Two-stage designs are especially efficient when which condition applies?

• A. The study is cross-sectional
• B. Covariate data are expensive to obtain
• C. Covariate data are cheap
• D. The outcome is rare

Answer: (B)

Two-stage designs maximize information while minimizing cost by using cheap data to guide the collection of expensive measurements. In the first stage you gather inexpensive data on a large group, then you selectively obtain costly covariate information only on a sub-sample chosen based on what you learned from that initial data. This targeted approach concentrates the expensive measurements where they matter most, preserving statistical efficiency (precision and bias properties) without having to pay for expensive data on everyone. If covariate data are cheap, there’s little advantage to this approach because you’d gain little by limiting expensive measurements. If the outcome is rare, two-stage designs can still be used, but the primary benefit comes from saving the costly covariate data rather than from the rarity of the outcome.