Sunday, 21 November 2010

The analysis of tumorigenicity data using a frailty effect

Yang-Jin Kim, Chung Mo Nam, Youn Nam Kim, Eun Hee Choi and Jinheum Kim have a new paper in the Journal of the Korean Statistical Society. This concerns the analysis of tumorigenicity data where a three-state model with states representing tumour-free, with tumour and death is used. The main characteristic of the data is that disease status (presence of tumour) can only be determined at either death or sacrifice - meaning we have data with possible observations: sacrifice without tumour, sacrifice with tumour, death without tumour and death with tumour.
Note that while the time of the tumour is always interval censored, if the mouse dies before sacrifice this death time is taken to be known exactly.

Kim et al extend the model proposed by Lindsey and Ryan (1993, Applied Statistics) by allowing a shared-frailty term that affects both tumour onset rate and the hazard of death given the presence of a tumour. Like Lindsey and Ryan, piecewise constant intensities are used to model the baseline intensities, with a Cox proportional hazards model for the effect of covariates. The same baseline hazard is used for pre- and post-tumour hazard of death, with the presence of tumour changing the effect of covariates. For some reason the introduction talks about n^{1/3} convergence rates of the non-parametric survival distribution for current status data. This doesn't seem relevant here given that the piecewise constant intensities model is parametric.

An EM algorithm is used to maximize the likelihood. Gauss-Hermite quadrature is required to perform the M-step due to the presence of the frailty terms. The authors appear to be basing standard error estimates on the complete data (rather than observed data) likelihood.

The new model is applied to the same data as used in Lindsey and Ryan. In addition, in a simulation it is shown that there is some reduction in bias compared to Lindsey and Ryan's method is the proposed model is correctly specified.

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