C1.1 Introduction to Prevalence, Risk, Odds and Rates

Risks 

Calculate the overall risk of death by using a combination of ‘table()’ and ‘prop.table()’ commands:

table(df$death)

prop.table(table(df$death))

Examine the pattern of risk of death in relation to increasing age. The margins option in the ‘prop.table()’ command needs to be set to “2” because we want to report the proportions per group. For example, for age and death, this command would be:

table(df$age_grp, df$death)

prop.table(table(df$age_grp, df$death), margins=2)

• Question C1.1a.i: What does your table suggest about the risk of death overall?

• Question C1.1a.ii: What does your table suggest about the risk death across levels of age?

The epitools R package

A good R package to calculate basic epidemiologic analysis is the epitools R package, which includes commands for the design of two-way and multi-way contingency tables and epidemiologic measures, such as risk ratios and odds ratios. You can find more details on the commands included in the epitools R package here.

Install and load the epitools R package with the following commands:

install.packages(“epitools”)

library(epitools)

The epitab() command

A good command in R to explore risk and odds ratios is the epitab() command from the epitools R package. This command is used to produce epidemiological tables with point estimates and CI for risk ratios, and odds ratios.

The syntax for the command is:

epitab(x, y, method)

where x is the vector of the exposure, y is the vector of the outcome and method can be either “oddsratio” to calculate an odds ratio or “riskratio” to calculate a risk ratio. This command works with either binary or categorical exposures. For categorical exposures, R uses by default the lowest value of the exposure as the reference category.

Using the epitab() command to calculate a risk ratio

We want to obtain the risk ratio of mortality for individuals that are current smokers compared to non-smokers. We type the command:

epitab(x = df$currsmoker, y = df$death, method = “riskratio”)

Use the help file for the epitab() command to find out how to obtain an odds ratio.

• • Question C1.1b.i: What is the risk ratio and 95% CI of death for individuals that are current smokers compared with individuals that are non-smokers?

• • Question C1.1b.ii: What is the odds ratio for death in individuals that are current smokers vs non-smokers? State and interpret the 95% confidence interval.

The ‘ir’ command for rates

 Now let’s have a look at the rate ratio for death in smokers vs non-smokers.  This will require the ‘rateratio’ method in the ‘epitab()’  command.

Type the following command to produce the rate and rate ratio:

> death_no_smokers <- sum(df$death[df$currsmoker==”0″])
> death_no_smokers 
[1] 1290 

> death_smokers <- sum(df$death[df$currsmoker==”1″])
> death_smokers 
[1] 215

> fup_no_smoker <- sum(df$fu_years[df$currsmoker==”0″])
> fup_no_smoker
[1] 25460.25

> fup_smoker <- sum(df$fu_years[df$currsmoker==”1″])
> fup_smoker
[1] 3593.209

> epitab(x=c(death_no_smokers, death_smokers), y= c(fu_no_smoker, fu_smoker),
method = c(“rateratio”))

          Outcome
Predictor  c(death_no_smokers, death_smokers) c(fup_no_smoker, fup_smoker) 
  Exposed1                               1290                    25460.250  
  Exposed2                                215                     3593.209  
          
Predictor    rateratio     lower      upper       p.value
  Exposed1   1.000000         NA         NA            NA
  Exposed2   1.180943   1.022177   1.364369    0.02633476

$measure
[1] “wald”

$conf.level
[1] 0.95

$pvalue
[1] “midp.exact”

• • Question C1.1c: What is the rate of death in current smokers compared to non-smokers (i.e. what is the rate ratio of ‘currsmoker’)? Is the rate of death in current smokers significantly different from that in non-smokers?