Semi-parametric and non-parametric methods for clinical trials with incomplete data

Peter C. O'Brien, David Zhang, Kent R. Bailey

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Last observation carried forward (LOCF) and analysis using only data from subjects who complete a trial (Completers) are commonly used techniques for analysing data in clinical trials with incomplete data when the endpoint is change from baseline at last scheduled visit. We propose two alternative methods. The semi-parametric method, which cumulates changes observed between consecutive time points, is conceptually similar to the familiar life-table method and corresponding Kaplan-Meier estimation when the primary endpoint is time to event. A non-parametric analogue of LOCF is obtained by carrying forward, not the observed value, but the rank of the change from baseline at the last observation for each subject. We refer to this method as the LRCF method. Both procedures retain the simplicity of LOCF and Completers analyses and, like these methods, do not require data imputation or modelling assumptions. In the absence of any incomplete data they reduce to the usual two-sample tests. In simulations intended to reflect chronic diseases that one might encounter in practice, LOCF was observed to produce markedly biased estimates and markedly inflated type I error rates when censoring was unequal in the two treatment arms. These problems did not arise with the Completers, Cumulative Change, or LRCF methods. Cumulative Change and LRCF were more powerful than Completers, and the Cumulative Change test provided more efficient estimates than the Completers analysis, in all simulations. We conclude that the Cumulative Change and LRCF methods are preferable to LOCF and Completers analyses. Mixed model repeated measures (MMRM) performed similarly to Cumulative Change and LRCF and makes somewhat less restrictive assumptions about missingness mechanisms, so that it is also a reasonable alternative to LOCF and Completers analyses.

Original languageEnglish (US)
Pages (from-to)341-358
Number of pages18
JournalStatistics in Medicine
Issue number3
StatePublished - Feb 15 2005


  • Clinical trials
  • Missing data
  • Non-parametric
  • Semi-parametric

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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