Panel count data arise when a recurrent event process is observed only at
intermittent examination times, so that the number of events between
consecutive examinations is known but the event times themselves are not.
pcdreg() fits either of the two standard semiparametric models to such
data, allowing the covariates \(X(t)\) to vary over time:
$$\textrm{rate:} \quad E[dN(t) \mid X(t)] = \exp(\beta' X(t)) \, d\Lambda(t)$$
$$\textrm{mean:} \quad E[N(t) \mid X(t)] = \mu(t) \exp(\beta' X(t))$$
The rate model treats the baseline cumulative rate \(\Lambda\) nonparametrically and maximises the likelihood that a nonhomogeneous Poisson process would imply, using an EM algorithm that augments the observed counts with latent per-examination-time Poisson counts. The Poisson assumption is a working device only: the estimator stays consistent and asymptotically normal when it fails, and the default covariance estimator is robust to that failure. The means model is fitted by an estimating equation and is provided as the comparator.
References
Sun, D., Guo, Y., Li, Y., Tu, W. and Sun, J. (2024). A robust approach for regression analysis of panel count data. Bernoulli 30(4), 3251–3275. doi:10.3150/23-BEJ1713
Author
Maintainer: Dayu Sun dayusun@iu.edu