Fertility Biomarkers Predict Differential Survival in a Long-Term Follow-Up Study of Male Fertility: Capturing and Treating Heterogeneity

Ronny Westerman, University of Marburg
Katharina Pyka, University of Marburg
Martina Schmidt-Stolte, University of Marburg
Markus Thiede, University of Marburg
Sabine Groos, University of Marburg
Walter Krause, University of Marburg

We found that low sperm counts and other impaired biomarkers predict differences in survival among otherwise healthy subjects in a long-term fertility follow-up. Here we report on possible hidden effects of the heterogeneous decomposition of the sample. Thus, the differences in lifespan for men with a lower sperm concentration might be an artifact because of the heterogeneity. A convenient way to demonstrate the intensity of hetereogeneity on the population hazard is to use frailty models regarding the individual frailty. Heterogeneity can be indicated by the variance of frailty. If sigma square = 0 indicates no heterogeneity, with increasing value of sigma square, the effect of heterogeneity becomes more relevant and leads to an unimodal shape of the hazard function. The final intention of the research is the estimation of the survival function for both subgroups under consideration of different age-structure and the hidden effects of co-morbidity regarding to the diseases of the genitourinary system.