I have two questions regarding methods for a pending project:

I will have an outcome "yscale" that has values 0 - 5. I am interested in the treatment effect on yscale of treatment "treatx," in which a subject may have a value that ranges from 1 (no treatments) to 5 (four treatments) over time. Many subjects will receive no treatments and will always have the 1 value.

I will have an unbalanced panel of observations over time per subject, at each of which a treatment may occur, adding to the total count for the subset of patients who ever receive the treatment.

A beneficial treatment effect would be a reduction in yscale from one observation to the next.

We also are controlling for continuous variables varq and varz in both treatment and outcome models.

One challenge we face is that it is almost impossible to download custom code packages for Stata due to particulars of the research setting. We will use whatever is already a part of Stata 16.


Goals:

A) Ideally, I wish to know the effect of each treatx value compared to having the next-lowest value in order to capture a dose-response effect.

B) If that is not possible, the next-best does-response-related effect to reveal would be that of any treatx count compared to the 1 value.


Questions in boldface:

1) What is the best model under the teffects family to reveal either or both of these effects?

For now, we have assessed that teffects with the AIPW option might let us address goal B. Most of the teffects options seem to require a two-level treatment, which doesn't work here. It seems unclear if any of the effects packages will let us answer goal A.

We also assume the robust SE inherent to AIPW helps this option serve well for the panel data with serial observations for the same subjects.

2) Assuming AIPW is appropriate, we are trying to ascertain the appropriate interpretation of the regression coefficients from AIPW from findings so far in test data, when the multinomial logit is specified for the treatment and the linear model is specified for the outcome. Here is some sample output from a modeling exercise. Are the interpretations of the output correct? I've omitted uncertainty metrics for simplicity; assume all findings are significant:


Interpretations:

ATE interpretations:

Having three treatments (treatx value 4) is associated with a mean reduction in yscale of 0.8 for subjects with three treatments compared to those with none (treatx value 1).

Having four treatments (treatx value 5) is associated with a mean reduction in yscale of 1.7 for subjects with four treatments compared to those with none (treatx value 1).

POmean interpretation:

At observations with no treatments, the mean potential outcome is a yscale value of 3.7.

OME1 interpretation:

In the absence of any treatments, a one-unit increase in varq is associated with a -0.001 decrease in the yscale value when controlling for varz.

TME2 interpretation (here is where we become especially confused):

A one-unit increase in varq is associated with a 0.002 increase in the probability of receiving 1 treatment compared to receiving none.

TME3 interpretation (also confused):

A one-unit increase in varq is associated with a 0.003 increase in the probability of receiving 2 treatments compared to receiving none.
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yscale |
------------------+---------------
ATE |
treatx |
(2: one |
vs |
1: none) | -.04
(3: two |
vs |
1: none) | -.06
(4: three |
vs |
1: none) | -.8
(5: four |
vs |
1: none) | -1.7
------------------+----------------------------------------------------------------
POmean |
treatx |
1: none | 3.7
OME1 |
varq | -.001
varz | -.01
_cons | 4.0
------------------+----------------------------------------------------------------
OME2 |
varq | -.0004
varz | .002
_cons | 3.3
------------------+----------------------------------------------------------------
OME3 |
varq | -.005
varz | -.006
_cons | 3.7
------------------+----------------------------------------------------------------
OME4 |
varq | .03
varz | -.006
_cons | 2.6
------------------+----------------------------------------------------------------
OME5 |
varq | .006
female | -.09
_cons | .7
------------------+----------------------------------------------------------------
TME2 |
varq | .002
varz | -.7
_cons | -6.8
------------------+----------------------------------------------------------------
TME3 |
varq | .003
varz | -.5
_cons | -8.4
------------------+----------------------------------------------------------------
TME4 |
varq | -.2
varz | -.1
_cons | -9.1
------------------+----------------------------------------------------------------
TME5 |
varq | -.8
varz | -.57
_cons | -10.3