# Example: Confidence Limits for Incidence Rate Difference and Incidence Rate Ratio

The data in Table 9-2 are taken from a study by Feychting et al.^{1} that compared cancer occurrence among the blind with occurrence among those who were not blind but had severe visual impairment. The study hypothesis was that a high

*Table 9-2* Incidence Rate of Cancer Among a Blind Population and a Population That Is Visually Severely Impaired but not Blind

Totally Blind |
Visually Severely Impaired but Not Blind |

Cancer cases 136 |
1,709 |

Person-years 22,050 |
127,650 |

Data from Petitti et al.^{2}

circulating level of melatonin protects against cancer. Melatonin production is greater among the blind because visual detection of light suppresses melatonin production by the pineal gland.

From these data, we can calculate a cancer rate of 136/22,050 person-years = 6.2/1000 person-years among the blind, compared with 1709/127,650 person- years = 13.4/1000 person-years among those who were visually impaired but not blind. The incidence rate difference (ID) is (6.2 — 13.4)/1000 person- years = —7.2/1000 person-years. The minus sign indicates that the rate is lower among the group with total blindness, which is here considered to be the exposed group. To get a 90% confidence interval for this estimate of rate difference, we use Equations 8-1 in combination with Equation 9-4, as follows.

This calculation gives 90% confidence limits around the rate difference, -7.2/1000 person-years, of -8.2/1000 person-years and -6.2/1000 person-years.

The incidence rate ratio for the data in Table 9-2 is (136/22,050)/ (1709/127,650) = 0.46, indicating a rate among the blind that is less than one half that among the comparison group. The lower limit of the 90% confidence interval for this rate ratio is calculated as follows:

A corresponding calculation for the upper limit gives IRU = 0.53, for a 90% confidence interval around the incidence rate ratio of 0.46 of 0.40 to 0.53.