COMPARISON OF ONE-SAMPLE 2-SIDED SEQUENTIAL T-TESTS FOR APPLICATION IN EPIDEMIOLOGIC STUDIES

In epidemiological prospective cohort studies, exposure levels of case s with disease and disease-free control subjects can be measured by la boratory analysis of previously stored biological specimens. In such s tudies, a sequential t-test can be used for preliminary evaluations, a t the expense of the smallest possible number of specimens, of whether a new aetiological hypothesis is worth further investigation or wheth er specimens should rather be spared to test other, more fruitful, hyp otheses. For this purpose, we recently compared two sequential probabi lity ratio tests (SPRTs), in which the log-likelihood ratio was either based on an approximation, or computed exactly, and which were adapte d to account for various control-to-case matching ratios. The tests tu rned out relatively conservative, particularly in terms of the signifi cance level achieved. In the present paper, we compare an SPRT for mat ched or paired data based on Rushton's approximation to the log-likeli hood ratio with a profile log-likelihood method developed by Whitehead . The comparison is partly mathematical, and partly based on computeri zed simulations. Average sample size for a sequential test is already smaller than for the equivalent fixed sample test. Increasing the numb er of controls matched per case further reduces the average sample siz e necessary to come to a decision. We show that, irrespective of the n umber of controls per case, pre-specified levels of statistical power and significance are respected closely by Whitehead's method, but not by Rushton's SPRT. This last procedure can lead to a significant loss in power. Since, in addition, Whitehead's method has been implemented in a commercially available computer program (PEST), we conclude that this method can be preferred to the methods we described earlier. More over, compared with the method of Rushton, Whitehead's method has the advantage that it can also be applied to groupwise inspection of the d ata and that it can also be converted easily into a truncated procedur e.