A semi-Markov model for stroke with piecewise-constant hazards in the presence of left, right and interval censoring.

This paper presents a parametric method of fitting semi-Markov models with piecewise-constant hazards in the presence of left, right and interval censoring. We investigate transition intensities in a three-state illness-death model with no recovery. We relax the Markov assumption by adjusting the intensity for the transition from state 2 (illness) to state 3 (death) for the time spent in state 2 through a time-varying covariate. This involves the exact time of the transition from state 1 (healthy) to state 2. When the data are subject to left or interval censoring, this time is unknown. In the estimation of the likelihood, we take into account interval censoring by integrating out all possible times for the transition from state 1 to state 2. For left censoring, we use an Expectation-Maximisation inspired algorithm. A simulation study reflects the performance of the method. The proposed combination of statistical procedures provides great flexibility. We illustrate the method in an application by using data on stroke onset for the older population from the UK Medical Research Council Cognitive Function and Ageing Study

Most Likely Transformations

We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a cascade of increasingly complex transformation models that can be estimated, compared and analysed in the maximum likelihood framework. Models for the unconditional or conditional distribution function of any univariate response variable can be set-up and estimated in the same theoretical and computational framework simply by choosing an appropriate transformation function and parameterisation thereof. The ability to evaluate the distribution function directly allows us to estimate models based on the exact likelihood, especially in the presence of random censoring or truncation. For discrete and continuous responses, we establish the asymptotic normality of the proposed estimators. A reference software implementation of maximum likelihood-based estimation for conditional transformation models allowing the same flexibility as the theory developed here was employed to illustrate the wide range of possible applications.Comment: Accepted for publication by the Scandinavian Journal of Statistics 2017-06-1

Prediction of remaining life of power transformers based on left truncated and right censored lifetime data

Prediction of the remaining life of high-voltage power transformers is an important issue for energy companies because of the need for planning maintenance and capital expenditures. Lifetime data for such transformers are complicated because transformer lifetimes can extend over many decades and transformer designs and manufacturing practices have evolved. We were asked to develop statistically-based predictions for the lifetimes of an energy company's fleet of high-voltage transmission and distribution transformers. The company's data records begin in 1980, providing information on installation and failure dates of transformers. Although the dataset contains many units that were installed before 1980, there is no information about units that were installed and failed before 1980. Thus, the data are left truncated and right censored. We use a parametric lifetime model to describe the lifetime distribution of individual transformers. We develop a statistical procedure, based on age-adjusted life distributions, for computing a prediction interval for remaining life for individual transformers now in service. We then extend these ideas to provide predictions and prediction intervals for the cumulative number of failures, over a range of time, for the overall fleet of transformers.Comment: Published in at http://dx.doi.org/10.1214/00-AOAS231 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

HIV dynamics and natural history studies: Joint modeling with doubly interval-censored event time and infrequent longitudinal data

Hepatitis C virus (HCV) coinfection has become one of the most challenging clinical situations to manage in HIV-infected patients. Recently the effect of HCV coinfection on HIV dynamics following initiation of highly active antiretroviral therapy (HAART) has drawn considerable attention. Post-HAART HIV dynamics are commonly studied in short-term clinical trials with frequent data collection design. For example, the elimination process of plasma virus during treatment is closely monitored with daily assessments in viral dynamics studies of AIDS clinical trials. In this article instead we use infrequent cohort data from long-term natural history studies and develop a model for characterizing post-HAART HIV dynamics and their associations with HCV coinfection. Specifically, we propose a joint model for doubly interval-censored data for the time between HAART initiation and viral suppression, and the longitudinal CD4 count measurements relative to the viral suppression. Inference is accomplished using a fully Bayesian approach. Doubly interval-censored data are modeled semiparametrically by Dirichlet process priors and Bayesian penalized splines are used for modeling population-level and individual-level mean CD4 count profiles. We use the proposed methods and data from the HIV Epidemiology Research Study (HERS) to investigate the effect of HCV coinfection on the response to HAART.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS391 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Assessing the Impact of a Wage Subsidy for Single Parents on Social Assistance

