Comparing "all active dose" to placebo - do we treat "all active dose" as one group or separate groups?

A randomized clinical trial has 4 treatment groups (1:1:1:1 randomization to placebo, dose level 1, dose level 2, and dose level 3), and there is interest in understanding the following treatment comparisons:

  • dose level 1: placebo
  • dose level 2: placebo
  • dose level 3: placebo
  • any active dose: placebo

For the “any active dose to placebo” comparison, one could fit a separate model where treatment group is coded to 2 levels, or one could extract the comparison from the same model where treatment group is coded to 4 levels via a separate ESTIMATE statement in SAS. Note that the two approaches will give slightly different estimates and p values due to the different degrees of freedom.


  • What are the pros and cons of either approach, or is one preferred over the other? What is the rationale of the latter approach other than convenience (or perhaps efficiency)?
  • Would interpretation differ for the two approaches?
  • Are there any references that discuss this?

Many thanks,

Fitting a separate model will result in the wrong estimate of \sigma^2. Use contrasts within the overall model. You’ll need to define the “any active dose” contrast, e.g. placebo vs. the average of the active groups. If doing a Bayesian analysis more options would be available, e.g., Pr(average > placebo and at least one active arm more than 10% greater than placebo) or Pr(monotonic dose effect) = Pr(placebo <= dose 1 <= dose 2 <= dose 3).

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This is really helpful. Thank you, Prof Harrell!