| 474 | 0 | 39 |
| Downloads | Citas | Reads |
Relative risk(RR) is a commonly used indicator in epidemiological randomized controlled trials to compare morbidity or mortality between two groups.Interval estimation of RR is an effective statistical inference method that reflects uncertainty and confidence.However, traditional interval estimation methods, such as Wald's interval, Wilson interval, Fisher interval, etc.,have certain limitations: large error, low coverage, long interval length, and unreasonable interval.In order to overcome these shortcomings, an interval estimation method based on saddle point approximation is proposed: in the context of Poisson distribution, the approximation formula of RR is derived by using Taylor expansion and Laplace integral, and the corresponding confidence interval construction method is given.Through Monte Carlo simulation and empirical analysis, the saddle point approximation method is compared with some existing interval estimation methods, and the results show that the saddle point approximation method can obtain the shortest confidence interval in the case of small or large samples, and the interval coverage is closer to the nominal level, which provides a superior interval estimation method for RR.Finally, the advantages and limitations of the saddle point approximation method, as well as its application value and prospect in epidemiological research are discussed.
[1] BRESLOW N E,DAY N E,HESELTINE E.Statistical methods in cancer research - The analysis of case-control studies[M].Lyon:IARC Scientific Publications,1980:85-115.
[2] SEDGWICK P,MARSTON L.Relative risks[J].BMJ,2010,341:c3983.
[3] WANG W,LU S,XIE T.Optimal confidence intervals for the relative risk and odds ratio[J].Statistics in medicine,2023,42(3):281-296.
[4] TANG M L,TIAN M.Approximate confidence interval construction for risk difference under inverse sampling[J].Statistics and computing,2010,20:87-98.
[5] 夏丽丽，田茂再，朱钰.二项分布下基于鞍点逼近的总体成数置信区间的构造[J].统计与信息论坛，2019,34(9):3-9.
[6] 孟令宾，李二倩，田茂再.基于鞍点逼近的二项抽样下优势比的置信区间构造[J].数理统计与管理，2017,36(1):85-102.
[7] 白永昕，田茂再.Poisson分布下基于鞍点逼近的慢性病风险差的置信区间构造[J].高校应用数学学报A辑，2017,32(3):253-266.
[8] 王维贤，田茂再.鞍点逼近下相关差的置信区间构造[J].高校应用数学学报A辑，2019,34(3):264-272.
[9] CANNON-ALBRIGHT L A,FOSTER N L,SCHLIEP K,et al.Relative risk for Alzheimer disease based on complete family history[J].Neurology,2019,92(15):e1745-e1753.
[10] BYERLEY C O N,HORNE D,GONG M,et al.An effective COVID-19 vaccine hesitancy intervention focused on the relative risks of vaccination and infection[J].Scientific reports,2024,14(1):7419.
[11] EDERER F,MANTEL N.Confidence limits on the ratio of two Poisson variables[J].American journal of epidemiology,1974,100(3):165-167.
[12] CROW E L.Confidence intervals for a proportion[J].Biometrika,1956,43(3/4):423-435.
[13] KATZ D,BAPTISTA J,AZEN S P,et al.Obtaining confidence intervals for the risk ratio in cohort studies[J].Biometrics,1978,34(3):469-474.
[14] PAPANICOLAOU A.Taylor approximation and the delta method [R/OL].(2009-04-28)[2024-03-21].https://www.stat.rice.edu/～dobelman/notes_papers/math/TaylorAppDeltaMethod.pdf.
[15] BARKER L,CADWELL B L.An analysis of eight 95 percent confidence intervals for a ratio of Poisson parameters when events are rare[J].Statistics in medicine,2008,27(20):4030-4037.
[16] MURPHY S A.Likelihood ratio-based confidence intervals in survival analysis[J].Journal of the American Statistical Association,1995,90(432):1399-1405.
[17] FIELLER E C.Some problems in interval estimation[J].Journal of the royal statistical society series B:statistical methodology,1954,16(2):175-185.
[18] FAY M P.Confidence intervals that match Fisher’s exact or Blaker’s exact tests[J].Biostatistics,2010,11(2):373-374.
[19] WOOLF B.On estimating the relation between blood group and disease[J].Annals human genetics,1955,19(4):251-253.
[20] FELLER W.An introduction to probability theory and its applications,Volume 2[M].New York:John Wiley & Sons,1991:500-510.
[21] DANIELS H E.Saddlepoint approximations in statistics[J].The annals of mathematical statistics,1954,25(4):631-650.
[22] 田茂再，吴喜之，李远，等.逆抽样下流行病发病率的逼近与渐近置信区间[J].系统科学与数学，2008(5):513-523.
[23] ZHANG W,BRAVINGTON M V,FEWSTER R M.Fast likelihood-based inference for latent count models using the saddlepoint approximation[J].Biometrics,2019,75(3):723-733.
[24] JENSEN J L.Saddlepoint approximations[M].Oxford:Clarendon Press,1995:32.
[25] 钱政超，张晨阳，孟令宾，等.二项抽样下基于鞍点逼近方法的流行病相对风险置信区间构造[J].数学的实践与认识，2014,44(21):204-217.
[26] 闵素芹，张宁.鞍点逼近法在NNT区间估计中的应用与模拟研究[J].统计与信息论坛，2014,29(9):11-14.
[27] ASIF F,AHMAD M R,MAJID A.Risk factors for thyroid cancer in females using a logit model in Lahore,Pakistan[J].Asian Pacific journal of cancer prevention,2015,16(15):6243-6247.
[28] BELARDINELLI R,GEORGIOU D,CIANCI G,et al.Randomized,controlled trial of long-term moderate exercise training in chronic heart failure:effects on functional capacity,quality of life,and clinical outcome[J].Circulation,1999,99(9):1173-1182.
[29] DOLL R,HILL A B.Smoking and carcinoma of the lung[J].British medical journal,1950,2:739-748.
[30] ARMITAGE P,BERRY G,MATTHEWS J N S.Statistical methods in medical research[M].New York:John Wiley & Sons,2008:648-716.
[31] 郭冰清，姚强.新时代中国居民健康保障获得感变化趋势及影响因素研究[J].统计与信息论坛，2023,38(9):95-111.
[32] 田梓璇，谢小月.大数据序贯检验方法及其应用[J].统计与信息论坛，2024,39(9):13-22.
[33] 熊巍，王娟，潘晗，等.多重稳健的高维缺失数据插补研究[J].统计与信息论坛，2023,38(2):3-15.
Basic Information:
DOI：10.20207/j.cnki.1007-3116.20250703.001
China Classification Code:O212.1
Citation Information:
[1]HOU Jian,LIU Shuo,TIAN Maozai.Relative Risk Confidence Interval Construction Based on Saddle Point Approximation under Poisson Distribution[J].Journal of Statistics and Information,2025,40(08):3-13.DOI:10.20207/j.cnki.1007-3116.20250703.001.
Fund Information:
国家自然科学基金项目“基于分位回归的当代统计学逆问题重大基础理论和方法及其应用”(11861042); 中国人民大学科学研究基金(中央高校基本科研业务费专项资金资助)项目成果“当代复杂大数据的动态稳健建模及应用研究”(22XNL016)
2025-07-03
2025-07-03
2025-07-03