  The usual development cycles are too slow for the development of vaccines,
diagnostics and treatments in pandemics such as the ongoing SARS-CoV-2
pandemic. Given the pressure in such a situation, there is a risk that findings
of early clinical trials are overinterpreted despite their limitations in terms
of size and design. Motivated by a non-randomized open-label study
investigating the efficacy of hydroxychloroquine in patients with COVID-19, we
describe in a unified fashion various alternative approaches to the analysis of
non-randomized studies. A widely used tool to reduce the impact of
treatment-selection bias are so-called propensity score (PS) methods.
Conditioning on the propensity score allows one to replicate the design of a
randomized controlled trial, conditional on observed covariates. Extensions
include the g-computation approach, which is less frequently applied, in
particular in clinical studies. Moreover, doubly robust estimators provide
additional advantages. Here, we investigate the properties of propensity score
based methods including three variations of doubly robust estimators in small
sample settings, typical for early trials, in a simulation study. R code for
the simulations is provided.
