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I want to identify predictors of a binary healthcare outcome in a purely observational study, and some of my participants have 1 recorded outcome timepoint, while others have 2 recorded outcome timepoints. I do not care about time at all and I am not interested in within-person variation - time is not part of the research question, there is no conceptual reason that outcome time (1st vs 2nd) would matter, and the distribution of outcome variable values does not vary by time. I just want to be able to use ALL of my observations to make a statement about what variables predict the outcome in general.

I thought I would use GEE (generalized estimating equations) but then I read that with GEE every individual in the study needs to have at least 2 timepoints, so if that's correct, GEE would not serve my purpose. My sample size is very small (N total=79, N with 2 follow ups=40) and my outcome is binary. I welcome general statistics/model type selection tips, or software-specific tips as well. I was going to use PROC GEE in SAS with weighting via a missingness model before I found out it couldn't handle having unpaired response observations. Any tips are much appreciated. Thank you.

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  • $\begingroup$ Please say more about what differs between the 2 timepoints when they are available. Is the binary outcome for an individual identical between the 2 time points? (It's not clear what you mean when you say the "distribution" is the same for the 2 times.) How many patients have the outcome? Are there predictor variables that are collected at both times whose values might differ between times? What specific hypothesis are you testing? $\endgroup$
    – EdM
    Commented Aug 14, 2020 at 15:25
  • $\begingroup$ I am not testing a specific hypothesis. It's an exploratory analysis for a purely observational study and I'm looking at which variables on a survey predict a positive drug test result for a prescribed medication (i.e., recent adherence). At the first time point, 49 of 63 had a positive result and at the second time point, 41 of 56 had a positive result [ignore my earlier N from the prior post, it was intentionally approximate]. The study was designed to collect a baseline survey, and a survey and drug test result at 3 months and 6 months. $\endgroup$
    – L.S.
    Commented Aug 14, 2020 at 19:06
  • $\begingroup$ However, a lot of people did their survey and drug tests at quite different times (~30% were >1 week apart at both time points), so the data does not support comparing survey and drug test data within person over time. For this reason, I wanted to use baseline survey data to predict later drug tests results. The only time-variant variable would be the outcome. Does this help make it more possible to make methods recommendations? I appreciate any more thoughts you can share. thanks. $\endgroup$
    – L.S.
    Commented Aug 14, 2020 at 19:07

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You have a single survey response from each individual to consider, but either 1 or 2 observations of a binary outcome for each. If you don't care about the time between taking the survey and the adherence observation, or about systematic differences with time for those having 2 observations, this could in principle be simply handled by a mixed logistic regression model, with a fixed effect for the survey response and patient having random intercepts.

Say that your survey results are put together on a combined scale such that the mean response is 0. Then a logistic regression model with just 1 observation per patient would return an intercept representing the log-odds of being adherent if the survey response were 0, and the slope would be how much the log-odds changed per unit change in the survey response.

The possibility of having more than 1 observation per patient, with patient adherence likely to be correlated between the observations, is handled by allowing each patient to have a different random intercept: the estimated log-odds of adherence if their survey response had been 0. The distribution of intercepts among patients is taken to be Gaussian. Fitting the model simultaneously finds the best estimates of the overall intercept, the distribution of individual-patient intercepts around that, and the overall slope with respect to survey response. That pools information from all observations, effectively weighting patients with 2 observations more than those with a single observation.

This approach might be extended to consider time post-survey as a continuous predictor, if there were adequate data and you could assume a linear change in log-odds of adherence with time or some other simple relationship. That could take advantage of the actual survey-to-observation time differences from all your cases, not just those having 2 observations.

That said, your ability to evaluate predictors in a binary-outcome analysis is limited by the number of cases in the minority class, here the 29 non-adherence observations. The usual rule of thumb is you can examine about 1 predictor per 15 members of the minority class without overfitting. So don't go overboard in "looking at which variables on a survey predict a positive drug test result." The risk in examining too many predictors is that you might find a relationship that works very well in your current data set but doesn't work well on a new data set. I'd recommend using your knowledge of the subject matter to put together aspects of the survey into a small set of predictors, each of which combines related survey answers. Think about how individual Likert items are combined into a Likert scale.

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