Question:

Restenosis – narrowing of the blood vessels – frequently occurs after coronary angioplasty, but accurate prediction of which individuals will have the problem is problematic. In a study by Simmons et al. (1993), the authors hypothesized that restenosis is more likely to occur if activated smooth-muscle cells in coronary lesions at the time of surgery are present. They used the number of reactive nuclei in the coronary lesions as an indicator of the presence of the activated smooth-muscle cells. The number of reactive nuclei in the lesions and the degree of stenosis at follow-up for 16 patients who underwent a second angiography are shown below.

Are you suspicious of any of these data points? If so, why? Does there appear to be a linear relation between the degree of stenosis and the number of reactive nuclei? If there is, describe the relation. Are there any points that have a large influence on the estimated regression line?

If there are, eliminate the point with the greatest leverage and refit the equation.

Is there much difference between the two regression equations?

Are there any points that have a large standardized residual?

Explain why the residuals are large for these points.

Do you think the Simons et al. have a promising lead for predicting which patients will undergo restenosis?

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