I am generally interested in Bayesian inference and computation. Over the years, I have developed Bayesian models and computational methods to address applied problems in a variety of settings. Currently, my research is focused in methodology development for design and analysis of modern clinical trials such as Bayesian adaptive trials.
A few of my recent research projects are showcased below.
Gaussian process regression for estimating the design operating characteristics in clinical trials
More flexible designs that allow for adjustments and early stopping have gained popularity in clinical trials as more efficient and ethical alternatives to the conventional fixed size randomized clinical trials (RCT). Bayesian analysis become specifically attractive in this setting since sequential updating of the results is facilitated under the Bayesian framework. Despite the common use of Bayesian inference in clinical trials, the regulatory and funding agencies mainly rely on frequentist operating characteristics for assessment of trial design. Unlike in RCT, however, the sampling distribution of the test statistic in a Bayesian adaptive trial is not known and therefore analytic forms for the power and false positive rates do not exist. Evaluation of design operating characteristics (DOC), therefore, relies on simulation studies.
Simulation studies for design of Bayesian adaptive trial can be time consuming since the combination of plausible ranges of model parameters (effect size and baseline measure assumptions) together with possible design parameters (efficacy and futility thresholds, sample sizes, frequency of interim looks, etc.) can result in a large number of simulation scenarios. In many cases, a complex trial design and/or models without analytically tractable posteriors involve a significant amount of computation for a single trial simulation which is multiplied by the number of simulation scenarios as well as the number of simulation iterations.
I propose to use techniques commonly used in computer experiments – such as Gaussian process regression – for estimation of DOC based on an initial number of simulations. The goal is to “predict” the sampling distribution of a Bayesian test statistic throughout the parameter space and derive a number of operating characteristics such as power, false positive rate, probability of stopping early for futility, etc.
Use of Historical Individual Patient Data in Analysis of Clinical Trials
Historical data from previous clinical trials, observational studies and health records may be utilized in analysis of clinical trials data to strengthen inference. Under the Bayesian framework incorporation of information obtained from any source other than the current data is facilitated through construction of an informative prior. The existing methodology for defining an informative prior based on historical data relies on measuring similarity to the current data at the study level and does not take advantage of individual patient data (IPD). This paper proposes a family of priors that utilize IPD to strengthen statistical inference. It is demonstrated that the proposed prior construction approach outperforms the existing methods where the historical data are partially exchangeable with the present data. The proposed method is applied to IPD from a set of trials in non-small cell lung cancer.
Sequential Monte Carlo for design of Bayesian adaptive clinical trials
The Bayesian framework facilitates the sequential analysis required in Bayesian adaptive designs by updating the posterior distribution according to the most recently collected data at each interim analysis treating all that came before as the prior. In more complex modelling scenarios where a conjugate prior is not available and analytic updating is not possible, the prior needs to be estimated/approximated at every step. In this paper, I propose using sequential Monte Carlo for updating the samples drawn from the previous step posterior incorporating the last batch of data.