Modeling and prediction of advanced prostate cancer

Abstract

Background: Prostate cancer (PCa) is the most commonly diagnosed cancer and second leading cause of cancer-related deaths for men in Western countries. The advanced form of the disease is life-threatening with few options for curative therapies. The development of novel therapeutic alternatives would greatly benefit from a more comprehensive and tailored mathematical and statistical methodology. In particular, statistical inference of treatment effects and the prediction of time-dependent effects in both preclinical and clinical studies remains a challenging yet interesting opportunity for applied mathematicians. Such methods are likely to improve the reproducibility and translatability of results and offer possibility for novel holistic insights into disease progression, diagnosis, and prognosis.

Methods: Several novel statistical and mathematical techniques were developed over the course of this thesis work for the in vivo modeling of PCa treatment responses. A matching-based, blinded randomized allocation procedure for preclinical experiments was developed that provides assistance for the statistical design of animal intervention studies, e.g., through power analysis and accounting for the stratification of individuals. For the post-intervention testing of treatment effects, two novel mixed-effects models were developed that aim to address the characteristic challenges of preclinical longitudinal experiments, including the heterogeneous response profiles observed in animal studies. Subsequently, a Finnish clinical PCa hospital registry cohort was inspected with a strong emphasis on prostate-specific antigen (PSA), the most commonly used PCa marker. After exploring the PSA trends using penalized splines, a generalized mixed-effects prediction model was implemented with a focus on the ultra-sensitive range of the PSA assay. Finally, for metastatic, aggressive PCa, an ensemble Cox regression methodology was developed for overall survival prediction in the DREAM 9.5 mCRPC Challenge based on open datasets from controlled clinical trials.

Results: The advantages of the improved experimental design and two proposed statistical models were demonstrated in terms of both increased statistical power and accuracy in simulated and real preclinical testing settings. Penalized regression models applied to the clinical patient datasets support the use of PSA in the ultra-sensitive range together with a model for relapse prediction. Furthermore, the novel ensemble-based Cox regression model that was developed for the overall survival prediction in advanced PCa outperformed the state-of-the-art benchmark and all other models submitted to the Challenge and provided novel predictors of disease progression and treatment responses.

Conclusions: The methods and results provide preclinical researchers and clinicians with novel tools for comprehensive modeling and prediction of PCa. All methodology is available as open source R statistical software packages and/or web-based graphical user interfaces.