Natural cubic splines for the analysis of Alzheimer's clinical trials

for the Alzheimer's Disease Neuroimaging Initiative

Research output: Contribution to journalArticlepeer-review


Mixed model repeated measures (MMRM) is the most common analysis approach used in clinical trials for Alzheimer's disease and other progressive diseases measured with continuous outcomes over time. The model treats time as a categorical variable, which allows an unconstrained estimate of the mean for each study visit in each randomized group. Categorizing time in this way can be problematic when assessments occur off-schedule, as including off-schedule visits can induce bias, and excluding them ignores valuable information and violates the intention to treat principle. This problem has been exacerbated by clinical trial visits which have been delayed due to the COVID19 pandemic. As an alternative to MMRM, we propose a constrained longitudinal data analysis with natural cubic splines that treats time as continuous and uses test version effects to model the mean over time. Compared to categorical-time models like MMRM and models that assume a proportional treatment effect, the spline model is shown to be more parsimonious and precise in real clinical trial datasets, and has better power and Type I error in a variety of simulation scenarios.

Original languageEnglish (US)
Pages (from-to)508-519
Number of pages12
JournalPharmaceutical Statistics
Issue number3
StatePublished - May 1 2023


  • DPM
  • MMRM
  • cLDA
  • constrained longitudinal data analysis
  • disease progression models
  • mixed model repeated measures
  • natural cubic splines

ASJC Scopus subject areas

  • Statistics and Probability
  • Pharmacology
  • Pharmacology (medical)


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