One of the main differences between individual animal medicine and population medicine is the different approach to diagnostics in individuals compared to the approach to the herd. However, it is good to remember that population medicine does not exclude care for the individual, especially as a herd cannot perform or exist without healthy individuals.

This article will describe how to sample a proportion of a herd to estimate the prevalence of disease in a population.

## Why do we need herd sampling for infectious diseases?

The need for the sampling of proportions started because the number of cattle kept in a single herd has increased significantly in recent years. This is happening all over the world. It is not uncommon for farm animal veterinarians to work with herds comprising 30 to 3,000 heads of cattle or more. In 2018, the average dairy herd size in the United Kingdom was 148 milking cows (Uberoi, 2021), and this figure does not include followers.

The need for the sampling of proportions started because the number of cattle kept in a single herd has increased significantly in recent years

The average number of animals in the herd has increased over the years, as many producers with smaller herds have left the industry. This reflects the reality that, to be able to make a living from dairy cows only, it is often not economically viable to farm a small number of milking cows.

When animals like cattle are kept in larger herds, it is crucial to recognise that infectious diseases can spread easily and that individual cows can be clinically or sub-clinically affected. Also, some infectious diseases such as leptospirosis and infectious bovine rhinotracheitis can create carrier animals that are clinically healthy but shed the infectious organism.

## The use of diagnostic tests

Performing diagnostic tests on all individual animals in a large herd is labour-intensive and costly. Therefore, it is important to think of strategies to diagnose a disease in a herd. When a disease is diagnosed, an assessment of the number of infected animals is important for control and possible eradication.

It is only possible to eradicate a disease when the reproductive rate of the disease is less than one. Therefore, the farm animal veterinarian needs to know how the disease is spread and how to reduce the spread in the herd they are dealing with.

## Diagnosis of an infectious disease in a herd

Some diseases are easier to diagnose than others. The presence of a virus or bacterium in a bovine does not always mean that that pathogen is actually causing the clinical signs observed. Many pathogens can be present without causing disease.

The presence of a virus or bacterium in a bovine does not always mean that that pathogen is actually causing the clinical signs observed

Take this clinical scenario: a milk sample taken from the back left quarter of a cow with a persistently high somatic cell count (SCC) cultured *Corynebacterium bovis*. When followed up, it is noticed that the SCC of this cow is persistently high, so the same quarter of this cow is resampled and cultured one month later. In the second milk sample, *Staphylococcus aureus* was identified.

Experience and expertise are needed to pinpoint the reason for the high SCCs in this cow. The farm veterinarian needs to know the epidemiology and typical clinical presentation of these pathogens. Also, previous and current results of the rest of the population in question provide vital information for interpretation of the results.

### Is there a “gold-standard” test?

Post-mortem and identification (eg culture) is often the “gold standard” for the identification of various infectious diseases. Although gold-standard tests are often highly accurate, they are not always very sensitive.

For example, the gold-standard test for diagnosing Johne’s disease (*Mycobacterium avium *subspecies* paratuberculosis*) is a culture of the bacterium in the faeces of an adult cow. As this bacterium is difficult to culture and shedding can be intermittent, the sensitivity of this test is low. This means that the chance of a positive result (even when the animal is truly infected) is unlikely. Nevertheless, this test has a very high specificity. Therefore, when the result of the culture is positive the chance that the cow is truly infected is high.

## Serology

Milk and blood serology are common ways to diagnose the presence of a disease on-farm. Before going down this path, however, it is important to discuss the relevance of antibodies for a certain disease with the farmer.

Bulk milk tank testing is a cost-effective way of assessing whether a herd has been exposed to a certain disease. Before the sample is taken and analysed it is important to ask the following questions:

- Does this disease have clinical significance?
- Have the milking cows been vaccinated for this particular disease? If so, does this influence the test and test results?
- What is the minimal prevalence of the disease when the test is positive?
- Does the minimal prevalence change with herd size?
- When testing, which cows are included in the sample, and are any left out?
- Do low, medium or high positive results have meaning?
- What is the next step after the test result comes back?

## The test is positive! What’s the next step?

When the bulk milk tank test comes back positive, the next step can be either to test all individual animals, or if that’s not feasible, to test a proportion of the herd randomly to estimate the prevalence of the disease in the herd.

The next step can be either to test all individual animals, or if that’s not feasible, to test a proportion of the herd randomly to estimate the prevalence of the disease

To get a true idea of the prevalence it is important to sample the animals randomly. By selecting specific cows (for example, older, sick or only young and healthy ones) the estimated prevalence can be either artificially higher or lower than the true prevalence.

## Sample size estimations

The sample size estimate is determined for a given level of precision or an interval on either side of the estimate within which the true prevalence will fall by convention in many cases with a 95 percent confidence interval.

The formula for a 95 percent confidence interval is *n = 1.96 ^{2} P(1−P) / d^{2}* when (Radostits, 2001):

- “n” equals the sample size for an “infinite” population
- “P” equals the expected prevalence in the population
- “d” equals the largest acceptable difference from the true prevalence

### Example of herd population size estimate for diagnosis of an infectious disease

The following example shows how a veterinarian can approximately estimate the prevalence of *Neospora caninum* on a dairy farm that milks 800 cows.

To be able to do this calculation the prevalence needs to be estimated before testing. This can be done by either looking at the literature, finding out what the typical prevalence is on other farms in the area or doing an estimate on experience.

If the prevalence is unknown, then 50 percent needs to be used as this will create the largest sample size. For *N. caninum*, a prevalence of 10 percent could be predicted in the population and a 2 percent error either side of this value might be acceptable (Radostits, 2001).

When a 95 percent confidence is used the formula will be filled in like this:* n = 1.96 ^{2} (0.10) (1−0.10) / (0.02)^{2} = 864.36*.

As this number is for an infinite population and more than the number of cows in the herd, the last step is to adjust n for the herd size with the following formula:* n _{adj} = (N x n) / (N + n)*. For this equation, “N” equals herd size and “n” is the sample size for an infinite population.

Therefore, for this herd, the equation would be:* n _{adj} = (800 x 864.36) / (800 + 864.36) = 691488 / 1664.36 = 415.47*

This means that a sample of 416 (all numbers are rounded up) of the 800 cows is needed to be 95 percent confident that the prevalence of serologically positive animals is within ±2 percent of the sample estimate (Radostits, 2001).

## Helpful technology

This formula is only one example of a selection of different formulas available to tailor samples for serology and disease identification. To make life easier, several free epidemiological programs are available online. The programs Winepi and Epitools, for example, both do the calculations when the right numbers have been entered.

Even while using these programs, it is important to realise what the different formulas mean and how to interpret the results. This is because it is essential that veterinarians give tailored and appropriate advice to their farm clients.