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# New Epidemiologic Measures in Multilevel Study: Median Risk Ratio, Median Hazard Ratio and Median Beta

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New Epidemiologic Measures in Multilevel Study - 역학회발표

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### New Epidemiologic Measures in Multilevel Study: Median Risk Ratio, Median Hazard Ratio and Median Beta

1. 1. Introduction Formula Examples Discussion References New Epidemiologic Measures in Multilevel Study: Median Risk Ratio, Median Hazard Ratio and Median Beta Jinseob Kim1 Graduate School of Public Health, Seoul National University, Korea Apr 4, 2014 Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
2. 2. Introduction Formula Examples Discussion References Contents 1 Introduction ICC & VPC Multilevel analysis: binomial case This study 2 Formula Brief review of median OR Median RR, Median HR, Median Beta 3 Examples Data Count data Cox proportional hazard model 4 Discussion Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
3. 3. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study 목표 1 Multilevel study에서 그룹변수의 효과를 설명하는 방법을 소개한다. 2 그룹변수의 효과를 직관적으로 설명할 수 있는 새로운 지표를 제시한다. 3 실제로 어떻게 계산하고 해석되는지 예제를 통해 알아본다. 4 새로운 역학지표로서의 의의. Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
4. 4. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study 예시 Health survey conducted in 2000 in the county of Scania, Sweden[11] 1 10,723 persons, 18-80 age, 60 areas 2 Individual propensity of consulting private physicians VS Area. 3 Y: 최근 1년간 private physicians consulting 경험유무: binomial 4 X: individual level variables, area level variables, area Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
5. 5. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
6. 6. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study Eﬀect of group variable 1 Repeated measure, random eﬀect, multilevel, hierarchial GLM, GEE, GLMM... 2 그룹변수의 beta값 못구하겠다. (그룹이 너무 많다.. 50개 100 개...) 3 구해본들.. 해석난감.. (50개 그룹 → 49개 베타값) 4 그룹변수의 효과를 숫자 하나로 표시한다: Vgroup 5 분산이 얼마나 크냐?? 0: 그룹은 의미없다, 클수록 그룹의 의미가 크다. Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
7. 7. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study Intraclass correlation coeﬃcient, variance partition coeﬃcients Yi = Xi β + Groupi + i (1) ICC = VGroup VY = VGroup VGroup + V (2) 1 그룹변수의 효과를 나타내는 지표[1, 6]. 2 0: 그룹변수는 의미없는 변수, 1: 그룹변수가 Y 의 모든 것을 설명한다. Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
8. 8. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study ICC example lmer(formula = TG ~ age + sex + BMI + (1 | FID), data = a) Estimate Std. Error t value (Intercept) -65.222107 35.8720093 -1.8181894 age 0.109564 0.3318413 0.3301699 sex -41.942137 11.3684264 -3.6893529 BMI 8.648601 1.2917159 6.6954362 Groups Name Std.Dev. FID (Intercept) 39.356 Residual 72.007 Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
9. 9. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study ICC = 39.3562 39.3562 + 72.0072 0.23 (3) 해석: age, sex, BMI를 보정한 후에도 FID가 TG의 23%를 설명한다. Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
10. 10. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study Diﬀerent scale: ICC?? Var(Yi ) = pi (1 − pi ) (4) logit(pi ) = Xi β + Groupi (5) Proportional scale VS Logistic scale[3] Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
11. 11. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study Example: binomial case glmer(formula = hyperTG ~ age + sex + BMI + (1 | FID), data = a, family = binomial) Estimate Std. Error z value Pr(>|z|) (Intercept) -6.65451749 1.48227814 -4.4893852 7.142904e-06 age 0.01052907 0.01206682 0.8725635 3.829010e-01 sex -1.48506920 0.60773433 -2.4436158 1.454090e-02 BMI 0.19131619 0.05022612 3.8090977 1.394749e-04 Groups Name Std.Dev. FID (Intercept) 1.1163 Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
