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Br J Math Stat Psychol. 2016 Nov;69(3):276-290. doi: 10.1111/bmsp.12071.

Properties of bootstrap tests for N-of-1 studies.

Author information

Southampton Statistical Sciences Research Institute (S3RI), University of Southampton, UK.
National Institute for Health Research (NIHR) Wessex Collaboration for Leadership and Research in Health Care (CLAHRC), University of Southampton, UK.
Academic Unit of Psychology, University of Southampton, UK.
Southampton Statistical Sciences Research Institute (S3RI), University of Southampton, UK.
Electronics and Computer Science, University of Southampton, UK.


N-of-1 study designs involve the collection and analysis of repeated measures data from an individual not using an intervention and using an intervention. This study explores the use of semi-parametric and parametric bootstrap tests in the analysis of N-of-1 studies under a single time series framework in the presence of autocorrelation. When the Type I error rates of bootstrap tests are compared to Wald tests, our results show that the bootstrap tests have more desirable properties. We compare the results for normally distributed errors with those for contaminated normally distributed errors and find that, except when there is relatively large autocorrelation, there is little difference between the power of the parametric and semi-parametric bootstrap tests. We also experiment with two intervention designs: ABAB and AB, and show the ABAB design has more power. The results provide guidelines for designing N-of-1 studies, in the sense of how many observations and how many intervention changes are needed to achieve a certain level of power and which test should be performed.


N-of-1 studies; Type I error rate; Wald test; power; semi- and parametric bootstrapping

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