Statistical analysis of end-points in cancer clinical trials

The major end-points arising from cancer clinical trials are reviewed. These are: tumour response, treatment morbidity, survival with related data, and quality of life. A survey of tumour response data from 81 published clinical trials found the most common statistical test in use to be a Chi squared test of the total response rate, but a total of 21 different statistical methods were used. The various statistical tests available are reviewed, including the Mann-Whitney test and the Chi squared test for trend which make use of all the categories of response and their intrinsic order. The assumptions underlying the tests are described. Theoretical considerations support the Mann-Whitney test as the optimum choice for the analysis of tumour response data. Methods for comparing alternative statistical tests are summarised, and a new method is described which uses a number of typical sets of data to estimate the relative efficiency of two statistical tests by the median value of the square of the ratio of the z-values. Using this technique, and data from the 81 trials, the Mann-Whitney test is found to be around 40% more efficient than the Chi squared test of the total response rate (this increased efficiency is equivalent to increasing the recruitment to the trial by 40%). This practical result is confirmed by mathematical modelling of tumour response using the power relation of the Mann-Whitney test for ordered categorical data, which is derived. Clinical data is found to fit best a shift model which assumes homogeneity of treatment effect across the different grades of response. On the basis of this model, the Mann-Whitney test is found to be 30% to 110% more efficient than a Chi squared test of the total response rate. The similarities of acute morbidity data to tumour response data lead to similar general conclusions on the optimum method of statistical analysis. In a survey of 36 published clinical trials, the most common method of statistical analysis was again a Chi squared test of a dichotomy (such as no morbidity versus morbidity of any grade). Analysis of data from these trials shows the Mann-Whitney test to be more efficient by around 30%. A survey of 81 papers reporting tumour response in clinical trials found that few of them used methods of estimation of the difference between the treatments, or derived confidence intervals of the size of such a difference. Methods of estimation and calculation of confidence intervals were found even less often in a survey of methods of presentation of morbidity results. The possible reasons for this are discussed. It is concluded that the current methods of analysis of tumour response data and many sets of acute treatment morbidity data are not optimum, and a change should be made from the Chi squared test to the Mann-Whitney test. Such a change could be equivalent to an increase in recruitment into many cancer clinical trials of around 40%