests are a linear nonparametric test, an L2-norm-based test and a Kolmogorov–Smirnov-type test. Significance level assessment is based on rigorous procedures, which are justified through the use of modern empirical process theory. Moreover, the L2-norm and the Kolmogorov–Smirnov-type tests are shown to be consistent for every fixed alternative hypothesis. The proposed tests are also extended to more complex situations such as cases with incompletely observed absorbing states and non-Markov processes. Simulation studies show that the test statistics perform well even with small sample sizes. Finally, the proposed tests are applied to data on the treatment of early breast cancer from the European Organization for Research and Treatment of Cancer (EORTC) trial 10854, under an illness-death model

Nonparametric analysis of nonhomogeneous multistate processes with clustered observations

Frequently, clinical trials and observational studies involve complex event history data with multiple events. When the observations are independent, the analysis of such studies can be based on standard methods for multistate models. However, the independence assumption is often violated, such as in multicenter studies, which makes standard methods improper. This work addresses the issue of nonparametric estimation and two-sample testing for the population-averaged transition and state occupation probabilities under general multistate models with cluster-correlated, right-censored, and/or left-truncated observations. The proposed methods do not impose assumptions regarding the within-cluster dependence, allow for informative cluster size, and are applicable to both Markov and non-Markov processes. Using empirical process theory, the estimators are shown to be uniformly consistent and to converge weakly to tight Gaussian processes. Closed-form variance estimators are derived, rigorous methodology for the calculation of simultaneous confidence bands is proposed, and the asymptotic properties of the nonparametric tests are established. Furthermore, I provide theoretical arguments for the validity of the nonparametric cluster bootstrap, which can be readily implemented in practice regardless of how complex the underlying multistate model is. Simulation studies show that the performance of the proposed methods is good, and that methods that ignore the within-cluster dependence can lead to invalid inferences. Finally, the methods are illustrated using data from a multicenter randomized controlled trial

Estimating optimal individualized treatment rules with multistate processes

Multistate process data are common in studies of chronic diseases such as cancer. These data are ideal for precision medicine purposes as they can be leveraged to improve more refined health outcomes, compared to standard survival outcomes, as well as incorporate patient preferences regarding quantity versus quality of life. However, there are currently no methods for the estimation of optimal individualized treatment rules with such data. In this article, we propose a nonparametric outcome weighted learning approach for this problem in randomized clinical trial settings. The theoretical properties of the proposed methods, including Fisher consistency and asymptotic normality of the estimated expected outcome under the estimated optimal individualized treatment rule, are rigorously established. A consistent closed-form variance estimator is provided and methodology for the calculation of simultaneous confidence intervals is proposed. Simulation studies show that the proposed methodology and inference procedures work well even with small sample sizes and high rates of right censoring. The methodology is illustrated using data from a randomized clinical trial on the treatment of metastatic squamous-cell carcinoma of the head and neck

Impact of dependent left truncation in semiparametric competing risks methods: A simulation study

In this study, we investigated the robustness of the methods that account for independent left truncation when applied to competing risks settings with dependent left truncation. We specifically focused on the methods for the proportional cause-specific hazards model and the Fine–Gray model. Simulation experiments showed that these methods are not in general robust against dependent left truncation. The magnitude of the bias was analogous to the strength of the association between left truncation and failure times, the effect of the covariate on the competing cause of failure, and the baseline hazard of left truncation time

Semiparametric regression on cumulative incidence function with interval-censored competing risks data

Many biomedical and clinical studies with time-to-event outcomes involve competing risks data. These data are frequently subject to interval censoring. This means that the failure time is not precisely observed but is only known to lie between two observation times such as clinical visits in a cohort study. Not taking into account the interval censoring may result in biased estimation of the cause-specific cumulative incidence function, an important quantity in the competing risks framework, used for evaluating interventions in populations, for studying the prognosis of various diseases, and for prediction and implementation science purposes. In this work, we consider the class of semiparametric generalized odds rate transformation models in the context of sieve maximum likelihood estimation based on B-splines. This large class of models includes both the proportional odds and the proportional subdistribution hazard models (i.e., the Fine-Gray model) as special cases. The estimator for the regression parameter is shown to be consistent, asymptotically normal and semiparametrically efficient. Simulation studies suggest that the method performs well even with small sample sizes. As an illustration, we use the proposed method to analyze data from HIV-infected individuals obtained from a large cohort study in sub-Saharan Africa. We also provide the R function ciregic that implements the proposed method and present an illustrative example

