A Proportional Hazards Model with Time-dependent Covariates and Time-varying Effects for Analysis of Fetal and Infant Death

Birth-weight- and gestational-age-specific perinatal mortality curves intersect when compared by race and maternal smoking. The authors propose a new measure to replace fetal and infant mortality and an analytic strategy to assess the effects of risk factors on this outcome. They used 1998 data for US Blacks and Whites. Age-specific post-last menstrual period (LMP) mortality rate was defined as the proportion of deaths (stillbirth, perinatal death, or infant death) at a given age post-LMP. The authors used extended Cox regression with time-varying covariates and hazard ratios to model the effects of race and smoking on post-LMP mortality. Perinatal mortality rates (conventional calculation) for Blacks and Whites showed the expected crossover. However, analyses of post-LMP mortality showed no crossover. For the Black-White comparison, a hazard ratio of 1.72 (95% confidence interval: 1.67, 1.77) was obtained. The hazard was higher for smokers than for nonsmokers, but the hazard ratio increased from 1.09 (95% confidence interval: 0.98, 1.22) at 22 weeks to 1.82 (95% confidence interval: 1.72, 1.92) at 40 weeks. The hazard ratio associated with birth was also time dependent: higher than 1 for preterm gestation and lower than 1 for term gestation. The increasing adverse effect of smoking with gestational age suggests an accumulating effect of smoking on mortality. Modeling post-LMP mortality eliminates the crossover paradox for race and maternal smoking in a single statistical model.