Tutorials : center effect
The center : a possible confounder
Clinical practices and/or patient profiles are often heterogeneous between centers. One can therefore suspect unobserved variables differently distributed between centres (socioeconomic level of patients, environmental pollution, etc.). Some of these variables may constiture confounders. Taking into account the center effect tends to adjust the results on these confounders.
Adjustement of the results on the center

In multivariate models (conditional approach), an adjustment on the center as an explanatory variable can be made (fixed effect). The centre can also be included as a random effect.

Also in the conditional context, but in the particular case of a Cox model, a stratification of the baseline hazard function on the center can be performed.

In the context of a marginal effect, the centre can be included in the propensity score, i.e. as an explanatory variable of the logistic model predicting the probability of exposure.