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I've been told that if all known prognostic factors are not adjusted for in a non linear model, in this case a Cox PH model, that because the error term is not estimated the treatment variable will necessarily be biased. However, I was wondering in this particular case, if my sample is balanced in both trial arms by all known prognostic factors and my sample matches the population I aim to use the treatment will a univariate model that does not control for these prognostic factors as covariates give an unbiased HR of the treatment effect in the target population?

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    $\begingroup$ If the prognostic factors have a causal effect on the explanatory variable (the treatment), then you should control for them. If, on the other hand, there is no causal effect from the prognostic factors to the treatment, then you should NOT control for them. $\endgroup$ – Adrian Keister Jun 1 '20 at 14:57
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I address this question here. The quick answer is that because the hazard ratio (HR) is not collapsible, the marginal and conditional HRs will differ even in the absence of confounding. If your sample is balanced (e.g., as a result of random assignment), you can estimate the marginal HR without including any covariates in the model, and it will be unbiased. You can estimate a conditional HR by including covariates in the model. How to proceed depends on whether you want the marginal or conditional HR. If you're a health policymaker deciding whether to implement a blanket policy recommending one treatment over another, you probably want the marginal HR; if you're a doctor figuring out which treatment to prescribe based on the covariates that are available in your dataset, then you probably want the conditional HR.

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