Essentials of Biostatistics in Public Health by Sullivan & Sullivan

Essentials of Biostatistics in Public Health by Sullivan & Sullivan

Author:Sullivan & Sullivan
Language: eng
Format: epub
Publisher: Jones & Bartlett Learning
Published: 2017-02-17T05:00:00+00:00


8.1.2 Sample Size for One Sample, Dichotomous Outcome

In studies where the plan is to estimate the proportion of successes in a dichotomous outcome variable in a single population, the formula for determining sample size is

where z is the value from the standard normal distribution reflecting the confidence level that will be used (e.g., z = 1.96 for 95%), E is the desired margin of error, and p is the proportion of successes in the population. Here we are planning a study to generate a 95% confidence interval for the unknown population proportion, p, and the formula to estimate the sample size needed requires p! Obviously, this is a circular problem—if we knew the proportion of successes in the population, then a study would not be necessary. To estimate the sample size, we need an approximate value of p. The range of p is 0 to 1 and the range of p(1 - p) is 0 to 0.25. The value of p that maximizes p(1 - p) is p = 0.5. Thus, if there is no information available to approximate p, then p = 0.5 can be used to generate the most conservative, or largest, sample size.

Example 8.3. An investigator wants to estimate the proportion of freshmen at his university who currently smoke cigarettes (i.e., the prevalence of smoking). How many freshmen should be involved in the study to ensure that a 95% confidence interval estimate of the proportion of freshmen who smoke is within 0.05 or 5% of the true proportion?

If we have no information on the proportion of freshmen who smoke, we use the following to estimate the sample size:

To ensure that the 95% confidence interval estimate of the proportion of freshmen who smoke is within 5% of the true proportion, a sample of size 385 is needed.

Suppose that a similar study was conducted two years ago and found that the prevalence of smoking was 27% among freshmen. If the investigator believes that this is a reasonable estimate of prevalence today, it can be used to plan the study:

To ensure that the 95% confidence interval estimate of the proportion of freshmen who smoke is within 5% of the true proportion, a sample of size 303 is needed. Notice that this sample size is substantially smaller than the one estimated previously. Having some information on the magnitude of the proportion in the population always produces a sample size that is less than or equal to the one based on a population proportion of 0.5. However, the estimate must be realistic.

Example 8.4. An investigator wants to estimate the prevalence of breast cancer among women who are between 40 and 45 years of age living in Boston. How many women must be involved in the study to ensure that the estimate is precise? National data suggest2 that 1 in 235 women are diagnosed with breast cancer by age 40. This translates to a proportion of 0.0043 (0.43%), or a prevalence of 43 per 10,000 women. Suppose the investigator wants the estimate to be within 10 per 10,000 women with 95% confidence.



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