How to control for within-subject covariate in a single-arm, mirror image study design?

Question

I have a mirror image study which consists of one group of subjects, and they have a measure before and another measure after an intervention.

Depiction:

Single group: Measure#1 -> (Intervention) -> Measure#2

Paired-t test is used to examine the statistical significance of the difference between measure #1 and measure #2.

I know this pre/post single-arm study is a weak study design due to the lack of control group and randomization. I also know that maturation (or natural changes) of subjects over this period (due to factors unrelated to the intervention itself) can lead to the difference between the 2 measures.

I have a covariate that I derived which is time-dependent, such that there is one covariate value before and another covariate value after the intervention.

I'm not aware that time-dependent covariates can be added in a paired-t test, are there any statistical test I can use to test the difference between the measure #1 and measure #2 but adjust for the time-dependent covariate?

Edited to provide more details below:

As a whole, the subjects are patients who initiated drug A (intervention). Pre-intervention and post-intervention measures refer to the number of doctor's visits within 1 year, such that pre-intervention is between 1 year before and up until the intervention period, while the post-intervention is between intervention and 1 year after the intervention.

The time-dependent covariate is a proxy disease severity indicator which has a value of Y (more severe) and N (less severe), and they are measured pre- and post-intervention.

Other time-independent covariates I have are age and sex. While another covariate which could be time-dependent but only measured during the pre-intervention is whether of not patient takes drug B and drug C.

An sample data would like the following:

Answer 1

You can see your situation as Repeated measures with a time-dependent covariate, and model the repeated measurements using linear mixed models. Also note that a paired t-test can be represented via mixed models also, see Paired t-test as a special case of linear mixed-effect modeling.

Your data file (in long format) could look like

ID   Time    Y      x
A     1      .      .
A     2      .      .
B     1      .      .
B     2      .      .
.
.

and your model (in R, with package lme4) something like

mod <- lme4::lmer(Y ~ x + Time + (1|ID), data=your_data_frame, ...)

This as a starting point, you didn't tell us much context.