epiR (version 2.0.95)

epi.ssclus2estb: Number of clusters to be sampled to estimate a binary outcome using two-stage cluster sampling

Description

Number of clusters to be sampled to estimate a binary outcome using two-stage cluster sampling.

Usage

epi.ssclus2estb(N.psu = NA, b, Py, epsilon, error = "relative", 
   rho, nfractional = FALSE, conf.level = 0.95)

Value

A list containing the following:

n.psu

the total number of primary sampling units (clusters) to be sampled for the specified level of confidence and relative error.

n.ssu

the total number of secondary sampling units to be sampled for the specified level of confidence and relative error.

DEF

the design effect.

rho

the intracluster correlation coefficient, as entered by the user.

Arguments

N.psu

scalar integer, the total number of primary sampling units eligible for inclusion in the study. If N = NA the eligible primary sampling unit population size is assumed to be infinite.

b

scalar integer or vector of length two, the number of individual listing units in each cluster to be sampled. See details, below.

Py

scalar number, an estimate of the unknown population proportion.

epsilon

scalar number, the maximum difference between the estimate and the unknown population value expressed in absolute or relative terms.

error

character string. Options are absolute for absolute error and relative for relative error.

rho

scalar number, the intracluster correlation coefficient.

nfractional

logical, return fractional sample size.

conf.level

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

Details

In many situations it is common for sampling units to be aggregated into clusters. Typical examples include individuals within households, children within classes (within schools) and cows within herds. We use the term primary sampling unit (PSU) to refer to what gets sampled first (clusters) and secondary sampling unit (SSU) to refer to what gets sampled second (individual listing units within each cluster). In this documentation the terms primary sampling unit and cluster are used interchangeably. Similarly, the terms secondary sampling unit and individual listing units are used interchangeably.

b as a scalar integer represents the total number of individual listing units from each cluster to be sampled. If b is a vector of length two the first element represents the mean number of individual listing units to be sampled from each cluster and the second element represents the standard deviation of the number of individual listing units to be sampled from each cluster.

The methodology used in this function follows the approach described by Bennett et al. (1991). At least 25 PSUs are recommended for two-stage cluster sampling designs. If less than 25 PSUs are returned by the function a warning is issued.

As a rule of thumb, around 30 PSUs will provide good estimates of the true population value with an acceptable level of precision (Binkin et al. 1992) when: (1) the true population value is between 10% and 90%; and (2) the desired absolute error is around 5%. For a fixed number of individual listing units selected per cluster (e.g., 10 individuals per cluster or 30 individuals per cluster), collecting information on more than 30 clusters can improve the precision of the final population estimate, however, beyond around 60 clusters the improvement in precision is minimal.

If a value is entered for N.psu a finite population correction factor (Cochran 1977) is applied to the calculated sample size estimate. That is:

$$n_{adj} = \frac{n}{1 + \left(\frac{n}{N}\right)}$$

References

Bennett S, Woods T, Liyanage W, Smith D (1991). A simplified general method for cluster-sample surveys of health in developing countries. World Health Statistics Quarterly 44: 98 - 106.

Binkin N, Sullivan K, Staehling N, Nieburg P (1992). Rapid nutrition surveys: How many clusters are enough? Disasters 16: 97 - 103.

Cochran WG (1977). Sampling Techniques. John Wiley and Sons, London.

Machin D, Campbell MJ, Tan SB, Tan SH (2018). Sample Sizes for Clinical, Laboratory ad Epidemiological Studies, Fourth Edition. Wiley Blackwell, London, pp. 195 - 214.

Examples

## EXAMPLE 1 (from Bennett et al. 1991 p 102):
## We intend to conduct a cross-sectional study to determine the prevalence 
## of disease X in a given country. The expected prevalence of disease is 
## thought to be around 20%. Previous studies report an intracluster 
## correlation coefficient for this disease to be 0.02. Suppose that we want 
## to be 95% certain that our estimate of the prevalence of disease is 
## within 5% of the true population value and that we intend to sample 20 
## individuals per cluster. How many clusters should be sampled to meet 
## the requirements of the study?

epi.ssclus2estb(N.psu = NA, b = 20, Py = 0.20, epsilon = 0.05, 
   error = "absolute", rho = 0.02, nfractional = FALSE, conf.level = 0.95)

## A total of 17 clusters need to be sampled to meet the specifications 
## of this study. epi.ssclus2estb returns a warning message that the number of 
## clusters is less than 25.