An adaptive design for updating the threshold value of a continuous biomarker.

Potential predictive biomarkers are often measured on a continuous scale, but in practice, a threshold value to divide the patient population into biomarker 'positive' and 'negative' is desirable. Early phase clinical trials are increasingly using biomarkers for patient selection, but at this stage, it is likely that little will be known about the relationship between the biomarker and the treatment outcome. We describe a single-arm trial design with adaptive enrichment, which can increase power to demonstrate efficacy within a patient subpopulation, the parameters of which are also estimated. Our design enables us to learn about the biomarker and optimally adjust the threshold during the study, using a combination of generalised linear modelling and Bayesian prediction. At the final analysis, a binomial exact test is carried out, allowing the hypothesis that 'no population subset exists in which the novel treatment has a desirable response rate' to be tested. Through extensive simulations, we are able to show increased power over fixed threshold methods in many situations without increasing the type-I error rate. We also show that estimates of the threshold, which defines the population subset, are unbiased and often more precise than those from fixed threshold studies. We provide an example of the method applied (retrospectively) to publically available data from a study of the use of tamoxifen after mastectomy by the German Breast Study Group, where progesterone receptor is the biomarker of interest. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Incorporating Functional Genomic Information in Genetic Association Studies Using an Empirical Bayes Approach.

There is a large amount of functional genetic data available, which can be used to inform fine-mapping association studies (in diseases with well-characterised disease pathways). Single nucleotide polymorphism (SNP) prioritization via Bayes factors is attractive because prior information can inform the effect size or the prior probability of causal association. This approach requires the specification of the effect size. If the information needed to estimate a priori the probability density for the effect sizes for causal SNPs in a genomic region isn't consistent or isn't available, then specifying a prior variance for the effect sizes is challenging. We propose both an empirical method to estimate this prior variance, and a coherent approach to using SNP-level functional data, to inform the prior probability of causal association. Through simulation we show that when ranking SNPs by our empirical Bayes factor in a fine-mapping study, the causal SNP rank is generally as high or higher than the rank using Bayes factors with other plausible values of the prior variance. Importantly, we also show that assigning SNP-specific prior probabilities of association based on expert prior functional knowledge of the disease mechanism can lead to improved causal SNPs ranks compared to ranking with identical prior probabilities of association. We demonstrate the use of our methods by applying the methods to the fine mapping of the CASP8 region of chromosome 2 using genotype data from the Collaborative Oncological Gene-Environment Study (COGS) Consortium. The data we analysed included approximately 46,000 breast cancer case and 43,000 healthy control samples.

Novel bayes factors that capture expert uncertainty in prior density specification in genetic association studies.

Bayes factors (BFs) are becoming increasingly important tools in genetic association studies, partly because they provide a natural framework for including prior information. The Wakefield BF (WBF) approximation is easy to calculate and assumes a normal prior on the log odds ratio (logOR) with a mean of zero. However, the prior variance (W) must be specified. Because of the potentially high sensitivity of the WBF to the choice of W, we propose several new BF approximations with logOR ∼N(0,W), but allow W to take a probability distribution rather than a fixed value. We provide several prior distributions for W which lead to BFs that can be calculated easily in freely available software packages. These priors allow a wide range of densities for W and provide considerable flexibility. We examine some properties of the priors and BFs and show how to determine the most appropriate prior based on elicited quantiles of the prior odds ratio (OR). We show by simulation that our novel BFs have superior true-positive rates at low false-positive rates compared to those from both P-value and WBF analyses across a range of sample sizes and ORs. We give an example of utilizing our BFs to fine-map the CASP8 region using genotype data on approximately 46,000 breast cancer case and 43,000 healthy control samples from the Collaborative Oncological Gene-environment Study (COGS) Consortium, and compare the single-nucleotide polymorphism ranks to those obtained using WBFs and P-values from univariate logistic regression.