Abstract
Using convenient stratification criteria such as geographical regions or other natural conditions like age, gender, etc., is not beneficial in order to maximize the precision of the estimates of variables of interest. Thus, one has to look for an efficient stratification design to divide the whole population into homogeneous strata that achieves higher precision in the estimation. In this paper, a procedure for determining Optimum Stratum Boundaries (OSB) and Optimum Sample Sizes (OSS) for each stratum of a variable of interest in health surveys is developed. The determination of OSB and OSS based on the study variable is not feasible in practice since the study variable is not available prior to the survey. Since many variables in health surveys are generally skewed, the proposed technique considers the readily-available auxiliary variables to determine the OSB and OSS. This stratification problem is formulated into a Mathematical Programming Problem (MPP) that seeks minimization of the variance of the estimated population parameter under Neyman allocation. It is then solved for the OSB by using a dynamic programming (DP) technique. A numerical example with a real data set of a population, aiming to estimate the Haemoglobin content in women in a national Iron Deficiency Anaemia survey, is presented to illustrate the procedure developed in this paper. Upon comparisons with other methods available in literature, results reveal that the proposed approach yields a substantial gain in efficiency over the other methods. A simulation study also reveals similar results.
Highlights
Stratified random sampling is an important sampling technique utilized in estimating the prevalence of diseases such as diabetes, anaemia, obesity hypertension, and smoking
This paper involves the usage of multiple auxiliary variables in determining the Optimum Stratum Boundaries (OSB) for the study variable
Stratified random sampling is an efficient and widely used sampling technique in health surveys to estimate the prevalence of diseases and many other parameters
Summary
Stratified random sampling is an important sampling technique utilized in estimating the prevalence of diseases such as diabetes, anaemia, obesity hypertension, and smoking. Optimum strata boundaries and sample sizes the study variable (y) vary little from each other and the precise estimate of y can be obtained from a small sample in that stratum. If the population mean of the study variable y is to be estimated over a range (a, b) under the allocation (3), the problem of determining the strata boundaries of y is to cut up the range, (a, b) at (L − 1) intermediate points a. . ., xp), the first term inside the square root function in (7) can be expressed as the functions of the boundary points (yh−1, yh) by finding the stratum weight Whxi, mean μhxi and variance s2 hxi of ith auxiliary variable xi using the following expressions: If f(xi) are known and integrable frequency functions of the auxiliary variables, for the given λ(x1, x2, . . ., xp), the first term inside the square root function in (7) can be expressed as the functions of the boundary points (yh−1, yh) by finding the stratum weight Whxi, mean μhxi and variance s2 hxi of ith auxiliary variable xi using the following expressions:
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