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Large scale electronic health records (EHRs) present an opportunity to quickly identify suitable individuals in order to directly invite them to participate in an observational study. EHRs can contain data from millions of individuals, raising the question of how to optimally select a cohort of size n from a larger pool of size N. In this paper we propose a simple selective recruitment protocol that selects a cohort in which covariates of interest tend to have a uniform distribution. We show that selectively recruited cohorts potentially offer greater statistical power and more accurate parameter estimates than randomly selected cohorts. Our protocol can be applied to studies with multiple categorical and continuous covariates. We apply our protocol to a numerically simulated prospective observational study using an EHR database of stable acute coronary disease patients from 82,089 individuals in the U.K. Selective recruitment designs require a smaller sample size, leading to more efficient and cost-effective studies.

Motivation: Epigenetic heterogeneity within a tumour can play an important role in tumour evolution and the emergence of resistance to treatment. It is increasingly recognised that the study of DNA methylation (DNAm) patterns along the genome -- so-called `epialleles' -- offers greater insight into epigenetic dynamics than conventional analyses which examine DNAm marks individually. Results: We have developed a Bayesian model to infer which epialleles are present in multiple regions of the same tumour. We apply our method to reduced representation bisulfite sequencing (RRBS) data from multiple regions of one lung cancer tumour and a matched normal sample. The model borrows information from all tumour regions to leverage greater statistical power. The total number of epialleles, the epiallele DNAm patterns, and a noise hyperparameter are all automatically inferred from the data. Uncertainty as to which epiallele an observed sequencing read originated from is explicitly incorporated by marginalising over the appropriate posterior densities. The degree to which tumour samples are contaminated with normal tissue can be estimated and corrected for. By tracing the distribution of epialleles throughout the tumour we can infer the phylogenetic history of the tumour, identify epialleles that differ between normal and cancer tissue, and define a measure of global epigenetic disorder.

Selective recruitment designs preferentially recruit individuals that are estimated to be statistically informative onto a clinical trial. Individuals that are expected to contribute less information have a lower probability of recruitment. Furthermore, in an information-adaptive design recruits are allocated to treatment arms in a manner that maximises information gain. The informativeness of an individual depends on their covariate (or biomarker) values and how information is defined is a critical element of information-adaptive designs. In this paper we define and evaluate four different methods for quantifying statistical information. Using both experimental data and numerical simulations we show that selective recruitment designs can offer a substantial increase in statistical power compared to randomised designs. In trials without selective recruitment we find that allocating individuals to treatment arms according to information-adaptive protocols also leads to an increase in statistical power. Consequently, selective recruitment designs can potentially achieve successful trials using fewer recruits thereby offering economic and ethical advantages.

We propose a novel adaptive design for clinical trials with time-to-event outcomes and covariates (which may consist of or include biomarkers). Our method is based on the expected entropy of the posterior distribution of a proportional hazards model. The expected entropy is evaluated as a function of a patient's covariates, and the information gained due to a patient is defined as the decrease in the corresponding entropy. Candidate patients are only recruited onto the trial if they are likely to provide sufficient information. Patients with covariates that are deemed uninformative are filtered out. A special case is where all patients are recruited, and we determine the optimal treatment arm allocation. This adaptive design has the advantage of potentially elucidating the relationship between covariates, treatments, and survival probabilities using fewer patients, albeit at the cost of rejecting some candidates. We assess the performance of our adaptive design using data from the German Breast Cancer Study group and numerical simulations of a biomarker validation trial.

The analysis of high dimensional survival data is challenging, primarily due to the problem of overfitting which occurs when spurious relationships are inferred from data that subsequently fail to exist in test data. Here we propose a novel method of extracting a low dimensional representation of covariates in survival data by combining the popular Gaussian Process Latent Variable Model (GPLVM) with a Weibull Proportional Hazards Model (WPHM). The combined model offers a flexible non-linear probabilistic method of detecting and extracting any intrinsic low dimensional structure from high dimensional data. By reducing the covariate dimension we aim to diminish the risk of overfitting and increase the robustness and accuracy with which we infer relationships between covariates and survival outcomes. In addition, we can simultaneously combine information from multiple data sources by expressing multiple datasets in terms of the same low dimensional space. We present results from several simulation studies that illustrate a reduction in overfitting and an increase in predictive performance, as well as successful detection of intrinsic dimensionality. We provide evidence that it is advantageous to combine dimensionality reduction with survival outcomes rather than performing unsupervised dimensionality reduction on its own. Finally, we use our model to analyse experimental gene expression data and detect and extract a low dimensional representation that allows us to distinguish high and low risk groups with superior accuracy compared to doing regression on the original high dimensional data.

We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates are regarded as the `inputs' and the event times are the `outputs'. This allows for highly flexible inference of non-linear relationships between covariates and event times. Many existing methods, such as the ubiquitous Cox proportional hazards model, focus primarily on the hazard rate which is typically assumed to take some parametric or semi-parametric form. Our proposed model belongs to the class of accelerated failure time models where we focus on directly characterising the relationship between covariates and event times without any explicit assumptions on what form the hazard rates take. It is straightforward to include various types and combinations of censored and truncated observations. We apply our approach to both simulated and experimental data. We then apply multiple output GP regression, which can handle multiple potentially correlated outputs for each input, to competing risks survival data where multiple event types can occur. By tuning one of the model parameters we can control the extent to which the multiple outputs (the time-to-event for each risk) are dependent thus allowing the specification of correlated risks. Simulation studies suggest that in some cases assuming dependence can lead to more accurate predictions.