arXiv subjects

Sankaran P. G.

Publications and source records attributed to Sankaran P. G..

6 recordsLinked to original sources

arXiv2026

A Family of Quantile Functions Useful in Clinical Studies

Motivated by upper-tail quantile-domain summaries, we study the quantile-based effectiveness persistence function defined as the ratio between the tail mean and the quantile function. We derive statistical properties of this measure and consider a rational (Möbius) specification of the quantilebased effectiveness persistence function. Under natural boundary conditions, this specification reduces to a canonical form. The resulting canonical family defines a two-parameter class of nonnegative distributions through its quantile function. Various properties, including descriptive measures, L-moments, and quantile-based reliability concepts, are derived for this class. Estimation of the model parameters using maximum likelihood is also developed. The proposed family is illustrated using a real survival dataset.

stat.ME↗

arXiv2026

Quantile-Based Effectiveness Persistence Function: A Tail-Focused Metric with Theory, Estimation, and Application to Biosimilar Evaluation

In clinical studies, persistence, which measures the duration of time a patient continues to take a prescribed medication without discontinuation, is increasingly recognized as a critical indicator of adherence to medication. Adherence encompasses not only whether a patient takes their medication as prescribed but also the consistency and duration with which they do so. Among the various metrics used to evaluate adherence, persistence stands out as a particularly robust measure because it provides a temporal dimension, reflecting the sustained commitment of patients to their therapeutic regimens. This focus on persistence offers unique insights into adherence-related quality and performance, shedding light on the challenges and opportunities to optimize long-term medication use. The comparison of upper-tail clinical performance, which measures the extent to which very large responses persist among top responders, is often more decisive in therapy evaluation than conventional summaries. In this paper, we introduce the quantile-based effectiveness persistence function defined as the ratio between the tail mean and the quantile function. The notion parallels expected shortfall in risk theory and is tailored to detect clinically meaningful deviations in the upper tail. We establish key properties and show that the function is equivalent to the first L-moment of the scaled tail, yielding robust inference tools. We derive a simple nonparametric estimator of the function and develop a bootstrap-calibrated two-sample (upper-tail) equivalence test. Simulation studies and real-data analysis illustrate that the proposed measures captures clinically relevant tail persistence that complements median and mean-based summaries.

stat.ME↗

arXiv2024

The Relative Information Generating Function-A Quantile Approach

Information generating functions have been used for generating various entropy and divergence measures. In the present work, we introduce quantile based relative information generating function and study its properties. The proposed generating function provides well-known Kullback-Leibler divergence measure. The quantile based relative information generating function for residual and past lifetimes are presented. A non parametric estimator for the function is derived. A simulation study is conducted to assess performance of the estimators. Finally, the proposed method is applied to a real life data.

math.ST↗

arXiv2021

Comparison of cause specific rate functions of panel count data with multiple modes of recurrence

Panel count data refer to the data arising from studies concerning recurrent events where study subjects are observed only at distinct time points. If these study subjects are exposed to recurrent events of several types, we obtain panel count data with multiple modes of recurrence. In the present paper, we propose a nonparametric test for comparing cause specific rate functions of panel count data with more than one mode of recurrence. The test can also be employed to assess whether the competing modes of recurrence are affecting the recurrence times identically. We carry out simulation studies to evaluate the performance of the test statistic in a finite sample setup. The proposed test is illustrated using two real life panel count data sets, one arising from a medical follow up study on skin cancer chemo prevention trial and the other on a warranty database for a fleet of automobiles.

stat.ME↗

arXiv2021

Proportional mean model for panel count data with multiple modes of recurrence

Panel count data is common when the study subjects are exposed to recurrent events, observed only at discrete time points. In this article, we consider the regression analysis of panel count data with multiple modes of recurrence. We propose a proportional mean model to estimate the effect of covariates on the underlying counting process due to different modes of recurrence. The simultaneous estimation of baseline cumulative mean functions and regression parameters of $(k>1)$ recurrence modes are studied in detail. Asymptotic properties of the proposed estimators are also established. A Monte Carlo simulation study is carried out to validate the finite sample behaviour of the proposed estimators. The methods are applied to a real data arising from skin cancer chemoprevention trial.

stat.ME↗

arXiv2021

Cause specific rate functions for panel count data with multiple modes of recurrence

Panel count data arise from longitudinal studies on recurrent events where each subject is observed only at discrete time points. If recurrent events of several types are possible, we obtain panel count data with multiple modes of recurrence. Such data is commonly encountered in medical studies, reliability experiments as well as in sociological studies. In this article, we present cause specific rate functions for the analysis of panel count data with multiple modes of recurrence and develop nonparametric estimation procedures for the same. We derive empirical estimators for the cause specific rate functions and also propose a smoothed version of the same estimators using kernel estimation method. Asymptotic properties of the proposed estimators are studied. A simulation study is conducted to assess the performance of the proposed estimators in finite samples. The practical utility of the proposed method is demonstrated using a real life data arising from skin cancer chemoprevention trial given in Sun and Zhao (2013).

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