Semiparametric Marshall-Olkin models applied to the occurrence of metastases at multiple sites after breast cancer.

It is noted that the bivariate exponential distribution introduced by Marshall and Olkin (1967, Journal of the American Statistical Association 62, 30-40) allows semiparametric generalizations along the lines of the Cox regression model for survival data. Partial likelihoods for the regression parameters may be derived (here illustrated by the use of the profile likelihood construction), and in most cases standard Cox regression model software may be applied for the analysis with minor modification of the input files. The study was initiated by data on occurrence of metastases from breast cancer. Metastases may occur at various sites, here grouped into ten categories, and simultaneous as well as consecutive occurrence at several sites in common. It is desired to identify and compare risk factors for development of metastases at each site, and we illustrate on some of these data that the above models may be useful for this purpose.