Analysis of N-of-1 trials using Bayesian distributed lag model with autocorrelated errors

TL;DR

This paper introduces a Bayesian distributed lag model with autocorrelated errors for analyzing N-of-1 trials, effectively estimating carryover effects and improving accuracy over existing methods.

Contribution

It presents a novel Bayesian approach that accounts for temporal correlations and collinearity in N-of-1 trials, enhancing carryover effect estimation.

Findings

Reduces root mean squared error in carryover effect estimation

Performs well in simulation compared to existing methods

Applied successfully to light therapy data in cancer survivors

Abstract

An N-of-1 trial is a multi-period crossover trial performed in a single individual, with a primary goal to estimate treatment effect on the individual instead of population-level 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 when no washout periods between treatment periods are instituted to reduce trial duration. To deal with this issue in situations where high volume of measurements is made during the study, we introduce a novel Bayesian distributed lag model that facilitates the estimation of carryover effects, while accounting for temporal correlations using an autoregressive model. Specifically, we propose a prior variance-covariance structure on the lag coefficients to address collinearity caused by the fact that treatment exposures are typically identical on successive days. A connection between the proposed Bayesian model and penalized regression is noted. Simulation results demonstrate that the proposed model substantially reduces the root mean squared error in the estimation of carryover effects and immediate effects when compared to other existing methods, while being comparable in the estimation of the total effects. We also apply the proposed method to assess the extent of carryover effects of light therapies in relieving depressive symptoms in cancer survivors.