Background: The hazard ratio of the Cox proportional hazards model is widely used in randomized controlled trials to assess treatment effects. However, two properties of the hazard ratio including the non-collapsibility and built-in selection bias need to be further investigated. Methods: We conduct simulations to differentiate the non-collapsibility effect and built-in selection bias from the difference between the marginal and the conditional hazard ratio. Meanwhile, we explore the performance of the Cox model with inverse probability of treatment weighting for covariate adjustment when estimating the marginal hazard ratio. The built-in selection bias is further assessed in the period-specific hazard ratio. Results: The conditional hazard ratio is a biased estimate of the marginal effect due to the non-collapsibility property. In contrast, the hazard ratio estimated from the inverse probability of treatment weighting Cox model provides an unbiased estimate of the true marginal hazard ratio. The built-in selection bias only manifests in the period-specific hazard ratios even when the proportional hazards assumption is satisfied. The Cox model with inverse probability of treatment weighting can be used to account for confounding bias and provide an unbiased effect under the randomized controlled trials setting when the parameter of interest is the marginal effect. Conclusions: We propose that the period-specific hazard ratios should always be avoided due to the profound effects of built-in selection bias.

翻译：背景：Cox比例风险模型的风险比被广泛用于随机对照试验以评估治疗效果。然而，风险比的两个性质——不可压缩性与内置选择偏倚——仍需进一步探究。方法：我们通过模拟实验来区分边际风险比与条件风险比差异中蕴含的不可压缩性效应和内置选择偏倚。同时，探究采用逆概率治疗加权Cox模型进行协变量调整时，估计边际风险比的性能表现。进一步评估时段特异性风险比中的内置选择偏倚。结果：由于不可压缩性性质，条件风险比对边际效应的估计存在偏倚。相反，基于逆概率治疗加权Cox模型估计的风险比，可无偏估计真实边际风险比。即使比例风险假设成立，内置选择偏倚也仅在时段特异性风险比中显现。当关注参数为边际效应时，逆概率治疗加权Cox模型可用于校正混杂偏倚，并在随机对照试验背景下提供无偏效应估计。结论：由于内置选择偏倚的深远影响，我们建议始终避免使用时段特异性风险比。