American Journal of Epidemiology Vol. 131, No. 3: 578
Copyright © 1990 by The Johns Hopkins University School of Hygiene and Public Health
correction |
ERRATUM
ABSTRACT
The Journal has been notified by Dr. Lawrence L. Kupper of several printer's errors that occurred in the article by Dr. Glen A. Satten and himself in the January 1990 issue of the Journal entitled, "Sample Size Requirements for Interval Estimation of the Odds Ratio" (Am J Epidemiol 1990;131:177–84).
One printer's error involved the inadvertent dropping of a line of text in line 6 of page 179 and a repetition here of a line of text that appeared earlier in the ‘Methods’ section. Also, theidentifying number ‘(2)’ for statement 2 on page 178 was accidentally dropped In addition, the radical for equation 5 on page 179 is incomplete
The section of the text of the paper with these errors corrected is given below:
Setting no = kn1 where k is to be specified by the investigator, we use statement 1to define the optimal sample size nx* to be the smallest positive integer value of nx satisfying the probabilistic statement
 |
where 0 
A n1 and 0 C kn1
For specified values of 
, k, and n1, the inequality inside the brackets of statement 2 defines a region Q in the (A, C) plane. Evaluating the probability statement 2then requires summing, over all integer pairs (a, c) in fi, the probability of each of these pairs, where the joint probability distribution of A and C is
 |
where 0 a n1 0 c kn1
The region 
is most easily specified by noting that, when either a or c is held constant, condition that (a, c) 
can be obtained by solving a quadratic equation. Solving the quadratic equation in c for fixed a gives the condition f–(a) : c f+(a).The minimum and maximum values of a, denoted by amin and amax1, can be found by observing that, for
, with equality holding when c = kn1/2. Then amin andamax can be found as the roots of the quadratic equation that arises when c is fixed at the value kn1/2. Thus, using equation 3, we can rewrite statement 2 as
 |
 |
 |
and where the sum is over integer values of a and c only.