Diagnostic tests can predict the efficacy of treatments without randomisation to control by solving simultaneous equations based on different test results: applied to assessing the effectiveness of test, trace and isolation

The efficacy of an intervention can be assessed by randomising patients to different diagnostic tests instead of to an intervention and control. The tests must have different predictive characteristics such as different sensitivities with respect to the outcome. The intervention is applied to a patient if a test result is on one side of a threshold (or if it is positive) and control applied if it is on the other side (or if the test result is negative). This can also be done with different dichotomising thresholds for one test. The frequencies of the outcome in those with each of the four observations are then used to calculate the risk reduction by solving a pair of simultaneous equations. This assumes that the risk reduction and the overall frequency of the outcome is the same in both groups. The calculations are illustrated by using data from the IRMA2 randomized controlled trial that assessed the efficacy of the angiotensin receptor blocker irbesartan in lowering the risk of diabetic nephropathy in patients conditional on different urinary albumin excretion rates. They are also illustrated with simulated data based on a suggested methodology for assessing the effectiveness of test, trace and isolate to reduce transmission of Covid-19 using RT-PCR and LFD tests.