12. 12. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study Solution 1 Linearization : logit → proportion 2 Simulation : proportion → logit 3 Latent variable Approximation of ICC, calculation issue[3, 15] Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
13. 13. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study Median Odds Ratio(MOR) Larsen et al.(2000, 2005) 임의의 두 group을 골랐을 때 (Odds가 큰 그룹: 작은 그룹) 의 OR이 대충(median) 얼마나 되는가?[8, 7, 11] MOR = exp ( 2VGroup × Φ−1 (0.75)) exp (0.95 VGroup) (6) 1 1 ∼ inf : Group효과 없다, 엄청 크다. 2 VGroup만 있으면 계산가능. 3 OR scale로 해석: age, sex 해석하듯이 하면 된다. Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
14. 14. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
15. 15. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
16. 16. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study Example: binomial case glmer(formula = hyperTG ~ age + sex + BMI + (1 | FID), data = a, family = binomial) Groups Name Std.Dev. FID (Intercept) 1.1163 MOR = exp( 2 × 1.11632 × 0.6745) = 3.67 (7) : 임의의 두 가족을 뽑으면 대충(median) OR이 3.67이다. Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
17. 17. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study If count data? survival analysis? Count data(rate, 자녀 수..) 1 poisson 분포때는 ICC계산가능 (similar to binomial case) 2 Gamma, neg-bin...???, Interpretation issue: 0-1 scale. Cox-proportional hazard model 1 ICC의 개념이 없다. Y: hazard function... 2 그냥 Vgroup 만 제시하는 정도.. Interpretation issue. Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
18. 18. Introduction Formula Examples Discussion References ICC & VPC Multilevel analysis: binomial case This study 목표 New measurement in multilevel analysis. 1 Count data(poisson, gamma, neg-bin...)[4, 14, 16] : Median Risk Ratio 2 Survival data : cox proportional hazard : Median Hazard Ratio 3 Continuous data : Median Beta 일반 변수 해석과 같은 Scale로 해석가능 & 계산이 간단하며 신뢰구간도 쉽게 구할 수 있다[5]. Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
19. 19. Introduction Formula Examples Discussion References Brief review of median OR Median RR, Median HR, Median Beta Multilevel logistic regression[8] Logit[Pr(Yij = 1|Xij , Gj )] = β0 + Xij β1 + Gj (8) (β0: intercept, β1: vector of ﬁxed regression coeﬃcients, Gj : random intercept Gj ∼ N(0, Vg )) Odds[Pr(Yij = 1|Xij , Gj )] = exp (β0) exp (Xij β1) exp (Gj ) (9) Odds[Pr(Yij = 1|X, Gj )] Odds[Pr(Yik = 1|X, Gk)] = exp (Gj − Gk) (10) Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
20. 20. Introduction Formula Examples Discussion References Brief review of median OR Median RR, Median HR, Median Beta Odds가 큰그룹을 Odds가 작은 그룹과 비교! OR = exp |Gj − Gk| (11) (Gj − Gk) ∼ N(0, 2Vg ) (12) 결국 임의로 두 그룹을 뽑았을 때 Odds가 큰 그룹과 Odds가 작은 그룹을 비교하여 OR의 median값을 계산하였을 때 그 결과는 MOR = exp ( 2Vg × Φ−1 (0.75)) exp (0.95 Vg) (13) (Φ: probability density function(PDF) of standard normal distribution) Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
21. 21. Introduction Formula Examples Discussion References Brief review of median OR Median RR, Median HR, Median Beta Multilevel poisson regression[9] Yij |λij ∼ Pois(λij ) (14) ln[(λij |Xij , Gj )] = β0 + Xij β1 + Gj (15) Risk[(λij |X, Gj )] Risk[(λik|X, Gk)] = exp (Gj − Gk) (16) Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
22. 22. Introduction Formula Examples Discussion References Brief review of median OR Median RR, Median HR, Median Beta Risk가 큰그룹을 Risk가 작은 그룹과 비교!! RR = exp |Gj − Gk| (17) (Gj − Gk) ∼ N(0, 2Vg ) (18) 임을 이용하면 결국 임의로 두 그룹을 뽑았을 때 Risk가 큰 그룹과 Risk가 작은 그룹을 비교하여 RR의 median값을 계산하였을 때 그 결과는 MRR = exp ( 2Vg × Φ−1 (0.75)) exp (0.95 Vg) (19) (Φ: probability density function(PDF) of standard normal distribution) Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
23. 23. Introduction Formula Examples Discussion References Brief review of median OR Median RR, Median HR, Median Beta Multilevel cox-proportional hazard analysis[10] ln[( hij (t) h0(t) |Xij , Gj )] = β0 + Xij β1 + Gj (20) (hij (t): hazard function of ith individual of jth group, h0(t): base hazard function) [(hij (t)|X, Gj )] [(hik(t)|X, Gk)] = exp (Gj − Gk) (21) MHR = exp ( 2Vg × Φ−1 (0.75)) exp (0.95 Vg) (22) Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
