10.2 Variance and confidence interval

The variance estimator in general use is due to Robins, Breslow and Greenland (1986). With \[ P_k = \frac {a_k + d_k}{n_k}, \quad Q_k = \frac {b_k + c_k}{n_k}, \quad R_k = \frac {a_k d_k}{n_k}, \quad S_k = \frac {b_k c_k}{n_k} , \] and \(R_+ = \sum _k R_k\), \(S_+ = \sum _k S_k\), \[ \widehat {\Var }(\log \widehat {\OR }_{\text {MH}}) = \frac {\sum _k P_k R_k}{2R_+^2} + \frac {\sum _k (P_k S_k + Q_k R_k)}{2R_+ S_+} + \frac {\sum _k Q_k S_k}{2S_+^2} . \] It is consistent under both kinds of asymptotics of Theorem 10.1.3, and the \(95\%\) interval is \[ \widehat {\OR }_{\text {MH}}\exp (\pm 1.96\,\text {SE}) . \]