How can I model association between participant risk threshold and their demographic characteristics

[lei]

Hi,

i li have a study of patients where we asked them to choose between two procedures of varying risk. One procedure had risk of 0 percent mortality but more side effects (call this A). The other procedure has no side effects but has a certain percent of mortality (call b).

in this case we started everyone on procedure B and asked them at what percent mortality from 0 to 100% will they switch to procedure A. The distribution of this switching threshold is left skewed. I want to determine the association between some demographic covariates like age, sex, etc with what mortality rate they would accept to switch to procedure A. One problem is that, if a person switches at 30% mortality rate that means they would also switch at any mortality greater than 30%. 

how would we model this. I am at s loss right now.

thank you.

[pearsoninst]

You can look bayes theorem and see if that helps

[lei]

Hi thank you for the response. I know Bayes theorem. Can you elaborate a bit further?

[SteveDenham]

Start with a simple model--the probability of switching as a function of mortality.  That could easily be fit with a logistic regression.  Since you have repeated and correlated measures of the response per subject, you would likely need to fit this with PROC GLIMMIX (or if going Bayesian, with PROC MCMC).  Once you get that model working, you could add covariates of interest.  Does that approach make sense?

Steve Denham

[PGStats]

I don't see your data as repeated measures. There is only one meaningful measure related to each subject (the switching treshold). Knowing that value for a subject determines all other measures for that subject.

[lei]

Hi pgstats you are absolutely right. It's not a repeated measure. Therefore I am stuck on what to use. The threshold is a continuous variable. If a person chooses for example a threshold of say 75% this means that they will switch their decision at this point. It also means they accept a risk of anything higher too.

[SteveDenham]

How about fitting the single response as a beta distributed response?  That would lead to PROC GLIMMIX as a possibility, although I would fit all of the covariates you are interested in as fixed effects, with no random effects in the mix.  Another possibility is that the endpoint is better described using a beta-binomial distribution, which would imply PROC FMM as a tool.

Steve Denham

[StatDave]

This sounds to me like a simple logistic or probit model with switch/don't switch as the response and the risk percent and demographics as predictors.  After fitting the model, you can estimate the risk percent that produces any given probability of switching. This is like estimating the ED50 in quantal bioassay studies, and can be done using the INVERSECL option in PROC PROBIT.  See the examples and in the PROBIT documentation and this note.

[SteveDenham]

Aha!!

That is exactly what this is, @StatDave.  I have to admit I was trying too hard.

Steve Denham

[lei]

Hi everyone,

Thank you for the responses. I'm not really sure if the solution you provided actually pertains to what I am looking for.

I think I can explain this problem a bit further:

We have two treatments A and B.

Treatment A removes the organ completely, so the probability of having the disease (site-specific) come back is 0% basically. Treatment B has some chances of the disease come back. However, treatment A is associated with a lot of side effects which includes both physical and psychological problems. On the other hand, Treatment B is not associated with these risk.

Therefore, we asked patients which treatment they would choose if for both treatments A and B, local recurrence is 0%. It's most likely that they would choose treatment B since there is no side effects. This is considered their initial choice. If the patient chose A at 0% recurrence, then their are not likely to accept any possibility of local recurrence and the questions stop. However, for the patients that chose B at the start, we increased the percentage of recurrence until the point where they said they cannot accept this risk and switched to A. This is the threshold that I mentioned in my original e-mail.

Now my task is to determine what predicts this threshold of switching. Therefore, I think for the dependent variable it'll be the threshold percentages of local recurrence where patients switched from B to A.  If patient chose A then their threshold will be 0%. 

I am quite confused as how I am going to get there. Would the beta distribution still work in the case I described above?

[StatDave]

I suppose you could fit a beta model (GLIMMIX) to the risk level at which switch occurs.  That is, the data would consist of one observation per subject containing the risk level at which they switched, along with the subject's demographics.  That would allow you to assess the association of the demographics with the switching risk level. 

[lei]

Thank you StatDave_sas. Quick question, why the beta distribution? I know it is to model proportions and percentages, is this the reason? Sorry for such a ridiculous and stupid question. I have never used beta model.

Thank you all again.

[StatDave]

Yes, the beta distribution has bounded support, so it is useful for modeling something like a proportion that is bounded in [0,1].  There are several ways to go about modeling continuous proportions which are discussed in this note and this one.