THE DIAGNOSTIC ACCURACY OF COMPOSITE INDICES IS ASSOCIATED WITH THE NUMBER OF PARTITIONS OF THEIR COMPONENTS: A SIMULATION STUDY

G. Kourlaba (Greece), D. Panagiotakos (Greece) and V. Stavrinos (Greece)

Received May 10, 2007

Abstract

In bio-medical research, simple or multi-component indices are widely used for the evaluation of various clinical conditions (e.g., presence of chronic diseases, severity of stroke, etc.) and people’s personal characteristics (e.g., psychological and dietary evaluation, etc.). Despite their wide use, the methodology of their construction is not utterly clarified. The main research hypothesis tested in this work is whether the number of partitions (i.e., classes) in each component influences the diagnostic accuracy of the index. To test the previous hypothesis, 10 random variables (r.vs.) –the components of an index- were generated. The components followed a discrete distribution, with values 1, 2, ..., 10 and with corresponding probabilities 0.05, 0.05, 0.1, 0.1, 0.2, 0.2, 0.1, 0.1, 0.05, 0.05. Each r.v. had sample size of 1000 and the previous procedure was simulated 1000 times. Then an index with values 10-100 (S10) was calculated, summing the values of these r.vs. Afterwards, 10 new variables were constructed using the 8-quantiles of the initial r.vs. Summing the aforementioned r.vs., another index, ranged 10-80, (S8) was created. Likewise, 5 new indices were constructed using 6-quantiles (S6), quintiles (S5), quartiles (S4), tertiles (S3) and median (S2) of 10 initial r.vs. Indices’ values higher than the median considered to reflect a pathological situation. Moreover, a r.v. that followed the Bernoulli distribution (p = 0.25)  and with odds ratio = 3 for the median of S10, was generated (D) in order to represent the presence of a disease. Based on D, sensitivity, specificity and area under the ROC curve (AUC) were calculated for each index. Finally, using the least square method the function that associates the number of partitions with indices’ accuracy was calculated. The sensitivity and AUC are proportional to the number of partitions of the components of an index, while the specificity is inversely associated. In the 1000 simulated samples, the sensitivity ranged from 48.7% to 69.7%, the AUC from 60.2% to 63.5% and the specificity from 66.4% to 59.3%, for S10 and S2, respectively. The function that best fitted the data was the natural logarithm (sensitivity = 0.432 + 0.108ln). Conclusively, the use of a large number of partitions in index components increases its diagnostic accuracy. Therefore, a large number of partitions are recommended in order to obtain high sensitivity and AUC, which have particular clinical interest.

Keywords and phrases: sensitivity, specificity, index.