24. 24. Introduction Formula Examples Discussion References Brief review of median OR Median RR, Median HR, Median Beta Gaussian multilevel regression Yij ∼ N(µij , σ2 ) (23) [(µij |Xij , Gj )] = β0 + Xij β1 + Gj (24) [(µij |X, Gj )] − [(µik|X, Gk)] = (Gj − Gk) (25) Median Beta = 2Vg × Φ−1 (0.75) 0.95 Vg (26) Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
25. 25. Introduction Formula Examples Discussion References Data Count data Cox proportional hazard model Minnesota Breast Cancer Study- kinship2 packages in R[13] 1 3725 obs. of 15 variables (female with non-missing) 2 education : 1-고졸이하, 2-대졸미만, 3-대졸이상 3 marstat : 1- 결혼 및 사실혼, 2- 사별 및 이혼, 3-미혼 4 yob(출생년도): 1: -1919, 2: 1920-1939, 3: 1940-1959, 4: 1960- 5 parity: 자녀 수 6 cancer: 1-유방암, 0-censored 7 endage: 마지막 f/u 또는 암발생 나이 8 famid: 가족 id Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
26. 26. Introduction Formula Examples Discussion References Data Count data Cox proportional hazard model See data famid endage cancer yob education marstat parity 16 4 64 0 2 2 1 2 20 4 69 0 2 2 1 2 22 4 59 0 3 3 2 2 23 4 59 0 3 3 2 2 31 4 62 0 2 2 2 1 35 4 61 0 3 2 1 2 Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
27. 27. Introduction Formula Examples Discussion References Data Count data Cox proportional hazard model Variables Model.1 Model.2 Model.3 (Intercept) 2.75 (2.67˜2.83) 3.53 (3.35˜3.71) 3.61 (3.35˜3.9) Education 1 . 1 1 2 . 0.84 (0.8˜0.89) 0.89 (0.84˜0.94) 3 . 0.67 (0.63˜0.71) 0.75 (0.7˜0.79) Marriage 1 . 1 1 2 . 1.03 (0.98˜1.08) 0.95 (0.9˜1) 3 . 0.07 (0.05˜0.11) 0.08 (0.05˜0.13) Year of birth ˜1919 . . 1 ˜1939 . . 1.13 (1.05˜1.21) ˜1959 . . 0.75 (0.7˜0.81) 1960˜ . . 0.52 (0.47˜0.59) V famid 0.03 0.02 0.01 Median RR 1.18 1.14 1.11 Table: Y: parity, Group: family ID, lme4 package in R Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
28. 28. Introduction Formula Examples Discussion References Data Count data Cox proportional hazard model Interpretation 1 일반적인 RR에 대한 해석 2 가족구조가 차지하는 분산이 각각 0.03, 0.02, 0.01 3 MRR: 임의로 두 가족을 골랐을때 high rate: low rate의 RR 값의 중간값은 각각 1.18, 1.14, 1.11 4 교육수준, 결혼상태, period eﬀect 를 고려한 후에도 가족자체의 효과는 남아있다?? Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
29. 29. Introduction Formula Examples Discussion References Data Count data Cox proportional hazard model Variables Model.1 Model.2 Model.3 Model.4 I(parity > 0)TRUE . 0.71 (0.66˜0.77) 0.72 (0.65˜0.79) 0.74 (0.67˜0.81) Education 1 . . 1 1 2 . . 1.32 (1.25˜1.4) 1.24 (1.17˜1.31) 3 . . 1.07 (0.99˜1.14) 0.97 (0.9˜1.04) Marriage 1 . . 1 1 2 . . 1.03 (0.99˜1.07) 1.15 (1.1˜1.2) 3 . . 1.08 (0.71˜1.64) 1.23 (0.81˜1.88) Year of birth ˜1919 . . . 1 ˜1939 . . . 1.41 (1.3˜1.52) ˜1959 . . . 2.52 (2.21˜2.87) 1960˜ . . . 1.5 (0.17˜13.14) V famid 0.18 0.18 0.18 0.17 Median HR 1.49 1.5 1.5 1.49 Table: Y: Breast cancer hazard, Group: family ID, coxme package in R Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
30. 30. Introduction Formula Examples Discussion References Data Count data Cox proportional hazard model Interpretation 1 일반적인 Hazard Ratio에 대한 해석. 2 가족구조가 차지하는 분산이 1.5정도 3 MHR: 임의로 두 가족을 골랐을때 high hazard: low hazard 의 HR값의 중간값은 1.5 4 출산경험, 교육수준, 결혼상태, period eﬀect와 상관없이 가족력이 일정하게 존재한다?? Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
31. 31. Introduction Formula Examples Discussion References Median OR의 count, survival 버전. 1 Poisson regression: ICC 계산가능 but, Neg-bin? Gamma? 2 Cox: ICC 개념적용어렵다, 그냥 그룹변수의 분산을 제시하고 끝이었다. 3 MRR, MHR: 다른 지표 해석과 같은 scale에서 해석이 가능하다[2, 12]. 4 계산이 간단하다. 그룹변수만 있으면 된다. 5 신뢰구간 구하기도 ICC보다 편하다. Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
32. 32. Introduction Formula Examples Discussion References Conclusion 1 New measurement explaining eﬀect of group variable in multilevel analysis with count data/survival data 2 Count data: ICC의 대안, 해석하고싶은 scale로 (proportion VS RR) 3 Cox: Best explaination?? 4 Median Beta도 ICC의 대안이 될 수 있다. 5 Multilevel study에서 Group level의 효과를 직관적으로 설명할 수 있어 의사결정과 소통에 도움이 될 것이다. Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
