On the Translation of a Treatment's Effect on Disease Progression Into an Effect on Overall Survival
Pages 72-78
Steven M. Snapinn and Qi Jiang
DOI: http://dx.doi.org/10.6000/1929-6029.2015.04.01.8
Published: 27 January 2015

Abstract: There are many examples of treatments for cancer that show a large and statistically significant improvement in progression-free survival (PFS) but fail to show a benefit in overall survival (OS). One recent example that has received considerable attention involves bevacizumab (Avastin) for the treatment of breast cancer. While it seems logical that slowing the rate of progression of a fatal disease would translate into an increase in survival, it is not clear what relative magnitudes of these two effects one should expect. One potential model for the translation of a benefit on disease progression into an OS benefit assumes that patients transition from a low-risk state (pre-progression) into a high-risk state (post-progression), and that the only impact of the treatment is to alter the rate of this transition. In this paper we describe this model and present quantitative results, using an assumption of constant hazards both pre-progression and post-progression. We find that an effect on progression translates into an effect on survival of a smaller magnitude, and that two key factors influence that relationship: the magnitude of the difference between the hazard rate for death in the pre- and post-progression states, and the duration of follow-up.

Some Useful Properties of Log-Logistic Random Variables for Health Care Simulations
Pages 79-86
David E. Clarkand Muhammad El-Taha
DOI: http://dx.doi.org/10.6000/1929-6029.2015.04.01.9
Published: 27 January 2015

Abstract:  A log-logistic (LL) random variable is one whose logarithm has a logistic distribution. Since the logistic distribution is similar to the normal distribution, log-logistic random variables are similar to log-normal (LN) random variables. However, many of the important properties of LN random variables can only be described using integrals, while the corresponding properties of LL random variables can be described using simple algebra. LL random variables may therefore be a useful alternative to LN random variable for computer simulation of operating room processes or other health care applications, especially when they fit the data more closely. We review the properties of LL random variables, and derive some relationships of the mean residual time to the median residual time. We describe methods of fitting LL distributions to observed data, and discuss potential advantages of using them for simulation of operating room utilization.

Inferential Procedures for Comparing the Accuracy and Intrinsic Measures of Multivariate Receiver Operating Characteristic (MROC) Curve
Pages 87-93
R. Vishnu Vardhan, G. Sameera, P.A. Chandrasekharan and Thulasi Beere
DOI: http://dx.doi.org/10.6000/1929-6029.2015.04.01.10
Published: 27 January 2015

Abstract:  A number of classification techniques are prevailing in literature. Of them, one of the most important techniques is the Receiver Operating Characteristic (ROC) curve. A multivariate extension of this technique is proposed in the recent years. This technique helps in classifying the objects/individuals into one of the two classes by considering two or more markers. The most important measure of an ROC curve is the Area Under the Curve (AUC) and it explains the accuracy and discriminating ability of the test under study. There are two intrinsic measures of ROC namely sensitivity (Sn) and specificity (Sp). Further, two ROC curves can be compared by comparing their measures. The practical application of the proposed inferential procedures is explained with the help of two real datasets namely, Indian Liver Patient (ILP) Dataset and Intra Uterine Growth Restricted Fetal Doppler Study (IUGRFDS) dataset. These inferential procedures are developed based on the measures of multivariate ROC (MROC) curve proposed by Sameera G, R Vishnu Vardhan and KVS Sarma [1].

The Hybrid ROC (HROC) Curve and its Divergence Measures for Binary Classification
Pages 94-102
S. Balaswamy, R. Vishnu Vardhan and K.V.S. Sarma
DOI: http://dx.doi.org/10.6000/1929-6029.2015.04.01.11
Published: 27 January 2015

Abstract:  In assessing the performance of a diagnostic test, the widely used classification technique is the Receiver Operating Characteristic (ROC) Curve. The Binormal model is commonly used when the test scores in the diseased and healthy populations follow Normal Distribution. It is possible that in real applications the two distributions are different but having a continuous density function. In this paper we considered a model in which healthy and diseased populations follow half normal and exponential distributions respectively, hence named it as the Hybrid ROC (HROC) Curve. The properties and Area under the curve (AUC) expressions were derived. Further, to measure the distance between the defined distributions, a popular divergence measure namely Kullback Leibler Divergence (KLD) has been used. Simulation studies were conducted to study the functional behavior of Hybrid ROC curve and to show the importance of KLD in classification.

Time Profile of Time-Dependent Area Under the ROC Curve for Survival Data
Pages 103-113
J. Lambert, R. Porcher and S. Chevret
DOI: http://dx.doi.org/10.6000/1929-6029.2015.04.01.12
Published: 27 January 2015

Abstract:  In the setting of survival analysis, the time-dependent area under the receiver operating characteristic curve (AUC) has been proposed as a discrimination measure of interest. In contrast with the diagnostic setting, the definitions of time-dependent sensitivity and specificity are required. This paper evaluates the time-dependent profile of the resulting AUC(t), which has not been previously assessed. We show that, even when the effect of a binary biomarker on the hazard rate is constant, the value of AUC(t) varies over time according to the prevalence of the marker. The Time-profile of the continuous biomarker is illustrated with numerical integration, and data on several prognostic factors in AML are examined.