Department of Obstetrics and Gynecology and Duke Global Health Institute, Duke University, Durham, NC, USA.
Stat Med. 2012 Aug 30;31(19):2098-109. doi: 10.1002/sim.5317. Epub 2012 Apr 11.
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 on large-sample theory and provided accurate estimates of the hazard ratio.
受先前发表的 HIV 治疗研究的启发，我们模拟了受先前治疗影响的时变混杂数据，以检查边缘结构 Cox 比例风险模型的一些有限样本性质。我们比较了（a）未调整、（b）回归调整、（c）未稳定和（d）稳定的边缘结构（逆处理概率 [IPT] 加权）模型估计值的偏差、标准误差、均方根误差 (MSE) 和 95%置信限覆盖范围，涵盖了一系列研究场景，包括相对较小的样本量和 10 次研究评估。在类似于激发示例的基本情况下，真实风险比为 0.5，IPT 加权分析均无偏差，而原始和调整分析均偏向于并跨越了零假设。在包括相对较小样本量在内的一系列情况下，稳定的 IPT 加权分析仍然无偏差；然而，在原始和调整模型中，标准误差通常较小。在许多情况下，与其他方法相比，未稳定加权分析的标准误差大幅增加。对于基本情况，IPT 加权分析的根均方误差最小。在不存在先前治疗影响的时变混杂的情况下，IPT 加权分析的精度较低，因此与调整分析相比，根均方误差更大。95%置信限覆盖范围接近所有稳定 IPT 加权分析的标称值，但在原始、调整和未稳定 IPT 加权分析中较差。在现实情况下，边缘结构 Cox 比例风险模型根据基于大样本理论的预期表现良好，并提供了风险比的准确估计。
