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 |
- 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).