Cb. Dean et R. Balshaw, EFFICIENCY LOST BY ANALYZING COUNTS RATHER THAN EVENT TIMES IN POISSON AND OVERDISPERSED POISSON REGRESSION-MODELS, Journal of the American Statistical Association, 92(440), 1997, pp. 1387-1398
Inference for point processes is most efficient if the event times for
each individual are available. Sometimes, the study design is such th
at only aggregated data are collected, consisting of the number of eve
nts or recurrences for each individual over the observation period. Th
is article discusses the loss in efficiency of an analysis of the aggr
egated counts versus an analysis of the actual event times. One partic
ular case is exemplified--that in which the purpose of the experiment
or trial is to compare the effects of treatments--and the loss in effi
ciency in the estimator of the treatment effect is computed. The speci
fic point process considered here is the nonhomogeneous Poisson proces
s, with a proportional intensity model for the treatment effects. Rand
om-effects models are also considered, with estimation via a quasi-lik
elihood approach. The quasi-likelihood analysis proposed here is an ex
tension of such techniques for the homogeneous Poisson process. The re
sulting estimating equations for the parameters in the random-effects
models are simple and intuitive. The results show that for many usual
situations, treatment effects are very efficiently estimated using agg
regated data, but the underlying intensity function is not.