Conditional maximum likelihood estimation in semiparametric transformation model with LTRC data.
Left-truncated data often arise in epidemiology and individual follow-up studies due to a biased sampling plan since subjects with shorter survival times tend to be excluded from the sample. Moreover, the survival time of recruited subjects are often subject to right censoring. In this article, a general class of semiparametric transformation models that include proportional hazards model and proportional odds model as special cases is studied for the analysis of left-truncated and right-censored data. We propose a conditional likelihood approach and develop the conditional maximum likelihood estimators (cMLE) for the regression parameters and cumulative hazard function of these models. The derived score equations for regression parameter and infinite-dimensional function suggest an iterative algorithm for cMLE. The cMLE is shown to be consistent and asymptotically normal. The limiting variances for the estimators can be consistently estimated using the inverse of negative Hessian matrix. Intensive simulation studies are conducted to investigate the performance of the cMLE. An application to the Channing House data is given to illustrate the methodology.
Institute of Public Health, School of Medicine, National Yang-Ming University, Taipei, Taiwan, ROC.
Chyong-Mei
CM
Chen
Department of Statistics, Tunghai University, Xitun District, Taichung, 40704, Taiwan, ROC. psshen@thu.edu.tw.
Pao-Sheng
PS
Shen
D000465:Algorithms; D015982:Bias; D003627:Data Interpretation, Statistical; D016021:Epidemiologic Studies; D016013:Likelihood Functions; D016016:Proportional Hazards Models; D016019:Survival Analysis
Maximum conditional likelihood; Proportional hazards model; Proportional odds model; Semiparametric transformation model; Truncation data