ageing and transition rates in multi-state model

[shelly]

Hi

I have two related questions regarding ageing and transition rates in a multi state model I’m working with to determine impacts of disease on survival and infection rates. Animal have been trapped and marked between two and four times per year from May 2005 to June 2007. Individuals are considered subadults for the second year of their life (1-2 years) and adults thereafter (reproductive maturity occurs at 2 years of age). As there is a synchronous breeding season in this species we assign yearly ‘ageing’ in jan/feb each year.

The model has 3 strata:
1= Subadult individuals (all healthy; can become either diseased (1to3) or healthy adults (1to2))
2= Healthy adults (can become diseased adults (2to3) or stay healthy (2to2))
3= Diseased adults (either stay diseased (3to3) or die, no recovery possible)

My question relates to how to correctly construct the transition rates out of the healthy subadult strata (S1). All individual must at some point transition to adults but the length of time an individual can stay in this stratum clearly depends on when that individual was first caught …

Eg…
If first caught in May 2005
May-05 Aug-05 Feb-06 May-06 Jul-06 Nov-06 Jan-07 Apr-07 Jun-07
Sub(1) Sub(1) Ad(2/3) Ad(2/3) Ad(2/3) Ad(2/3) Ad(2/3) Ad(2/3) Ad(2/3
If first caught in Feb 2006
__0_____0____ Sub(1) Sub(1) Sub(1) Sub(1) Ad(2/3) Ad(2/3) Ad(2/3)

The preliminary results with no parameters fix show that transitions from 1to2 and from 1to3 only occur in the 2nd and 6th intervals - ie at the start of each year - these interval are the only ones for which meaningful estimates are obtained. But in the data set there are clearly transitions which occur outside of these times
for example….
110202203
112200202
001101220
000111022
100030000

Why are there no estimates for transition rates at other times? and which intervals need the transition rate fixed to zero (obviously the first interval, but fixing all bar the 2nd and 6th improves the fit of the model) ?

Any help greatly appreciated.

Shelly

[ganghis]

Hi Shelly,

While it will make you problem somewhat ugly (in terms of PIMs, etc.), I'd suggest treating individuals first caught at different capture occasions as members of different groups. Then you can constrain transition rates to zero for every period except for when they advance to the next age class. See material in the gentle introduction on age structured models.

Paul