epiR (version 0.9-82)

epi.cohortsize: Sample size, power or minimum detectable effect for a cohort study

Description

Computes sample size, power or minimum detectable effect for a cohort study.

Usage

epi.cohortsize(exposed, unexposed, n, power, r = 1, design = 1, sided.test = 2, 
   conf.level = 0.95)

Arguments

exposed

the expected incidence risk (cumulative incidence) for exposed subjects (see below).

unexposed

the expected incidence risk (cumulative incidence) for unexposed subjects (see below).

n

scalar, defining the total number of subjects in the study (i.e. the number in the exposed and unexposed groups).

power

scalar, the required study power.

r

scalar, the number in the treatment group divided by the number in the control group. This argument is ignored when method = "proportions".

design

scalar, the estimated design effect.

sided.test

use a one- or two-sided test? Use a two-sided test if you wish to evaluate whether or not the treatment group is better or worse than the control group. Use a one-sided test to evaluate whether or not the treatment group is better than the control group.

conf.level

scalar, defining the level of confidence in the computed result.

Value

A list containing one or more of the following:

n.crude

the crude estimated total number of subjects required for the specified level of confidence and power.

n.total

the total estimated number of subjects required for the specified level of confidence and power, respecting the requirement for r times as many individuals in the treatment group compared with the control group.

delta

the minimum detectable difference given the specified level of confidence and power.

lambda

the minimum detectable risk ratio >1 and the maximum detectable risk ratio <1.

power

the power of the study given the number of study subjects, the expected risk ratio and level of confidence.

Details

The methodology in this function follows the approach described in Chapter 8 of Woodward (2005), pp 405 - 410.

References

Kelsey JL, Thompson WD, Evans AS (1986). Methods in Observational Epidemiology. Oxford University Press, London, pp. 254 - 284.

Woodward M (2005). Epidemiology Study Design and Data Analysis. Chapman & Hall/CRC, New York, pp. 381 - 426.

Examples

## EXAMPLE 1 (from Woodward 2005 p. 406):
## A cohort study of smoking and coronary heart disease (CHD) in middle aged men
## is planned. A sample of men will be selected at random from the population
## and those that agree to participate will be asked to complete a 
## questionnaire. The follow-up period will be 5 years. The investigators would 
## like to be 0.90 sure of being able to detect when the risk ratio of CHD 
## is 1.4 for smokers, using a 0.05 significance test. Previous evidence 
## suggests that the incidence risk of death rate in non-smokers is 413 per 
## 100,000 per year. Assuming equal numbers of smokers and non-smokers are 
## sampled, how many men should be sampled overall?

exposed = 1.4 * (5 * 413)/100000
unexposed = (5 * 413)/100000
epi.cohortsize(exposed = exposed, unexposed = unexposed, n = NA, power = 0.90, 
   r = 1, design = 1, sided.test = 1, conf.level = 0.95)

## A total of 12,130 men need to be sampled (6065 smokers and 6065 non-smokers).


## EXAMPLE 2 (from Woodward 2005 p. 406):
## Say, for example, we are only able to enrol 5000 subjects into the study
## described above. What is the minimum and maximum detectable risk ratio?

unexposed = (5 * 413)/100000
epi.cohortsize(exposed = NA, unexposed = unexposed, n = 5000, power = 0.90, 
   r = 1, design = 1, sided.test = 1, conf.level = 0.95)

## The minimum detectable risk ratio >1 is 1.65. The maximum detectable
## risk ratio <1 is 0.50.


## EXAMPLE 3:
## A study is to be carried out to assess the effect of a new treatment for
## anoestrus in dairy cattle. What is the required sample size if we expect 
## the proportion of cows responding in the treatment (exposed) group to be 
## 0.30 and the proportion of cows responding in the control (unexposed) group 
## to be 0.15? The required power for this study is 0.80 using a two-sided 
## 0.05 test.

epi.cohortsize(exposed = 0.30, unexposed = 0.15, n = NA, power = 0.80, 
   r = 1, design = 1, sided.test = 2, conf.level = 0.95)

## A total of 242 cows are required: 121 in the treatment (exposed) group and 
## 121 in the control (unexposed) group.

## Assume now that this study is going to be carried out using animals from a 
## number of herds. What is the required sample size when you account for the 
## observation that response to treatment is likely to cluster across herds. 

## For the exercise, assume that the intra-cluster correlation coefficient 
## (the rate of homogeneity, rho) is 0.05 and the average number of cows per
## herd is 30. Calculate the design effect, given 
## rho = (design - 1) / (nbar - 1), where nbar equals the average number of 
## individuals per cluster:

design <- 0.05 * (30 - 1) + 1
epi.cohortsize(exposed = 0.30, unexposed = 0.15, n = NA, power = 0.80, 
   r = 1, design = design, sided.test = 2, conf.level = 0.95)

## A total of 592 cows are required for this study: 296 in the treatment group
## and 296 in the control group.