17.4.2 Handling Missing Values
Unfortunately, the Poisson regression model cannot cope with missing values in
an integrated way. Missings are in general a problem in GLMs and Imbrahim et
al. [20] recently compared different techniques that can be used to handle missing
values in combination with GLMs. One of the best methods (leading to unbiased
estimates and reliable standard errors) in their comparison was multiple imputation
(MI) [41]. MI methods create a number of ‘complete’ data sets in which values for
originally missing values are drawn from a distribution conditionally on the nonmissing
values. These imputed data sets can be created using two different methods:
data augmentation [43] and sampling importance/resampling [26]. Although both methods lead to results having the same quality, the second method computes
these results much faster. Therefore, an algorithm based on the second approach,
namely the Amelia algorithm [26] which is available as a package [19] for the statistical
software environment R, is used in our approach. For a discussion about how
the regression coefficients and standard errors of these imputed datasets can be used
to estimate the parameters and standard errors of the Poisson regression model, we
refer to [22].