The long-term inverse Nakagami distribution: Properties, inference and application

In this paper, a new long-term survival distribution, the so-called long-term inverse Nakagami distribution, is presented. The proposed distribution allows us to fit data with unimodal hazard function, where a part of the population is not susceptible to the event of interest, the so-called long-term survival. This distribution can be used, for instance, in clinical studies where a portion of the population can be cured during a treatment. Some mathematical properties of the new distribution are derived. The inferential procedures for the parameters are discussed under the maximum likelihood estimators. A numerical simulation study is carried out to verify the performance of these estimators. Finally, an application to real data on patients’ lifetime after acute myocardial infarction illustrates the usefulness of the proposed distribution.

Ultrasound Assessment of Hepatic Steatosis by Using the Double Nakagami Distribution: A Feasibility Study

Ultrasound imaging is a first-line assessment tool for hepatic steatosis. Properties of tissue microstructures correlate with the statistical distribution of ultrasound backscattered signals, which can be described by the Nakagami distribution (a widely adopted approximation of backscattered statistics). The double Nakagami distribution (DND) model, which combines two Nakagami distributions, was recently proposed for using high-frequency ultrasound to analyze backscattered statistics corresponding to lipid droplets in the fat-infiltrated liver. This study evaluated the clinical feasibility of the DND model in ultrasound parametric imaging of hepatic steatosis by conducting clinical experiments using low-frequency ultrasound dedicated to general abdominal examinations. A total of 204 patients were recruited, and ultrasound image raw data were acquired using a 3.5 MHz array transducer for DND parametric imaging using the sliding window technique. The DND parameters were compared with hepatic steatosis grades identified histologically. A receiver operating characteristic (ROC) curve analysis was used to evaluate the diagnostic performance. The results indicated that DND parametric imaging constructed using a sliding window with the side length of five times the pulse length of the transducer provided stable and reliable DND parameter estimations and visualized changes in the backscattered statistics caused by hepatic steatosis. The DND parameter increased with the hepatic steatosis grade. The areas under the ROC curve for identifying hepatic steatosis were 0.76 (≥mild), 0.81 (≥moderate), and 0.82 (≥severe). When using low-frequency ultrasound, DND imaging allows the clinical detection of hepatic steatosis and reflects information associated with lipid droplets in the fat-infiltrated liver.