Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation

Michael Richard Crager

doi:doi:10.11648/j.ajam.20221005.11

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Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation

Michael Richard Crager

Published in American Journal of Applied Mathematics (Volume 10, Issue 5)

Received: 6 September 2022 Accepted: 4 October 2022 Published: 17 October 2022

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Abstract

Under the assumption of no unmeasured confounders, Cox proportional hazards regression with inverse probability of treatment (IPTW) weighting based on propensity scores can be used to produce approximately unbiased estimates of treatment effect hazard ratios and event risks using observational cohorts. Often the weights are treated as fixed even though they are random variables, typically derived from a logistic regression analysis applied to the same cohort with treatment use as the outcome. Bootstrapping the entire process of weight-derivation, Cox regression analysis and estimation produces valid confidence intervals that account for the variability in the weights, but this method may be time- and resource-intensive for large cohorts. Here the delta method is used to derive large sample interval estimates of treatment effects and event risks that account for variability in the weights analytically. External time-dependent covariates, left truncation, and cohort sampling study designs are accommodated. Simulation studies show that this method provides confidence interval coverage probabilities at or above nominal level for small and moderate sample sizes. Stabilization of the weights by multiplying them by the overall treatment rate noticeably improves confidence interval coverage probabilities. Software to perform the calculations is freely available.

Published in	American Journal of Applied Mathematics (Volume 10, Issue 5)
DOI	10.11648/j.ajam.20221005.11
Page(s)	176-204
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Cox Regression, IPTW, Propensity Score, Risk Estimation, Variability

References

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APA Style

Michael Richard Crager. (2022). Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation. American Journal of Applied Mathematics, 10(5), 176-204. https://doi.org/10.11648/j.ajam.20221005.11

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ACS Style

Michael Richard Crager. Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation. Am. J. Appl. Math. 2022, 10(5), 176-204. doi: 10.11648/j.ajam.20221005.11

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AMA Style

Michael Richard Crager. Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation. Am J Appl Math. 2022;10(5):176-204. doi: 10.11648/j.ajam.20221005.11

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@article{10.11648/j.ajam.20221005.11,
  author = {Michael Richard Crager},
  title = {Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation},
  journal = {American Journal of Applied Mathematics},
  volume = {10},
  number = {5},
  pages = {176-204},
  doi = {10.11648/j.ajam.20221005.11},
  url = {https://doi.org/10.11648/j.ajam.20221005.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20221005.11},
  abstract = {Under the assumption of no unmeasured confounders, Cox proportional hazards regression with inverse probability of treatment (IPTW) weighting based on propensity scores can be used to produce approximately unbiased estimates of treatment effect hazard ratios and event risks using observational cohorts. Often the weights are treated as fixed even though they are random variables, typically derived from a logistic regression analysis applied to the same cohort with treatment use as the outcome. Bootstrapping the entire process of weight-derivation, Cox regression analysis and estimation produces valid confidence intervals that account for the variability in the weights, but this method may be time- and resource-intensive for large cohorts. Here the delta method is used to derive large sample interval estimates of treatment effects and event risks that account for variability in the weights analytically. External time-dependent covariates, left truncation, and cohort sampling study designs are accommodated. Simulation studies show that this method provides confidence interval coverage probabilities at or above nominal level for small and moderate sample sizes. Stabilization of the weights by multiplying them by the overall treatment rate noticeably improves confidence interval coverage probabilities. Software to perform the calculations is freely available.},
 year = {2022}
}

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TY  - JOUR
T1  - Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation
AU  - Michael Richard Crager
Y1  - 2022/10/17
PY  - 2022
N1  - https://doi.org/10.11648/j.ajam.20221005.11
DO  - 10.11648/j.ajam.20221005.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 176
EP  - 204
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20221005.11
AB  - Under the assumption of no unmeasured confounders, Cox proportional hazards regression with inverse probability of treatment (IPTW) weighting based on propensity scores can be used to produce approximately unbiased estimates of treatment effect hazard ratios and event risks using observational cohorts. Often the weights are treated as fixed even though they are random variables, typically derived from a logistic regression analysis applied to the same cohort with treatment use as the outcome. Bootstrapping the entire process of weight-derivation, Cox regression analysis and estimation produces valid confidence intervals that account for the variability in the weights, but this method may be time- and resource-intensive for large cohorts. Here the delta method is used to derive large sample interval estimates of treatment effects and event risks that account for variability in the weights analytically. External time-dependent covariates, left truncation, and cohort sampling study designs are accommodated. Simulation studies show that this method provides confidence interval coverage probabilities at or above nominal level for small and moderate sample sizes. Stabilization of the weights by multiplying them by the overall treatment rate noticeably improves confidence interval coverage probabilities. Software to perform the calculations is freely available.
VL  - 10
IS  - 5
ER  -

