Home

Background

Reference intervals are frequently the only decision support tool provided to clinicians for the interpretation of clinical laboratory data. The direct derivation of reference intervals for an assay using a well-defined population of reference individuals can be a challenging and expensive process. In 1967 Bhattacharya described a method for resolving a distribution into its Gaussian components. In the original paper the method was applied to the distribution of fish length¹. The approach was later applied to the derivation of reference intervals from data mined from the laboratory information system².

Not all patient data can be resolved into Gaussian populations. Hemel et al.³ have proposed the use of the gamma distribution where patient data appears to be skewed and a Gaussian model is clearly not appropriate,. These authors also recommended inspection of the residuals to assess how well the data fits the assumed statistical model.

When developing this application my goal was to provide a cross platform software implementation to support the analysis of population data using these techniques. Like all my programming attempts, it is not pretty but it seems to work.

Requirements

The program requires a Java runtime environment (1.8 or later) in order to run. Java for various platforms including Microsoft Windows, Apple, or Linux can be downloaded from Adoptium. At the time of writing development was undertaken using JDK-11. Java virtual machines are also available from Oracle

Installation and Use

1. Unzip the distribution file (Bellview-1.2.5-RELEASE-bin.zip) to a suitable directory.
2. Locate the file Bellview-1.2.5-RELEASE.jar. The usual path will be <Installation Directory>/Bellview/ Bellview-1.2.5-RELEASE.jar
3. Open a command window to the same directory and execute the command 'java -jar rievaluator.jar'. On Windows or OSX based systems it should be sufficient to double click on the Bellview-1.2.5-RELEASE.jar file.

Using Bellview

Import Data

Import from a delimited text file using the Import menu item from the File menu.

The import parameters are specified in the Import File Dialog. Please ensure you select the field separator, whether or not the first row contains the field headings, and the field / column to import. Reading the data into the database can take a few seconds, and the row counter will be displayed in the bottom left corner of the main application window.

Data Analysis

Choose the desired model to be used for the analysis. Currently only three are supported:

1. Gaussian distribution
2. Log Gaussian distribution
3. Gamma distribution (experimental)

The data importer will read the data into the histogram model based on the default bin width. The default bin width is simply (maximum value - minimum value)/15. If the bin width is set before reading the data, this bin width will be used. If the default is not suitable (usually it won’t be), then enter the bin parameters in the fields provided and rebuild the histogram.

If a Gaussian or log Gaussian model has been selected, then the log difference plot is constructed by taking the log of the bin count for the n+1th bin minus log of the bin count for the nth bin and plotting this difference against the mid-point of the bins. Gaussian populations are resolved by finding points that form a straight line with a negative slope. The mean of the population can be calculated from the x-intercept, and the standard deviation is derived from the slope of the line. To perform the analysis using the Analyzer, select the index corresponding to the first point and the index corresponding to the last point forming the straight section (Note, the straight line must cover at least three points for a valid analysis). Enter the desired confidence interval to use for constructing the reference interval (Generally 95%), then click the Analyze button.

The application will perform a least squares regression analysis on the points delimited by the indexes and uses the results of this to calculate the mean and standard deviation. The residuals plot and the estimated parameters and other details can be seen in the 'Residuals' and 'Report' tabs respectively.

If a gamma distribution is selected, first update the bin parameters to some appropriate values. The x axis values for the log difference plot are a little different in this case each point is equal to ln(1 + h/x) where x is the mid-point of the nth bin, and h is the width of each bin used to construct the histogram. Therefore, the points on the log difference plot are in the reverse direction to those on the histogram. That is the first point at the left of the histogram corresponds to the last point on the right of the log difference plot.

The process of selecting the appropriate range of results in order to estimate the distribution parameters is essentially the same. Choose the index corresponding to the first point and the index corresponding to the last point of the group of linearly related points with a positive slope. Clicking on the analyze button will then trigger the program to estimate the statistical parameters which can then be viewed on the appropriate tabs.

How well the data fit a linear model can be assessed by inspecting the residuals plot where results should be randomly distributed around the zero point on the Y-axis.

The estimated model parameters and derived reference interval are shown on the "Report" tab and can be saved to PDF using the "Export" function under the "File" menu.

References

1. Bhattacharya CG. As simple method of resolution of a distribution into Gaussian components. Biometrics. 1967;23(1):115-135.
2. Baadenhuijsen H and Smit JC. Indirect Estimation of Clinical Chemical Reference Intervals from Total Hospital Patient Data: Application of a Modified Bhattacharya Procedure. Journal of Clinical Chemistry and Clinical Biochemistry. 1985;23:829-839.
3. Hemel JB, Hindriks FR, Van der Slik W. Critical discussion on a method for derivation of reference limits in clinical chemistry from a patient population. Journal of Automatic Chemistry. 1985;7(1):20-30.