Unbiased Estimation of the Standard Deviation

A clinician has conducted a randomized clinical trial of two treatments (1 and 2) for cancer. N patients have received each treatment. Criteria for considering that a patient has had a have been decided on, and it is agreed that a patient whose cancer has metastasized is not curable. The observed numbers of cures are n1 and n2, and the cure rates have been estimated as ri = ni/N and r2 = n2/N. The clinician is concerned about how to write the standard errors of these cure rates because he realizes that some of the original 2N patients had metastases before the beginning of treatment and that therefore the number of potential may iiot have been equal in the two groups and in neither case was equal to N. He is anxious not to attribute a difference in the observed number of cures to a difference in the treatments when it might be due solely to a difference in the unknown numbers of assigned to the two treatment groups. The question which he brings to the statistician is: How does the fact that there were only some unknown number, k1, of curables in the first group, and a similarly unknown number, k2, in the second, affect the standard error of the observed difference in the cure rates, r1 -r2 The clinician is rather surprised and most relieved