Modeling Two-state Disease Processes with Random Effects

Many chronic medical conditions are manifested by alternating sojourns in symptom-free and symptomatic states. In many cases, in addition to their relapsing and remitting nature, these conditions lead to worsening disease patterns over time and may exhibit seasonal trends. We develop a mixed-effect two-state model for such disease processes in which covariate effects are modeled multiplicatively on transition intensities. The transition intensities, in turn, are functions of three time scales: the semi-Markov scale involving the backward recurrence time for the cyclical component, the Markov scale for the time trend component, and a seasonal time scale. Multiplicative bivariate log-normal random effects are introduced to accommodate heterogeneity in disease activity between subjects and to admit a possible negative correlation between the transition intensities. Maximum likelihood estimation is carried out using Gauss-Hermite integration and a standard Newton-Raphson procedure. Tests of homogeneity are presented based on score statistics. An application of the methodology to data from a multi-center clinical trial of chronic bronchitis is provided for illustrative purposes.     

Fitting Weibull duration models with random effects

Duration time models often should include correlated failure times, due to clustered data. These random effects hierarchical models sometimes are called frailty models when used for survival analyses. The data analyzed here involve such correlations because patient level outcomes (the times until graft failure following kidney transplantation) are observed, but patients are clustered in different transplant centers. We describe fitting such models by combining two kinds of software, one for parametric survival regression models, and the other for doing Poisson regression in a hierarchical setting. The latter is implemented by using PRIMM (Poisson Regression and Interactive Multilevel Modeling) methods and software (Christiansen & Morris, 1994a). An illustrative example for profiling data is included withk=11 kidney transplant centers andN=412 patients.     

Profile likelihood approaches for semiparametric copula and frailty models for clustered survival data

ABSTRACT

In clustered survival data, the dependence among individual survival times within a cluster has usually been described using copula models and frailty models. In this paper we propose a profile likelihood approach for semiparametric copula models with different cluster sizes. We also propose a likelihood ratio method based on profile likelihood for testing the absence of association parameter (i.e. test of independence) under the copula models, leading to the boundary problem of the parameter space. For this purpose, we show via simulation study that the proposed likelihood ratio method using an asymptotic chi-square mixture distribution performs well as sample size increases. We compare the behaviors of the two models using the profile likelihood approach under a semiparametric setting. The proposed method is demonstrated using two well-known data sets.     

Clustered Survival Data with Left‐truncation

Left‐truncation occurs frequently in survival studies, and it is well known how to deal with this for univariate survival times. However, there are few results on how to estimate dependence parameters and regression effects in semiparametric models for clustered survival data with delayed entry. Surprisingly, existing methods only deal with special cases. In this paper, we clarify different kinds of left‐truncation and suggest estimators for semiparametric survival models under specific truncation schemes. The large‐sample properties of the estimators are established. Small‐sample properties are investigated via simulation studies, and the suggested estimators are used in a study of prostate cancer based on the Finnish twin cohort where a twin pair is included only if both twins were alive in 1974.     

EFFICIENT ESTIMATION IN REGRESSION FRAILTY OR TRANSFORMATION MODELS BASED ON AN ALGORITHM

This paper considers a regression frailty or transformation model in which the structural parameter is the vector of regression coefficients and the nuisance parameter is a vector of arbitrarily high dimension. It proposes jointly (implicitly) defined parameter estimators which have been proved to be consistent and asymptotically efficient, and develops an algorithmic procedure that provides these estimators. The behaviour of the algorithm is illustrated by analysing simulated and real data.     

Frailty Models for Arbitrarily Censored and Truncated Data

In this paper, we propose a frailty model for statistical inference in the case where we are faced with arbitrarily censored and truncated data. Our results extend those of Alioum and Commenges (1996), who developed a method of fitting a proportional hazards model to data of this kind. We discuss the identifiability of the regression coefficients involved in the model which are the parameters of interest, as well as the identifiability of the baseline cumulative hazard function of the model which plays the role of the infinite dimensional nuisance parameter. We illustrate our method with the use of simulated data as well as with a set of real data on transfusion-related AIDS.     

Non-mixture cure correlated frailty models in Bayesian approach

In this article, we develop a Bayesian approach for the estimation of two cure correlated frailty models that have been extended to the cure frailty models introduced by Yin [34]. We used the two different type of frailty with bivariate log-normal distribution instead of gamma distribution. A likelihood function was constructed based on a piecewise exponential distribution function. The model parameters were estimated by the Markov chain Monte Carlo method. The comparison of models is based on the Cox correlated frailty model with log-normal distribution. A real data set of bilateral corneal graft rejection was used to compare these models. The results of this data, based on deviance information criteria, showed the advantage of the proposed models.     

Shared frailty model for recurrent event data with multiple causes

The topic of heterogeneity in the analysis of recurrent event data has received considerable attention recent times. Frailty models are widely employed in such situations as they allow us to model the heterogeneity through common random effect. In this paper, we introduce a shared frailty model for gap time distributions of recurrent events with multiple causes. The parameters of the model are estimated using EM algorithm. An extensive simulation study is used to assess the performance of the method. Finally, we apply the proposed model to a real-life data.     

Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity

The proportional hazard model with unobserved heterogeneity gives the hazard function of a random variable conditional on covariates and a second random variable representing unobserved heterogeneity. This paper shows how to estimate the baseline hazard function and the distribution of the unobserved heterogeneity nonparametrically. The baseline hazard function and heterogeneity distribution are assumed to satisfy smoothness conditions but are not assumed to belong to known, finite-dimensional, parametric families. Existing estimators assume that the baseline hazard function or heterogeneity distribution belongs to a known parametric family. Thus, the estimators presented here are more general than existing ones.     

A Semi‐parametric Transformation Frailty Model for Semi‐competing Risks Survival Data

In the analysis of semi‐competing risks data interest lies in estimation and inference with respect to a so‐called non‐terminal event, the observation of which is subject to a terminal event. Multi‐state models are commonly used to analyse such data, with covariate effects on the transition/intensity functions typically specified via the Cox model and dependence between the non‐terminal and terminal events specified, in part, by a unit‐specific shared frailty term. To ensure identifiability, the frailties are typically assumed to arise from a parametric distribution, specifically a Gamma distribution with mean 1.0 and variance, say, σ². When the frailty distribution is misspecified, however, the resulting estimator is not guaranteed to be consistent, with the extent of asymptotic bias depending on the discrepancy between the assumed and true frailty distributions. In this paper, we propose a novel class of transformation models for semi‐competing risks analysis that permit the non‐parametric specification of the frailty distribution. To ensure identifiability, the class restricts to parametric specifications of the transformation and the error distribution; the latter are flexible, however, and cover a broad range of possible specifications. We also derive the semi‐parametric efficient score under the complete data setting and propose a non‐parametric score imputation method to handle right censoring; consistency and asymptotic normality of the resulting estimators is derived and small‐sample operating characteristics evaluated via simulation. Although the proposed semi‐parametric transformation model and non‐parametric score imputation method are motivated by the analysis of semi‐competing risks data, they are broadly applicable to any analysis of multivariate time‐to‐event outcomes in which a unit‐specific shared frailty is used to account for correlation. Finally, the proposed model and estimation procedures are applied to a study of hospital readmission among patients diagnosed with pancreatic cancer.