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

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:

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.

• To explore further, I do have some covariates available in the pre intervention (only) period, they don't have a post intervention value (unlike the example in my OP), can they somehow be adjusted for in repeated measure analysis? This would be adjusted for as between subject covariate though, right? Jan 10, 2020 at 4:07
• Are those extra covariates time-independent, or are they possibly time-dependent, but only measured pre, or are they not meaningful post? ... You should really update your post with context, telling us what are the measurements, what are the covariables, maybe include some plots, and could you share (a link to) the data? Jan 10, 2020 at 4:13
• I have updated with details. Jan 10, 2020 at 16:42