Stratified Analysis: Beginner Level

Confounding vs Effect Modification

Stratified Analysis to study association between stroke and angina with BMI as a 3rd variable

Exposure=Angina, Outcome= Stroke

framdata<-read.csv(file.choose(),header = T) names(framdata) attach(framdata)

Categorize individuals into 2 groups of BMI : normal or over weight

BMI_category<-ifelse(BMI >25,"Overweight","Normal Weight") table(BMI_category)

Output

BMI_category Normal Weight Overweight 1449 1785

Install and load epiR Package

install.packages("epiR") library(epiR)

Create contigency tables

epitables<-table(framdata$STROKE,framdata$ANGINA,BMI_category) rownames(epitables)<-c("ANGINA","NO ANGINA") #EXPOSURE colnames(epitables)<-c("STROKE","NO STROKE") #OUTCOME epitables

Output

, , BMI_category = Normal Weight STROKE NO STROKE ANGINA 1166 167 NO ANGINA 91 25

, , BMI_category = Overweight STROKE NO STROKE ANGINA 1343 280 NO ANGINA 126 36

Prepare the matrix table using the information from the output

for normal weight people (BMI<25)

normal_wt<-matrix(c(1166,167,91,25),nrow = 2,byrow = T) rownames(normal_wt)<-c("ANGINA","NO ANGINA") #EXPOSURE colnames(normal_wt)<-c("STROKE","NO STROKE") #OUTCOME normal_wt

for overweight individuals (BMI >25)

over_wt<-matrix(c(1341,280,126,36),nrow = 2,byrow = T) rownames(over_wt)<-c("ANGINA","NO ANGINA") #EXPOSURE colnames(over_wt)<-c("STROKE","NO STROKE") #OUTCOME over_wt

Stratified Odds Ratios and Risk Ratios

epi.2by2(epitables,method = "cohort.count") #crude/unadjusted epi.2by2(normal_wt,method = "cohort.count") #adjusted for normal weight individuals epi.2by2(over_wt,method = "cohort.count") #adjusted for overweight individuals

Output

epi.2by2(epitables,method = "cohort.count") #crude/unadjusted Outcome + Outcome - Total Exposed + 2509 447 2956 Exposed - 217 61 278 Total 2726 508 3234 Inc risk * Odds Exposed + 84.9 5.61 Exposed - 78.1 3.56 Total 84.3 5.37

Point estimates and 95% CIs:

Inc risk ratio (crude) 1.09 (1.02, 1.16) Inc risk ratio (M-H) 1.09 (1.02, 1.16) Inc risk ratio (crude:M-H) 1.00 Odds ratio (crude) 1.58 (1.17, 2.13) Odds ratio (M-H) 1.56 (1.15, 2.11) Odds ratio (crude:M-H) 1.01 Attrib risk (crude) * 6.82 (1.79, 11.85) Attrib risk (M-H) * 6.67 (-6.54, 19.89) Attrib risk (crude:M-H) 1.02

M-H test of homogeneity of RRs: chi2(1) = 0.504 Pr>chi2 = 0.48 M-H test of homogeneity of ORs: chi2(1) = 1.194 Pr>chi2 = 0.27 Test that M-H adjusted OR = 1: chi2(1) = 8.514 Pr>chi2 = 0.00 Wald confidence limits M-H: Mantel-Haenszel; CI: confidence interval

• Outcomes per 100 population units

epi.2by2(normal_wt,method = "cohort.count") #adjusted for normal weight individuals Outcome + Outcome - Total Exposed + 1166 167 1333 Exposed - 91 25 116 Total 1257 192 1449 Inc risk * Odds Exposed + 87.5 6.98 Exposed - 78.4 3.64 Total 86.7 6.55

Point estimates and 95% CIs:

Inc risk ratio 1.12 (1.01, 1.23) Odds ratio 1.92 (1.20, 3.07) Attrib risk * 9.02 (1.33, 16.71) Attrib risk in population * 8.30 (0.62, 15.98) Attrib fraction in exposed (%) 10.32 (1.13, 18.65) Attrib fraction in population (%) 9.57 (1.01, 17.39)

Test that OR = 1: chi2(1) = 7.559 Pr>chi2 = 0.01 Wald confidence limits CI: confidence interval

• Outcomes per 100 population units

epi.2by2(over_wt,method = "cohort.count") #adjusted for overweight individuals Outcome + Outcome - Total Exposed + 1341 280 1621 Exposed - 126 36 162 Total 1467 316 1783 Inc risk * Odds Exposed + 82.7 4.79 Exposed - 77.8 3.50 Total 82.3 4.64

Point estimates and 95% CIs:

Inc risk ratio 1.06 (0.98, 1.16) Odds ratio 1.37 (0.92, 2.03) Attrib risk * 4.95 (-1.71, 11.61) Attrib risk in population * 4.50 (-2.14, 11.14) Attrib fraction in exposed (%) 5.98 (-2.39, 13.67) Attrib fraction in population (%) 5.47 (-2.19, 12.56)

Test that OR = 1: chi2(1) = 2.474 Pr>chi2 = 0.12 Wald confidence limits CI: confidence interval

• Outcomes per 100 population units

detach(framdata)