Repeated assessment of results in clinical trials of cancer treatment

Abstract

A clinical trial comparing two treatments for cancer is bound to extend over several years, partly because of the time required to collect sufficient numbers of patients and partly because of the time required before the results of treatment can be assessed. It is, therefore, common practice to make surveys of the results to date at intermediate stages of the trial. These preliminary assessments may be used to stop the trial if a new unproven treatment method is seen to be unexpectedly much worse than the usual technique, or if the results from the new treatment are already found to be significantly better. While such surveys are ethically desirable, since their aim is to minimize the number of patients treated by an inferior method, it is not always appreciated that, as pointed out by Boag, Haybittle, Fowler and Emery (1971), the procedure may seriously invalidate the use of a conventional test of significance in comparing the results. Armitage, McPherson and Rowe (1969) have examined this effect in data having a binomial, normal or exponential distribution, and it is of equal interest to study the situation when survival rates are compared in a typical clinical trial of cancer treatment. This has been done by the simulation experiment described in the next section. SIMULATION EXPERIMENT-NULL HYPOTHESISThe model simulated was as follows. Suppose 2N patients enter a trial of maximum duration *T years, and suppose that T-year (T<*T) survival rate is taken as the parameter for comparing the two groups. After * T + T-years the difference *D in T-year rates can be obtained directly and compared with the standard error of the difference. If there is no real difference between the two treatment groups, then the probability of *D being greater than 1-96 times its standard error is P=0-05, i.e. in 1,000 such trials one would only find such a difference in about 50. By using the actuarial or lifetable method it is possible to estimate the T-year survival rate at an earlier stage in the trial, provided at least some of the patients have been followed for T-years. Suppose this is done at yearly intervals from T-\-l to *T-1 years after the beginning of the trial. Again the standard errors of the rates may be calculated (Greenwood, 1926) and the difference in rates compared with its standard error (taken to be the square root of the sum of the squares of the separate standard errors). The point of interest is how much the probability of finding a "significant" difference (i.e. difference more than 1-96 times its standard error) is increased by making these early analyses.To answer this question a computer program was written in Titan Autocode to simulate a large number of clinical trials on the Cambridge University Titan computer. The program randomly selected 2N survival times assuming a model for the survival curve having a proportion, c, cured and a lognormal distribution of survival times in the uncured group with logmean p and standard deviation a (Boag, 1948). The 2N patients were assumed to enter the trial regularly ov...

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