Semi‐parametric estimation of covariate effects using the positive stable frailty model

Many biological and medical studies have as a response of interest the time to occurrence of some event, such as the occurrence of a particular symptom or disease, remission, relapse, death due to some specific disease, or simply death. In this paper we study the problem of assessing the effect of potential risk factors on the outcome event of interest through a parametric or semi-parametric frailty model where the lifetimes have a reason to be considered dependent. This dependence may arise because of multiple endpoints within the same individual or because, when studying a single endpoint, there are natural groupings between study subjects. The objective of this paper is to extend both parametric and semi-parametric approaches to regression analysis in which the lifetimes of individuals in a group are effected by the same random frailty which follows a positive stable distribution. Some comparisons of the properties of this frailty distribution with other frailty distributions are made and an example which assesses the effect of a treatment in a litter-matched tumorigenesis study is presented.

[1]  J. Klein,et al.  Estimating Random Effects In the Framingham Heart Study , 1992 .

[2]  N. Mantel,et al.  Use of logrank scores in the analysis of litter-matched data on time to tumor appearance. , 1979, Cancer Research.

[3]  Philip Hougaard,et al.  Modelling multivariate survival , 1987 .

[4]  Philip Hougaard,et al.  Life table methods for heterogeneous populations: Distributions describing the heterogeneity , 1984 .

[5]  D. Clayton,et al.  Multivariate generalizations of the proportional hazards model , 1985 .

[6]  P. Hougaard.  A class of multivanate failure time distributions , 1986 .

[7]  John P. Klein,et al.  Effects of model misspecification in estimating covariate effects in survival analysis for small sample sizes , 1996 .

[8]  S. Johansen.  An Extension of Cox's Regression Model , 1983 .

[9]  N Mantel,et al.  Mantel-Haenszel analyses of litter-matched time-to-response data, with modifications for recovery of interlitter information. , 1977, Cancer research.

[10]  P. Hougaard.  Survival models for heterogeneous populations derived from stable distributions , 1986 .

[11]  Philip Hougaard,et al.  Measuring the Similarities between the Lifetimes of Adult Danish Twins Born between 1881–1930 , 1992 .

[12]  J P Klein,et al.  Semiparametric estimation of random effects using the Cox model based on the EM algorithm. , 1992, Biometrics.

[13]  P. Lee,et al.  Weibull distributions for continuous-carcinogenesis experiments. , 1973, Biometrics.

[14]  D. Oakes,et al.  Bivariate survival models induced by frailties , 1989 .

[15]  Nancy Flournoy,et al.  Assessment of Dependence In the Life Times of Twins , 1992 .

[16]  Richard D. Gill,et al.  A counting process approach to maximum likelihood estimation in frailty models , 1992 .