# Variable selection for Cox regression repeated for multiple covariates of interest

I am doing a retrospective analysis of the effect of various measures of haemodynamics in sepsis on mortality. I will separately look at the effect of 5 independent variables: 1) shock index 2) blood pressure 3) heart rate 4) arterial BP 5) non invasive BP

I plan to do use Cox regression analysis to calculate the odds ratio of each of the five above variables with respect to mortality. I will repeat my method 5 times, once for each of the 5 above independent variables. Each time, I will take 1 of the above independent variables and several other covariates to be adjusted for (ie. age, sex, source of admission, mean glucose, presence of positive blood culture, lactate, presence of CKD, hepatic failure, cancer, heart failure and diabetes). All will be included in the Cox regression model. Then, I will optimise the model by stepwise removing the covariate with the highest p-value, until all p-values for each covariate are p<0.2. The number I'm interested in will be the odds ratio of that independent variable (shock index, blood pressure, heart rate, arterial BP or non invasive BP) with respect to mortality.

Now, my problem is that each of the five calculations of my odds ratio, a different set of covariates is included. (EDIT: different covariates are included because each of the five independent variables interact different with the other covariates changing their multivariate significance and hence which ones are removed in the stepwise feature selection process). I think this creates bias and makes it difficult to compare the effect size of each of my 5 independent variables of interest. For example, overfitting will effect each of my 5 effect sizes differently.

Is this something I can avoid? Would it be better to not optimise my model each time? Or would there be some other way to ensure that my list of covariates are the same on each of the 5 repetitions?

• Please provide more information about your data and analysis. It's not clear why you have different sets of covariates depending on the particular predictor variable you are examining; is this some type of meta-analysis of separate studies? Also, as the values of those variables certainly change over time, are you treating them as time-dependent predictors or are you restricting analysis to values at some particular time, like at admission? How many cases and deaths are there? That could affect how best to handle the other covariates.
– EdM
Dec 24, 2019 at 17:58
– EdM
Dec 24, 2019 at 17:59
• I have different sets of covariates because each of the 5 independent variables interact differently with the other covariates, causing each to have different significance in the multivariate model. Covariates are stepwise removed if p<0.2, and this is a different set each time. Dec 25, 2019 at 22:14
• Thanks for your point @EdM. Due to the biases of stepwise selection and also my difficulty comparing independent variables, I will include a calculation skipping the predictor selection steps. However, I think there is some benefit from selecting predictors because it removes the extraneous ones without predictive power. Dec 25, 2019 at 22:18