Statistical Inference for Gompertz and Weibull Models under Doubly Interval-Censored Data

Authors

  • Himani Kotian Department of Community Medicine, Kasturba Medical College Mangalore, Manipal Academy of Higher Education, Manipal, India
  • Sunita Sharma Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India
  • Asha Kamath Department of Applied Statistics & Data Science, Prasanna School of Public Health, Manipal Academy of Higher Education, Manipal, India
  • Vasudeva Guddattu Department of Applied Statistics & Data Science, Prasanna School of Public Health, Manipal Academy of Higher Education, Manipal, India.

DOI:

https://doi.org/10.13052/jrss0974-8024.19216

Keywords:

Doubly interval censoring, likelihood ratio, Wald method, Gompertz model, coverage probability

Abstract

This study explores the statistical inference for the Gompertz model using doubly interval-censored data. In this framework, the initial event time is assumed to follow either a Weibull or uniform distribution, whereas the lifetime of interest is assumed to follow the Gompertz distribution. Confidence intervals for the model parameters were constructed using the Wald and likelihood ratio methods and compared in terms of coverage probability. A simulation study was conducted to examine the large-sample asymptotic behavior of the estimators and the interval procedures. The results indicate that the Wald method consistently provides more accurate and reliable coverage than the likelihood ratio method. A real-life dataset was analyzed to validate the proposed methodology and to demonstrate its practical relevance.

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Author Biographies

Himani Kotian , Department of Community Medicine, Kasturba Medical College Mangalore, Manipal Academy of Higher Education, Manipal, India

Himani Kotian received the bachelor’s degree in Statistics from Mangalore University in 2013, the master’s degree in Biostatistics from Manipal University in 2015, and Pursuing philosophy of doctorate degree in Survival Analysis (Doubly Interval-Censored Data) from Manipal University, respectively. She is currently working as a Lecturer cum Biostatistician in the Department of Community Medicine, Kasturba Medical College Mangalore. Her research areas include Inferential Statistics, Survival analysis, and Machine Learning Technique.

Sunita Sharma, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India

Sunita Sharma is an Assistant Professor in the Department of Mathematics at Manipal Institute of Technology, Manipal, Karnataka, India. She obtained her Ph.D. in Statistics from G. B. Pant University of Agriculture and Technology, Pantnagar, Uttarakhand, India.

Her research interests include Bayesian Statistics, Reliability Engineering, Statistical Inference, and Applied Probability. Dr. Sharma has published numerous research articles in reputed international journals indexed in SCI and Scopus databases. Her research primarily focuses on reliability analysis, Bayesian estimation, and stochastic modeling of complex systems.

In addition to her research contributions, Dr. Sharma actively serves as a reviewer for several national and international journals in Statistics, Reliability Engineering, and related disciplines.

Asha Kamath, Department of Applied Statistics & Data Science, Prasanna School of Public Health, Manipal Academy of Higher Education, Manipal, India

Asha Kamath is Associate Director and Professor of Department of Data Science, PSPH, Manipal Academy of Higher Education (MAHE), Manipal. Dr. Kamath is an expert in research methodology and biostatistics. She regularly undertakes statistical consultancy for medical researchers and supervises research among medical postgraduates. She is a panel member on the PhD committee of MAHE. Dr. Kamath has worked extensively in the designing and analysis of epidemiological studies, clinical trials, model building, Bayesian analysis, Time series analysis of health and climate data, and allied health fields such as adolescent health and geriatrics. She has been a part of several collaborations, both nationally and internationally and has been an investigator/co-investigator on several projects for ICMR and other reputed institutions grant from the University of Alabama at Birmingham International Training and Research in Environmental and Occupational Health program from the National Institutes of Health-Fogarty International Center (NIH-FIC) for developing R manual for time series analysis.

She is a Life member of the Indian Society for Medical Statistics (ISMS). Dr Kamath has published more than 175 articles in national and international journals which have been indexed in SCOPUS and PubMed databases. She has written six chapters in books and has served as a resource person in workshops as a research methodologist as well as a statistician.

Vasudeva Guddattu, Department of Applied Statistics & Data Science, Prasanna School of Public Health, Manipal Academy of Higher Education, Manipal, India.

Vasudeva Guddattu is a Professor in the Department of Applied Statistics and Data Science of Public Health at Manipal Academy of Higher Education. He is Coordinator for MSc Biostatistics Program. Professor Guddattu obtained his master’s degree in Statistics from Mangalore University in 2005 and completed his PhD in Count Data Regression from the same university in 2014. His areas of expertise encompass categorical data analysis, discrete data modelling, biostatistics, and statistical methods for health research. He is a distinguished researcher with an h-index of 23 and has made significant contributions to scientific literature through numerous publications, including randomized controlled trials and mixed-methods studies. His research has contributed substantially to advancing statistical applications in medical and public health research.

References

A. H. Peruski, B. Wu, L. Linley, K. P. Delaney, E. A. DiNenno, and A. S. Johnson, “Time from HIV infection to diagnosis in the U.S., 2014–2018,” IEEE Trans. Am. J. Prev. Med., vol. 61, no. 5, pp. 636–643, 2021, doi: 10.1016/j.amepre.2021.04.015.

