  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.
