The waiting game: how long is long enough?
The time it takes to recruit patients into a clinical trial has a major impact on whether a drug development programme completes on time. Here Byron Jones explains how simple statistical models can be very useful in predicting the time to complete recruitment.
The Poisson Distribution
Many rare events occur at random in time or space, for example, the number of radioactive disintegrations per minute or the number of bacteria per unit area of Petri dish. The probability of obtaining 0, 1, 2, 3, etc., events follows a simple mathematical formula developed by Poisson. After presenting the basic information, the chapter describes methods for setting confidence limits, determining sample size, and comparing groups. Ways of determining cumulative probabilities are given, for example, how many nurses are needed to staff a delivery room that on average has 12 deliveries per day.
Analysis of data from multiclinic experiments.
The analysis of data from multiclinic experiments is put in the framework of a mixed model in which the treatment effects are assumed to be fixed, and clinic and clinic by treatment effects are assumed to be random. The analysis in the unbalanced case is developed under the usual mixed model assumptions. The maximum likelihood estimates and likelihood ratio tests of the parameters are derived following the approach of Hemmerle and Hartley (1973). The T2 test is shown to be asymptotically equivalent to the analysis of variance F test in the balanced case. The distribution of the test statistic in the case of proportional cell frequencies is also discussed. Some investigation is made of the distribution of the test statistic by applying the method of Box (1954).