A framework for sequential monitoring of individual N-of-1 trials and combining results across a series of sequentially monitored N-of-1 trials.

Background: N-of-1 trials compare two or more treatment options for a single participant. These trials have been used to study options for chronic conditions such as arthritis and attention deficit hyperactivity disorder. In addition, they have been suggested as a means to study interventions in rare populations that may not be tractable to include in standard clinical trials, such as treatment options for HIV-positive patients in need of organ transplant. Sequential monitoring of accruing data has been well-studied in traditional clinical trials, but these methods have not yet been implemented in N-of-1 trials. However, the option to validly stop an N-of-1 trial early could deliver faster decisions that could directly improve the patient's health.

Methods: In this work, we propose and evaluate a framework to (1) facilitate sequential monitoring in individual N-of-1 trials with a continuous outcome and (2) combine results across a series of already-completed sequentially monitored N-of-1 trials. By employing the block structure common to N-of-1 trials, we suggest that existing approaches to sequential monitoring may be employed when data from one N-of-1 trial are analyzed with a linear mixed-effects model. To combine results across a series of already-completed sequentially monitored N-of-1 trials, we propose combining the naive estimates from constituent trials in a random-effects model with inverse-variance weighting. We evaluate these proposals via simulation.

Results: We find that type 1 error can be substantially inflated for N-of-1 trials with a small number of planned blocks but can reach the nominal rate for trials with more planned blocks or those with larger numbers of periods per block or by using a $t$-value correction. For those settings with acceptable type 1 error, sequential monitoring results in similar power and on average earlier stopping compared with trials with no sequential monitoring. And, as expected, we find that including a larger number of constituent trials in a series reduces the mean-squared error of the combined point estimator.

Conclusion: Under suitable design considerations, our proposed framework for sequential monitoring can support clinicians in providing important decisions earlier, on average, for patients engaged in N-of-1 trials.