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Comparison of two rates

	1st group	2nd group
Numerator (e.g. number of events counted):
Denominator (e.g. total person-years):
Express result as 1:X

Description

A rate is a ratio between a count and another measurement, for example the ratio of a number of events observed and the total number of person-years of observation.

This form allows to compare the rates in two groups.

Required input

Numerator: the observed number of events in each group.
Denominator: for example the total person-years for each group.
Option Express result as 1:X: when this option is selected the rate R will be displayed as 1:(1/R), e.g. the rate 10/200 equals 0.05 and can be represented as 1:20.

Results

MedCalc reports:

The (incidence) rate in the two groups with their Poisson 95% Confidence Interval.
The difference between the two rates R2-R1 with its 95% Confidence Interval and associated P-value. If the P-value is less than 0.05 it can be concluded that there is a statistical significant difference between the two rates.
The ratio of the two rates (the incidence rate ratio) R1/R2 with its 95% Confidence Interval and associated P-value. If the P-value is less than 0.05 it can be concluded that the ratio R1/R2 is significantly different from 1 (which is the case when the rates are equal).

Computational details

For the confidence interval of the difference between two rates, MedCalc uses the "Test based Method" given on page 169 of Sahai H, Khurshid A (1996). The P-value is obtained using the Chi²-statistic.

For the confidence interval of the incidence rate ratio, MedCalc uses the "Exact Poisson Method" given on page 172-174 of Sahai H, Khurshid A (1996). The P-value is the exact mid-P double sided P-value (Hanley, 1986).

Literature

Hanley H (1986) Analysis of Crude Data. In: Modern Epidemiology, ed Rothman KJ. Boston: Little, Brown & Co.
Sahai H, Khurshid A (1996) Statistics in epidemiology: methods, techniques, and applications. Boca Raton, FL: CRC Press, Inc.

How to cite this page

MedCalc Software Ltd. Comparison of two rates. https://www.medcalc.org/calc/rate_comparison.php (Version 22.013; accessed September 24, 2023)