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Medical papers contain reports based on the results of surveys conducted with local residents and patients (market and social surveys).

In this article, we explain the concept of n (sample size) required to conduct such surveys.

## Concept of n-number (sample size) setting

The fewer the people surveyed (small sample size), the wider the confidence interval and the larger the margin of error. The number of people required for the survey depended on the degree of error desired.

For example, to estimate the proportion (%) of drug X prescriptions in 100,000 patients with hypertension in an area, the number of patients with hypertension should be surveyed.

We estimate the proportion (%) of drug X prescriptions to hypertensive patients in this area by saying “between p1% and p2%.”

(See vol.2 for an estimation of the population mean.)

## Let’s estimate the population proportion (probability of an event occurring in the population: %)

n is the sample size of the survey, and p is the proportion of prescriptions (%) obtained from the survey.

The smaller the value of the sampling error in the formula, the higher the precision. The estimation results are considered good if the precision is < 10 %.

The values of the sampling error and precision decreased as n (sample size) increased. This relationship can be applied to determine n (sample size).

When the survey designer determines the number of n (sample size), the first step is to define the survey’s precision.

If the proportion (%) of the population prescribed drug X is defined as 50% and the precision as 10%, the sampling error is 5% (50% x 10%) and the confidence interval is 50% ± 5% (45-55%). We only needed to determine n (sample size) to obtain this confidence interval.

Expected ratio 50%⇒0.5

Expected precision 10%⇒0.1

Sampling error = expected ratio x expected precision = 0.5 x 0.1 = 0.05 (5%)

This means that the sample size is 384 persons.

## Determine the number of n (sample size) to estimate the population proportion

The number n (sample size) can be determined in the aforementioned manner. Additionally, it can be easily calculated using the following formula:

[ Calculation examples]

If the percentage (%) of prescriptions for drug X in the population is 50%, find the number of n (sample size) to obtain a confidence interval of 50% ± 5%.

From the above, we can see that we only needed to find approximately 384 persons.

However, we know in advance that the proportion (%) of prescriptions for drug Z, which is different from drug X in the same area, for hypertensive patients will not exceed 10% because it has been newly launched recently.

In this case, we assumed that the proportion of prescriptions of drug Z in this area was 5%, and we wanted to find the n number (sample size) to obtain a confidence interval of 5% ± 0.5%.

The number of n (sample size) in this example is 7,299.

Under the same accuracy, a smaller assumed ratio corresponds to a larger n (sample size).

## Determine n (sample size) to estimate the population mean (mean of the population)

If the value to be estimated is the population mean, then the formula for determining n (sample size) differs from that above.

[ Calculation examples]

The question is, “How many physicians should be surveyed to estimate how many patients per physician in an area are prescribed drug A?”

If the number of prescribed patients in the population is 20, then n (sample size) is calculated to obtain a confidence interval of 20 ± 2 (precision is 2÷20 ⇒10%).

If the standard deviation (s) is unknown, the number of people is assumed the standard deviation (20 in this example).

Population size (N) is the number of physicians in the target area.

(48,000 in this example)

The number of n (sample size) is 381.

The smaller the standard deviation to be predicted, the smaller the n (sample size).

Thus, this formula was applied to determine the sample size (n) at the survey design stage.

Even if the sample size is 215, it is advisable to design a slightly larger n (sample size), for example, 230, in anticipation of including some inapplicable samples, such as defective responses.

In this issue, we introduce the sample size (n) required to conduct a survey (market or social survey) of local residents and patients.

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