interval length, survival estimates, and precision

[Todd]

I have a quick question regarding estimating survival between two intervals.

If you have collected data semi-annually and model survival over these 6-month intervals, you will obtain one estimate. Presumably you would square this estimate to then produce a yearly survival estimate (which is often of more useful for various reasons).

However, if you ignore half of your data and just model survival over 1-year intervals, you will obtain a different estimate of yearly survival.

In nearly all cases in which I've tried this, a modeled 1-year survival estimate is greater than a squared 6-month survival estimate.

I cannot figure out why this occurs or what to make of it. Does it stem from the fact that by squaring shorter survival estimates you are compounding the uncertainty (limitations to precision) of those estimates?

Philosophically, it seems you'd want to use all of your data in analyses, necessitating modeling 6-month survival intervals. But if this underestimates yearly survival, what good are the resulting estimates? This problem gets exponentially worse when you have data collected every month and want to derive a yearly survival estimate.

Any clarity on why the disparity exists and how to interpret this problem would be greatly appreciated.

Many thanks,
Brian Todd

[cooch]

I have a quick question regarding estimating survival between two intervals.

If you have collected data semi-annually and model survival over these 6-month intervals, you will obtain one estimate. Presumably you would square this estimate to then produce a yearly survival estimate (which is often of more useful for various reasons).

However, if you ignore half of your data and just model survival over 1-year intervals, you will obtain a different estimate of yearly survival.

In nearly all cases in which I've tried this, a modeled 1-year survival estimate is greater than a squared 6-month survival estimate.

I cannot figure out why this occurs or what to make of it. Does it stem from the fact that by squaring shorter survival estimates you are compounding the uncertainty (limitations to precision) of those estimates?

Philosophically, it seems you'd want to use all of your data in analyses, necessitating modeling 6-month survival intervals. But if this underestimates yearly survival, what good are the resulting estimates? This problem gets exponentially worse when you have data collected every month and want to derive a yearly survival estimate.

Any clarity on why the disparity exists and how to interpret this problem would be greatly appreciated.

Many thanks,
Brian Todd

Have a read of the - sidebar - beginning on p. 13 of Chapter 4. It covers some of the underlying issues with unequal time-intervals.

THere have also been postings on this forum about what options are available (if any) if comparing groups with different sampling intervals.

[Todd]

Thanks Evan. The sidebar from chapter 4 does shed some light on the subject but I'm not sure it really answers my question.

Briefly, when using a complete dataset with 6-month time intervals I obtain semi-annual survival estimates that scale to a lower than expected yearly survival rate. In contrast, if I ignore half of the data and only model survival over yearly sampling periods by removing all of the capture histories from the second sampling period of each year, I obtain a more realistic estimate of yearly survival, the square root of which does not match the estimates obtained from a complete capture history that includes all 6-month sampling periods.

[ganghis]

Hi Todd,

The invariance property of MLE's makes your argument somewhat implausible in the general sense. Could you provide a description the dataset you are using? It could be that 6 month sampling exposes some 'lower quality' individuals or transients that would otherwise go undetected.

If you want to check if the 6 month/12 month phenomenon applies more generally, I'd suggest simulating some data where you know the true answer.

Cheers, Paul Conn

[caspar]

Hi all,

I have been in a similar situation where I experienced the same issue of interval length and estimates, so I followed Paul's advice and simulated some data. The data were simulated semiannually with phi= 0.7 and p= 0.3, and I used the "dot" models to compare.

Here's what I got:

Semi year estimates (need to be squared to get the yearly estimates):
estimate se lcl ucl fixed
0.7162424 0.0103631 0.6954996 0.7361082
0.2891476 0.0127953 0.2647273 0.3148560

Yearly estimates (a 1 in the encounter history if seen within that year=violation of duration):

estimate se lcl ucl fixed
0.5073719 0.0156352 0.4767376 0.5379509
0.5086082 0.0255431 0.4586245 0.5584204

Yearly estimates (a 1 in the encounter history if seen within the first half of the year and disregard any other encounters):

estimate se lcl ucl fixed
0.4886469 0.0253451 0.4392445 0.5382720
0.3155842 0.0303666 0.2592827 0.3778745

The recapture estimates are similar in cases 1 and 3 but not 2 (when violating the recapture duration assumption)! Survival estimates are highly comparable though in all three cases. So I conclude (but correct me if I'm wrong) that when such a disparity as observed in my data (and possible Todd's) indeed uncovers some information that goes undetected when using yearly interval lengths.

Cheers

Caspar

[ganghis]

Caspar,

That is one possible explanation at least, although differences may also result from stochasticity in the encounter process.

FYI there are a few papers that deal with the sampling period mortality & interval length issue in greater detail that might be of interest:

Hargrove & Borland 1994, Biometrics 50 1129-1141
O'Brien et al. 2005 J. App Ecol 1096-1104
Tavecchia et al. 2001. Ecology 82:165-174

Beware that these studies in effect assume constant forces of mortality and capture within individual periods so their results are limited to that case.

Cheers, Paul Conn