Latent Class Analysis - Interpretation and integration with survival analysis?

Question

I am approaching to Latent Class Analysis to identify "classes" of patients based on some variables.

Question 1: diagnostics of the results. I already gone through the discussion on whether it is better to use BIC, cAIC, etc.: I reach the conclusion that evaluating several metrics, along with entropy and clinical judgment, probably is the best approach to choose the number of classes.

Now, several sources report that a "good entropy" is when entropy >0.8. But I have also found some other people saying that even a lower entropy (around 0.5) could be acceptable, if the classes makes sense, given that in certain areas reaching such high values of entropy (i.e., >0.8) may not be feasible. As the entropy for my latent class model is around 0.45, I want to ask whether "relaxing" the demand for high entropy is acceptable or not.

Question 2: I am wondering whether I can use the classes allocation according to modal posterior probability as a covariate into a Cox-regression model, to analyse hazards across different class? To me, this sound like a suitable approach, but I would like a confirmation that this approach is ok, as I can't find much on this site.

Let's say (with R):

library(poLCA)
library(survival)
data <- whatever # Whatever dataset
    
form <- as.formula(cbind(X1, X2, X3 ...) ~ 1) 
  # Where X1, X2, X3 etc. are the variables used to run the latent 
  # class analysis
    
lc <- poLCA(form, data=data, nclass=3, nrep=5, maxiter=3000) 
  # Let's assume I have already evaluated BIC, entropy etc. and 
  #  found 3 as the best number of classes
    
data$class <- lc$predclass 
  # I use the class membership assigned by modal posterior probability
    
coxph(Surv(time, event) ~ class + Y1 + Y2 + Y3 ..., data=data) 
 # Where Y1, Y2, Y3 are other covariates I want to use in the 
 # Cox regression model.

Would this approach be sound?

Answer 1

I want to ask whether "relaxing" the demand for high entropy is acceptable or not.

Your purpose in identifying the classes provides the best answer to that question.

Decide on a measure of model performance that makes the most sense for your application. There's a potential problem with entropy, as that term seems to get used in different ways among implementations of latent class analysis (LCA). The poLCA package you use reports the standard Shannon definition of entropy calculated over the cells $c$ of the cross-classification table, $-\sum_c p_c \ln p_c$, with an upper limit equal to the log of the number of cells. The cutoffs you cite seem to be based on values re-scaled into a range of 0 to 1 like Mplus reports. I'm not an expert in LCA, but I suspect that there might be a better measure of model performance than entropy.

It would seem that a measure of the stability of class assignments among resampled data sets would be most useful for a clinical application. I don't think that you can get that from your single model fit, but you could get that by repeating your entire modeling process on multiple bootstrapped samples of your data. That mimics the process of taking your original sample from the underlying population. A process that tends to co-identify the same cases into the same classes would be most reliable.

Save the predictions of each bootstrap-based model on the full data set. See how well the multiple models tend to match the same cases into the same classes. Then decide if that performance is good enough for your purpose. If so, report the results of your original model along with your measure of model-process performance.

In terms of application to survival analysis, LCA might provide a type of data reduction, unsupervised with respect to survival outcomes, to convert a large number of X categorical variables into a smaller number of predictors for modeling an event-limited survival data set. Frank Harrell discusses similar data-reduction approaches in Section 4.7 of Regression Modeling Strategies. Using the modal class assignment would seem to be the most appropriate choice. If you have enough events to include all of your variables into the model, however, the pre-assignment to classes would seem to lead to a loss of precision.