The notes for the topics on this page can be found in the lectures 5 and 7 folders on Canvas.
Odds ratios and risk ratios can be calculated from contingency tables using the functions oddsratio() and riskratio() from the epitools package. Risk difference can be calculated from contingency tables using the riskdiff() function from the catfun package. For further help, please watch the video example.
library(epitools)
library(catfun)
trial <- tibble(
disease = c(rep("yes", 2), rep("no", 2)),
treatment = c(rep(c("estrogen", "placebo"), 2)),
count = c(751, 623, 7755, 7479)
)
trial <- trial %>%
mutate(disease = as.factor(disease),
treatment = as.factor(treatment),
disease = fct_relevel(disease, "yes", "no"),
treatment = fct_relevel(treatment, "estrogen", "placebo"))For these examples, the oddsratio() and riskratio() are used in combination with xtabs() while riskdiff() only calls upon the dataset.
xtabs(count ~ treatment + disease, data = trial) %>%
oddsratio(method = "wald")## $data
## disease
## treatment yes no Total
## estrogen 751 7755 8506
## placebo 623 7479 8102
## Total 1374 15234 16608
##
## $measure
## odds ratio with 95% C.I.
## treatment estimate lower upper
## estrogen 1.000000 NA NA
## placebo 1.162555 1.04056 1.298853
##
## $p.value
## two-sided
## treatment midp.exact fisher.exact chi.square
## estrogen NA NA NA
## placebo 0.007681115 0.008067297 0.007702585
##
## $correction
## [1] FALSE
##
## attr(,"method")
## [1] "Unconditional MLE & normal approximation (Wald) CI"xtabs(count ~ treatment + disease, data = trial) %>%
riskratio()## $data
## disease
## treatment yes no Total
## estrogen 751 7755 8506
## placebo 623 7479 8102
## Total 1374 15234 16608
##
## $measure
## risk ratio with 95% C.I.
## treatment estimate lower upper
## estrogen 1.0000 NA NA
## placebo 1.0125 1.003305 1.021779
##
## $p.value
## two-sided
## treatment midp.exact fisher.exact chi.square
## estrogen NA NA NA
## placebo 0.007681115 0.008067297 0.007702585
##
## $correction
## [1] FALSE
##
## attr(,"method")
## [1] "Unconditional MLE & normal approximation (Wald) CI"trial %>%
riskdiff("treatment", "disease", weight = "count")##
## Risk difference: 0.0114
## 95% confidence interval: 0.003 0.0198
##
## Proportion 1 = 0.0883
## Proportion 2 = 0.0769
## ---------------------------------------------
##
## Contingency table:
##
## disease
## treatment yes no
## estrogen 751 7755
## placebo 623 7479To caculate measures of association from a contingency table in SAS you use the frequency procedure with the relrisk argument in table statement to generate the relative risk/odds ratio and the riskdiff argument to generate the risk difference. This will always produce confidence intervals for generated measures. The syntax is:
proc freq data = <dataset>;
table <row variable>*<column variable> / <relrisk> <riskdiff>;
weight <weighting variable if summary data>;
run; For further help, please watch the video example.
data trial;
input disease $ treatment $ count;
cards;
yes estrogen 751
yes placebo 623
no estrogen 7755
no placebo 7479
;
run;
proc freq data = trial order = data;
table treatment*disease / riskdiff relrisk;
weight count;
run; ## The FREQ Procedure
##
## Table of treatment by disease
##
## treatment disease
##
## Frequency|
## Percent |
## Row Pct |
## Col Pct |yes |no | Total
## ---------+--------+--------+
## estrogen | 751 | 7755 | 8506
## | 4.52 | 46.69 | 51.22
## | 8.83 | 91.17 |
## | 54.66 | 50.91 |
## ---------+--------+--------+
## placebo | 623 | 7479 | 8102
## | 3.75 | 45.03 | 48.78
## | 7.69 | 92.31 |
## | 45.34 | 49.09 |
## ---------+--------+--------+
## Total 1374 15234 16608
## 8.27 91.73 100.00
##
##
## Statistics for Table of treatment by disease
##
## Column 1 Risk Estimates
##
## (Asymptotic) 95% (Exact) 95%
## Risk ASE Confidence Limits Confidence Limits
## -----------------------------------------------------------------------------
## Row 1 0.0883 0.0031 0.0823 0.0943 0.0823 0.0945
## Row 2 0.0769 0.0030 0.0711 0.0827 0.0712 0.0829
## Total 0.0827 0.0021 0.0785 0.0869 0.0786 0.0870
##
## Difference 0.0114 0.0043 0.0030 0.0198
##
## Difference is (Row 1 - Row 2)
##
##
## Column 2 Risk Estimates
##
## (Asymptotic) 95% (Exact) 95%
## Risk ASE Confidence Limits Confidence Limits
## -----------------------------------------------------------------------------
## Row 1 0.9117 0.0031 0.9057 0.9177 0.9055 0.9177
## Row 2 0.9231 0.0030 0.9173 0.9289 0.9171 0.9288
## Total 0.9173 0.0021 0.9131 0.9215 0.9130 0.9214
##
## Difference -0.0114 0.0043 -0.0198 -0.0030
##
## Difference is (Row 1 - Row 2)
##
##
## Odds Ratio and Relative Risks
##
## Statistic Value 95% Confidence Limits
## ------------------------------------------------------------------
## Odds Ratio 1.1626 1.0406 1.2989
## Relative Risk (Column 1) 1.1482 1.0371 1.2712
## Relative Risk (Column 2) 0.9877 0.9787 0.9967
##
## Sample Size = 16608