The document describes a multi-level discrete time hazard model for estimating the impact of a health program (GEHIP) on child survival. The model captures the underlying hazard of death by months of age between 1 and 60 months using a three knot linear spline function. It also estimates the conditional effects of the treatment by permitting interactions of independent variables with age, to estimate effects on newborns, infants, and post-infants separately. The model further adjusts for household, parental, community, and village level confounding factors.

1. ,
Estimating the impact of GEHIP (T) on the survival of
children is given by the multi-level discrete time hazard
model…
Where:
𝛂(t) = a three knot linear spline function of age in months, t, that captures the
underlying hazard of death by months of age between 1 and 60 months., such
that
𝛂(t) = {𝐭−𝐜𝐚 }, where {} means, take the positive value and zero otherwise,
c defines knots for three segments of age (a) of child for 𝐜𝟏=1 (neonates), zero
otherwise, 𝐜𝟐= 2, children over one months of age, and 𝐜𝟑= 13 for the months of
post infancy, permitting the estimation of interactions of independent variables
with t , thereby estimating the conditional effects of treatment or health
strengthening with mortality risks among newborns, infants, or post-infant
children.

2. ,
The odds of childhood
death relative to the
underlying risk of death
over months of age t

3. ,
Adjustment for the confounding
effects of J household and
parental characteristics (H) for
individual I in village v

4. ,
Adjustment for the
confounding effects of K
community characteristics in
village v

5. ,
An adjustment for the
confounding effects of
treatment village v
characteristics

6. ,

7. ,

8. ,
The main effects of the
index of health systems
strength on childhood
survival in village v

9. ,
The end of project
conditional effect of
health systems strength
in treatment villages v

10. ,