My goal is to model waiting times between recurrent events with time-dependent covariats with parametric models (Poisson, Weibull, log-normal etc.). This is not an issue time-dependent covaraits as long as they are constant between the events.
Though, in my case i have 1) sparse number of events and 2) covariats that may change between events (i.e. within gaps). To be concrete, I have accounting data which is updated yearly whereas there often goes 2-3 years between the events. Hence, I end up with quite out of date accouting data if I fix the accounting data after each event until the next. Further, this is complicated by the fact that I only have accounting data from primarily 2010+ but event data from 2007+ so I have a tons of missing values with this approach. I have a large number of firms - i.e. multiple series
My idea so fare is to right censor the intervals whenever I have new accounting data with a stop time at the end of that particular date. Then I create a new interval with a start value at this date. E.g. say that two concurrent events occur at times $t_1$ and $t_2$, $t_1<t_2$. Normally this will yield one gap time $(t_1,t_2]$ with an event at the end. Then say I get have new accounting data at time $s$ with $t_1<s<t_2$. I now have two intervals for my data with my suggested setup. One for $(t_1,s]$ that is right censored and one for $(s,t_2]$ that have an event at the end.
Though, I have not encountered any references that state whether or not this is a good idea. The only thing close to this issue so fare is in The Statistical Analysis of Recurrent Events by Richard J. Cook and Jerald F. Lawless. They write: "If covariates are fixed over the intervals ... then parametric survival analysis software such as censorReg in S-PLUS or survreg in R may be used" (page 65)
"Covariates that vary within gaps are harder to handle with AFT [accelerated failure time] models, but are easily dealt with by the Cox model ..." (page 123)
I prefer using parametric models as I plan to use them in combination with other models. I know that I may as well model the count as Poisson distribution if I use exponential distribution for the gab time. Though, I loose the flexiblity to model gab times with other models, right?
Any suggestion or comments are appreciated!