Proportions: Correlated and Paired
Sample size for a matched case-control study testing the association between a binary exposure and a binary outcome using the score test from conditional logistic regression. Based on the matched-set formulation described by Lachin and.
This calculator uses the score-test sample-size formulation for a binary exposure in a matched case-control study analyzed with conditional logistic regression. this method describes the regression coefficient as the log odds ratio, so the effect-size parameter is θ = log(OR).
For a two-sided test, the required number of matched sets is calculated from the normal approximation:
Here, N is the number of matched sets, MD is the number of cases per set, MH is the number of controls per set, and PE is the probability of exposure in the population. The matching contribution is MDMH/(MD+MH).
When other covariates are included in the conditional logistic regression, the exposure information is reduced according to 1−R2. Thus, a larger R2 produces a larger required sample size. Note that this adjustment assumes that covariates having strong effects on the outcome have already been handled through the matching process rather than simply relying on this R2 adjustment.
Once the required number of matched sets is obtained, the total evaluable sample size is N × (MD + MH). If a dropout rate is specified, the enrollment target is inflated as Nenroll = Nsubjects/(1−dropout), rounded upward.
This worked example: Power = 0.90, α = 0.05, OR = 1.5, PE = 0.30, R² = 0.20, one case and one control per matched set. Expected result: 761 matched sets, or 1,522 evaluable subjects.
This worked example: Power = 0.85, α = 0.05, OR = 0.4444, PE = 0.15, R² = 0, one case and two controls per matched set. Expected result: 161 matched sets, or 483 evaluable subjects.
The calculated sample size is the number of matched strata required under the specified assumptions. Each matched set contains the specified number of cases and controls. The calculation concerns the test of the exposure odds ratio; it does not replace considerations such as matching feasibility, exposure prevalence within matched sets, model specification, or losses that may affect the final analyzable sample.
Lachin, J. M. (2008). Sample size evaluation for a multiply matched case-control study using the score test from a conditional logistic (discrete Cox PH) regression model. Statistics in Medicine, 27(14), 2509–2523. doi:10.1002/sim.3057.
Tang, Y. (2009). Comments on “Sample size evaluation for multiply matched case-control study using the score test from the conditional logistic (discrete Cox PH) regression model.” Statistics in Medicine, 28, 175–177.
the software, LLC. this method Sample Size Software: Tests for the Odds Ratio in a Matched Case-Control Design with a Binary X, Chapter 156.