C.I. Calculator: Single Incidence Rate

Data Input: (Help) (Example)

Input	Result
1-α	Rate
a	Lower
N	Upper

Note:

Variables	Descriptions
1-α	Two-sided confidence level
a	Number of clinical events
N	Person-time at risk
Rate	Incidence rate
Lower	Lower C.I.
Upper	Upper C.I.

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Description:

Incidence rate is the rate at which new clinical events occur in a population.

It is the number of new events divided by the population at risk of an event in a specific time period, sometimes it is the person-time at risk.

Procedure:

1. Enter

a)    Value of 1-α, the two-sided confidence level

b)    Value of a, the number of clinical events

c)    Value of N, the person-time at risk

2. Click the button “Calculate” to obtain the lower and upper endpoints of 100(1-α)% confidence interval

3. Click the button “Reset” for another new calculation

Formula:

Define:

Define the standard error:

The 100(1-α)% confidence interval is defined as:

Notation:

100(1-α)% confidence interval: We are 100(1-α)% sure the true value of the parameter is included in the confidence interval

: The z-value for standard normal distribution with left-tail probability

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Example

Suppose the number of new cases is 9 (a = 9)

Person-year at risk is 4028.16 (N = 4028.16)

Then the incidence rate is 0.0022343 and

The 95% confidence interval ((1-α) =0.95) is (0.0011634, 0.004291)

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