Jackknife-based diagnostics for non-monotonic hazard survival model with interval-censored data

Jayanthi  Arasan

doi:https://doi.org/10.59139/stattrans-2026-008

Jackknife-based diagnostics for non-monotonic hazard survival model with interval-censored data

Jayanthi Arasan 1Department of Mathematics and Statistics, Universiti Putra Malaysia, Malaysia ORCID:https://orcid.org/0000-0003-1805-9601 Statistics in Transition new series, vol. 27, 2026, 1, pages: 137-153 Published online: 11 March 2026 https://doi.org/10.59139/stattrans-2026-008 Citation: Arasan J., 2026. Jackknife-based diagnostics for non-monotonic hazard survival model with interval-censored data. Statistics in Transition new series, 27(1), pp. 137- 153 https://doi.org/10.59139/stattrans-2026-008

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ABSTRACT

This study focuses on jackknife-based model diagnostics for a non-monotonic twoparameter hazard survival regression model (TBPR) when data is interval and rightcensored. This distribution is very flexible, because it accommodates both monotonic and bathtub-shaped hazard rates. This research proposes a bias-corrected jackknife harmonic mean and a ran-dom imputation technique to obtain the altered Cox-Snell (r^*_i), adjusted Martingale (r^*_i) and Schoenfeld (r^*_{S_i} ) residuals. Two simulation studies were conducted to assess the perfor-mances of the altered residuals and their ability to detect extreme observations and outliers at various censoring proportions (cp) and sample sizes (n) for this model. The results indicated that the altered residuals based on jackknife outperformed other residuals at cp and n levels. The proposed methods are then illustrated using a real dataset on Hodgkin’s Disease with the prior treatment group as the covariate. The results showed that the altered residuals work well to address model adequacy and identify potential outliers in the dataset.

KEYWORDS

Jackknife, interval-censored, outliers, covariate.

REFERENCES

Al-Hakeem, H. A., Arasan, J., Mustafa, M. S. B. and Peng, L. F., (2023). Generalized exponential distribution with interval-censored data and time dependent covariate. Communications in Statistics-Simulation and Computation, 52(12), pp. 6149–6159.

Alharbi, N., Jayanthi, A., Haizum, A. and Ling, W., (2022). Assessing performance of the generalized exponential model in the presence of the interval censored data with covariate. Austrian Journal of Statistics, 51(1), pp. 52–69.

Arasan, J., Ehsani, S., (2011). Modeling repairable system failures with interval failure data and time dependent covariate. Journal of Modern Applied Statistical Methods, 10, pp. 618–624.

Arasan, J., Lunn, M., (2008). Alternative interval estimation for parameters of bivariate exponential model with time varying covariate. Computational Statistics, 23, pp. 605–622.

Arasan, J., Lunn, M., (2009). Survival model of a parallel system with dependent failures and time varying covariates. Journal of Statistical Planning and Inference, 139(3), pp 944–951.

Arasan, J., Midi, H., (2021). Jackknife and bootstrap estimates for modified residuals of the log-logistic model. in AIP Conference Proceedings, Vol. 2423(1), AIP Publishing LLC, p. 070009.

Arasan, J., Midi, H., (2023). Bootstrap based diagnostics for survival regression model with interval and right-censored data. Austrian Journal of Statistics, 52(2), pp. 66–85.

Bartolucci, A. A., Dickey, J. M., (1977). Comparative bayesian and traditional inference for gamma-modeled survival data. Biometrics pp. 343–354.

Chen, Z., (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics & Probability Letters, 49(2), pp. 155–161.

Cox, D. R., Snell, E. J., (1968). ‘A general definition of residuals. Journal of the Royal Statistical Society: Series B (Methodological), 30(2), pp. 248–265.

Crowley, J., Hu, M., (1977). Covariance analysis of heart transplant survival data. Journal of the American Statistical Association, 72(357), pp. 27–36.

