Problem of Survival estimations by using initial.age levels

[scha]

Dear all,

I am interesting in senescence. So, I am using “Age models” a lot. Until there, everything is ok. I need to use the initial.age level definition. The problem is there.

If I understand the concept of initial.age, “initial.age” level definition correspond to an automatic creation of groups with as much groups as initial age.

Nevertheless, I have a little problem with the age survival estimations when I use initial.age levels. This method create more age than in reality but the model succeed in estimating survival for impossible age. To give you an example, I have a dataset with animals collected over 50 years (with around 8000 individuals). I have individuals which are captured for the first time between 1 and 18 years old. So basically, I use initial age in consequence (between 1 and 18 years old). The model computes a theoretical maximum age of 68 years old (50 + 18 = the model considers the release of 18 years old animal at t=1; Which is not true in reality but quite normal). My problem : if I do a simple model like S(age), Mark estimates survival parameter (whith confidence intervals) until more than 50 years old, which is not possible because the older individual live until 23 years old. So my questions:

How mark can estimate survival without informations? (between 23 and 68 years old)
What I am supose to do ? Use estimations just until 23 years old ?
Could it be an artefact of no 1 probability of detection?

I work on differents dataset, and I always have this problem.

How can I interprete these results?

I hope that my explanation are clear

Thanks in advance for your help

Stephane

[jlaake]

I suggest that you bin ages in some way that makes sense to you. Due to the length of sampling in your example, animals could be 68 but it doesn't mean they will reach that age and from what you said they do not. Therefore, MARK has no observations of animals that old and survival for ages >23 will hit the boundary of 0. To avoid that problem, you may want to use something like 20 to 68 as your last age bin. See Appendix C of the RMark workshop report for examples of binning with age.

--jeff

[RudyJonker]

Dear Jeff,

I have a related question to this. When I use the age models (as TSM) in my analysis (data from 23 years, maximum lifespan approx. 13-14 years), I get estimates for age classes that seem wrong. So for the 1st cohort, which at some moment reaches the age of 20 or so, I get very high survival estimates (+/- 0.. But, these individuals are no longer alive. How can Mark get these high estimates?

Would creating age classes manually solve this issue, by not having one class for all ages higher than the maximum age? Ideally I want to make a linear function for age, but then I cannot create these classes manually.

Thanks in advance

[jlaake]

I'm not sure what you are not understanding as this seems to be the same question that you posed earlier. If you don't assign initial.age then the age variable is the time since it first entered. age is a factor variable with as many levels as there are ages (years most likely). Likewise it creates a variable Age which is a numeric field and could be used to fit a linear trend on the link scale (most likely logit). You could fit a linear and quadratic with Age+I(Age^2). If you use age, the factor variable, then it will try to fit a survival for each of the levels and there is probably too little data to do that and many of the estimates will hit boundary values of 0 or 1. The other alternative is to bin the ages as I suggested earlier. The only difference between TSM and age is when you assign initial ages that differ across groups and you can only do that if you know the ages of the animals when they were first marked.

--jeff

[RudyJonker]

Thanks Jeff, (that earlier question wasn't me)

Difference between TSM and Age was clear. The problem was that with the linear predictor of Age, the model also predicts a value for Ages that do not exist. I solved that by using the factor age. And indeed most estimates hit either 0 or 1. But at least there are no estimates for age classes that do not exist, and thus I know that I included the model that I intended to.

[jlaake]

Thanks Jeff, (that earlier question wasn't me)

I see that now That makes more sense.

If you are getting estimates going to boundaries with a factor variable then you need to bin your ages. Regardless of how you model the age effect it will give estimates for ages which are not "possible" but that doesn't mean that it is a bad model. Consider that any regression line truly extends beyond the range of the data mathematically but the regression is based on the data and you needn't use estimates outside the range of the data. In the case of survival what matters is cumulative survival. Presumably the estimated cumulative survival is essentially 0 at the "impossible" ages. Since there are no observations at those ages the are no data there and obviously won't have any influence on the estimates. Now that doesn't mean that a linear model is the best and I'd expect you would need to add a quadratic as well.

regards --jeff