Comparison of one-sample two-sided sequential t-tests for application in epidemiological studies.

In epidemiological prospective cohort studies, exposure levels of cases with disease and disease-free control subjects can be measured by laboratory analysis of previously stored biological specimens. In such studies, a sequential t-test can be used for preliminary evaluations, at the expense of the smallest possible number of specimens, of whether a new aetiological hypothesis is worth further investigation or whether specimens should rather be spared to test other, more fruitful, hypotheses. For this purpose, we recently compared two sequential probability ratio tests (SPRTs), in which the log-likelihood ratio was either based on an approximation, or computed exactly, and which were adapted to account for various control-to-case matching ratios. The tests turned out relatively conservative, particularly in terms of the significance level achieved. In the present paper, we compare an SPRT for matched or paired data based on Rushton's approximation to the log-likelihood ratio with a profile log-likelihood method developed by Whitehead. The comparison is partly mathematical, and partly based on computerized simulations. Average sample size for a sequential test is already smaller than for the equivalent fixed sample test. Increasing the number of controls matched per case further reduces the average sample size necessary to come to a decision. We show that, irrespective of the number 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. Moreover, compared with the method of Rushton, Whitehead's method has the advantage that it can also be applied to groupwise inspection of the data and that it can also be converted easily into a truncated procedure.