Statistical Methods for Cancer Biomarkers

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Project Summary/Abstract Individualized prognostic models abound in clinical biomedicine. They are used to make predictions of the future, derived from individual patient characteristics, and will play increasingly important roles in the move towards per- sonalized medicine. They can be used in the settings of early detection and screening, or after a cancer diagnosis to help decide on treatment, or after treatment to monitor for progression and recurrence. While some models are well established, they likely have the potential to be improved through the use of additional variables. Larger and better quality training datasets and improved statistical models and methods will improve their accuracy, but the potential for largest improvement is through new biomarkers. Since cancer is a heterogenous disease with multifactorial etiology, many clinical and molecular factors will likely aid in predicting the future for a patient, and would be candidates for inclusion in a new model. The challenge we will address in this research is how to de- velop a new model that both includes the new biomarkers and makes use of the knowledge implicit in the existing models, when the datasets that are available containing the new biomarkers are only of modest size. To develop a new model from a new dataset of modest size that contains the new biomarkers, the typical approach will be to analyze these data, as a separate entity, and build a model based on that analysis. However, this approach does not utilize the external information from an established model. Such external information will often be available, however it may come in the form of regression coefficients, odds ratios or other summary statistics for a subset of the variables, or in the form of a prediction from an online calculator. We will consider a variety of statistical methods for incorporating the external information. The methods we propose to develop are motivated by specific head and neck cancer and prostate cancer stud- ies, but have much broader applicability to other cancers and other diseases. In the head and neck study the additional new biomarkers to be incorporated in to the prediction models are HPV status and other molecular biomarkers. For the prostate cancer risk prediction model the new bimarkers are based on proteins measured from urine. The research is separated into three specific aims. The first aim considers the situation in which there is a modest sized new dataset, that includes a new biomarker, and there is an existing prediction model, that does not include this new biomarker. The external information comes in the form of estimates and standard errors of regression parameters from an established prediction model based on a subset of the predictors. We propose a number of different frequentist and Bayesian methods, in which the information on the lower dimensional parameter space is used via inequality constraints and Lagrange multipliers, through prior distributions and through a novel transformation approach. The properties of the approaches will be compared in the situation of continuous and binary response variables. In the second aim the external information comes in the form of a prediction from one or more calculators, and specifically the predictions for each individual in our own data are used. We include in this aim consideration of the situation where there are multiple established prediction models and where the outcome variable is the survival time. We consider different possible methodological approaches, one is an adaptation of the methods in the first aim, a second very general method is to incorporate synthetic data generated from the existing models and a third general method uses weights that enable the new biomarker to have a stronger role for observations that were were not predicted well by the existing models. In the third aim we consider the situation where there may be a panel of new biomarkers, and there is also knowledge about the unadjusted association between each new biomarker and the outcome variable, as might be available from a genome-wide association study. A novel nonparametric Bayes approach is proposed to solve this problem.