Survival mixture modelling of recurrent infections (original) (raw)

A computer graphical user interface for survival mixture modelling of recurrent infections

Computers in Biology and Medicine, 2009

Recurrent infections data are commonly encountered in medical research, where the recurrent events are characterised by an acute phase followed by a stable phase after the index episode. Twocomponent survival mixture models, in both proportional hazards and accelerated failure time settings, are presented as a flexible method of analysing such data. To account for the inherent clustering and dependency of the recurrent observations, random effects are incorporated within the conditional hazard function, in the manner of generalised linear mixed models. Assuming a Weibull or log-logistic baseline hazard in both mixture components of the survival mixture model, an EM algorithm is developed for the residual maximum quasi-likelihood estimation of fixed effect and variance components parameters. The methodology is implemented as a graphical user interface coded using Microsoft visual C++. Application to model recurrent urinary tract infections for elderly women is illustrated, where significant individual variations are evident at both acute and stable phases. The survival mixture methodology developed enable practitioners to identify pertinent risk factors affecting the recurrent times and to draw valid conclusions inferred from these clustered and heterogeneous survival data.

A Logistic Weibull Mixture Models with Long-Term Survivors

2009

1,2,3&4 Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia Email: mrizam@putra.upm.edu.my, isa@putra.upm.edu.my, nakma@putra.upm.edu.my, desirahmatina@yahoo.com Abstract. The mixture model postulates a mixed population with two types of individuals, the susceptible and long-term survivors. The susceptibles are at the risk of developing the event under consideration. However, the long-term survivors or immune individuals will never experience the event. This paper focuses on the covariates associated with individuals such as age, surgery and transplant related to the probability of being immune in a logistic Weibull model and to evaluate the effect of heart transplantation on subsequent survival.

Bayesian compartmental model for an infectious disease with dynamic states of infection

Journal of Applied Statistics, 2018

Population-level proportions of individuals that fall at different points in the spectrum [of disease severity], from asymptomatic infection to severe disease, are often difficult to observe, but estimating these quantities can provide information about the nature and severity of the disease in a particular population. Logistic and multinomial regression techniques are often applied to infectious disease modeling of large populations and are suited to identifying variables associated with a particular disease or disease state. However, they are less appropriate for estimating infection state prevalence over time because they do not naturally accommodate known disease dynamics like duration of time an individual is infectious, heterogeneity in the risk of acquiring infection, and patterns of seasonality. We propose a Bayesian compartmental model to estimate latent infection state prevalence over time that easily incorporates known disease dynamics. We demonstrate how and why a stochastic compartmental model is a better approach for determining infection state proportions than multinomial regression is by using a novel method for estimating Bayes factors for models with high-dimensional parameter spaces. We provide an example using visceral leishmaniasis in Brazil and present an empirically-adjusted reproductive number for the infection.

Generalized cure rate model for infectious diseases with possible co-infections

PLOS ONE

This research mainly aims to develop a generalized cure rate model, estimate the proportion of cured patients and their survival rate, and identify the risk factors associated with infectious diseases. The generalized cure rate model is based on bounded cumulative hazard function, which is a non-mixture model, and is developed using a two-parameter Weibull distribution as the baseline distribution, to estimate the cure rate using maximum likelihood method and real data with R and STATA software. The results showed that the cure rate of tuberculosis (TB) patients was 26.3%, which was higher than that of TB patients coinfected with human immunodeficiency virus (HIV; 23.1%). The non-parametric median survival time of TB patients was 51 months, while that of TB patients co-infected with HIV was 33 months. Moreover, no risk factors were associated with TB patients co-infected with HIV, while age was a significant risk factor for TB patients among the suspected risk factors considered. Furthermore, the bounded cumulative hazard function was extended to accommodate infectious diseases with co-infections by deriving an appropriate probability density function, determining the distribution, and using real data. Governments and related health authorities are also encouraged to take appropriate actions to combat infectious diseases with possible co-infections.

