A flexible parametric approach for analyzing arbitrarily censored data that are potentially subject to left truncation under the proportional hazards model.

The proportional hazards (PH) model is, arguably, the most popular model for the analysis of lifetime data arising from epidemiological studies, among many others. In such applications, analysts may be faced with censored outcomes and/or studies which institute enrollment criterion leading to left truncation. Censored outcomes arise when the event of interest is not observed but rather is known relevant to an observation time(s). Left truncated data occur in studies that exclude participants who have experienced the event prior to being enrolled in the study. If not accounted for, both of these features can lead to inaccurate inferences about the population under study. Thus, to overcome this challenge, herein we propose a novel unified PH model that can be used to accommodate both of these features. In particular, our approach can seamlessly analyze exactly observed failure times along with interval-censored observations, while aptly accounting for left truncation. To facilitate model fitting, an expectation-maximization algorithm is developed through the introduction of carefully structured latent random variables. To provide modeling flexibility, a monotone spline representation is used to approximate the cumulative baseline hazard function. The performance of our methodology is evaluated through a simulation study and is further illustrated through the analysis of two motivating data sets; one that involves child mortality in Nigeria and the other prostate cancer.

An extended proportional hazards model for interval-censored data subject to instantaneous failures.

The proportional hazards (PH) model is arguably one of the most popular models used to analyze time to event data arising from clinical trials and longitudinal studies. In many such studies, the event time is not directly observed but is known relative to periodic examination times; i.e., practitioners observe either current status or interval-censored data. The analysis of data of this structure is often fraught with many difficulties since the event time of interest is unobserved. Further exacerbating this issue, in some such studies the observed data also consists of instantaneous failures; i.e., the event times for several study units coincide exactly with the time at which the study begins. In light of these difficulties, this work focuses on developing a mixture model, under the PH assumptions, which can be used to analyze interval-censored data subject to instantaneous failures. To allow for modeling flexibility, two methods of estimating the unknown cumulative baseline hazard function are proposed; a fully parametric and a monotone spline representation are considered. Through a novel data augmentation procedure involving latent Poisson random variables, an expectation-maximization (EM) algorithm is developed to complete model fitting. The resulting EM algorithm is easy to implement and is computationally efficient. Moreover, through extensive simulation studies the proposed approach is shown to provide both reliable estimation and inference. The motivation for this work arises from a randomized clinical trial aimed at assessing the effectiveness of a new peanut allergen treatment in attaining sustained unresponsiveness in children.

Study design with staggered sampling times for evaluating sustained unresponsiveness to peanut sublingual immunotherapy.

In this work, we delineate an altered study design of a pre-existing clinical trial that is currently being implemented in the Department of Pediatrics at the University of North Carolina at Chapel Hill. The purpose of the ongoing investigation of the desensitized pediatric cohort is to address the effectiveness of sublingual immunotherapy in achieving sustained unresponsiveness (SU) as assessed by repeated double-blind placebo-controlled food challenges (DBPCFC). With scarce published literature characterizing SU, the length of time off-therapy that would represent clinically meaningful benefit remains undefined. We use the new design features to assess time to loss of SU, an important efficacy endpoint, that to our knowledge, no prior study has investigated. Our work has two-fold objectives: first is to propose and discuss aspects of the altered design that would allow us to study SU and second is to explore methodology to evaluate the time to loss of SU and its association with risk factors in the context of the data originating from the trial. The salient feature of the new design is the allocation scheme of study subjects to staggered sampling timepoints when a subsequent DBPCFC is administered. Due to this feature, the time to loss of SU is either left or right censored. Additionally, some participants at study entry fail the DBPCFC, leading to what can be construed as an instantaneous failure. Through in-depth numerical studies, we examine the performance and power of a recently proposed mixture proportional hazards model specifically designed for the analysis of interval-censored data subject to instantaneous failures.