33. 33. Introduction Formula Examples Discussion References Packages 1 lme4, nlme, coxme.. in R 2 Conﬁdence interval for MHR, MRR: calculation issue.. 3 Using Bayesian hierarchical model with OpenBUGS, JAGS, Stan.. 4 R2OpenBUGS, BRugs, rjags, R2jags, rstan Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
34. 34. Introduction Formula Examples Discussion References Reference I [1] Bartko, J. J. (1966). The intraclass correlation coeﬃcient as a measure of reliability. Psychological reports, 19(1):3–11. [2] Bolker, B. M., Brooks, M. E., Clark, C. J., Geange, S. W., Poulsen, J. R., Stevens, M. H. H., and White, J.-S. S. (2009). Generalized linear mixed models: a practical guide for ecology and evolution. Trends in ecology & evolution, 24(3):127–135. [3] Browne, W. J., Subramanian, S. V., Jones, K., and Goldstein, H. (2005). Variance partitioning in multilevel logistic models that exhibit overdispersion. Journal of the Royal Statistical Society: Series A (Statistics in Society), 168(3):599–613. [4] Coxe, S., West, S. G., and Aiken, L. S. (2009). The analysis of count data: A gentle introduction to poisson regression and its alternatives. Journal of personality assessment, 91(2):121–136. [5] Do Ha, I. and Lee, Y. (2005). Multilevel mixed linear models for survival data. Lifetime data analysis, 11(1):131–142. [6] Goldstein, H., Browne, W., and Rasbash, J. (2002). Partitioning variation in multilevel models. Understanding Statistics: Statistical Issues in Psychology, Education, and the Social Sciences, 1(4):223–231. [7] Larsen, K. and Merlo, J. (2005). Appropriate assessment of neighborhood eﬀects on individual health: integrating random and ﬁxed eﬀects in multilevel logistic regression. American journal of epidemiology, 161(1):81–88. [8] Larsen, K., Petersen, J. H., Budtz-Jørgensen, E., and Endahl, L. (2000). Interpreting parameters in the logistic regression model with random eﬀects. Biometrics, 56(3):909–914. [9] Lee, A. H., Wang, K., Scott, J. A., Yau, K. K., and McLachlan, G. J. (2006). Multi-level zero-inﬂated poisson regression modelling of correlated count data with excess zeros. Statistical Methods in Medical Research, 15(1):47–61. Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
35. 35. Introduction Formula Examples Discussion References Reference II [10] Liu, L. and Huang, X. (2008). The use of gaussian quadrature for estimation in frailty proportional hazards models. Statistics in medicine, 27(14):2665–2683. [11] Merlo, J., Chaix, B., Ohlsson, H., Beckman, A., Johnell, K., Hjerpe, P., R˚astam, L., and Larsen, K. (2006). A brief conceptual tutorial of multilevel analysis in social epidemiology: using measures of clustering in multilevel logistic regression to investigate contextual phenomena. Journal of Epidemiology and Community Health, 60(4):290–297. [12] Therneau, T. (2012). Mixed eﬀects cox models. R-package description. URL: http://cran. r-project. org/web/packages/coxme/vignettes/coxme. pdf. [13] Therneau, T., Atkinson, E., Sinnwell, J., Schaid, D., and McDonnell, S. (2014). kinship2: Pedigree functions. R package version 1.5.7. [14] Ver Hoef, J. M. and Boveng, P. L. (2007). Quasi-poisson vs. negative binomial regression: how should we model overdispersed count data? Ecology, 88(11):2766–2772. [15] Vigre, H., Dohoo, I., Stryhn, H., and Busch, M. (2004). Intra-unit correlations in seroconversion to actinobacillus pleuropneumoniae and mycoplasma hyopneumoniae at diﬀerent levels in danish multi-site pig production facilities. Preventive veterinary medicine, 63(1-2):9–28. [16] Winkelmann, R. and Zimmermann, K. F. (1995). Recent developments in count data modelling: theory and application. Journal of economic surveys, 9(1):1–24. Jinseob Kim1 New Epidemiologic Measures in Multilevel Study:
36. 36. Introduction Formula Examples Discussion References END Email : secondmath85@gmail.com Jinseob Kim1 New Epidemiologic Measures in Multilevel Study: