  We propose a way to remove the bias of a Poisson regression when the subjects
are partially observed. In this paper we address this issue under certain
assumptions about the missing-data generating process. We fix the total number
of observed subjects and allow individual subjects to be observed randomly.
This theme is relevant when a researcher is provided with a survey data not
covering the whole population. A highlighting result is that if subjects are
observed according to a random sampling without replacement, a Poisson
distribution with sampling-ratio-adjusted mean is an asymptotically consistent
model of the observed count variable. An innovative asymptotic regime is
employed to derive the results.
