"effective" sample sizes in multi-stratum analyses

[steven]

I'm doing a study in which the parametric form of an age-specific survival curve is a central issue.

FIRST, I fit a model for which the individuals are NOT stratified (with respect to reproductive state). Let's say that the best fit is that

logit(Si) = a + b x i + c x i2)

where Si is the survival rate for age i, i2 is the square of i, and a, b, and c are constants. This is a standard exercise.

SECOND, I fit a stratified model (with, say, three reproductive states: producing a small, medium, or large clutch) in order to calculate the age-specific survival rates conditional on being in one of the three reproductive strata. Again, this is standard exercise. Keep in mind that the stratum "identity" of each individual can change over time, that is, individuals canNOT be divided into those that always produce small clutches, those that always produce medium clutches, and those that always produce large clutches.

In this multistratum analysis, let's say that the best fit model is such that the stratum-specific parametric forms are:

SMALL: logit(Si) = a + b x i
MEDIUM: logit(Si) = a + b x i
LARGE: logit(Si) = a + b x i

We see that the qualitative nature of the forms differ in that the UNstratified analysis says there is a quadratic dependency, whereas the stratified analysis says there is a linear dependency for each stratum. Suppose I believe this is an important finding (that the forms are different depending on whether there is stratification).

Is there a way in which one an calculate an "effective" sample size associated with EACH of the parametric forms in the stratified analysis? Such a number would allow one to do a power calculation in which one could assess the power to detect the "missing" part of the parametric form described by the UNstratified analysis (that is, the quadratic dependency).
Of course, I am open to hearing about other approaches that would allow one to assess the confidence I should have in the claim that different qualitative forms have been revealed by the two analyses.

Note again, that the UNstratified and stratified analyses are both based on the same number of individual records.

I have never seen any discussion of this issue. Any thoughts, comments, suggestions, clarifications are most welcome.

many thanks,

S.