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Table 3 Example of calculations from data in Baker and Lindeman [Reference 9]

From: The Paired Availability Design for Historical Controls

hospital before" group data after group data estimate std error weight
  n1 e1 P1 n2 e2 p2 y s w
1 116 .586 .172 103 .223 .184 -.033 .143 44
2 180 .290 .080 180 .440 .090 .067 .196 24
3 373 .131 .110 421 .587 .100 -.022 .048 208
4 1000 .100 .040 1000 .450 .050 .029 .026 313
5 1298 .000 .074 1084 .480 .065 -.019 .022 333
6 1919 .000 .275 2073 .316 .229 -.146 .044 225
7 3195 .010 .030 3733 .290 .031 .004 .015 365
8 4778 .008 .194 4859 .586 .190 -.006 .014 369
9 4685 .187 .149 6170 .551 .125 -.046 .015 352
10 8108 .467 .248 9918 .678 .280 .152 .031 288
11 11159 .328 .209 11869 .499 .209 .000 .031 288
  1. n1 (n2) = number of subjects in "before" ("after") group. el (e2) = fraction of subjects in "before" ("after") group that had epdiural analgesia, p1 (p2) = fraction of subjects in "before" ("after") group that had a Cesarean section, y= estimated effect of epidural analgesia on the probability of Cesarean section = (p2-p1)/(e2-e1), s= standard error of y= square root of (p2 (1-p2))/n2 + p1 (1-p1)/n1) /(e2-e1)2, w* = weight used in random effects meta-analysis. We computed the weights as follows. Let i index studies, so yi and si are the values of y and s for study i. It is convenient to define w1 = I/ si 2. Following DerSimonian and Laird [Reference 19], to compute v, the variance of the true effect among the k studies, we set v equal to the larger of (Q-(k-1)) / (Σwi - Σwi 2/Σwi) and 0, where Q = Σwi (yi - m)2, m = Σyi wi/Σwi. The random-effects weights are w* i= 1/(si 2 + v), and the summary statistic is y* = Σyi w* i/Σw* i, with standard error s* = square root of 1/Σw* i. Following Proschan and Follman [reference 20], the 95% confidence interval is (y* - tk- s*, y*+ tk-1 s*), where tk-1 is the value of the 97 ½ percentile of a t-distribution with k-1 degrees of freedom. In this example, k = 11, Q = 50.1, v = .0025, m =-.007, s* = .019 y* = -.005, t10 = 2.23, y* = -.005 and the 95% confidence interval is (-.047, .037).