Multiple comparison issue in multivariate logistic regression I am assessing a bunch of risk factors related to HIV infection by logistic regression.
First I will conduct a couple of chi square tests or t-tests to see if each factor is associated with HIV infection or not.
Then I will pick those factors with p value less than 0.1 out of the bivariate analysis above and include them in the multivariable logistic regression model (adjusted model).
In this case, is multiple comparison a concern for me? Why and why not?
 A: Testing each of the risk factors individually is probably not the best idea: what if a combination of two predictors that individually are not good, predict very well together? There are many methods available to do more proper variable selection, most of them some form of penalized regression, like (adaptive) lasso.
Apart from that: If you are willing to throw variables back out after adding them to the logistic regression, it doesn't really matter whether you do multiple testing correction or not: the unconditional strong association of a variable is not necessarily a good predictor of the conditional association (that is: conditional on all the other predictors included in the model). If you insist on doing this univariate variable selection: pick any criterion that gives you a reasonable set of variables (e.g.: the 20 variables with the smallest univariate p-values, or all variables that have p-values less than a threshold you think is nice), fit the model with those 20 variables (assuming you have enough data) and then throw the ones that don't perform conditionally in the model, back out.
Be aware, though: I did not tell you to do it this way. My advice is to use a proper variable selection method.
