Elizabeth Parker, BVSc, MPH, PhD, DACVPM∗     Department of Veterinary Preventive Medicine, The Ohio State University, 1920 Coffey Road, Columbus, OH 43210, USA
∗ Corresponding author. 
email address: parker.1224@osu.edu

Sample size; Cluster sampling; Sampling unit; Sampling frame; Variance; Precision; Confidence

Veterinarians conduct clinical examinations on individual animals every day, sometimes taking samples for laboratory testing, to make decisions on the cause and treatment of adverse results. At the same time, they may be scanning the rest of the herd, checking body condition, and looking for lameness, respiratory disease, or diarrhea while also checking the environment, airflow, temperature, and feed and pasture quality. Any information gathering activity, clinical examinations, taking measurements, or collecting samples is considered a diagnostic test. Sometimes this information is collected from the entire population, a census. In large populations, however, a census is often not possible and collecting measurements from a subset or sample of the population is more convenient and practical. Before embarking on any diagnostic investigation in a ruminant population, the veterinarian and the producer must first agree on the diagnostic question, and how the results of the investigation will be used. The farmer and the veterinarian must also consider the availability of resources, including appropriate animal handling and restraint facilities, unique identification of all the animals or sampling units in the population of interest, and the time and money required for sampling and diagnostic tests. Diagnostic test sensitivity (Se) and specificity (Sp) should also be considered when calculating the sample size. Generally, if all other diagnostic objectives remain the same, as Se decreases, the required sample size increases. If, however, the test Sp is also less than 100%, sampling more animals decreases the herd Sp and it is even more likely that disease-free animals may, incorrectly, test positive. A common solution to this problem is to submit positive animals to a second diagnostic test to confirm the diagnosis. Only animals that test positive on both tests are declared diseased. Considerations when using and interpreting “imperfect” diagnostic tests are discussed in greater detail elsewhere.1 This review demonstrates, using formulae described by Dohoo and colleagues 2009,2 how the required sample size changes depending on statistical considerations, such as the required precision of the estimate, the expected variation in the estimate to be measured, the desired level of confidence, and power of the test. For the scenarios discussed in this review we assume perfect Se and Sp. Computer software and free online sample size calculators provide a more exact sample size and also adjust the sample size for diagnostic tests with imperfect test Se and Sp.3,4 We also assume that the farmer and veterinarian have the time, money, facilities, and other resources available to complete this investigation and that the farmer has a complete list of all animals (or sampling units), in the target population along with their unique identification number and other animal characteristics, such as age, sex, and parity as appropriate for each case study.

Epidemiologic studies may be either descriptive or analytical. Descriptive studies are commonly used to estimate a population parameter, such as a proportion or mean. For the veterinarian in clinical practice the population of interest is most likely to be animals within a farm, whereas veterinarians in government practice may investigate a “population” of regions within a country, or farms within a region. Descriptive studies may be used to determine the presence, absence, or prevalence of a disease or to measure production performance, such as the mean weaning weight of beef calves, or the mean somatic cell counts of dairy cows, in a population of animals. Often, the purpose of prevalence and “freedom from disease” studies is to support trade and the movement of animals at local, interstate, and international levels.5 This may simply be a matter of testing the entire consignment of animals at a single point in time. For example, the veterinarian may be required to test rams for the presence of ovine brucellosis before introducing them to a new farm. Sometimes, however, certification requires evidence that the herd of origin is free of the disease. Sampling the entire herd is often not feasible. The challenge, therefore, is selecting an appropriate sample from the herd. Sampling strategies differ depending on the desired outcome, a disease prevalence estimate or certification of freedom from disease, and if there is clustering of the outcome within the population. Different sampling strategies for descriptive studies are discussed using case studies related to enzootic bovine leucosis in dairy cattle (Case Study 1), Q fever in goats (Case Study 2), and Salmonella prevalence in feedlot cattle (Case Study 3). Analytical studies aim to test associations between outcomes and exposures and may be conducted at a herd, farm, or regional level to support management decisions or to assess risk factors associated with disease or poor production performance. For example, the veterinarian may be required to measure the effect of different management strategies, such as housing or nutrition, on the prevalence of disease or daily liveweight gain. Different disease sampling strategies for analytical studies are described in Case Study 4a, sampling to assess the difference in disease prevalence, and Case Study 4b, sampling to assess the difference in mean liveweight gain.

Enzootic bovine leukosis is a disease caused by bovine leukemia virus (BLV), a retrovirus that is spread horizontally via virus-infected lymphocytes. Overt clinical signs are rare affecting 0.1% to 10% of infected individuals. Bovine leukemia virus may, however, predispose the animal to opportunistic pathogens that cause mastitis and hoof problems leading to suboptimal production. Infection with BLV is also a barrier to local and international trade in many jurisdictions. Reports indicate an increase in BLV prevalence in the United States.6 A US herd-level study found that 94.2% of US dairy herds had at least one BLV antibody-positive cow in the herd. The within herd prevalence was between 0% and 96.9% with an average of 42.5%. The prevalence increased from 29.7% in first lactation cows to 58.9% for cows in their fourth or later lactation.7 All cattle are susceptible to BLV. Infection can occur at any stage of life and may occur naturally at parturition. Infection with the virus is lifelong and gives rise to a persistent antibody response. However, it may take up to 16 weeks for antibodies to appear postinfection and maternally derived antibodies can take up to 7 months to disappear. Antibody detection is the preferred method of testing.8 Your client is interested in exporting her prized dairy cows to Europe and wants to know the prevalence of BLV in her dairy herd of 4000 females older than 7 months of age.

The sampling frame is a list of all sampling units in the source population. The sampling unit is the basic element of the population to be sampled. If the aim of this project was to estimate, for example, the prevalence of BLV antibody-positive dairy herds in a region, the sampling unit would be the herd and the sampling frame would be a list of all dairy herds. In this case, the sampling frame lists all cattle on the farm more than 7 months of age, along with their unique identification, their age, and parity.

Equation 1 is the formula for calculating the sample size to estimate a single proportion.

n is the sample size.

Zα is the value from the standard normal distribution corresponding to the desired level of confidence. α, the type one...