TY - JOUR

T1 - Conditional logistic regression with sandwich estimators

T2 - Application to a meta-analysis

AU - Fay, Michael P.

AU - Graubard, Barry I.

AU - Freedman, Laurence S.

AU - Midthune, Douglas N.

PY - 1998/3

Y1 - 1998/3

N2 - Motivated by a meta-analysis of animal experiments on the effect of dietary fat and total caloric intake on mammary tumorigenesis, we explore the use of sandwich estimators of variance with conditional logistic regression. Classical conditional logistic regression assumes that the parameters are fixed effects across all clusters, while the sandwich estimator gives appropriate inferences for either fixed effects or random effects. However, inference using the standard Wald test with the sandwich estimator requires that each parameter is estimated using information from a large number of clusters. Since our example violates this condition, we introduce two modifications to the standard Wald test. First, we reduce the bias of the empirical variance estimator (the middle of the sandwich) by using standardizid residuals. Second, we approximately account for the variance of these estimators by using the t-distribution instead of the normal distribution, where the degrees of freedom are estimated using Satterthwaite's approximation. Through simulations, we show that these sandwich estimators perform almost as well as classical estimators when the true effects are fixed and much better than the classical estimators when the true effects are random. We achieve simulated nominal coverage for these sandwich estimators even when some parameters are estimated from a small number of clusters.

AB - Motivated by a meta-analysis of animal experiments on the effect of dietary fat and total caloric intake on mammary tumorigenesis, we explore the use of sandwich estimators of variance with conditional logistic regression. Classical conditional logistic regression assumes that the parameters are fixed effects across all clusters, while the sandwich estimator gives appropriate inferences for either fixed effects or random effects. However, inference using the standard Wald test with the sandwich estimator requires that each parameter is estimated using information from a large number of clusters. Since our example violates this condition, we introduce two modifications to the standard Wald test. First, we reduce the bias of the empirical variance estimator (the middle of the sandwich) by using standardizid residuals. Second, we approximately account for the variance of these estimators by using the t-distribution instead of the normal distribution, where the degrees of freedom are estimated using Satterthwaite's approximation. Through simulations, we show that these sandwich estimators perform almost as well as classical estimators when the true effects are fixed and much better than the classical estimators when the true effects are random. We achieve simulated nominal coverage for these sandwich estimators even when some parameters are estimated from a small number of clusters.

KW - Generalized estimating equations

KW - Random effects

KW - Robust variance

KW - Satterthwaite's formula

KW - Standardized residuals

UR - http://www.scopus.com/inward/record.url?scp=0031919927&partnerID=8YFLogxK

U2 - 10.2307/2534007

DO - 10.2307/2534007

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C2 - 9544516

AN - SCOPUS:0031919927

SN - 0006-341X

VL - 54

SP - 195

EP - 208

JO - Biometrics

JF - Biometrics

IS - 1

ER -