Fig. 3

Schematic of pooling strategy for a 1:3 matched case-control study with three nodes, numbered 1–3 and 10 matched sets distributed over these nodes. For each matched set, case is indicated by filled red circle, three matched controls are indicated by shaded green circles. A line joins the case and controls in each matched stratum. Boxes represent the nodes. In the table on the right hand side, the first column indicates the node number and the second column indicates the matched set number. The 3rd column titled “Current” indicates the pool id if the current strategy of Saha-Chaudhuri and Weinberg (2017) is applied directly. The 4th and 5th column indicates the pool ids for two variants of the proposed within-node pooling strategy. In “New - 1” (4th column), poolsize g = 2 is used. The first two pools are formed within node 1, third pool is formed within node 2 and the fourth pool is formed within node 3. Since g = 2 is used and nodes 2 and 3 have odd number of matched sets, within-node pooling leads to exclusion of one matched set each from node 2 and node 3. In Scheme 2 (4th column, titled “New - 2”), poolsizes g = 2 and 3 are used. The first two pools are formed within node 1 (g = 2), third pool is formed within node 2 (g = 3) and the fourth pool is formed within node 3 (g = 3). Consequently, all participant data were used for analysis. Secure summation is not required for within-node stratified pooling as only the aggregate covariate levels are released from the nodes