Die Messung des Einflusses von Heterogenität bei der Überlebenszeitanalyse von fertilen und subfertilen Männern

The present thesis will discuss the effect of unobserved hetero-geneity in the context of modelling the association between fer-tility and the post-reproductive life span of males. Unobserved heterogeneity must eventually be taken into account for successive data analyses and might be useful for the explana-tion of unexpected results, or for alternative interpretations. In the worst case one can detect the mortality cross-over for the hazard functions. The influence of unobserved covariates in a proportional hazard model can be treated by a positive latent random variable, the frailty . The frailty concept implies a mixture of individuals in populations varying in their susceptibility to common risks. In homogeneous populations the frailty variance is small, the value for the frailty Z converges to 1. But when increases the frailty variable Z becomes more relevant for affecting the individual hazard intensively by unob-served heterogeneity. The unexplained heterogeneity can be unshared or shared among individuals. If the individuals or groups of individuals share, then the frailty the individuals risk is common to all group members. The frailty concept requires, for the parametric paradigm, the specification of one statistical distribution. The most popular parametric specification for the frailty variance follows the gamma distribution. This is one of the most flexible statistical distributions and can be used as an approximation for any other parametric version. It must be mentioned, that there are no bio-logical or empirical arguments justifying the use of the gamma distribution, its simply computational or mathematical conven-ience that determines the preference of any parametric version for the frailty. The dataset contains 1408 patients born before 1942 who at-tended the fertility and sterility office of the department of an-drology at Marburg University Hospital for semen analysis be-tween 1949 and 1985. The assignment into subgroups was carried out by the analysis of semen samples on the basis of medical records of sperm con-centrations according to the WHO (2010) classification: to infer-tile at sperm concentrations of <15*106 per mL, and to fertile men at ≥15*106 per mL. The patients can also be classified into three groups: azoo-spermics, with none sperms in ejaculate; in oligozoospermics, with less than 15 Mio. per mL but more than zero sperms in ejaculate; and in normozoospermics with more than 15 Mio. sperms per mL. Regarding to the findings of the statistical analysis, we conclude that the fertility status of males is not a powerful predictor for differences in survival. Using numerical and graphical tests we showed, that the propor-tional hazard assumption is not violated in any PH-Model. Hence the impact of the frailty variance could not be verified in the unshared parametric regression models. In general, frailty models, as well as all other parametric models are afflicted by the problem of finding the right specification for the most informative statistical distribution. In spite of these drawbacks frailty models perform as a sophisti-cated tool for the analysis of event history data, especially in epidemiology, demography, biology and other life sciences. They can be easily used as alternatives to the traditional survival models.