Question

"Doctors Praise Device That Aids Ailing Hearts" (Associated Press, November 9,2004 ) is the headline of an article describing a study of the effectiveness of a fabric device that acts like a support stocking for a weak or damaged heart. People who consented to treatment were assigned at random to either a standard treatment consisting of drugs or the experimental treatment that consisted of drugs plus surgery to install the stocking. After two years, \(38 \%\) of the 57 patients receiving the stocking had improved, and \(27 \%\) of the 50 patients receiving the standard treatment had improved. The researchers used these data to determine if there was evidence to support the claim that the proportion of patients who improve is higher for the experimental treatment than for the standard treatment.

Short answer

The experimental treatment which involves a combination of device and drugs appears to be more effective by 11% compared to the standard treatment of drugs alone. However, statistical analysis is required to confirm if this difference is statistically significant.

Step-by-step solution

Identify the proportions

First identify the proportions of patients who improved in each group. For the experimental treatment group, 38% of 57 patients improved, which is approximately 0.38 × 57 = 21.66, which simplifies to about 22 patients. For the standard treatment group, 27% of 50 patients improved, which is approximately 0.27 × 50 = 13.5, which simplifies to about 14 patients.

Calculate the difference between proportions

Next, calculate the difference between the two proportions. Subtract the proportion of patients who improved with standard treatment from the proportion who improved with the experimental treatment. The difference is 0.38 - 0.27 = 0.11 or 11%.

Interpret the result

The difference in proportions indicates the relative effectiveness of the treatments. A positive difference of 11% suggests that the experimental treatment (device plus drugs) is more effective than the standard treatment (only drugs). An increase of 11% in the improvement rate implies that approximately 11 more patients out of every 100 patients would improve with the experimental treatment compared to the standard one. However, this alone doesn't provide evidence of statistical significance. Further analysis using confidence intervals or hypothesis testing should be performed to reach a statistically valid conclusion.