Designs for synthetic case-control studies in open cohorts

Several designs are proposed for case-control studies within cohorts when the cohort is open to late entry. These and previously proposed designs are examined with respect to consistency and efficiency of relative risk parameter estimation, and a small simulation study is reported. If study costs increase in proportion to the total number of "at-risk" controls, the most efficient design, Design C, is as follows. For a case failing at time t, controls are selected at random (and without regard to "at-risk" status) from among cohort members who are (i) known not to have failed prior to t and (ii) have not been previously selected as controls. At each t, control sampling proceeds until a prespecified number of controls who are "at risk" at t have been obtained. The efficiency advantage of Design C over that of the standard case-control design proposed by Thomas (in Appendix to Liddell, McDonald, and Thomas, 1977, Journal of the Royal Statistical Society, Series B 140, 469-490) will often be small. If, on the other hand, the costs increase in proportion to the number of distinct "at-risk" controls, Design C is no longer the most efficient design. In this case, several alternative designs are proposed.