The generalized exponential cure rate model with covariates

Journal of Applied Statistics, 2010

In this article, we consider a parametric survival model that is appropriate when the population of interest contains long-term survivors or immunes. The model referred to as the cure rate model was introduced by Boag [1] in terms of a mixture model that included a component representing the proportion of immunes and a distribution representing the life times of the susceptible population. We propose a cure rate model based on the generalized exponential distribution that incorporates the effects of risk factors or covariates on the probability of an individual being a long-time survivor.

Approximate Bayesian inference for mixture cure models

TEST

Cure models in survival analysis deal with populations in which a part of the individuals cannot experience the event of interest. Mixture cure models consider the target population as a mixture of susceptible and non-susceptible individuals. The statistical analysis of these models focuses on examining the probability of cure (incidence model) and inferring on the time-to-event in the susceptible subpopulation (latency model). Bayesian inference on mixture cure models has typically relied upon Markov chain Monte Carlo (MCMC) methods. The integrated nested Laplace approximation (INLA) is a recent and attractive approach for doing Bayesian inference. INLA in its natural definition cannot fit mixture models but recent research has new proposals that combine INLA and MCMC methods to extend its applicability to them 2;8;9. This paper focuses on the implementation of INLA in mixture cure models. A general mixture cure survival model with covariate information for the latency and the incidence model within a general scenario with censored and non-censored information is discussed. The fact that non-censored individuals undoubtedly belong to the uncured population is a valuable information that was incorporated in the inferential process.

Bayesian Weibull Mixture Models for Dengue Fever

Dengue fever disease has become common problem in developing countries including Indonesia. Mixture models are usually used in modelling data consisting of several groups, where each group has different properties and characteristics of the one family but uses the same distribution. Weibull mixture models have received increasing attention in recent statistical research with applications in the field of survival analysis. The advances in the Bayesian paradigm have substantially expanded the methodology and application of Weibull mixture models. One problem of current interests is the analysis of survival times of patients. Dengue hemorrhagic fever data can be used to make inference about patient survival. In this study, we focus on the use of Bayesian Weibull mixture models for estimating survival. A simulation study that investigates the impact of censoring on these models is also described.

Cross-sectional and Longitudinal Approaches in a Survival Mixture Model

Mathematika, 2008

In this article, we explore the performance of estimators in mixture sur- vival model using simulated data recorded cross-sectionally and longitudinally. We use the maximum likelihood estimation approach in estimating the unknown model parameters. We found, in particular, that the maximum likelihood estimator for the proportion of long-term survivors in longitudinal setting gain better efficiency and precision for a certain distance of recording time.

Joint Modelling of Recurrent Infections and Antibody Response by Bayesian Data Augmentation

Scandinavian Journal of Statistics, 2003

A joint dynamic model for the interdependence between infection, immunity and risk of disease is presented. Recurrent latent infections are modelled as realizations from a renewal process and antibody dynamics as a diffusion with a decreasing drift modified by the stimulating effect of the random infections. The augmented submodels are estimated simultaneously in one large Markov chain Monte Carlo algorithm. As an example, we consider the risk of recurrent ear infections when having only partially observed information on bacterial carriage and antibody concentrations.

Use of Bayesian Mixture Models in Analyzing Heterogeneous Survival Data: A Simulation Study

Journal of Biostatistics and Epidemiology, 2020

Background and Aim: One of the statistical methods used to analyze the time-to-event medical data is survival analysis. In survival models, the response variable is time to the occurrence of an event. The main characteristic of survival data is the existence of censored data. When we have the distribution of survival time, we can use parametric methods. Among the important and popular distributions that can be used, we can mention the Weibull distribution. If the data derives from a heterogeneous population, simple parametric models (such as Weibull) would not fit the data appropriately. One of the methods which have been introduced to overcome this problem is the use of mixture models. Methods: To assess the validity of the two-component Weibull mixture model, we use a simulation method on heterogeneous survival data. For this purpose, data with different sample sizes were produced in a batch of 1000. Then, the validity of the model is checked using root mean square error (RMSE...