Trend

[Owen]

In section 6.8.1 of "Gentle Intro.", a trend covariate (1,2,3, etc.) is used to model survival and there's talk of constrining survial to be a linear function of time. My question is pretty basic, but aren't you constraining the logit(survival) to be linear, not the survial itself? (that's if you use the logit link of course). I think the question may be moot if your survivals are in the middle of the 0-1 range, but when they get closer to zero (or 1) it seems that you wouldn't be looking at a linear effect of time on survial itself (?). Thanks for any advice.

[cooch]

In section 6.8.1 of "Gentle Intro.", a trend covariate (1,2,3, etc.) is used to model survival and there's talk of constraining survival to be a linear function of time. My question is pretty basic, but aren't you constraining the logit(survival) to be linear, not the survival itself? (that's if you use the logit link of course).

Correct - linear on the logit scale.

I think the question may be moot if your survivals are in the middle of the 0-1 range, but when they get closer to zero (or 1) it seems that you wouldn't be looking at a linear effect of time on survival itself (?). Thanks for any advice.

Its still effectively linear. I wouldn't worry about that too much. You can prove this to yourself by simulating a linear trend in survival over a range of values from (say) 0.85 -> 0.95. You'll see that the reconstituted estimates are pretty darned close to the underlying true values.

But, perhaps more to the point, inference is based on fit on the transformed scale. This is nothing new. If you do ANOVA on arcsin transformed count data, and find a 'significant' difference, then the difference is 'significant' on that scale. So, we say something is linear, or additive or what have you on a particular scale -- in this case, logit.