Good day everyone.

I'm having difficulties in generating a similar output found in an article that reports on relative change in probabilities among the number of people with a prior response who change it to a particular post-treatment response.

Summary of my data:
I have 14 treatment arms (in the form of a message), 1 of which is the control arm (arm 8). I'll call this categorical variable "Arm".

Participants are asked a pre-treatment question which has 4 ordinal levels ("Definitely No", Probably No", "Probably Yes", and "Definitely Yes"). I'll call this variable W.

Participants are then exposed to 1 or 2 messages, depending on the arm they are in. After that, they are then asked the same question as the pre-treatment question (I'll call this variable Y).

I ran an ordinal logistic regression with the control arm as the comparator:

ologit Y W ib8.Arm

Ordered logistic regression Number of obs = 5,784
LR chi2(14) = 6002.02
Prob > chi2 = 0.0000
Log likelihood = -2162.2764 Pseudo R2 = 0.5812

------------------------------------------------------------------------------
Y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Arm |
1 | -.3515066 .2239792 -1.57 0.117 -.7904979 .0874846
2 | .1390929 .226348 0.61 0.539 -.304541 .5827269
3 | -.0402385 .2271925 -0.18 0.859 -.4855275 .4050505
4 | -.4568252 .2253801 -2.03 0.043 -.8985621 -.0150883
5 | .1046006 .2228341 0.47 0.639 -.3321463 .5413475
6 | -.0366926 .2236594 -0.16 0.870 -.4750569 .4016716
7 | -.1334436 .2257624 -0.59 0.554 -.5759297 .3090426
9 | -.1544665 .2223191 -0.69 0.487 -.5902039 .2812709
10 | -.1488834 .2247939 -0.66 0.508 -.5894713 .2917045
11 | -.4866269 .226059 -2.15 0.031 -.9296944 -.0435593
12 | -.2457011 .2234472 -1.10 0.272 -.6836495 .1922473
13 | -.0185866 .2262289 -0.08 0.935 -.4619871 .4248139
14 | -.2465563 .2278901 -1.08 0.279 -.6932127 .2001
|
W | 4.487208 .0823932 54.46 0.000 4.32572 4.648696
-------------+----------------------------------------------------------------
/cut1 | 6.497468 .2666616 5.974821 7.020115
/cut2 | 10.07818 .2704226 9.548164 10.6082
/cut3 | 14.82019 .3187617 14.19543 15.44496


After that, I ran the margin and over() code, with the condition of at(W=1) to obtain predicted probability differences between each arm with the control arm, given that a respondent were to answer "Definitely No" in W.

margins, at(W==1) over(rb8.Arm)

| Delta-method
| Contrast Std. Err. [95% Conf. Interval]
----------------------+------------------------------------------------
Arm@_predict |
(1 vs 8) 1 | .0319949 .0211312 -.0094216 .0734113
(1 vs 8) 2 | -.030896 .0204181 -.0709147 .0091227
(1 vs 8) 3 | -.0010892 .0007269 -.0025139 .0003354
(1 vs 8) 4 | -9.64e-06 6.54e-06 -.0000225 3.17e-06
(2 vs 8) 1 | -.0152769 .0249436 -.0641653 .0336116
(2 vs 8) 2 | .0147245 .0240433 -.0323995 .0618484
(2 vs 8) 3 | .0005475 .0008963 -.0012091 .0023042
(2 vs 8) 4 | 4.86e-06 7.96e-06 -.0000107 .0000205
............

By computing this, I realised that this method will only provide probability differences, given if a person answers "Definitely No" during pre-treatment, in general. It does not provide information on the relative change in probabilities in the number of people who answered "Definitely No" in W who change it to a certain level of answer in Y,post-treatment, relative to the control group.

As a reference, I am trying to generate similar outputs found in Figure 2 and Supplementary Table 2 in this article (link provided). I understand that the author used Bayesian techniques. I do not wish to thread with that much complexity and prefer with the frequentist approach.

https://www.nature.com/articles/s415...-01056-1#Sec14

https://static-content.springer.com/...MOESM1_ESM.pdf

Does anyone here know how to perform such analysis in STATA?

Your kind advice and guidance on this matter is much appreciated. Thank you very much.