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© 1980 Oxford University Press

research-article

Bias and Efficiency in Logistic Analyses of Stratified Case-Control Studies

M C PIKE1, A P HILL2 and and P G SMITH3

1,2 Department of Community and Family Medicine, University of Southern California School of Medicine 2025 Zonal Avenue, Los Angeles, California 90033, USA.
3 ICRF Cancer Epidemiology and Clinical Trials Unit, 9 Keble Road, Oxford UK. Present address: Department of Medical Statistics and Epidemiology, London School of Hygiene and Tropical Medicine, London WC1E 7HT

Pike M C [University of Southern California School of Medicine, 2025 Zonal Avenue, Los Angeles, California 90033, USA], Hill A P, and Smith P G. Bias and efficiency in logistic analyses of stratified case-control studies. International Journal of Epidemiology 1980, 9: 89–95.

Two approaches to the estimation of the parameters in the logistic model applied to the analysis of stratum matched case-control studies are compared. It is shown that the ‘unconditional likelihood method’ gives estimates of odds ratios which may be severely exaggerated if the stratum sizes are not large; however, if stratum sizes are not small, the ‘conditional likelihood method’ is computationally prohibitive. The use of small stratum sizes (e.g., 1-to-1 matching) leads to some loss of efficiency if the matching is irrelevant but it is shown that the loss is small for odds ratios up to at least 3. There would seem to be strong arguments for the routine use of matched designs as the reduction in confounding bias produced by such matching may be considerable whereas there is only a small loss in efficiency compared with unmatched designs.

Received 29 August 1979


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