Question

Is injecting medical cement effective in reducing pain for people who have suffered fractured vertebrae? A paper describes an experiment to compare patients who underwent vertebroplasty (the injection of cement) to patients in a placebo group who underwent a fake procedure in which no cement was actually injected. Because the placebo procedure was similar to the vertebroplasty procedure except for the actual injection of cement, patients participating in the experiment were not aware of which treatment they received. All patients were asked to rate their pain at three different times—3 days, 14 days, and 1 month after the procedure. Summary statistics are given in the accompanying table. Pain Intensity Vertebroplasty Group Placebo Group n = 68 n = 63 mean sd mean sd 3 days 4.2 2.8 3.9 2.9 14 days 4.3 2.9 4.5 2.8 1 month 3.9 2.9 4.6 3.0

(a) Briefly explain why the researchers may have chosen to include a placebo group that underwent a fake procedure rather than just comparing the vertebroplasty group to a group of patients who did not receive any treatment.

(b) Construct and interpret a 95% confidence interval for the difference in mean pain intensity 3 days after treatment for the vertebroplasty treatment and the fake treatment. (Use μVertebroplasty − μPlacebo. Round your answers to two decimal places.) to Interpret the interval. There is a 95% chance that the true mean pain intensity 3 days after treatment for the vertebroplasty treatment is directly in the middle of these two values. We are 95% confident that the true mean pain intensity 3 days after treatment for the fake treatment is between these two values.

(c) Construct and interpret 95% confidence intervals for the difference in mean pain intensity at 14 days after treatment. (Use μVertebroplasty − μPlacebo. Round your answers to two decimal places.) to Interpret the interval. There is a 95% chance that the true mean pain intensity 14 days after treatment for the vertebroplasty treatment is directly in the middle of these two values.

(d) Based on the confidence intervals from parts (b) and (c), comment on the effectiveness of injecting cement as a way of reducing pain for those with fractured vertebrae.

Answer 1

(a)

Using placebo, researcher can have true comparison between pain reduction scores. That is researcher can identified that whether treatment is truly beneficial or not because patient of placebo group do not have any knowledge that they did not get any treatments. So there will be no psychological effect on scores.

(b)

Let population 1: 3 days after treatment for the vertebroplasty treatment

population 2: 3 days after treatment for the fake treatment

We are 95% confident that the true mean pain difference intensity 3 days after treatment for the fake treatment is between these two values.

(c)

Let population 1: 14 days after treatment for the vertebroplasty treatment

population 2: 14 days after treatment for the fake treatment

(d)

It does not seem that treatment is effective because both confidence interval contains zero.