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Estimation Based on Case-Control Designs with Known Prevalence Probability

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  • van der Laan Mark J.

    (University of California, Berkeley)

Abstract

Regular case-control sampling is an extremely common design used to generate data to estimate effects of exposures or treatments on a binary outcome of interest when the proportion of cases (i.e., binary outcome equal to 1) in the population of interest is low. Case-control sampling represents a biased sample of a target population of interest by sampling a disproportional number of cases. Case-control studies are also commonly employed to estimate the effects of genetic markers or biomarkers on binary phenotypes.In this article we present a general method of estimation relying on knowing the prevalence probability, conditional on the matching variable if matching is used.Our general proposed methodology, involving a simple weighting scheme of cases and controls, maps any estimation method for a parameter developed for prospective sampling from the population of interest into an estimation method based on case-control sampling from this population.We show that this case-control weighting of an efficient estimator for a prospective sample from the target population of interest maps into an efficient estimator for matched and unmatched case-control sampling. In particular, we show how application of this generic methodology provides us with double robust locally efficient targeted maximum likelihood estimators of the causal relative risk and causal odds ratio for regular case control sampling and matched case control sampling.Various extensions and generalizations of our methods are discussed.

Suggested Citation

  • van der Laan Mark J., 2008. "Estimation Based on Case-Control Designs with Known Prevalence Probability," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-59, September.
    • Handle: RePEc:bpj:ijbist:v:4:y:2008:i:1:n:17
    DOI: 10.2202/1557-4679.1114
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    References listed on IDEAS

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    1. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, vol. 49(5), pages 1289-1316, September.
    2. Anthony P. Morise & George A. Diamond & Robert Detrano & Marco Bobbio & Erdogan Gunel, 1996. "The Effect of Disease-prevalence Adjustments on the Accuracy of a Logistic Prediction Model," Medical Decision Making, , vol. 16(2), pages 133-142, June.
    3. Manski, Charles F & Lerman, Steven R, 1977. "The Estimation of Choice Probabilities from Choice Based Samples," Econometrica, Econometric Society, vol. 45(8), pages 1977-1988, November.
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    Citations

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    Cited by:

    1. Sjolander Arvid & Vansteelandt Stijn & Humphreys Keith, 2010. "A Principal Stratification Approach to Assess the Differences in Prognosis between Cancers Caused by Hormone Replacement Therapy and by Other Factors," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-37, June.
    2. van der Laan Mark J., 2010. "Targeted Maximum Likelihood Based Causal Inference: Part I," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-45, February.
    3. Brooks Jordan C. & van der Laan Mark J. & Singer Daniel E. & Go Alan S., 2013. "Targeted Minimum Loss-Based Estimation of Causal Effects in Right-Censored Survival Data with Time-Dependent Covariates: Warfarin, Stroke, and Death in Atrial Fibrillation," Journal of Causal Inference, De Gruyter, vol. 1(2), pages 235-254, November.
    4. van der Laan Mark J., 2014. "Targeted Estimation of Nuisance Parameters to Obtain Valid Statistical Inference," The International Journal of Biostatistics, De Gruyter, vol. 10(1), pages 29-57, May.
    5. van der Laan Mark J. & Gruber Susan, 2012. "Targeted Minimum Loss Based Estimation of Causal Effects of Multiple Time Point Interventions," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-41, May.
    6. Brooks Jordan & van der Laan Mark J. & Go Alan S., 2012. "Targeted Maximum Likelihood Estimation for Prediction Calibration," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-35, October.
    7. Rose Sherri & van der Laan Mark J., 2008. "Simple Optimal Weighting of Cases and Controls in Case-Control Studies," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-26, September.
    8. Amanda Coston & Edward H. Kennedy, 2022. "The role of the geometric mean in case-control studies," Papers 2207.09016, arXiv.org.
    9. van der Laan Mark J. & Petersen Maya & Zheng Wenjing, 2013. "Estimating the Effect of a Community-Based Intervention with Two Communities," Journal of Causal Inference, De Gruyter, vol. 1(1), pages 83-106, June.
    10. van der Laan Mark J., 2014. "Causal Inference for a Population of Causally Connected Units," Journal of Causal Inference, De Gruyter, vol. 2(1), pages 13-74, March.
    11. Wei Zhao & Ying Qing Chen & Li Hsu, 2017. "On estimation of time-dependent attributable fraction from population-based case-control studies," Biometrics, The International Biometric Society, vol. 73(3), pages 866-875, September.

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