The Presentation and Analysis of the Results of Radiotherapy. Part II

If the experiment is incomplete, the dot diagram will include a number of cases which have been under observation for a relatively short time after treatment. In any such experiment we can divide the patients treated into the four groups already discussed. Group (1) Those who have died with cancer present at time t, reckoned from the commencement of treatment. Group (2) Those who have died of intercurrent disease at time t. Group (3) Those who remain alive and symptom free after time t. Group (4) Those who remain alive but with cancer progressing at time t. Each patient in one of the above groups makes his own individual contribution to the likelihood of the sample, depending on the value of t. The likelihood function is not the same for patients in different groups, however, so we shall consider each in turn. Let the frequency distribution of the survival times of patients who subsequently die with cancer present be given by The probability that a patient will die from cancer between times t and (t + dt) is the product of the probability that he will live at least as long as t, and the probability that, not having been cured, he will die from cancer in the given interval.