Data Visualization and Data Summary

Data Visualization and Data Summary

Patricia Cerrito (University of Louisville, USA)
DOI: 10.4018/978-1-60566-752-2.ch002
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Abstract

Patients in a clinic or geographic area are very heterogeneous. Therefore, the distribution of patient factors will not have a normal distribution. Generally, the distribution will have a heavy tail since every patient population will have those extreme patients who need extraordinary care; there will be more patients who need considerable care than those whose treatment can be discontinued early. Thus, unlike the normal distribution assumption, distributions of patient populations will not be symmetric. Therefore, great care must be used when considering a model that assumes normality, or even symmetry. We will look at alternative methods of analysis and visualization that do not depend upon the assumption of normality.
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Background

Bar Graphs of Population Distributions

We start with Figure 1, the bar graph of the hospital length of stay for all patients with diabetes. In the National Inpatient Sample, that includes just over 1 million patient stays. Note that the distribution has a very heavy tail with the maximum stay of about 354 days. The average length of stay is equal to 5 days with a standard deviation of 5.8 days. Figure 2 reduces the values on the x-axis to a maximum of 50 days so that we can focus on this part of the graph.

Figure 1.

Length of hospital stay for patients with diabetes

Figure 2.

Length of stay limited to 50 days maximum

In Figure 2, note the gaps that occur because of rounding in the length of stay. It suggests that the information is not completely accurate because of this rounding.

Figure 3 gives the best normal estimate of the population distribution. It significantly under-values the probability at the low end, but also does not adequately estimate the outliers, or extreme patient outcomes.

Figure 3.

Normal estimate of population distribution

Figure 4 gives an exponential distribution estimate. It better follows the pattern of the bar graph, but it still under-values the height of the bars.

Figure 4.

Exponential estimate of population distribution

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