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

American Journal of Epidemiology, Aug 2004

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.

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

Robert W. Platt ) 1 2 K. S. Joseph 0 Cande V. Ananth 3 Justin Grondines 2 Michal Abrahamowicz 1 Michael S. Kramer 1 2 0 Perinatal Epidemiology Research Unit, Department of Obstetrics and Gynecology and Pediatrics, Faculty of Medicine, Dalhousie University , Halifax, Nova Scotia , Canada 1 Department of Epidemiology and Biostatistics, Faculty of Medicine, McGill University , Montreal, Quebec , Canada 2 Department of Pediatrics, Faculty of Medicine, McGill University , Montreal, Quebec , Canada 3 Section of Epidemiology and Biostatistics, Department of Obstetrics, Gynecology and Reproductive Sciences, Robert Wood Johnson Medical School, University of Medicine and Dentistry of New Jersey , New Brunswick, NJ 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 timevarying 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. birth weight; gestational age; infant mortality; proportional hazards models Abbreviation: LMP, last menstrual period. - Over 30 years ago, Yerushalmy et al. (1) identified a paradoxical relation between maternal smoking and birthweight-specific neonatal mortality. Neonatal death rates for infants of smokers were lower than those for infants of nonsmokers at birth weights of 3,000 g or less; the reverse was true at higher birth weights. In the last three decades, this observation has been corroborated in many studies, including comparisons based on race, infant sex, and country (24), as well as other factors. Intersecting neonatal mortality curves present an inferential challenge. The argument that fetuses of women who smoke during pregnancy (or of a disadvantaged group such as twins or Blacks) are healthier than fetuses of nonsmokers (or an advantaged group) at some birth weights but not others lacks biologic plausibility and coherence. Sophisticated statistical approaches (59) have been proposed to address this phenomenon and include explanations based on relative birth weight (57) or relative gestational age (9). For instance, Wilcox and Russell (7) showed that examining perinatal mortality rates across categories of relative birth weight, that is, birth weight expressed in terms of the population mean and standard deviation, eliminates the crossover paradox. However, the relative birth weight formulation has been criticized because it fails to distinguish the contributions of birth weight differences due to maturity (i.e., higher gestational age) versus fetal growth (represented by birth weight for gestational age) (10). Although use of relative birth weight (6) or relative gestational age (9) resolves the perinatal mortality crossover, these approaches require that birth weight or gestational age be treated differently from other predictors. More importantly, relative birth weight or gestational age fails to account for the temporal nature of gestational age. Gestational ages are not exchangeable; that is, an infant born at 40 weeks was at risk of being born at 30 weeks, but an infant born at 30 weeks of gestation is not at risk of being born at 40 weeks. Thus, gestational age should be considered a time axis rather than an independent variable in the model. Research to date on perinatal outcomes has all but ignored the fact that gestational age is a time-to-event variable and has treated gestational age and birth weight as having the same potential causal effect on outcomes. Perinatal mortality has been criticized as an outcome because it is the combination of two etiologically heterogeneous events, stillbirth and early neonatal death (11, 12). In addition, an arbitrary restriction of early neonatal mortality to the firs (...truncated)


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Robert W. Platt, K. S. Joseph, Cande V. Ananth, Justin Grondines, Michal Abrahamowicz, Michael S. Kramer. A Proportional Hazards Model with Time-dependent Covariates and Time-varying Effects for Analysis of Fetal and Infant Death, American Journal of Epidemiology, 2004, pp. 199-206, 160/3, DOI: 10.1093/aje/kwh201