Hello JMP community,
I am currently analysing data from an experiment where flies were exposed to 4 doses of insecticide and a solvent control. Furthurmore, I am comparing mortality response between different fly populations. I have the data organized according to Survival Statistics: Cage mortality I have been using non-parametric approach to compare surival between doses within a group and between groups using Log Rank and Kaplan Meier, but I am interested in potentially doing parametric modeling to look at the median lethal times for each population at each dose. As an aside, I have been doing other GLM probit work on the data set (formatted differently) and have seen a signifigant effect of populationxdose interaction term and this makes me feel more confident about using parametric where I can include the interaction term.
I have been reading that I need to see which distribution best fits the dataset and have been analyzing in the Life Distribution JMP feature looking at distributions. Based on what I have read, with the lowest AICc, Lognormal has the best fit of the three. I know the classic maxim of "all models are wrong but some are useful" and that it is based on the integrity of the data I collected but I am curious of when a model is good enough to be interpreted. The picture bellow shows the total dataset (without segregation) in the Life Distribution model comparison. Perhaps I should look at the distributions for each population and treatment too? Again my goal is to get the most accurate median lethal time for each population at each dose.
Also is using a log-rank (nonparametric) and a parametric test on the same dataset a no-no? I am not familiar with a parametric distribution comparison but I am sure I could use a likeleyhood ratio test to a similar effect.
Yes, the model with the smallest AICc is judged to be the best model based on the empirical evidence provided by the sample of data. You might also consider prior evidence and theoretical findings if available to temper your decision.
The difference in AICc between the best model and any other model can give you an idea of the support for the other model. If the difference is less than 4, then the other model has substantial support. If the difference is between 4 and 7, then the other model has considerably less support. Finally, if the difference is more than 10, then the other model has essentially no support. The smallest AICc difference in your case is about 300, so based on this evidence alone, the Lognormal model is the best model of those in the comparison.
You can use AICc to compare different kinds of models (e.g., linear model versus neural network model) as along as AICc is meaningful for each model and the criterion was calculated for the same data set.
You could now use the Parametric Survival model through the Fit Model dialog. Select lognormal for the error distribution and add your five-level treatment (Insecticide). I recommend, if possible, that you represent these levels with a continuous variable for more information. The linear predictor can include transformations of Insecticide, such as powers, to address non-linear response. That model will get your LRT going!