Efron, B., Tibshirani, R. J., (1994). An Introduction to the Bootstrap, Chapman&Hall/CRC, New York.

Fang, L. Y., Arasan, J., Midi, H. and Bakar, M. R. A., (2015). Jackknife and bootstrap inferential procedures for censored survival data. in AIP Conference Proceedings, Vol. 1682(1), AIP Publishing.

Farrington, C. P., (2000). Residuals for proportional hazards models with interval-censored survival data. Biometrics, 56(2), pp. 473–482.

García Meixide, A., Lema, M. and Vilar, J. M., (2024). A bayesian semiparametric mixture cure model for doubly interval-censored data. Computational Statistics & Data Analysis, 190, p. 107925.

Huber, P. J., (1981). Robust Statistics, Wiley Series in Probability and Mathematical Statistics, Wiley, New York.

Ismail, I., Arasan, J., Safie, M. and Mohd Safari, M. A., (2022). Bathtub hazard model with covariate and right censored data. Journal of Quality Measurement and Analysis JQMA, 18(3), pp. 1–15.

Kiani, K., Arasan, J., (2013). Gompertz model with time-dependent covariate in the presence of interval-, right-and left-censored data. Journal of Statistical Computation and Simulation, 83(8), pp. 1472–1490.

Kiani, K., Arasan, J., Midi, H. et al., (2012). Interval estimations for parameters of gompertz model with time-dependent covariate and right censored data. Sains Malaysiana, 41(4), pp. 471–480.

Lai, M. C., Arasan, J., (2020). Single covariate log-logistic model adequacy with right and interval censored data. Journal of Quality Measurement and Analysis, 16(2), pp. 131–140.

Lawless, J. F., (1982). Statistical Models and Methods for Lifetime Data, Wiley, New York.

Lou, Y., Li, G. and Sun, J., (2024). Interval-censored quantile regression based on fractional counting process. Statistical Analysis and Modeling, XX(XX), pp. 1–20.

Manoharan, T., Arasan, J., Midi, H. and Adam, M. B., (2015). A coverage probability on the parameters of the log-normal distribution in the presence of left-truncated and rightcensored survival data. Malaysian Journal of Mathematical Sciences, 9(1).

Manoharan, T., Arasan, J., Midi, H. and Adam, M. B., (2017). Bootstrap intervals in the presence of left-truncation, censoring and covariates with a parametric distribution. Sains Malaysiana, 46(12), pp. 2529–2539.

Manoharan, T., Arasan, J., Midi, H. and Adam, M. B., (2020). Influential measures on log-normal model for left-truncated and case-k interval censored data with time-dependent covariate. Communications in Statistics-Simulation and Computation, 49(6), pp. 1445–1466.

Naslina, A. M. N. N., Jayanthi, A., Syahida, Z. H. and Bakri, A. M., (2020). Assessing the goodness of fit of the gompertz model in the presence of right and interval censored data with covariate. Austrian Journal of Statistics, 49(3), pp. 57–71.

Pal, N., Peng, Y. and Aselisewine, S., (2023). Bayesian cure rate modeling of interval censored data based on negative binomial distribution. Statistics & Probability Letters, 204, p. 109984.

Schoenfeld, D., (1982). Partial residuals for the proportional hazards regression model. Biometrika, 69(1), pp. 239–241.

Sun, J., (2006). The statistical analysis of interval-censored failure time data, Vol. 3, No. 1, Springer.

Zhang, J., Li, G. and Weng, C., (2023). A semiparametric transformation model for multivariate interval-censored failure time data. Lifetime Data Analysis, 30, pp. 41–65.

Zhou, H., Sun, J., (2021). Semiparametric transformation model for interval-censored survival data with covariate measurement error. Biometrics, 77(2), pp. 523–535.

Zhou, H., Sun, J. and Ibrahim, J. G., (2021). A review on interval-censored survival data: models, inference methods, and applications. Statistical Methods in Medical Research, 30(5), pp. 1312–1336.