Estimating Drug Effects in the Presence of Placebo Response: Causal Inference Using Growth Mixture Modeling

Stat Med. 2009 Nov 30;28(27):3363-85. doi: 10.1002/sim.3721.


Placebo-controlled randomized trials for antidepressants and other drugs often show a response for a sizeable percentage of the subjects in the placebo group. Potential placebo responders can be assumed to exist also in the drug treatment group, making it difficult to assess the drug effect. A key drug research focus should be to estimate the percentage of individuals among those who responded to the drug who would not have responded to the placebo ('Drug Only Responders'). This paper investigates a finite mixture model approach to uncover percentages of up to four potential mixture components: Never Responders, Drug Only Responders, Placebo Only Responders, and Always Responders. Two examples are used to illustrate the modeling, a 12-week antidepressant trial with a continuous outcome (Hamilton D score) and a 7-week schizophrenia trial with a binary outcome (illness level). The approach is formulated in causal modeling terms using potential outcomes and principal stratification. Growth mixture modeling (GMM) with maximum-likelihood estimation is used to uncover the different mixture components. The results point to the limitations of the conventional approach of comparing marginal response rates for drug and placebo groups. It is useful to augment such reporting with the GMM-estimated prevalences for the four classes of subjects and the Drug Only Responder drug effect estimate.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Antidepressive Agents / therapeutic use
  • Antipsychotic Agents / therapeutic use
  • Computer Simulation
  • Depression / drug therapy
  • Humans
  • Models, Statistical*
  • Monte Carlo Method
  • Placebo Effect*
  • Randomized Controlled Trials as Topic / methods*
  • Schizophrenia / drug therapy


  • Antidepressive Agents
  • Antipsychotic Agents