An Analysis of Equally Weighted and Inverse Probability Weighted Observations in the Expanded Program on Immunization (EPI) Sampling Method

Abstract

Performing health surveys in developing countries and humanitarian emergencies can be challenging work because the resources in these settings are often quite limited and information needs to be gathered quickly. The Expanded Program on Immunization (EPI) sampling method provides one way of selecting subjects for a survey. It involves having field workers proceed on a random walk guided by a path of nearest household neighbours until they have met their quota for interviews. Due to its simplicity, the EPI sampling method has been utilized by many surveys. However, some concerns have been raised over the quality of estimates resulting from such samples because of possible selection bias inherent to the sampling procedure. We present an algorithm for obtaining the probability of selecting a household from a cluster under several variations of the EPI sampling plan. These probabilities are used to assess the sampling plans and compute estimator properties. In addition to the typical estimator for a proportion, we also investigate the Horvitz-Thompson (HT) estimator, an estimator that assigns weights to individual responses. We conduct our study on computer-generated populations having different settlement types, different prevalence rates for the characteristic of interest and different spatial distributions of the characteristic of interest. Our results indicate that within a cluster, selection probabilities can vary largely from household to household. The largest probability was over 10 times greater than the smallest probability in 78% of the scenarios that were tested. Despite this, the properties of the estimator with equally weighted observations (EQW) were similar to what would be expected from simple random sampling (SRS) given that cases of the characteristic of interest were evenly distributed throughout the cluster area. When this was not true, we found absolute biases as large as 0.20. While the HT estimator was always unbiased, the trade off was a substantial increase in the variability of the estimator where the design effect relative to SRS reached a high of 92. Overall, the HT estimator did not perform better than the EQW estimator under EPI sampling, and it involves calculations that may be difficult to do for actual surveys. Although we recommend continuing to use the EQW estimator, caution should be taken when cases of the characteristic of interest are potentially concentrated in certain regions of the cluster. In these situations, alternative sampling methods should be sought.