  With the evolution of single-cell RNA sequencing techniques into a standard
approach in genomics, it has become possible to conduct cohort-level causal
inferences based on single-cell-level measurements. However, the individual
gene expression levels of interest are not directly observable; instead, only
repeated proxy measurements from each individual's cells are available,
providing a derived outcome to estimate the underlying outcome for each of many
genes. In this paper, we propose a generic semiparametric inference framework
for doubly robust estimation with multiple derived outcomes, which also
encompasses the usual setting of multiple outcomes when the response of each
unit is available. To reliably quantify the causal effects of heterogeneous
outcomes, we specialize the analysis to standardized average treatment effects
and quantile treatment effects. Through this, we demonstrate the use of the
semiparametric inferential results for doubly robust estimators derived from
both Von Mises expansions and estimating equations. A multiple testing
procedure based on Gaussian multiplier bootstrap is tailored for doubly robust
estimators to control the false discovery exceedance rate. Applications in
single-cell CRISPR perturbation analysis and individual-level differential
expression analysis demonstrate the utility of the proposed methods and offer
insights into the usage of different estimands for causal inference in
genomics.
