Generalized regerssion (left censored data)
When using the generalized regression platform to analyze left censored data, where detection is not possible due to a lower detection limit, how JMP handles the censored data?
Please confirm that i understand correctly. Is the left censored data treated as if it lies between zero and the detection limit through missing imputation (simulation) assuming entire dataset is non-normal distribution (such as log-normal)?
Or, instead of using simulation for imputation, are specific statistical rules or methods applied to impute values for left censored data?
The reason I'm asking this question is because yesterday, during a session introducing generalized regression for JMP Pro, a customer mentioned that they are currently analyzing censored data in JMP Basic by simulating missing values between zero and the detection limit. They asked if genreg platform could be a better approach.
I can say GENREG could be appropriate to suggest that assuming a specific distribution for simulation might be more suitable in our case. right?
Re: Generalized regerssion (left censored data)About how censored data are handled, here is a good reference: "Statistical Methods for Reliability Data" by Meeker and others. https://www.amazon.com/Statistical-Reliability-Analysis-Probability-Statistics/dp/1118115457
For your question, see Section 2.4 Likelihood.
In short, the left censored observation has a contribution to the total likelihood. And that contribution is the probability of the left censored observation is between zero (if distribution is lognormal, Weibull, etc.) and the detection limit.
You may understand it by comparing with what imputation does. After imputation, the contribution of the observation is the "density" of the imputed value. Problem is how the value is imputed. It is closely related to the simulation approach.
Simulation is a reasonable thought, but how one determines the distribution from which observations should be drawn from? It is a chicken-egg problem.
The proper approach does not have such a dilemma.
Re: Generalized regerssion (left censored data)Thank you. resolved
