Title: Bayesian Modeling in Personalized Medicine with Applications to N-of-1 Trials
Description: The ultimate goal of personalized or precision medicine is to identify the best treatment for each patient. An N-of-1 trial is a multiple-period crossover trial performed within a single individual, which focuses on individual outcome instead of population or group mean responses. As in a conventional crossover trial, it is critical to understand carryover effects of the treatment in an N-of-1 trial, especially in situations where there are no washout periods between treatment periods and high volume of measurements are made during the study. Existing statistical methods for analyzing N-of-1 trials include nonparametric tests, mixed effect models and autoregressive models. These methods may fail to simultaneously handle measurements autocorrelation and adjust for potential carryover effects. Distributed lag model is a regression model that uses lagged predictors to model the lag structure of exposure effects. In the dissertation, we first introduce a novel Bayesian distributed lag model that facilitates the estimation of carryover effects for single N-of-1 trial, while accounting for temporal correlations using an autoregressive model.

In the second part, we extend the single N-of-1 trial model to multiple N-of-1 trials scenarios. In the third part, we again focus on single N-of-1 trials. But instead of modeling comparison with one treatment and one placebo (or active control), multiple treatments and one placebo (or active control) is considered. In the first part, we propose a Bayesian distributed lag model with autocorrelated errors (BDLM-AR) that integrate prior knowledge on the shape of distributed lag coefficients and explicitly model the magnitude and duration of carryover effect. Theoretically, we show the connection between the proposed prior structure in BDLM-AR and frequentist regularization approaches. Simulation studies were conducted to compare the performance of our proposed BDLM-AR model with other methods and the proposed model is shown to have better performance in estimating total treatment effect, carryover effect and the whole treatment effect coefficient curve under most of the simulation scenarios.

Data from two patients in the light therapy study was utilized to illustrate our method. In the second part, we extend the single N-of-1 trial model to multiple N-of-1 trials model and focus on estimating population level treatment effect and carryover effect. A Bayesian hierarchical distributed lag model (BHDLM-AR) is proposed to model the nested structure of multiple N-of-1 trials within the same study. The Bayesian hierarchical structure also improve estimates for individual level parameters by borrowing strength from the N-of-1 trials of others. We show through simulation studies that BHDLM-AR model has best average performance in terms of estimating both population level and individual level parameters. The light therapy study is revisited and we applied the proposed model to all patients’ data. In the third part, we extend BDLM-AR model to multiple treatments and one placebo (or active control) scenario. We designed prior precision matrix on each treatment. We demonstrated the application of the proposed method using a hypertension study, where multiple guideline recommended medications were involved in each single N-of-1 trial.