The probabilities of an outcome on intervention and control can be estimated by randomizing subjects to different testing strategies, required for assessing diagnostic tests, test trace and isolation and for natural randomisation (1808.09169v15)

Abstract: The efficacy of an intervention can be assessed by randomizing patients to different diagnostic tests instead of directly to an intervention and control. This principle is applied by allocating individuals to intervention if the test result is positive (or on one side of a threshold) but allocating individuals to a control if the result is negative (or on the other side of the threshold). This can also be done with different dichotomizing thresholds for one test. The frequencies of the outcome in those with each of the four resulting observations are then used to calculate the risk ratio (RR) for the marginal probabilities by solving simultaneous equations. This assumes that the RR due to intervention compared to control is the same in both test groups created by randomization. The calculations are illustrated by using data from a randomized controlled trial (RCT) that assessed the efficacy of an angiotensin receptor blocker (ARB) in lowering the risk of diabetic nephropathy in patients conditional on urinary albumin excretion rates (AERs). The calculations are also illustrated with simulated data for assessing the effectiveness of test, trace and isolation to reduce transmission of the SARS-Cov-2 virus by randomizing to RT-PCR or LFD tests. This approach allows the probabilities of outcomes, their RRs and odds ratios (OR) conditional on the results of covariates to be determined, also suggesting a way forward for natural as opposed to active randomization.