How do covariates influence the sample sizes for survival and binary outcomes? Currently, I try to wrap my head around the concept of how covariates influence non-normal outcomes like survival and binary outcomes. I know that in linear models the unexplained variance shrinks according to the squared Pearson correlation. This in turn influences the test statistic when testing a coefficient. This is a concept I now understand well enough.
I now try to understand the same concept when conducting logistic regression for binary outcomes or cox-regression for survival outcomes. Can someone explain to me how the commonly used test statistics are effected or could suggest some papers/books that explain this?

For logistic regression, the covariate changes the log-odds. For Cox regression model, the covariate changes the log-hazard. It might help to read this.
