Question

Much discussion has taken place concerning possible health hazards from exposure to anesthetic gases. In one study conducted in 1972, 525 Michigan nurse anesthetists were surveyed by mail questionnaires and telephone inter-views to determine the incidence rate of cancer [8]. Of this group, 7 women reported having a new malignancy other than skin cancer during 1971.

6.33 What is the best estimate of the 1971 incidence rate from these data?

6.34 Provide a 90% CI for the true incidence rate.

Answer 1

The best estimate of the 1971 incidence rate is 1.33%. The 90% confidence interval for the true incidence rate is approximately 1.30% to 1.36%.

Step-by-step explanation:

The best estimate of the 1971 incidence rate can be calculated by dividing the number of women who reported a new malignancy (7) by the total number of nurse anesthetists surveyed (525), and then multiplying by 100 to convert to a percentage.

Incidence Rate = (Number of women with new malignancy / Total number of nurse anesthetists surveyed) x 100

Incidence Rate = (7 / 525) x 100 = 1.33%

To provide a 90% confidence interval (CI) for the true incidence rate, we can use the formula:

CI = Incidence Rate ± (Z-value x Standard Error)

The Z-value for a 90% confidence interval is approximately 1.645. The standard error can be calculated using the formula:

Standard Error = √(Incidence Rate x (1 - Incidence Rate) / Sample Size)

Using the calculated incidence rate of 1.33% and a sample size of 525, we can calculate the standard error:

Standard Error = √(0.0133 x (1 - 0.0133) / 525) ≈ 0.0179

Finally, we can calculate the 90% confidence interval:

CI = 1.33% ± (1.645 x 0.0179)

CI = 1.33% ± 0.0295

Therefore, the 90% confidence interval for the true incidence rate is approximately 1.30% to 1.36%.