Estimating the result of randomized controlled trials without randomization in order to assess the ability of diagnostic tests to predict a treatment outcome
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A randomised controlled trial (RCT) is accepted as the best way of assessing the efficacy of a treatment. However randomization may be impractical, especially when assessing the ability of new diagnostic tests to predict the outcome of a treatment if the latter has shown to be superior to placebo already in a previous RCT. Such tests may be based on multivariable scores or other factors that may be studied to assess the external validity of a RCT. The method described here is based on allocating subjects to a control limb if the results of the test used to select subjects for the trial are on one side of some cut-off point and allocating subjects to a treatment limb if the results are on the other side of the cut-off point. The results are interpreted by assuming that the distribution of pre-treatment test results in those with a subsequent outcome are the same irrespective of whether the subjects with that outcome were in the treatment or placebo limbs. The resulting likelihood ratios are then used in conjunction with the proportion with an outcome on one side of the cut-off to estimate the proportion with that outcome on both sides of the cut-point by using a rearrangement of Bayes rule. The approach is illustrated with a data set from a RCT where the diagnostic test was the albumin excretion rate, the treatment was an angiotensin receptor blocker and the outcome was nephropathy. When curves are constructed to show the probabilities of an outcome (nephropathy) on placebo and treatment for each diagnostic test result by using all the data from the RCT and from only the part of the data that would have been available from a cut-off trial, the results were very similar, the small differences being readily explicable due to minor stochastic variation. Provided that suitable controls are in place, (e.g. double blinding) it appears that a cut-off study can predict the result of an RCT.
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