Computer simulation to compare three sampling plans for health and production surveillance in California dairy herds

Abstract

Computer simulation was carried out to determine the optimal combination of sampling plan and sample size for estimation of four health and production variables in California Dairy Herd Improvement Association (DHIA), member herds. Three sampling plans i.e. simple random, stratified (by herd size) random with proportional allocation and stratified random with Neyman allocation, called hereafter Sampling plans 1,2 and 3, respectively, and 8 levels of sample size (10–80, in increments of 10 herds) were used to estimate parameters of 4 production and health variables: average milk production, California Mastitis Test (CMT) score, average days open and services per conception. The sampling frame used was the list of California DHIA member dairy herds in June 1984. Simulation involved generating 1000 random samples for each comparison variable for the 24 combinations of sampling plan and sample size. Three bounds on the error of estimation (5,10 and 20%) of the 4 comparison variables were specified to compute the frequency of sample means falling within these bounds for each strategy. Based on the frequency criterion, no difference was found between Sampling plans 1 and 2 for all comparison variables except average milk production. For average milk production with a 5% bound on the error of estimation, Sampling plan 2 gave more precise estimates than Sampling plan 1 for sample sizes of 40–70. However, this difference did not exist using either a 10 or 20% bound on the error of estimation. For average milk production, Sampling plan 3 yielded a substantially larger percentage of point estimates within a 5 or 10% bound on the error for all sample sizes considered than Sampling plans 1 and 2. Similar results were observed for CMT score using sample sizes between 30 and 80 dairy herds. For average days open, Sampling plan 3, relative to Sampling plan 1 and 2, yielded 4–8% more point estimates of population parameter within a 5% bound on the error of estimation with sample sizes of 40–80. No meaningful difference was noticed among the three sampling plans for estimation of mean services per conception. Sampling plan 3 was the most efficient sampling plan for the health and production variables considered in this study. With respect to sample size, the mean of such production variables as average milk production, services per conception and average days open could be estimated with precision using a sample size of 80 or less dairy herds. For disease variables with variance structure similar to CMT score, precise estimates cannot be obtained using sample sizes of up to 80 herds; a sample size substantially larger than 80 herds would be required to provide a precise estimate of the central value.