Smoothed landmark estimators of the transition probabilities

One important goal in clinical applications of multi-state models is the estimation of transition probabilities. Recently, landmark estimators were proposed to estimate these quantities, and their superiority with respect to the competing estimators has been proved in situations in which the Markov condition is violated. As a weakness, it provides large standard errors in estimation in some circumstances. In this article, we propose two approaches that can be used to reduce the variability of the proposed estimator. Simulations show that the proposed estimators may be much more efficient than the unsmoothed estimator. A real data illustration is included

Presmoothed Landmark estimators of the transition probabilities

Multi-state models can be successfully used to model complicated event history data, for example, describing stages in the disease progression of a patient. In these models one important goal is the estimation of the transition probabilities since they allow for long term prediction of the process. There have been several recent contributions for the estimation of the transition probabilities. Recently, de Uña- Álvarez and Meira-Machado (2015) proposed new estimators for these quantities, and their superiority with respect to the competing estimators has been proved in situations in which the Markov condition is violated. In this paper, we propose a modification of the estimator proposed by de Uña-Álvarez and Meira-Machado based on presmoothing. Simulations show that the presmoothed estimators may be much more efficient than the completely nonparametric estimator.This project was funded by FEDER Funds through “Programa Operacional Factores de Competitividade - COMPETE” and by Portuguese Funds through FCT - “Fundação para a Ciência e a Tecnologia”, in the form of grant PEst-OE/MAT/UI0013/2014.info:eu-repo/semantics/publishedVersio

p3state.msm: Analyzing Survival Data from an Illness-Death Model

In longitudinal studies of disease, patients can experience several events across a followup period. Analysis of such studies can be successfully performed by multi-state models. In the multi-state framework, issues of interest include the study of the relationship between covariates and disease evolution, estimation of transition probabilities, and survival rates. This paper introduces p3state.msm, a software application for R which performs inference in an illness-death model. It describes the capabilities of the program for estimating semi-parametric regression models and for implementing nonparametric estimators for several quantities. The main feature of the package is its ability for obtaining nonMarkov estimates for the transition probabilities. Moreover, the methods can also be used in progressive three-state models. In such a model, estimators for other quantities, such as the bivariate distribution function (for sequentially ordered events), are also given. The software is illustrated using data from the Stanford Heart Transplant Study.

Estimation of multivariate distributions for recurrent event data

In many longitudinal studies information is collected on the times of different kinds of events. Some of these studies involve repeated events, where a subject or sample unit may experience a well-defined event several times along his history. Such events are called recurrent events. In this work we consider the estimation of the marginal and joint distribution functions of two gap times under univariate random right censoring. We also consider the estimation of the bivariate survival function.This research was financed by Portuguese Funds through FCT - “Funda¸c˜ao para a Ciˆencia e a Tecnologia”, within Project UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio

Methods for checking the Markov condition in multi-state survival data

The inference in multi-state models is traditionally performed under a Markov assumption that claims that past and future of the process are independent given the present state. This assumption has an important role in the estimation of the transition probabilities. When the multi-state model is Markovian, the Aalen-Johansen estimator gives consistent estimators of the transition probabilities but this is no longer the case when the process is non-Markovian. Usually, this assumption is checked including covariates depending on the history. Since the landmark methods of the transition probabilities are free of the Markov assumption, they can also be used to introduce such tests by measuring their discrepancy to Markovian estimators. In this paper, we introduce tests for the Markov assumption and compare them with the usual approach based on the analysis of covariates depending on history through simulations. The methods are also compared with more recent and competitive approaches. Three real data examples are included for illustration of the proposed methods.This research was financed by Portuguese Funds through FCT - “Fundação para a Ciencia e a Tecnologia”, within the research grants PTDC/MAT-STA/28248/2017 and PD/BD/142887/2018

Analysis of complex survival data: a tutorial using the Shiny MSM.app application

The development of applications for obtaining interpretable results in a simple and summarized manner in multi-state models is a research field with great potential, namely in terms of using open source tools that can be easily implemented in biomedical applications. In this tutorial, we introduce MSM.app, an interactive web application using the Shiny package for the R language. In the following sections, we present the main functionalities of the MSM.app and an explanation of the outputs obtained for better understanding, independent of the statistical knowledge of users.This research was financed within the research grants PTDC/MAT-STA/28248/2017 and PD/BD/142887/2018

An R package for inference and prediction in an illness-death model

Multi-state models are a useful way of describing a process in which an individual moves through a number of nite states in continuous time. The illness-death model plays a central role in the theory and practice of these models, describing the dynamics of healthy subjects who may move to an intermediate `diseased' state before entering into a terminal absorbing state. In these models one important goal is the modeling of transition rates which is usually done by studying the relationship between covariates and disease evolution. However, biomedical researchers are also interested in reporting other interpretable results in a simple and summarized manner. These include estimates of predictive probabilities, such as the transition probabilities, occupation probabilities, cumulative incidence functions, prevalence and the sojourn time distributions. An R package was built providing answers to all these topics

Nonparametric estimation of the distribution of gap times for recurrent events

In many longitudinal studies, information is collected on the times of different kinds of events. Some of these studies involve repeated events, where a subject or sample unit may experience a well-defined event several times throughout their history. Such events are called recurrent events. In this paper, we introduce nonparametric methods for estimating the marginal and joint distribution functions for recurrent event data. New estimators are introduced and their extensions to several gap times are also given. Nonparametric inference conditional on current or past covariate measures is also considered. We study by simulation the behavior of the proposed estimators in finite samples, considering two or three gap times. Our proposed methods are applied to the study of (multiple) recurrence times in patients with bladder tumors. Software in the form of an R package, called survivalREC, has been developed, implementing all methods.This research was financed by Portuguese Funds through FCT - “Fundação para a Ciência e a Tecnologia”, within Projects projects UIDB/00013/2020, UIDP/00013/2020 and the research grant PD/BD/142887/2018