Semiparametric Competing Risks Regression Under Interval Censoring Using the R Package intccr

Background and objective: Competing risk data are frequently interval-censored in real-world applications, that is, the exact event time is not precisely observed but is only known to lie between two time points such as clinic visits. This type of data requires special handling because the actual event times are unknown. To deal with this problem we have developed an easy-to-use open-source statistical software. Methods: An approach to perform semiparametric regression analysis of the cumulative incidence function with interval-censored competing risks data is the sieve maximum likelihood method based on B-splines. An important feature of this approach is that it does not impose restrictive parametric assumptions. Also, this methodology provides semiparametrically efficient estimates. Implementation of this methodology can be easily performed using our new R package intccr. Results: The R package intccr performs semiparametric regression analysis of the cumulative incidence function based on interval-censored competing risks data. It supports a large class of models including the proportional odds and the Fine-Gray proportional subdistribution hazards model as special cases. It also provides the estimated cumulative incidence functions for a particular combination of covariate values. The package also provides some data management functionality to handle data sets which are in a long format involving multiple lines of data per subject. Conclusions: The R package intccr provides a convenient and flexible software for the analysis of the cumulative incidence function based on interval-censored competing risks data

Semiparametric regression and risk prediction with competing risks data under missing cause of failure

The cause of failure in cohort studies that involve competing risks is frequently incompletely observed. To address this, several methods have been proposed for the semiparametric proportional cause-specific hazards model under a missing at random assumption. However, these proposals provide inference for the regression coefficients only, and do not consider the infinite dimensional parameters, such as the covariatespecific cumulative incidence function. Nevertheless, the latter quantity is essential for risk prediction in modern medicine. In this paper we propose a unified framework for inference about both the regression coefficients of the proportional cause-specific hazards model and the covariate-specific cumulative incidence functions under missing at random cause of failure. Our approach is based on a novel computationally efficient maximumpseudo-partial-likelihood estimationmethod for the semiparametric proportional cause-specific hazards model.Using modern empirical process theorywe derive the asymptotic properties of the proposed estimators for the regression coefficients and the covariate-specific cumulative incidence functions, and provide methodology for constructing simultaneous confidence bands for the latter. Simulation studies show that our estimators perform well even in the presence of a large fraction of missing cause of failures, and that the regression coefficient estimator can be substantially more efficient compared to the previously proposed augmented inverse probability weighting estimator. The method is applied using data from an HIV cohort study and a bladder cancer clinical trial

Nonparametric inference for Markov processes with missing absorbing state

This study examines nonparametric estimations of a transition proba- bility matrix of a nonhomogeneous Markov process with a nite state space and a partially observed absorbing state. We impose a missing-at-random assumption and propose a computationally e cient nonparametric maximum pseudolikelihood estimator (NPMPLE). The estimator depends on a parametric model that is used to estimate the probability of each absorbing state for the missing observations based, potentially, on auxiliary data. For the latter model, we propose a formal goodness- of- t test based on a residual process. Using modern empirical process theory, we show that the estimator is uniformly consistent and converges weakly to a tight mean-zero Gaussian random eld. We also provide a methodology for constructing simultaneous con dence bands. Simulation studies show that the NPMPLE works well with small sample sizes and that it is robust against some degree of misspec- i cation of the parametric model for the missing absorbing states. The method is illustrated using HIV data from sub-Saharan Africa to estimate the transition probabilities of death and disengagement from HIV care

Semiparametric regression on cumulative incidence function with interval-censored competing risks data and missing event types

Competing risk data are frequently interval-censored, that is, the exact event time is not observed but only known to lie between two examination time points such as clinic visits. In addition to interval censoring, another common complication is that the event type is missing for some study participants. In this article, we propose an augmented inverse probability weighted sieve maximum likelihood estimator for the analysis of interval-censored competing risk data in the presence of missing event types. The estimator imposes weaker than usual missing at random assumptions by allowing for the inclusion of auxiliary variables that are potentially associated with the probability of missingness. The proposed estimator is shown to be doubly robust, in the sense that it is consistent even if either the model for the probability of missingness or the model for the probability of the event type is misspecified. Extensive Monte Carlo simulation studies show good performance of the proposed method even under a large amount of missing event types. The method is illustrated using data from an HIV cohort study in sub-Saharan Africa, where a significant portion of events types is missing. The proposed method can be readily implemented using the new function ciregic_aipw in the R package intccr