Question

Errors in medical prescriptions occur and a study1 examined whether electronic prescribing may help reduce errors. Two groups of doctors used written prescriptions and had similar error rates before the study. One group switched to e-prescriptions while the other continued to use written prescriptions, and error rates were measured one year later. The results are given in Table 1.

Err No Error Total
Electronic 254 3594 3848
Written 1478 2370 3848

Table 1 Are prescription error rates different?

Find a 99% confidence interval for the difference in the two proportions, pw-pe, where pw is the proportion of errors using written prescriptions and pe is the proportion of errors using e-prescriptions.

Answer 1

The 99% confidence interval is (0.219, 0.417).

Step-by-step explanation:

To find the 99% confidence interval for the difference in the two proportions, we can use the formula:

CI = (pw - pe) ± Z * sqrt((pw * (1 - pw)) / nw + (pe * (1 - pe)) / ne)

where:

pw = proportion of errors using written prescriptions

pe = proportion of errors using e-prescriptions

nw = total number of written prescriptions

ne = total number of e-prescriptions

Z = Z-value corresponding to the desired confidence level (in this case, 99%)

From the given table, we have:

pw = 1478 / 3848

= 0.384

pe = 254 / 3848

= 0.066

nw = 3848

ne = 3848

Using a Z-value of 2.58 for a 99% confidence level, we can calculate the confidence interval:

CI = (0.384 - 0.066) ± 2.58 * sqrt((0.384 * (1 - 0.384)) / 3848 + (0.066 * (1 - 0.066)) / 3848)

Calculating the values, we get:

CI = (0.318) ± 2.58 * sqrt(0.000744 + 0.000714)

CI = (0.318) ± 2.58 * sqrt(0.001458)

CI = (0.318) ± 2.58 * 0.03817

CI = (0.318) ± 0.0984

CI = (0.219, 0.417)