Comparison of methods for the analysis of longitudinal interval count data.

Longitudinal studies are often concerned with estimating the recurrence rate of a non-fatal event. In many cases, only the total number of events occurring during successive time intervals is known. We compared a mixed Poisson-gamma regression method proposed by Thall and a quasi-likelihood method proposed by Zeger and Liang for the analysis of such data, in the case where the mean was correctly specified, using simulation techniques with large samples. Both methods produced similar standard errors in most situations, except in the case of time-dependent covariates with non-Poisson-gamma data where they were seriously underestimated by the Thall method. A simple method for discriminating between the variance forms of the two methods is described. The findings are applied to the analyses of clinical trials of non-melanoma skin cancer and familial polyposis. This study extends the findings of Breslow concerning variance misspecification in overdispersed Poisson and quasi-likelihood models to the longitudinal setting.

[1]  P. Albert,et al.  Models for longitudinal data: a generalized estimating equation approach. , 1988, Biometrics.

[2]  M. Lesser,et al.  Effect of wheat fiber and vitamins C and E on rectal polyps in patients with familial adenomatous polyposis. , 1989, Journal of the National Cancer Institute.

[3]  B W Turnbull,et al.  Analysis of multi-type recurrent events in longitudinal studies; application to a skin cancer prevention trial. , 1990, Biometrics.

[4]  James F. Nelson.  Multivariate Gamma-Poisson Models , 1985 .

[5]  J. Lawless.  Regression Methods for Poisson Process Data , 1987 .

[6]  John M. Lachin,et al.  Analysis of Recurrent Events: Nonparametric Methods for Random-Interval Count Data , 1988 .

[7]  J. Lawless.  Negative binomial and mixed Poisson regression , 1987 .

[8]  L. J. Wei,et al.  Regression analysis of multivariate incomplete failure time data by modeling marginal distributions , 1989 .

[9]  G G Koch,et al.  A general methodology for the analysis of experiments with repeated measurement of categorical data. , 1977, Biometrics.

[10]  H. D. Miller,et al.  The Theory Of Stochastic Processes , 1977, The Mathematical Gazette.

[11]  P. Thall,et al.  Some covariance models for longitudinal count data with overdispersion. , 1990, Biometrics.

[12]  Scott L. Zeger,et al.  Generalized linear models with random e ects: a Gibbs sampling approach , 1991 .

[13]  T. Stukel,et al.  The Skin Cancer Prevention Study: design of a clinical trial of beta-carotene among persons at high risk for nonmelanoma skin cancer. , 1989, Controlled clinical trials.

[14]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .

[15]  Norman E. Breslow,et al.  Tests of Hypotheses in Overdispersed Poisson Regression and other Quasi-Likelihood Models , 1990 .

[16]  T. Stukel,et al.  A clinical trial of beta carotene to prevent basal-cell and squamous-cell cancers of the skin. The Skin Cancer Prevention Study Group. , 1990, The New England journal of medicine.

[17]  D O Stram,et al.  Analysing repeated measurements with possibly missing observations by modelling marginal distributions. , 1988, Statistics in medicine.

[18]  A. Buist,et al.  The use of lung function tests in identifying factors that affect lung growth and aging. , 1988, Statistics in medicine.

[19]  A. V. Peterson,et al.  On the regression analysis of multivariate failure time data , 1981 .

[20]  J. Ware,et al.  Issues in the analysis of repeated categorical outcomes. , 1988, Statistics in medicine.

[21]  R. Gill,et al.  Cox's regression model for counting processes: a large sample study : (preprint) , 1982 .

[22]  D. Byar,et al.  Using permutation tests and bootstrap confidence limits to analyze repeated events data from clinical trials. , 1989, Controlled clinical trials.

[23]  K Y Liang,et al.  Longitudinal data analysis for discrete and continuous outcomes. , 1986, Biometrics.

[24]  A. Agresti.  Analysis of Ordinal Categorical Data , 1985 .

[25]  Niels Keiding,et al.  Linear Nonparametric Tests for Comparison of Counting Processes, with Applications to Censored Survival Data, Correspondent Paper , 1982 .

[26]  T. Louis,et al.  General methods for analysing repeated measures. , 1988, Statistics in medicine.

[27]  P F Thall,et al.  Mixed Poisson likelihood regression models for longitudinal interval count data. , 1988, Biometrics.

[28]  G. Seeber.  On the regression analysis of tumour recurrence rates. , 1989, Statistics in medicine.

[29]  T. Santner,et al.  An analysis of comparative carcinogenesis experiments based on multiple times to tumor. , 1980, Biometrics.