3 years ago

Partial factorial trials: comparing methods for statistical analysis and economic evaluation

Richard W. Morris, Alastair M. Gray, David W. Murray, Helen A. Dakin, Graeme S. MacLennan



Partial factorial trials compare two or more pairs of treatments on overlapping patient groups, randomising some (but not all) patients to more than one comparison. The aims of this research were to compare different methods for conducting and analysing economic evaluations on partial factorial trials and assess the implications of considering factors simultaneously rather than drawing independent conclusions about each comparison.


We estimated total costs and quality-adjusted life years (QALYs) within 10 years of surgery for 2252 patients in the Knee Arthroplasty Trial who were randomised to one or more comparisons of different surgical types. We compared three analytical methods: an “at-the-margins” analysis including all patients randomised to each comparison (assuming no interaction); an “inside-the-table” analysis that included interactions but focused on those patients randomised to two comparisons; and a Bayesian vetted bootstrap, which used results from patients randomised to one comparison as priors when estimating outcomes for patients randomised to two comparisons. Outcomes comprised incremental costs, QALYs and net benefits.


Qualitative interactions were observed for costs, QALYs and net benefits. Bayesian bootstrapping generally produced smaller standard errors than inside-the-table analysis and gave conclusions that were consistent with at-the-margins analysis, while allowing for these interactions. By contrast, inside-the-table gave different conclusions about which intervention had the highest net benefits compared with other analyses.


All analyses of partial factorial trials should explore interactions and assess whether results are sensitive to assumptions about interactions, either as a primary analysis or as a sensitivity analysis. For partial factorial trials closely mirroring routine clinical practice, at-the-margins analysis may provide a reasonable estimate of average costs and benefits for the whole trial population, even in the presence of interactions. However, such conclusions will be misleading if there are large interactions or if the proportion of patients allocated to different treatments differs markedly from what occurs in clinical practice. The Bayesian bootstrap provides an alternative to at-the-margins analysis for analysing clinical or economic endpoints from partial factorial trials, which allows for interactions while making use of the whole sample. The same techniques could be applied to analyses of clinical endpoints.

Trial registration

ISRCTN, ISRCTN45837371. Registered on 25 April 2003.

Publisher URL: https://link.springer.com/article/10.1186/s13063-018-2818-x

DOI: 10.1186/s13063-018-2818-x

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