Individual (N-of-1) trials can be combined to give population comparative treatment effect estimates: methodologic considerations

Abstract

Objective: To compare different statistical models for combining N-of-1 trials to estimate a population treatment effect.

Study design and setting: Data from a published series of N-of-1 trials comparing amitriptyline (AMT) therapy and combination treatment (AMT+fluoxetine [FL]) were analyzed to compare summary and individual participant data meta-analysis; repeated-measure models; Bayesian hierarchical models; and single-period, single-pair, and averaged outcome crossover models.

Results: The best-fitting model included a random intercept (response on AMT) and fixed treatment effect (added FL). Results supported a common, uncorrelated within-patient covariance structure that is equal between treatments and across patients. Assuming unequal within-patient variances, a random-effect model was favored. Bayesian hierarchical models improved precision and were highly sensitive to within-patient variance priors.

Conclusion: Optimal models for combining N-of-1 trials need to consider goals, data sources, and relative within- and between-patient variances. Without sufficient patients, between-patient variation will be hard to explain with covariates. N-of-1 data with few observations per patients may not support models with heterogeneous within-patient variation. With common variances, models appear robust. Bayesian models may improve parameter estimation but are sensitive to prior assumptions about variance components. With limited resources, improving within-patient precision must be balanced by increased participants to explain population variation.

Figure 1

Density plots of the prior and posterior distributions for the population level parameters used for analyses in Table 2. Graphs represent estimates for the mean parameters (α and β) and 3 variance parameters, within (σ_i²) and between (${\tau }_{\alpha }^2$ and ${\tau }_{\beta }^2$) patients. Each plot shows the weakly informative priors given in footnotes 2 and 4 of Table 2, the empirical posterior from the MCMC analysis and the approximated normal (for means) or inverse gamma (for variances) distributions found by matching means and variances.