chapter  35
Spatiotemporal Modeling of Preterm Birth
ByJoshua L. Warren, Montserrat Fuentes, Amy H. Herring, Peter H. Langlois
Pages 36

Φ−1 (pi) = xTi β+ m∑

z {si, ti (k) , j} θ (si, j, k) , (35.1)

T&F Cat #K23899 — K23899 C035 — page 653 — 2/16/2016 — 22:53

where Yi, pi, Φ−1 (.), xi, and β have been previously described. Pregnancy period k is associated with a diﬀerent calendar date for each woman due to diﬀerences in the date of conception. Therefore, we introduce ti (.), which maps an input pregnancy period to the appropriate calendar date of pregnancy for woman i and ensures that the correct exposures are selected. The exposure j at pregnancy period k corresponding to the calendar date of pregnancy for birth i at location si is represented by z {si, ti (k) , j}. The corresponding parameter that describes the association of interest is given by θ (si, j, k). These spatially, temporally, and exposure-varying parameters describe the association between a single exposure at a speciﬁc location and pregnancy time period. This allows for the possibility that the association is changing among the diﬀerent exposures, locations, and temporal windows. The general form of the model allows for multiple time-varying exposures (m) and ﬂexibility when choosing the number of exposure periods of interest during the pregnancy (d). We prohibit exposures occurring after the pregnancy from aﬀecting the probability of PTB through use of min {d, gai}, where gai is the gestational age in the appropriate timescale for birth i (e.g., days, weeks, or months).