# Should I include post-treatment data from the wait-list control group in the final analyses?

This is my first time dealing with RCT using wait-list control group. I'm planning to use linear mixed model for treatment effectiveness analysis.

Flowchart (edited):

My questions are: 1. Should I include post-treatment data from the wait-list control group in my analysis? (N=(23+10+12?) for pre-test/baseline, N=(22+9) for 7-day, N=(17+5) for 3month)? 2. Does it make sense if I use two separate models (mixed effect) using proc mixed for "pre and post test" for between subject variation and within-subject variation combining intervention and waitlist participants together as I mentioned in my first question?

• I would definitely recommend conducting a main analysis including the wait-list control and a sensitivity analysis excluding it (or the other way round). Depending on the pre-hoc protocol, you should consider one of the two as the main one for hypothesis testing and the other as exploratory. – Joe_74 May 17 '17 at 8:12
• Does that flowchart represent your final enrollment figures? What enrollment targets had you set originally, based on your power analysis? What sort of disease do you study here? Can you say more about the equipoise that rendered wait-listing 1/3 of patients ethical? Does the disease sometimes have a self-limiting character? Was the wait-time fixed, or do you have a time-to-event phenomenon to model in that regard, also? – David C. Norris May 17 '17 at 11:06
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• @Joe_74 Using waitlist observations for pre-test/baseline would look like this (N=(23+10+12=T1i+T1w+T2w) to compare to more straightforward for other time poitns N=(22+9) for 7-day, N=(17+5) for 3month)? Does it make sense to you? Potential effect of time (4 weeks) that would make T1w different from T2w is still there. Right? – Maggie May 18 '17 at 22:47
• @DavidC.Norris Q1: Yes. Q2:Target was equal sample sizes of 25 (N=50). 0.92 if change score=8 and 0.66 if change score=7. Q3-5:Primary outcome measure is the quality of life tested using SF36 questionnaire. Study subjects were Gulf War veterans who were interested in 4wk intervention (sauna detoxication, exercise) that study proposed. However, wait-list participants showed higher drop after told as not covered for the first-round. Pls note I edited in the flowchart. Could you also please look at my second question in my post too? – Maggie May 18 '17 at 22:58

You have a problem of missing data here, in which the missing-data mechanism hopelessly confounds the mechanism of the treatment effect. This likely represents a failed trial, which you should report honestly as such.

In this study (ostensibly) of 'detoxification', you chose to measure not objective pre- and post-treatment serum or sweat concentrations of 'toxins', but rather subjective reports on a survey instrument. This tells me that you did not take at face value the 'detoxification' concept, or at least did not intend to examine scientifically the claim embedded in that word. Thus, at the very least, you demonstrate an agnosticism to your sauna 'detoxification' intervention that leaves open the possibility that it exerts its effects through psychosocial and similar 'placebo' mechanisms of the kind frequently described in connection with 'complementary and alternative medicine' treatments such as 'detox'.

Can you argue persuasively that the mechanism driving the severe loss to follow up (LTFU) in your wait-listed group operated entirely separately from (placebo) mechanisms of 'detoxification'? I myself would tend to read psychological factors into this, like disappointment among those wait-listed and feeling lucky for those not wait-listed. How could you disentangle such phenomena from placebo mechanisms of the sauna treatment? I see that you list Bayesian methods as an area of interest in your bio; you would in fact be able to examine questions such as this using Bayesian methods that posit informative missingness mechanisms in your data set. See e.g. Greenland's work on quantitative bias analysis [1] and Chapter 8 in BDA3 [2].

I understand your original question as reflecting a hope that following one or more statistical 'best practices' might help you produce a credible analysis of this trial. As I have indicated with this answer, I consider that hope misplaced. Indeed, the only purely statistical advice that seems relevant at this point regards correct reporting of loss to follow up. From your earlier comment, I gather that you actually randomized on a 1:1 basis, so that the $N=12$ in your diagram counts only half of the veterans actually assigned to the wait-list. By correcting this under-counting, thus making clear the actual magnitude of LTFU in your study, you will begin the process of convincing the various people involved that the study has failed.

1. Greenland S. Multiple-bias modelling for analysis of observational data (with discussion). J R Stat Soc A. 2005;168(2):267-306. doi:10.1111/j.1467-985X.2004.00349.x.

2. Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian Data Analysis. Third edition. Boca Raton: CRC Press; 2014.

• This pilot hopes to get to a biological monit eventually. However, as a graduate assistant I noticed and agree with you on the evident failure Nevertheless I can use the data for learning Because, we have no control for 3mo FU, I'd think of 2 sep analyses. 1. Pre-post test for 7-day after intervention(int) and 4 wk after wait compare to pre-test? Within and btw subject var should be accounted here. Mixed effect or ANCOVA? 2). aggregate data longitudinally by time points: pre-test, 4 wk wait, 7day after int and 3mo after int and look at how slopes changed across time? Make sense? – Maggie May 24 '17 at 5:11