Counting process models for life history data: A review. (English) Zbl 0584.62176

Andersen, Per Kragh; Borgan, Ørnulf

Scand. J. Stat., Theory Appl. 12, 97-158 (1985).

A survey is given of the development of statistical models for life history data based on counting processes. This development was initiated by O. O. Aalen, Statistical inference for a family of counting processes. Ph. D. Diss., Dept. Stat., Univ. Calif., Berkeley (1975); see also Ann. Stat. 6, 701-726 (1978; Zbl 0389.62025). We review non-parametric estimation and testing procedures for counting process intensities, kernel function smoothing, parametric inference and various regression techniques, including a generalization of the Cox regression model for censored survival data.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
62G05	Nonparametric estimation
62G10	Nonparametric hypothesis testing
62M02	Markov processes: hypothesis testing
62M05	Markov processes: estimation; hidden Markov models

Keywords:

competing risks; Nelson-Aalen estimator; k-sample problem; Markov chain; martingale; multiplicative intensity model; multivariate counting process; stochastic integral; survival analysis; survey; life history data; counting processes; intensities; kernel function smoothing; generalization of the Cox regression model; censored survival data