# 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?

The Wald test on coefficients is probably closest to what you're familiar with from linear regression. It's based on an assumption that the distribution of coefficient estimates is multivariate normal. Coefficient variance estimates thus tend to scale inversely with the number of observations $$n$$ and their standard deviations with $$\sqrt n$$, as you might expect.