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On Modeling and Estimation for the Relative Risk and Risk Difference

Author

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  • Thomas S. Richardson
  • James M. Robins
  • Linbo Wang

Abstract

A common problem in formulating models for the relative risk and risk difference is the variation dependence between these parameters and the baseline risk, which is a nuisance model. We address this problem by proposing the conditional log odds-product as a preferred nuisance model. This novel nuisance model facilitates maximum-likelihood estimation, but also permits doubly-robust estimation for the parameters of interest. Our approach is illustrated via simulations and a data analysis. An R package {\tt brm} implementing the proposed methods is available on CRAN. Supplementary materials for this article are available online.

Suggested Citation

  • Thomas S. Richardson & James M. Robins & Linbo Wang, 2017. "On Modeling and Estimation for the Relative Risk and Risk Difference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1121-1130, July.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:519:p:1121-1130
    DOI: 10.1080/01621459.2016.1192546
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    Citations

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    Cited by:

    1. Linbo Wang & Eric Tchetgen Tchetgen & Torben Martinussen & Stijn Vansteelandt, 2023. "Rejoinder to discussions on “Instrumental variable estimation of the causal hazard ratio”," Biometrics, The International Biometric Society, vol. 79(2), pages 564-568, June.
    2. Linbo Wang & Xiang Meng & Thomas S. Richardson & James M. Robins, 2023. "Coherent modeling of longitudinal causal effects on binary outcomes," Biometrics, The International Biometric Society, vol. 79(2), pages 775-787, June.
    3. Stijn Vansteelandt & Oliver Dukes, 2022. "Authors' reply to the Discussion of ‘Assumption‐lean inference for generalised linear model parameters’ by Vansteelandt and Dukes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 729-739, July.
    4. Maria Cuellar & Edward H. Kennedy, 2020. "A non‐parametric projection‐based estimator for the probability of causation, with application to water sanitation in Kenya," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1793-1818, October.
    5. Thomas S. Richardson, 2022. "Thomas S. Richardson’s contribution to the Discussion of ‘Assumption‐lean inference for generalised linear model parameters’ by Vansteelandt and Dukes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 719-720, July.
    6. Linbo Wang & Eric Tchetgen Tchetgen & Torben Martinussen & Stijn Vansteelandt, 2023. "Instrumental variable estimation of the causal hazard ratio," Biometrics, The International Biometric Society, vol. 79(2), pages 539-550, June.
    7. Tyler J. VanderWeele, 2020. "Optimal approximate conversions of odds ratios and hazard ratios to risk ratios," Biometrics, The International Biometric Society, vol. 76(3), pages 746-752, September.

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