## Abstract

Motivated by a previously published study of HIV treatment, we simulated data subject to time-varying confounding affected by prior treatment to examine some finite-sample properties of marginal structural Cox proportional hazards models. We compared (a)unadjusted, (b)regression-adjusted, (c)unstabilized, and (d)stabilized marginal structural (inverse probability-of-treatment [IPT] weighted) model estimators of effect in terms of bias, standard error, root mean squared error (MSE), and 95% confidence limit coverage over a range of research scenarios, including relatively small sample sizes and 10 study assessments. In the base-case scenario resembling the motivating example, where the true hazard ratio was 0.5, both IPT-weighted analyses were unbiased, whereas crude and adjusted analyses showed substantial bias towards and across the null. Stabilized IPT-weighted analyses remained unbiased across a range of scenarios, including relatively small sample size; however, the standard error was generally smaller in crude and adjusted models. In many cases, unstabilized weighted analysis showed a substantial increase in standard error compared with other approaches. Root MSE was smallest in the IPT-weighted analyses for the base-case scenario. In situations where time-varying confounding affected by prior treatment was absent, IPT-weighted analyses were less precise and therefore had greater root MSE compared with adjusted analyses. The 95% confidence limit coverage was close to nominal for all stabilized IPT-weighted but poor in crude, adjusted, and unstabilized IPT-weighted analysis. Under realistic scenarios, marginal structural Cox proportional hazards models performed according to expectations based onlarge-sample theory and provided accurate estimates of the hazard ratio.

Original language | English (US) |
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Pages (from-to) | 2098-2109 |

Number of pages | 12 |

Journal | Statistics in Medicine |

Volume | 31 |

Issue number | 19 |

DOIs | |

State | Published - Aug 30 2012 |

Externally published | Yes |

## Keywords

- Bias
- Causal inference
- Marginal structural models
- Monte Carlo study

## ASJC Scopus subject areas

- Epidemiology
- Statistics and Probability