General Process of Statistical Investigation:

Case study: using stents to prevent strokes

An experiment that studies effectiveness of stents in treating patients at risk of stroke.

Treatment and Control Group

Each volunteer patient(of 451) was randomly assigned to one of two groups:

Treatment group(224) - Patients in the treatment group received a stent and medical management. The medical management included medications, management of risk factors, and help in lifestyle modification.

Control group(227) - Patients in the control group received the same medical management as the treatment group, but they did not receive stents.

A Data Table

Researchers studied the effect of stents at two time points: 30 days after enrollment and 365 days after enrollment.

A Data Summary

Considering data from each patient individually would be a long, cumbersome path towards answering the original research question. Instead, performing a statistical data analysis allows us to consider all of the data at once.

A Summary Statistics

A summary statistic is a single number summarizing a large amount of data.3 For instance, the primary results of the study after 1 year could be described by two summary statistics: the proportion of people who had a stroke in the treatment and control groups.

Proportion who had a stroke in the treatment (stent) group: 45/224 = 0.20 = 20%.

Proportion who had a stroke in the control group: 28/227 = 0.12 = 12%.

These two summary statistics are useful in looking for differences in the groups, and we are in for a surprise: an additional 8% of patients in the treatment group had a stroke! This is important for two reasons. First, it is contrary to what doctors expected, which was that stents would reduce the rate of strokes. Second, it leads to a statistical question: do the data show a “real” difference between the groups.

Random Fluctuation

"Do the data show a “real” difference between the groups?" 

Suppose you flip a coin 100 times. While the chance a coin lands heads in any given coin flip is 50%, we probably won’t observe exactly 50 heads. This type of fluctuation is part of almost any type of data generating process.

It is possible that the 8% difference in the stent study is due to this natural variation. However, the larger the difference we observe (for a particular sample size), the less believable it is that the difference is due to chance. So what we are really asking is the following: is the difference so large that we should reject the notion that it was due to chance?

Be careful: do not generalize the results of this study to all patients and all stents. This study looked at patients with very specific characteristics who volunteered to be a part of this study and who may not be representative of all stroke patients.