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 easuring
the quality of care being provided to hospital patients is a vexing—albeit important—problem
facing health care researchers. As hospitals are more exposed to market forces, it
has become increasingly necessary to understand how competitive factors have affected
the quality of hospital care provided by different types of institutions and to different
types of patients. Patient discharge databases allow researchers to measure hospital-specific
mortality and use these as outcome-based measures of quality. Hospitals with higher
mortality (after controlling for other factors) would be found to have lower quality.
This analysis is complicated by one important fact—more severely ill patients are
more likely, all else being equal, to choose higher quality hospitals. Thus, hospital-specific
mortality rates will reflect both the quality of the hospital and the severity of
illness of the patients. As hospital choice is correlated with severity of illness,
and severity of illness cannot be perfectly observed, standard estimation techniques
will give incorrect estimates of hospital-specific quality.
Professors Gautam Gowrisankaran and John Geweke of the Economics Department at the
University of Minnesota and Professor Robert Town of the School of Management at
the University of California in Irvine, California are developing a selection model
technique to consistently estimate hospital-specific mortality in the presence of
unobservable severity of illness by using geographical data from the United States
Census. The basis for this estimation process is to model patient choice of hospital
using distance as the principal predictor. If a hospital is drawing patients from
further away than other hospitals, that hospital is attracting patients with relatively
high severity of illness. In this way, the use of geographical measures allow a separation
of the two confounding effects, severity of illness and hospital quality, that both
affect hospital mortality. This simple insight is then used in Bayesian econometrics
to develop accurate estimates and predictions as to hospital quality.
Preliminary results indicate that selection is an important determinant of hospital
mortality, and controlling for selection yields substantially different predictions
as to hospital quality. For instance, the estimated distribution of predicted mortality
rates is compared for a randomly selected patient if that patient were to seek treatment
at two different hospitals, Los Angeles County / University of Southern California
(USC) Medical Center (a large, public teaching hospital located in East Los Angeles)
and the University of California–Los Angeles (UCLA) Medical Center (a well-regarded,
private teaching hospital located in West Los Angeles). Figure 1 shows the results
controlling for unobserved patient selection while Figure 2 shows the results with
standard methods. Points above the 45° line indicate a lower estimated mortality
(higher estimated quality) for UCLA. One can see from Figure 1 that, by controlling
for selection, UCLA Medical Center is revealed to be of higher quality than LA County
/ USC Medical Center. In contrast, standard methods from Figure 2 give exactly the
opposite prediction. A long-run goal is to further explore the determinants of hospital
quality by ownership type and to examine how competition and costs affect quality.
Because of the large size of the data set (20 thousand patients per year for 4 years
and 100 hospitals just in Los Angeles County), these methods are very computationally
intensive. Furthermore, the Bayesian estimates are computed using an iterative process,
with approximately 10,000 iterations required for convergence. Using a Sun UltraSparc
II 300 MHz computer, these researchers were able to compute each iteration in approximately
30 minutes. Using the IBM SP supercomputer and ESSL library routines for matrix multiplication,
these researchers computed the algorithm in approximately 6 minutes per iteration.
They then rewrote the code to take advantage of the parallel architecture of the
IBM SP making use of the Message Passing Interface paradigm. The use of parallel
algorithms resulted in substantial speed increases that made the algorithm feasible.
For instance, the algorithm takes 100 seconds per iteration with 4 processors, 60
seconds per iteration with 8 processors, 40 seconds per iteration with 16 processors,
and 33 seconds per iteration with 20 nodes.
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| Figure 1: Probability of death by
hospital using the Bayesian selection model. |
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Figure 2: Probability of death by
hospital using standard (non-selection) methods. |
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