Sankhya: The Indian Journal of Statistics

2007, Volume 69, Pt. 3, 494--513

Semiparametric Estimation of Hazard Function for Cancer Patients

Ivana Horov\'{a}, Zden\v{e}k Posp\'{i}\v{s}il and Ji\v{r}\'{i} Zelinka, Masaryk University, Brno, Czech Republic

SUMMARY. The main aim of this paper is to model and study the survival of cancer patients. First, a parametric form of hazard function is proposed. This model results from a recent model of cancer cells population dynamics given in the paper Kozusko and Bajzer (Mathematical Biosciences, 2003) and depends on several parameters. The method of estimating such parameters is described as well. On the other hand, the nonparametric methods seem to be appropriate for survival data. Among them, the methods of kernel estimation of hazard functions are very effective ones. But there is a serious difficulty with them, namely the choice of a smoothing parameter. We propose an alternative method for the bandwidth selection based on the aforementioned parametric method. The theory developed is applied to four data sets.

AMS (2000) subject classification. Primary 62F99, 62G99, 62P10.

Key words and phrases. Hazard function, kernel estimation, Gompertzian growth, parameter estimation.

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