Incidence-rate ratio calculator

Sometimes, we are given summary data and asked to estimate the incidence rate, incidence-rate difference, incidence-rate ratio, and confidence intervals.

This is common in prospective cohort studies where a sample of people without a condition (noncases) is followed over time to see who develops the condition (cases). The sample is typically divided into one group who were exposed to a possible risk factor and another group who were not exposed. Exposure to the risk factor is typically measured in "person-time". A person who is followed for two years contributes two "person-years", while a person who is followed for five years contributes five "person-years".

For example, we could follow a healthy group of people who are exposed to a possible carcinogen and a healthy group who are not exposed. Then we can count the number of people in each group who develop cancer. We can estimate the incidence rate metrics using Stata's iri command command followed by four numbers:

The number of cases in the exposed group (41)
The number of cases in the unexposed group (15)
The number of person-years in the exposed group (28,010)
The number of person-years in the unexposed group (19,017)

. iri 41 15 28010 19017


                
   Exposed   Unexposed  
      Total
           Cases 
        41          15  
         56
     Person-time 
     28010       19017  
      47027
                 
                        
           
  Incidence rate 
  .0014638    .0007888  
   .0011908
                 
                        
           
                 
      Point estimate    
    [95% conf. interval]
 Inc. rate diff. 
          .000675       
    .0000749    .0012751        
 Inc. rate ratio 
         1.855759       
    1.005684      3.6093 (exact)
 Attr. frac. ex. 
         .4611368       
    .0056519     .722938 (exact)
 Attr. frac. pop 
          .337618       
                        
Mid-p-values for tests of incidence-rate difference:
  Adj Pr(Exposed cases <= 41) = 0.9823 (lower one-sided)
  Adj Pr(Exposed cases >= 41) = 0.0177 (upper one-sided)
            Two-sided p-value = 0.0355

The output gives us a lot of information.

The overall incidence rate is .0012 cases per person-year. The incidence rate in the exposed group is .0015 cases per person-year, and the incidence rate in the unexposed group is .0008 cases per person-year.

The incidence rate difference (IRD) is the difference between the incidence rate in the exposed group and the incidence rate in the unexposed group. Here the IRD and 95% confidence interval is 0.0007 (0.0001 - 0.0013).

The incidence rate ratio (IRR) is the incidence rate in the exposed group divided by the incidence rate in the unexposed group. Here the IRR and 95% confidence interval is 1.86 (1.01 - 3.61).

The attributable fraction among the exposed (AFE) is an estimate of the proportion of exposed cases attributable to exposure. Here the AFE and 95% confidence interval is 0.46 (0.01 - 0.72).

The attributable fraction for the population (AFP) is the net proportion of all cases attributable to exposure. Here the AFP is 0.34.

At the bottom of the table, iri reports one- and two-sided tests of the IRD. For the one-sided test of the number of exposed cases being 41 or greater, the p-value is 0.0177. The two-sided test is twice the smallest one-sided p-value and is 0.0355. These p-values are calculated using the mid-p adjustment to exact p-values.

We can use the exact option to report exact p-values.

. iri 41 15 28010 19017, exact


                
   Exposed   Unexposed  
      Total
           Cases 
        41          15  
         56
     Person-time 
     28010       19017  
      47027
                 
                        
           
  Incidence rate 
  .0014638    .0007888  
   .0011908
                 
                        
           
                 
      Point estimate    
    [95% conf. interval]
 Inc. rate diff. 
          .000675       
    .0000749    .0012751        
 Inc. rate ratio 
         1.855759       
    1.005684      3.6093 (exact)
 Attr. frac. ex. 
         .4611368       
    .0056519     .722938 (exact)
 Attr. frac. pop 
          .337618       
                        
Exact p-values for tests of incidence-rate difference:
  Pr(Exposed cases <= 41) = 0.9884 (lower one-sided)
  Pr(Exposed cases >= 41) = 0.0238 (upper one-sided)
        Two-sided p-value = 0.0477

You can watch a demonstration of these commands by clicking on the link to the YouTube video below. You can read more about these commands by clicking on the links to the Stata manual entries below.

See it in action

Watch Stata® tutorial: Incidence-rate ratios calculator.