What specific endpoint(s) were used in determining the efficacy of the Pfizer and Moderna Covid-19 vaccines during the FDA trials?

I have been searching over various articles and pages from the CDC and elsewhere, but I haven't yet found a specific description of what endpoint(s) were used to define efficacy in the FDA Covid-19 vaccine trials for the Pfizer or Moderna vaccines. There are multiple articles suggesting reasonable primary and secondary endpoints to determine efficacy but nothing showing what they actually used.

Some possible endpoints:

• percentage who contracted Covid-19
• percentage who developed no, mild, or severe symptoms
• percentage hospitalized
• percentage who died
• transmissibility
• viral load a certain number of days after infection

If this info is available I'd like to know what combination of the above endpoints was used to get the 90-somehing percent efficacy results, and if possible how the math would have been done (ie. are multiple endpoints combined in some weighted fashion e.g. where hospitalization/death are primary endpoints but then secondary endpoint of viral-load is factored in).

In short, when we say a vaccine was found to be N% efficacious, what does that specifically mean?

TL;DR: The N% efficacy reported for a vaccine means that N% of the cases in the controls could have been prevented had they been vaccinated.

You have a few different question mushed together, so here are some key insights (you can read the first of many publications on safety and efficacy for both vaccines linked in my references as the end of my answer):

Vaccine efficacy, also termed the preventable fraction (Rothman and Greenland, 2008), is defined as:

$$\text{vaccine efficacy} = \frac{\text{rate}_{\text{controls}} - \text{rate}_{\text{vaccinated}}}{\text{rate}_{\text{controls}}}$$

Sometimes this fraction is expressed as the mathematically equivalent:

$$\text{vaccine efficacy} = 1 - \frac{\text{rate}_{\text{vaccinated}}}{\text{rate}_{\text{controls}}}$$

In these formulas $$\text{rate}$$ is a measure of the risk of COVID-19 infection as the studies' primary endpoints:

• For the Pfizer mRNA vaccine, that specifically was "confirmed Covid-19 with onset at least 7 days after the second dose in participants who had been without serologic or virologic evidence of SARS-CoV-2 infection up to 7 days after the second dose," Polack, F. P., et al., 2020.
• For the Moderna mRNA vaccine, that specifically was "a first occurrence of symptomatic Covid-19 with onset at least 14 days after the second injection in the per-protocol population, among participants who were seronegative at baseline," Baden L. R., et al., 2021.

Risks are always expressed for a given unit of time—like a year, or 90 days, or for both these vaccine trials, cases per 1000-person years.

The vaccine efficacy fraction expresses how much of the risk for COVID-19 infection in the unvaccinated (controls—participants receiving a placebo in these studies) could be prevented via vaccination. Risk (also known as an "incidence rate") can generally be measured in two ways (incidence densities or incidence proportions), but in randomized control trials, they are very often measured as incidence densities, which is a way of averaging observed risk across study participants who have been observed for differing lengths of time (for example, one subject may have been observed for 27 days before contracting COVID-19, while another may have been observed for 67 days before contracting COVID-19).

The 90-something percent efficacies reported for both the mRNA vaccines means that more than 90 of the cases of COVID-19 in the controls could have been prevented had they been vaccinated. Of course, there's lots of additional details and assumptions (e.g., what strain was prevalent during the randomized control trials, and so forth).

Different endpoints require different measurements and will necessarily have different efficacy measures. For example, efficacy against COVID-19 mortality is not the same as efficacy against COVID-19 infection. And the 1 year efficacy is not the same thing as the 30-day efficacy (for many reasons, including prevalence of COVID-19 infections, prevalent strains, reproductive rate of infection, behavioral changes due to perceived risk and distributions of such behaviors, decay in immune response from acquired immunity, etc.).

References

Baden, L. R. et al., (2021). Efficacy and Safety of the mRNA-1273 SARS-CoV-2 Vaccine. The New England Journal of Medicine. 384(5), 403–416.

Polack, F. P., et al., (2020). Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine. The New England Journal of Medicine, 383(27), 2603–2615.

Rothman, K. J., Greenland, S., & Lash, T. L. (2008). Modern Epidemiology (3rd ed.). Lippincott Williams & Wilkins.

As mentioned, a vaccine’s efficacy is measured in a controlled clinical trial and is based on how many people who got vaccinated developed the ‘outcome of interest’ (usually disease) compared with how many people who got the placebo (dummy vaccine) developed the same outcome. It’s important to note that the various clinical trials relating to vaccines is merely a rough probabilistic measurement of efficacy – even in a well defined study with control groups, there are numerous independent biological variables that cannot be measured quantifiably.