One reason for wanting to conduct a randomized control trial is that it provides evidence of the causal effect of a new drug or treatment. However, if we define "causal effect" as the difference in outcomes a patient would receive on the new drug and the outcome the patient would have received on the alternative, then it is not clear RCTs can provide this information.

Don Rubin points out in this paper that the problem is that we cannot observe the same patient's outcome for both the new drug and for the alternative. We are limited to observing only the patient's outcome for the treatment that the patient actually received.

We cannot observe the "causal effect."

Rubin states that all is not lost because it is possible to measure the average treatment effect with an ideal randomized control trial. The problem, is that the average treatment effect may not provide information on the effect of the treatment on the average patient, the majority of patients or even a plurality of patients. The average treatment effect averages over the treatment effects of the different patients.

In the comment to this post, Bill provides an example in which 99% of patients live one month shorter on the new drug and 1% of patients live 200 months. Such a trial will show that on average patients live 1 month longer on the new drug. This example shows that the average does not have to reflect the outcome for majority of patients or even for a plurality of patients.

In the comment to this post, Bill provides an example in which 99% of patients live one month shorter on the new drug and 1% of patients live 200 months. Such a trial will show that on average patients live 1 month longer on the new drug. This example shows that the average does not have to reflect the outcome for majority of patients or even for a plurality of patients.

In most cancer trials the authors present the difference in median survival between the treatment arms. I show in this unpublished working paper, that for arbitrary differences in median survival it is easy to find examples in which almost all patients (every patient except 1) their individual outcomes is the opposite of the median difference.

So a positive average treatment effect does not imply even a significant proportion of patient will benefit from the drug and a positive difference in median survival does not imply that a significant proportion of patients will benefit from the drug.

What about other measures, hazard ratios, Kaplan-Meier plots, can any information from the randomized control trial tell us if any reasonable number of patients will benefit from the drug?

Hazard ratios are based on "regression techniques" that make strong parametric assumptions that may not be true in practice. But even assuming that the parametric assumptions were correct the results only show that some positive number of patients will have some positive benefit from the drug. Like with the average treatment effect, a proportional hazard ratio is calculated by "averaging" over patients, some of whom may benefit from the drug and some of whom may not.

Kaplan-Meier plots are potentially representations of the marginal probability of survival for each treatment. If the trial does not suffer from attrition bias or participation bias then the difference in the survival curve at each point in time provides an estimate of the minimum number of people who would benefit from the drug.

If there is attrition bias or selection-into-sample bias then the results from the Kaplan-Meier plots can still be used to provide the minimum number of people who would benefit from the drug.

Kaplan-Meier plots are potentially representations of the marginal probability of survival for each treatment. If the trial does not suffer from attrition bias or participation bias then the difference in the survival curve at each point in time provides an estimate of the minimum number of people who would benefit from the drug.

If there is attrition bias or selection-into-sample bias then the results from the Kaplan-Meier plots can still be used to provide the minimum number of people who would benefit from the drug.

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