Bayesian statistics in oncology: a guide for the clinical investigator

The rise of evidence-based medicine as well as important progress in statistical methods and computational power have led to a second birth of the >200-year-old Bayesian framework. The use of Bayesian techniques, in particular in the design and interpretation of clinical trials, offers several substantial advantages over the classical statistical approach. First, in contrast to classical statistics, Bayesian analysis allows a direct statement regarding the probability that a treatment was beneficial. Second, Bayesian statistics allow the researcher to incorporate any prior information in the analysis of the experimental results. Third, Bayesian methods can efficiently handle complex statistical models, which are suited for advanced clinical trial designs. Finally, Bayesian statistics encourage a thorough consideration and presentation of the assumptions underlying an analysis, which enables the reader to fully appraise the authors' conclusions. Both Bayesian and classical statistics have their respective strengths and limitations and should be viewed as being complementary to each other; we do not attempt to make a head-to-head comparison, as this is beyond the scope of the present review. Rather, the objective of the present article is to provide a nonmathematical, reader-friendly overview of the current practice of Bayesian statistics coupled with numerous intuitive examples from the field of oncology. It is hoped that this educational review will be a useful resource to the oncologist and result in a better understanding of the scope, strengths, and limitations of the Bayesian approach.

Male reproductive pattern in a polygynous ungulate with a slow life-history: the role of age, social status and alternative mating tactics

According to life-history theory age-dependent investments into reproduction are thought to co-vary with survival and growth of animals. In polygynous species, in which size is an important determinant of reproductive success, male reproduction via alternative mating tactics at young age are consequently expected to be the less frequent in species with higher survival. We tested this hypothesis in male Alpine ibex (Capra ibex), a highly sexually dimorphic mountain ungulate whose males have been reported to exhibit extremely high adult survival rates. Using data from two offspring cohorts in a population in the Swiss Alps, the effects of age, dominance and mating tactic on the likelihood of paternity were inferred within a Bayesian framework. In accordance with our hypothesis, reproductive success in male Alpine ibex was heavily biased towards older, dominant males that monopolized access to receptive females by adopting the 'tending' tactic, while success among young, subordinate males via the sneaking tactic 'coursing' was in general low and rare. In addition, we detected a high reproductive skew in male Alpine ibex, suggesting a large opportunity for selection. Compared with other ungulates with higher mortality rates, reproduction among young male Alpine ibex was much lower and more sporadic. Consistent with that, further examinations on the species level indicated that in polygynous ungulates the significance of early reproduction appears to decrease with increasing survival. Overall, this study supports the theory that survival prospects of males modulate the investments into reproduction via alternative mating tactics early in life. In the case of male Alpine ibex, the results indicate that their life-history strategy targets for long life, slow and prolonged growth and late reproduction.

Colonization history of the Swiss Rhine basin by the bullhead (Cottus gobio): inference under a Bayesian spatially explicit framework

The present distribution of freshwater fish in the Alpine region has been strongly affected by colonization events occurring after the last glacial maximum (LGM), some 20,000 years ago. We use here a spatially explicit simulation framework to model and better understand their colonization dynamics in the Swiss Rhine basin. This approach is applied to the European bullhead (Cottus gobio), which is an ideal model organism to study fish past demographic processes since it has not been managed by humans. The molecular diversity of eight sampled populations is simulated and compared to observed data at six microsatellite loci under an approximate Bayesian computation framework to estimate the parameters of the colonization process. Our demographic estimates fit well with current knowledge about the biology of this species, but they suggest that the Swiss Rhine basin was colonized very recently, after the Younger Dryas some 6600 years ago. We discuss the implication of this result, as well as the strengths and limits of the spatially explicit approach coupled to the approximate Bayesian computation framework.