In 2002 the Quebec government implemented the “Action Emploi" (AE) program aimed at making work pay for long-term social assistance recipients (SA). AE offered a generous income supplement that could last up to three years to recipients who found a full-time job within twelve months. The program was implemented for a trial period of one year. Based on little empirical evidence, a slightly modified version of the program was implemented on a permanent basis in May 2008. The paper investigates the impact of the temporary program by focusing on the labour market transitions of the targeted population starting one year before the implementation of the program and up until the end of 2005. We use a multi-state multi-episode model. The endogeneity of the participation status is accounted for by treating AE as a distinct state and by allowing correlated unobserved factors to affect the transitions. The model is estimated by the method of simulated moments. Our results show that AE has indeed increased the duration of Off-SA spells and decreased the duration of SA spells slightly. There is also some evidence that the response to the program varies considerably with unobserved individual characteristics. En 2002, le gouvernement du Québec a mis sur pied le programme Action emploi (AE) qui visait à mieux rémunérer le travail des prestataires de l’aide sociale (AS) de longue durée. AE offrait un supplément de revenu généreux pouvant s’échelonner sur une période d’au plus trois ans aux prestataires ayant trouvé un emploi à temps plein à l’intérieur de 12 mois. Le programme a été mis en œuvre pendant une période d’essai d’un an. Sur la base d’une faible évidence empirique, une version légèrement modifiée du programme a été adoptée de façon permanente en mai 2008. Le document examine l’incidence du programme temporaire en mettant l’accent sur les transitions de la population ciblée sur le marché du travail, à compter de l’année précédant la mise en œuvre du programme jusqu’à la fin de 2005. Nous utilisons un modèle multi-états et multi-épisodes. Afin de prendre en compte l’endogénéité du statut de participation, nous considérons que le programme AE est un état distinct et nous permettons à des facteurs latents corrélés d’influencer les transitions. Le modèle est évalué par la méthode du maximum de vraisemblance simulée. Nos résultats démontrent que le programme a effectivement augmenté la durée des périodes de sortie de l’AS et diminué légèrement la durée des périodes de recours à l’AS. Le document montre également que la réponse au programme varie considérablement en fonction des caractéristiques individuelles latentes., assistance sociale, supplément de revenu, modèle de transition multi-états et multi-épisodes.

Regression Modeling of Complex Survival Data based on Pseudo-Observations

The restricted mean survival time (RMST) is a clinically meaningful summary measure in studies with survival outcomes. Statistical methods have been developed for regression analysis of RMST to investigate impacts of covariates on RMST, which is a useful alternative to the Cox regression analysis. However, existing methods for regression modeling of RMST are not applicable to left-truncated right-censored data that arise frequently in prevalent cohort studies, for which the sampling bias due to left truncation and informative censoring induced by the prevalent sampling scheme must be properly addressed. Meanwhile, statistical methods have been developed for regression modeling of the cumulative incidence function for left-truncated right-censored competing risks data. Nevertheless, existing methods typically involve complicated weighted estimating equations or nonparametric conditional likelihood function and often require a restrictive assumption that censoring and/or truncation times are independent of failure time. Andersen et al. introduced an approach of using pseudo observations (POs) in regression analysis of right-censored data. In this dissertation, we develop statistical methods for regression modeling of complex survival data based on POs. In Chapter 1, we propose to directly model RMST as a function of baseline covariates based on POs for left-truncated right-censored data under general censoring mechanisms. We adjust for the potential covariate-dependent censoring or dependent censoring by the inverse probability of censoring weighting method. We establish large sample properties of the proposed estimators and assess their finite sample performances by simulation studies under various scenarios. We apply the proposed methods to a prevalent cohort of women diagnosed with stage IV breast cancer identified from Surveillance, Epidemiology, and End Results-Medicare linked database. In Chapter 2, we extend the PO approach to left-truncated right-censored competing risks data and propose to directly model the cumulative incidence as a function of baseline covariates based on POs, under general truncation and censoring mechanisms. We adjust for potential covariate-dependent truncation and/or covariate-dependent censoring by incorporating covariate-adjusted weights into the inverse probability weighted estimator of the cumulative incidence function. We derive large sample properties of the proposed estimators under reasonable model assumptions and regularity conditions and assess their finite sample performances by simulation studies under various scenarios. We apply the proposed methods to a cohort study on HIV disease progression and a cohort study on pregnancy exposed to coumarin derivatives for illustration