CLUSTER SAMPLE SIZE FOR ILZE

Sample size

library(epiR)

Data

p <- 0.50 #expected prevalence
b <- 25 # units to be examined per cluster

EXAMPLE 1

The expected prevalence of disease in the population is 0.5. We wish to conduct a survey, sampling 25 persons per school. No data are available to provide an estimate of rho, though we suspect the intra-cluster correlation for this disease to be moderate. We wish to be 95% certain of being within 10% of the true population prevalence of disease. How many schools should be sampled?

D <- 4
rho <- (D - 1) / (b - 1)
cluster_ss <- epi.clustersize(p = p, # expected prevalence
                b = b, # sampling per school
                rho = rho, # difference among variance inside the clusters vs between clusters, i.e. caries prevalence inside every school expected to be homogeneous, and prevalence between schools expected to be homogenous also. 
                epsilon.r = 0.2, #the acceptable relative error. Relative error is error / expected prevalence
                conf.level = 0.95)

We need to sample 16 schools (400 samples in total)

Reference: Otte J, Gumm I (1997). Intra-cluster correlation coefficients of 20 infections calculated from the results of cluster-sample surveys. Preventive Veterinary Medicine 31: 147 - 150.

EXAMPLE 2

A cross-sectional study is to be carried out to determine the prevalence of a given disease in a population using a two-stage cluster design. We estimate prevalence to be 0.5 and we expect rho to be in the order of 0.02. We want to take sufficient samples to be 95% certain that our estimate of prevalence is within 5% of the true population value (that is, a relative error of 0.05 / 0.50 = 0.1). Assuming 25 responses from each cluster, how many clusters do we need to be sample?

cluster_ss_2 <- epi.clustersize(p = p, # expected prevalence
                b = b, # participants per cluster
                rho = 0.02,
                epsilon.r = 0.1,
                conf.level = 0.95)

We need to sample 24 clusters (600 samples in total)

Reference: Bennett S, Woods T, Liyanage WM, Smith DL (1991). A simplified general method for clustersample surveys of health in developing countries. World Health Statistics Quarterly 44: 98 - 106.

Sampling procedure (if required)

library(sampling)

Two-stage cluster sampling Uses the ‘swissmunicipalities’ data the variable ‘REG’ (region) has 7 categories; it is used as clustering variable in the first-stage sample the variable ‘CT’ (canton) has 26 categories; it is used as clustering variable in the second-stage sample 4 clusters (regions) are selected in the first-stage 1 canton is selected in the second-stage from each sampled region the method is simple random sampling without replacement in each stage (equal probability, without replacement)

data(swissmunicipalities)
c = swissmunicipalities
c = c[order(c$REG,c$CT),]
attach(c)

m = mstage(c,
           stage = list("cluster","cluster"),
           varnames = list("REG","CT"),
           size = list(4,c(1,1,1,1)),
           method = list("srswor","srswor"))

the first stage is m[[1]], the second stage is m[[2]] the selected regions

unique(m[[1]]$REG)

[1] 2 3 5 6

the selected cantons

unique(m[[2]]$CT)

[1] 26 12 16  6

extracts the observed data

x = getdata(c,m)[[2]]

check the output

table(x$REG,x$CT)