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

Sharon X Lin,Peter W F Smith,Leanne Morrison,Lucy Yardley,Charlie Hargood,Mark Weal

doi:10.1111/bmsp.12071

Abstract

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.

Highlights

N-of-1 study designs involve the collection and analysis of repeated measures of an individual unit using an intervention and not using an intervention
We compare the properties of the bootstrap tests to those of a Wald test for coefficients estimated by using generalized least squares (GLS) with restricted maximum likelihood (REML)
For Design 2 (D2) with an autocorrelation value of .2 and normal errors, to achieve a power of .8 for the parametric bootstrap test a b-value >1.5 is required; for a larger autocorrelation value, .5 or .7, a b of 2.5 or 3 is required (Table A3). These results suggest the power under D2 is low

Summary

Introduction

N-of-1 study designs involve the collection and analysis of repeated measures of an individual unit using an intervention and not using an intervention. DOI:10.1111/bmsp.12071 between periods that are subject to no interventions (phase A) and those that are subject to interventions (phase B) By and large these methods can be divided into two categories: non-regression-based (Borckardt, Nash, Murphy, Moore, Shaw, & O’Neil, 2008; Nourbakhsh & Ottenbacher, 1994; Parker, Vannest, & Brown, 2009); and regression-based (Huitema & McKean, 2000; McKnight, McKean, & Huitema, 2000). The former methods are simpler and easier to implement without formal statistical modelling, while the latter are based on regression theory, where parameters are formally estimated.

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