The article, "Heart Bypasses Are Safer, Study Shows," by Elizabeth
Rosenthal, reports data from the latest annual survey of cardiac bypass
operations in New York State. The survey is conducted by the State
Health Department and "each year evaluates 31 hospitals and dozens of
cardiac surgeons performing bypass surgery."
The variable is the "risk-adjusted mortality rate" for coronary artery
bypass surgery. "The rate is adjusted for the fact that some hospitals
have higher-risk patient populations." The statewide rate in 1993, based
on "more than 16,000" patients, is reported as 2.71, but the article does
not give the denominator for the rate; perhaps it's 100, so the rate is a
percentage.
In the accompanying graphic, a detailed diagram credited to The New York
Times, the scale for the rate appears as a horizontal line labeled 0 at
the left with the notation that a lower rate is "better." Intersecting
the scale is a vertical line at 2.71, the statewide rate. Running down
the graph is an irregular series of dots, some to the left of the line,
some to the right. The 31 dots show the risk-adjusted rates for the 31
hospitals, and each dot appears toward the center of a horizontal gray bar
that the graph labels "margin of error." A notation reads, "The State
Health Department says that based on statistical variation they are 95%
confident that the rate falls within the margin of error. Where gray bars
overlap there is no statistically significant difference in the rates."
Some bars are much wider than others, which is to say that some
confidence intervals are much wider, presumably because they are based on
smaller N's.
For two hospitals with a rate lower than the statewide, the gray bar does
not extend to the right as far as the statewide figure, and the diagram
calls this "variation from the statewide rate" "significantly lower." For
another three hospitals with a higher rate, the gray bar does not extend
to the left as far as the statewide figure, and the diagram calls this
variation "significantly higher."
By coincidence, on the day the article appeared I lectured on interval
estimation to my summer statistics class and put a similar diagram on the
board to illustrate the confidence interval and sampling variation in
estimates of a percentage characterizing a population.
The article leaves some questions unanswered. An important one is why
there is uncertainty about the mortality rate for a given hospital. Is
it because the entire population of patients who underwent the surgery in
that hospital in 1993 was not studied, and the Health Department relied
on a (hopefully) random sample of that population? Or did they study the
entire population for each hospital but encounter uncertainty in
the adjustment for how sick the patients in that population were?
Whatever the case, the article certainly shows statistics in action and
engaged my students' interest.
Perhaps someone familiar with the methodology of the research will post
an explanation of it.
Gordon Bear School of Science Ramapo College Mahwah NJ 07430-1680
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Voice: 201 529-7754 Fax: 201 529-7508 E-Mail: gbear@ultrix.ramapo.edu