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Author Information

Michael Richard Crager

Department of Biostatistics, Exact Sciences Corporation, Redwood City, United States

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Plain Text BibTeX RIS

APA Style

Michael Richard Crager. (2022). Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation. American Journal of Applied Mathematics, 10(5), 176-204. https://doi.org/10.11648/j.ajam.20221005.11

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ACS Style

Michael Richard Crager. Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation. Am. J. Appl. Math. 2022, 10(5), 176-204. doi: 10.11648/j.ajam.20221005.11

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AMA Style

Michael Richard Crager. Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation. Am J Appl Math. 2022;10(5):176-204. doi: 10.11648/j.ajam.20221005.11

Copy | Download

@article{10.11648/j.ajam.20221005.11,
  author = {Michael Richard Crager},
  title = {Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation},
  journal = {American Journal of Applied Mathematics},
  volume = {10},
  number = {5},
  pages = {176-204},
  doi = {10.11648/j.ajam.20221005.11},
  url = {https://doi.org/10.11648/j.ajam.20221005.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20221005.11},
  abstract = {Under the assumption of no unmeasured confounders, Cox proportional hazards regression with inverse probability of treatment (IPTW) weighting based on propensity scores can be used to produce approximately unbiased estimates of treatment effect hazard ratios and event risks using observational cohorts. Often the weights are treated as fixed even though they are random variables, typically derived from a logistic regression analysis applied to the same cohort with treatment use as the outcome. Bootstrapping the entire process of weight-derivation, Cox regression analysis and estimation produces valid confidence intervals that account for the variability in the weights, but this method may be time- and resource-intensive for large cohorts. Here the delta method is used to derive large sample interval estimates of treatment effects and event risks that account for variability in the weights analytically. External time-dependent covariates, left truncation, and cohort sampling study designs are accommodated. Simulation studies show that this method provides confidence interval coverage probabilities at or above nominal level for small and moderate sample sizes. Stabilization of the weights by multiplying them by the overall treatment rate noticeably improves confidence interval coverage probabilities. Software to perform the calculations is freely available.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Accounting for Propensity Score Variability in IPTW Weighted Cox Proportional Hazards Regression and Risk Estimation
AU  - Michael Richard Crager
Y1  - 2022/10/17
PY  - 2022
N1  - https://doi.org/10.11648/j.ajam.20221005.11
DO  - 10.11648/j.ajam.20221005.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 176
EP  - 204
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20221005.11
AB  - Under the assumption of no unmeasured confounders, Cox proportional hazards regression with inverse probability of treatment (IPTW) weighting based on propensity scores can be used to produce approximately unbiased estimates of treatment effect hazard ratios and event risks using observational cohorts. Often the weights are treated as fixed even though they are random variables, typically derived from a logistic regression analysis applied to the same cohort with treatment use as the outcome. Bootstrapping the entire process of weight-derivation, Cox regression analysis and estimation produces valid confidence intervals that account for the variability in the weights, but this method may be time- and resource-intensive for large cohorts. Here the delta method is used to derive large sample interval estimates of treatment effects and event risks that account for variability in the weights analytically. External time-dependent covariates, left truncation, and cohort sampling study designs are accommodated. Simulation studies show that this method provides confidence interval coverage probabilities at or above nominal level for small and moderate sample sizes. Stabilization of the weights by multiplying them by the overall treatment rate noticeably improves confidence interval coverage probabilities. Software to perform the calculations is freely available.
VL  - 10
IS  - 5
ER  -

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