G. Pantaleo et al., “The qualitative nature of the primary immune response to HIV infection is a prognosticator of disease progression independent of the initial level of plasma viremia,” Proc. Natl. Acad. Sci. U.S.A., vol. 94, no. 1, pp. 254–258, 1997, doi: 10.1073/pnas.94.1.254.

M. L. Calle, “The analysis of interval censoring and double censoring via Markov chain Monte Carlo methods,” Working document, Universitat de Vic, Vic, Spain, 2002.

L. P. Chen and B. Qiu, “Analysis of length-biased and partly interval-censored survival data with mismeasured covariates,” Biometrics, vol. 79, no. 4, pp. 3929–3940, 2023, doi: 10.1093/biomtc/ujad117.

K. Kiani and J. Arasan, “Gompertz model with time dependent covariate in the presence of interval-, right- and left-censored data,” J. Stat. Comput. Simul., vol. 83, no. 8, pp. 1472–1490, 2013, doi: 10.1080/00949655.2012.662979.

Y. F. Loh, J. Arasan, H. Midi, and M. R. A. Bakar, “Inferential procedures for log logistic distribution with doubly interval-censored data,” J. Mod. Appl. Stat. Methods, vol. 16, no. 2, pp. 581–603, 2017, doi: 10.22237/jmasm/1509496320.

K. Kiani and J. Arasan, “Survival model with doubly interval-censored data and timedependent covariates,” in Proc. World Congr. Eng., London, U.K., 2018, pp. 135–140.

M. Z. Yin, Q. W. Zhu, and X. Lü, “Parameter estimation of the incubation period of COVID-19 based on the doubly interval-censored data model,” Nonlinear Dyn., vol. 106, no. 2, pp. 1347–1358, 2021, doi: 10.1007/s11071-021-06587-w.

J. Sun, “Statistical analysis of doubly interval-censored failure time data,” in Handbook of Statistics: Advances in Survival Analysis, vol. 23. Amsterdam, The Netherlands: Elsevier, 2004, pp. 105–122, doi: 10.1016/S0169-7161(03)23006-6.

W. Pan, “A multiple imputation approach to regression analysis for doubly censored data with application to AIDS studies,” Biometrics, vol. 57, no. 4, pp. 1245–1250, 2001, doi: 10.1111/j.0006-341X.2001.01245.x.

V. De Gruttola and S. W. Lagakos, “The analysis of doubly censored data,” Biometrics, vol. 45, no. 1, pp. 1–11, 1989, doi: 10.2307/2532031.

K. Kiani and J. Arasan, “Simulation of interval-censored data in medical and biological studies,” Int. J. Mod. Phys. Conf. Ser., vol. 9, pp. 112–118, 2012, doi: 10.1142/S2010194512005168.

P. Bacchetti, “Estimating the incubation period of AIDS by comparing population infection and diagnosis patterns,” J. Amer. Stat. Assoc., vol. 85, no. 412, pp. 1002–1008, 1990, doi: 10.2307/2289596.

Y. F. Loh, J. Arasan, H. Midi, and M. R. Abu Bakar, “A parametric model for doubly interval-censored lifetime data,” J. Sci. Technol., vol. 9, no. 2, 2017.

J. Ramjith, C. Andolina, T. Bousema, and M. A. Jonker, “Flexible time-to-event models for double-interval-censored infectious disease data with clearance of the infection as a competing risk,” Front. Appl. Math. Stat., vol. 8, Art. no. 1035393, 2022, doi: 10.3389/fams.2022.1035393.

J. Kim, Y.-J. Kim, and C. M. Nam, “A generalized log-rank-type test for comparing survivals with doubly interval-censored data,” Biom. J., vol. 51, no. 4, pp. 689–696, 2009, doi: 10.1002/bimj.200800253.

M. Y. Kim, V. De Gruttola, and S. W. Lagakos, “Analyzing doubly censored data with covariates, with application to AIDS,” Biometrics, vol. 49, no. 1, pp. 13–22, Mar. 1993.

N. G. Reich, J. Lessler, D. A. T. Cummings, and R. Brookmeyer, “Estimating incubation period distributions with coarse data,” Statistics in Medicine, vol. 28, no. 22, pp. 2769–2784, 2009, doi: 10.1002/sim.3659.

R. Oller, G. Gómez, and M. L. Calle, “Interval censoring: Model characterizations for the validity of the simplified likelihood,” Canadian Journal of Statistics, vol. 32, no. 3, pp. 315–326, 2004.

K. Sruthi and M. Kumar, “Fuzzy reliability estimation within a stress-strength framework incorporating distortion functions,” Journal of Reliability and Statistical Studies, vol. 19, no. 1, pp. 3–24, 2026, doi: 10.13052/jrss0974-8024.1913.

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Published

2026-09-15

How to Cite

Kotian , H., Sharma, S., Kamath, A., & Guddattu, V. (2026). Statistical Inference for Gompertz and Weibull Models under Doubly Interval-Censored Data. Journal of Reliability and Statistical Studies, 19(02), 635–664. https://doi.org/10.13052/jrss0974-8024.19216

Issue

2026: Vol 19 Iss 2

Section

Articles