Estimating the hazard rate difference from case-cohort studies

The case-cohort design, among many two-phase sampling designs, substantially reduces the cost of an epidemiological study by selecting more informative participants within the full cohort for expensive variable measurements. Despite their benefits, additive hazards models, which estimate hazard differences, have rarely been used for the analysis of case-cohort studies due to the lack of software and application examples. In this paper, we describe a newly developed estimation method that fits the additive hazards models to general two-phase sampling studies along with the R package addhazard that implements it. It allows for missing covariates among cases, cohort stratification, robust variances, and the incorporation of auxiliary information from the full cohort to enhance inference precision. We demonstrate the use of this tool to estimate the association of the risk of coronary heart disease (CHD) with biomarkers high-sensitivity C-reactive protein (hs-CRP) and Lipoprotein-associated phospholipase A₂ (Lp-PLA₂) by analyzing the Atherosclerosis Risk in Communities Study, which adopted a two-phase sampling design for studying these two biomarkers. We show that the use of auxiliary variables from the full cohort based on calibration techniques improves the precision of the hazard difference being estimated. We observe a synergistic effect of the two biomarkers among participants with lower LDL cholesterol (LDL-C): the CHD hazard rate attributable to the combined action of high hs-CRP and high Lp-PLA₂ exceeded the sum of the CHD hazard rate attributable to each one independently by 11.58 (95% CI 2.16-21.01) cases per 1000 person-years. With higher LDL-C, we observe the CHD hazard rate attributable to the combined action of high hs-CRP and medium Lp-PLA₂ was less than the sum of their individual effects by 13.42 (95% CI 2.44-24.40) cases per 1000 person-years. This demonstration serves the dual purposes of illustrating analysis techniques and providing insights about the utility of hs-CRP and Lp-PLA₂ for identifying the high-risk population of CHD that the traditional risk factors such as the LDL-C may miss. Epidemiologists are encouraged to use this new tool to analyze other case-cohort studies and incorporate auxiliary variables embedded in the full cohort in their analysis.