# Is the Breslow estimator over-adjusted?

In a proportional hazard model with a Breslow estimator, I wondered why do we adjust on covariates in the cumulative hazard and in the model. On these few lines from Xia et al.[2], we can see that the linear predictors are used twice in the survival function.

I ran some simulations on a Cox model with a Breslow estimator and my variance was far too small. So I wondered if the cause was not because the model was over-adjusted ...

Why do we need to multiply $$\hat{\Lambda}_{0,BR}(t)$$ by $$\exp(\hat{\beta} z)$$ knowing that $$\exp(\hat{\beta} z)$$ was already used for the calculation of $$\hat{\Lambda}_{0,BR}(t)$$?

I am sorry if this question seems naive!

[2]:J Biom Biostat 2018, 9:2 DOI: 10.4172/2155-6180.1000392