Hi all,
I need an advise on the correct statistical approach for a sequence of events.
1. I have a data collected from a group of individuals at baseline (BL) and follow-up (FU).
2. There are traits A, B and C measured at BL and FU. The traits are categorical (yes, no).
3. The question is what trait comes first? Say, individuals first develop trait A and this increases the risk of the appearance of the traits B and C. Or, trait C comes first and increases the risk of A and B. Etc.
I am thinking of time series forecasting, but not sure it is applicable.
An advise from experienced statisticians would be much appreciated.
If trait A is the case for a person at BL, can it be also the case for the same person at FL? For instance, if "trait" means to "develop the trait", or "newly recorded trait", then a person can have a recorded "yes" for a trait only at one of the time-points but not at both.
If "trait" just means that the trait is there, no matter when it was developed, then having trait A at BL as well as at FU can mean that this trait did not change on FU or that the trait at BL disappeared but caused the appearance of A at FU. Not sure how these things could be distangled then - especially when more than one trait can be the case at each time-point.
In general, a time-to-event analysis would be better to tackle such questions, so it might be worth to think if you have a chance to get more appropriate data or do a better experiment (I know the answer is likely negative, but I had to mention...).
You might get some ideas from Fuller and Grandjean, in Cross Cultural Research 2001. Full text is posted in my pubs here on Research Gate. We tried to tease out causal order for a number of dichotomous variables. We were limited by small sample size (and time order was not very clear). Our research topic was likely very different from yours, but some of our approach might be applicable to your problem.
Hello Maxim. What kind of sample size do you have? Assuming it is large enough, I wonder if a series of 3 logistic regression models would help address your question. Let A0, B0 and C0 be the baseline indicator variables for the 3 traits; and A1 to C1 be the follow-up indicators. Estimate 3 separate logit models with A1 to C1 as the outcome variables, and with A0 to C0 as explanatory variables in all models. If you include the 3-way interaction plus all lower order terms, you'll be able to compute the odds of seeing a given trait at follow-up for each of the 8 possible combinations of baseline indicator variables. And I think those odds help you address your question, do they not?
HTH.
Many thanks, Bruce. Eventually, I have done the analysis in a way you proposed. Except for the interactions, which is a very good idea. I will see where it goes.
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