Known fate analysis and mortality rate by cause

[Atoq]

Hei! It's me again, dealing with telemetry data on roe deer.
Are you aware of any paper that is analysing the annual rate of mortality for different causes (for example predation, hunting, car accident) by using Mark? Do you know if it is possible at all?

Many thanks for any help!

Claudia Melis

[ganghis]

Hi Claudia,

Multiple sources of mortality can be modeled using the multistate framework. For an example having to do with tag recovery data, see

Schaub & Pradel ECOLOGY 85 (4): 930-938 APR 2004

As long as there is no censoring, you should be able to do this in MARK using the multistate data type, by fixing p=1, phi=1, and letting state transitions represent different survival and mortality parameters. You will need to code in several different states, such as 'alive' (call this state 'A'), 'dead because of cause B' (call this state B), 'dead because of cause C' (call this state C). For example, an individual that is known to be alive in sampling periods 1, 2, and 3, but dies of cause B between sampling periods 3 and 4 would receive the history AAABB in the case where there are 5 total sampling periods. The key here is that you need to fix some of the state transitions to 0 or 1 as well. For instance, the probability that an animal moves out of state B or C once they are dead is 0.

You might also check MSURGE documentation. The problem you're interested in is certainly doable, but if there's censoring I'm not sure there's software currently available.

Cheers, Paul Conn

[cooch]

Hi Claudia,

Multiple sources of mortality can be modeled using the multistate framework. For an example having to do with tag recovery data, see

Schaub & Pradel ECOLOGY 85 (4): 930-938 APR 2004

As long as there is no censoring, you should be able to do this in MARK using the multistate data type, by fixing p=1, phi=1, and letting state transitions represent different survival and mortality parameters. You will need to code in several different states, such as 'alive' (call this state 'A'), 'dead because of cause B' (call this state B), 'dead because of cause C' (call this state C). For example, an individual that is known to be alive in sampling periods 1, 2, and 3, but dies of cause B between sampling periods 3 and 4 would receive the history AAABB in the case where there are 5 total sampling periods. The key here is that you need to fix some of the state transitions to 0 or 1 as well. For instance, the probability that an animal moves out of state B or C once they are dead is 0.

That is correct. In fact, Pradel and colleagues have shown in a variety of cases that a particular model is often just a special case of a more general multi-state model. A number of examples of this are given in the multi-state chapter in the book. As Paul notes, the 'trick' in most cases is to figure out which states are 'absorbing', or not, and what the detection rates are in various states, and fix parameters as needed.

I share Paul's uncertainty about censoring. As noted in the known fate chapter, censoring is a general problem - hopefully one you can avoid.

[Atoq]

I wanted to be sure that you cannot use the known-fate analisys with staggered entries and censored data.

Thanks a lot for your help!

Claudia

[cooch]

I wanted to be sure that you cannot use the known-fate analisys with staggered entries and censored data.

Thanks a lot for your help!

Claudia

Seems as if reading the known fate chapter would help - the issue of staggered entries and censored data are covered in some detail.

[Bill Kendall]

Paul Conn provided a good suggestion for using the Multistate feature of MARK for telemetry, and left open the question of dealing with censoring. It seems to me this can be handled by the "deaths on capture" coding (e.g., a -1 for the frequency of that history). The last entry in the history would be for the time period before censoring occurred (e.g., if you determine the radio had failed when you go out to search in week t, then the last entry in the history would be for week t-1). More complications arise if your detection probability for the device is <1, but it can still be handled.