# low sample size - causal study using multiple outcome analysis

I am trying to do a healthcare analysis project (observational research) using retrospective data for the first time. Let's say I would like to study the effect of drug A. The primary outcome is death and secondary outcome (unintended effect of the drug) is chest pain (for example).

My question is about the sample size.

Let's say my dataset has 3000 patients... And I have info on the primary outcome for 3000 patients. Meaning, I know whether a patient is dead or not...So, 3000 is a good sample number. (indicating good statistical power)

However, when I look at the secondary outcome, I have info only for about 430 patients. For the rest of the patients, it is NA.

In this case, how should I analyze the data for secondary outcomes?

Should I impute the missing data? Doesn't make sense to impute using the usual fillna() approaches.

I am interested to know on the below

a) How do we address the lack of enough info from the secondary outcome? Does secondary outcome need to have a good sample size too? (or is it because we are only interested in the effect of a drug on the primary outcome, what kind of info can be reported about the secondary outcome?

b) Since, we have 430 patients with the secondary outcomes, is it possible to extrapolate it for 3000 patients?

c) Does primary and secondary outcome analysis have to be on the same count of patients (3000)? Is it okay to do the below? First, I will do my primary outcome analysis on 430 patients... 2nd, I will do my primary outcome analysis on 3000 patients... Compare the result from these two methods (not sure how can I compare though)

d) If the comparison output produces same results, can I say that my secondary outcome analysis on 430 patients will generalize to 3000 patients?

Can someone guide me to a related topic where I can read about this (especially on lack of enough sample size for secondary outcome) and how to do this correctly? how to handle uneven sample sizes for primary and secondary outcome?