Assessing the variability of the attributable causes of death

Wenjiang J Fu1, Tianshuang Wu2, Yu Wang3, Haiying Meng4, Jianshi Huang3 1Department of Epidemiology, 2Department of Mathematics, Michigan State University, East Lansing, MI, USA; 3Department of Epidemiology, Institute of Basic Medical Sciences, Chinese Academy of Medical Sciences; School of Basic Medicine, Peking Union Medical College, Beijing, People’s Republic of China; 4Center for Disease Control and Prevention of Chaoyang District, Beijing, People’s Republic of China "This article is dedicated to the memory of Professor Jianshi Huang, who passed away suddenly during the final proofreading of this article. We thank him for his inspiration and encouragement for this work, as well as his leadership and commitment to public health." Abstract: The study of attributable causes of death (ACD) provides a new venue to quantify the external (nongenetic) causes of mortality, and may guide policymaking to address emerging issues in public health by focusing on the largely preventable risk factors. Given such importance, systematic methods to assess the variability of the attributable number of deaths (AND), including the standard errors and confidence intervals, need to be developed. In this article, we develop two statistical methods of the estimation of the standard errors and confidence intervals for the ANDs, one using multinomial distribution and the other using bootstrap sampling, and study the effect of the size of the mortality through simulations. Both methods are easy to implement and provide valid and efficient estimation of the standard errors and confidence intervals. While AND estimates and their standard errors increase with the size of the mortality, the ratio of the standard error to the AND estimate decreases. We demonstrate the methods with two data sets, the US national mortality data during the year 2006 and the mortality data of Chaoyang district of Beijing, China during the year 2007. We conclude that assessment of the variability is needed for small size mortality as the uncertainty is relatively large, but not for large size mortality. Keywords: attributable causes, bootstrap, confidence interval, mortality, population attributable fraction