The procedure used for analyzing child mortality, Poisson regression, has been described in detail in the volume entitled *Demographic Effects of Economic Reversals in Sub-Saharan Africa* (Working Group on Demographic Effects of Economic and Social Reversals, 1993:42-43) and is reiterated in large part here.

Poisson regression is essentially a methodology for the multivariate analysis of counts of occurrences, in this case, of child deaths. The method assumes some underlying risk or hazard of the event occurring in some category of duration of exposure, in this case an age group of children. In our model, the natural logarithm of the hazard, h _{ia}, for observation *i* of age group *a* is assumed to be given by an additive expression including the base hazard for the age group, h_{a}, and the effects of a series of other variables, *X*, that are assumed to influence the hazard:

In(h_{ia}) = h_{a} + τ'X_{i} .

Note that in our model, the effects of the variables *X* are assumed not to vary with age.

The expected number of events or deaths, D'_{ia}, observed for individuals with a particular set of characteristics in duration-of-exposure category *a*, will be the hazard multiplied by the exposure time of such individuals in the exposure category, E_{ia}. Thus for individuals with characteristics *i* and age *a*,

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Population Dynamics of Senegal
Appendix C
Methodology for Analysis of Child Mortality
The procedure used for analyzing child mortality, Poisson regression, has been described in detail in the volume entitled Demographic Effects of Economic Reversals in Sub-Saharan Africa (Working Group on Demographic Effects of Economic and Social Reversals, 1993:42-43) and is reiterated in large part here.
Poisson regression is essentially a methodology for the multivariate analysis of counts of occurrences, in this case, of child deaths. The method assumes some underlying risk or hazard of the event occurring in some category of duration of exposure, in this case an age group of children. In our model, the natural logarithm of the hazard, h ia, for observation i of age group a is assumed to be given by an additive expression including the base hazard for the age group, ha, and the effects of a series of other variables, X, that are assumed to influence the hazard:
In(hia) = ha + τ'Xi .
Note that in our model, the effects of the variables X are assumed not to vary with age.
The expected number of events or deaths, D'ia, observed for individuals with a particular set of characteristics in duration-of-exposure category a, will be the hazard multiplied by the exposure time of such individuals in the exposure category, Eia. Thus for individuals with characteristics i and age a,

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Population Dynamics of Senegal
In(D'ia) - In(Eia) = ha + τ'Xi .
The logarithm of the exposure term Eia is commonly referred to as the ''offset," which standardizes cell counts for varying exposure times. We set up the data for Poisson analysis by counting events (deaths) and exposure time in each cell of a matrix defined by age a, time t, and a vector of control variables X.