Heterogeneity in survival analysis

I discuss the impact of individual heterogeneity in survival analysis. It is well known that this phenomenon may distort what is observed. A general class of mixing (or frailty) distributions is applied, extending a model of Hougaard. The extension allows part of the population to be non-susceptible, and contains the traditional gamma distribution as a special case. I consider the mixing of both a constant and a Weibull individual rate, and also discuss the comparison of rates from two populations. A number of practical examples are mentioned. Finally, I analyse two data sets, the main one containing data from the Norwegian Cancer Registry on the survival of breast cancer patients. The statistical analysis is of necessity speculative, but may still provide some insight.