# JEL Ratio Test for Independence of Time to Failure and Cause of Failure in Competing Risks Data

## DOI:

https://doi.org/10.6092/issn.1973-2201/13836## Keywords:

Chi square distribution, Competing Risks, Conditional probability, Jackknife empirical likelihood, U-statistics## Abstract

In the present article, we propose a Jackknife empirical likelihood (JEL) ratio test for testing the independence of time to failure and cause of failure in competing risks data. We use the U-statistics theory to derive the JEL ratio test. The asymptotic distribution of the test statistic is shown to be the standard chi-square distribution. A Monte Carlo simulation study is carried out to assess the finite sample behavior of the proposed test. The performance of the proposed JEL test is

compared with the test given by Dewan et al. (2004). Finally, we illustrate our test procedure using two real data sets.

## References

S. ANJANA, I. DEWAN, K. SUDHEESH (2019). Test for independence between time to failure and cause of failure in competing risks with k causes. Journal of Nonparametric Statistics, 31, no. 2, pp. 322–339.

J. BEYERSMANN, A. ALLIGNOL, M. SCHUMACHER (2011). Competing Risks and Multistate Models with R. Springer Science & Business Media, New York.

M. J. CROWDER (2012). Multivariate Survival Analysis and Competing Risks. CRC Press, Boca Raton.

I. DEWAN, J. DESHPANDE, S. KULATHINAL (2004). On testing dependence between time to failure and cause of failure via conditional probabilities. Scandinavian Journal of Statistics, 31, no. 1, pp. 79–91.

I. DEWAN, S. KULATHINAL (2007). On testing dependence between time to failure and cause of failure when causes of failure are missing. PloS one, 2, no. 12, p. e1255.

I. DEWAN, P. SANKARAN, P. ANISHA (2013). On testing independence of failure time and cause of failure using subquantiles. Journal of Statistical Theory and Practice, 7, no. 1, pp. 24–32.

R. DYKSTRA, S. KOCHAR, T. ROBERTSON (1998). Restricted tests for testing independence of time to failure and cause of failure in a competing-risks model. Canadian Journal of Statistics, 26, no. 1, pp. 57–68.

D. G. HOEL (1972). A representation of mortality data by competing risks. Biometrics, 28, no. 2, pp. 475–488.

H. HUANG, Y. ZHAO (2018). Empirical likelihood for the bivariate survival function under univariate censoring. Journal of Statistical Planning and Inference, 194, pp. 32–46.

B.-Y. JING, J. YUAN, W. ZHOU (2009). Jackknife empirical likelihood. Journal of the American Statistical Association, 104, no. 487, pp. 1224–1232.

J. D. KALBFLEISCH, R. L. PRENTICE (2011). The Statistical Analysis of Failure Time Data. John Wiley & Sons, New York.

J. F. LAWLESS (2011). Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New York.

A. J. LEE (2019). U-statistics: Theory and Practice. Routledge, Boca Raton.

E. L. LEHMANN (1951). Consistency and unbiasedness of certain nonparametric tests. The Annals of Mathematical Statistics, 22, no. 2, pp. 165–179.

G. LI, Q.-H. WANG (2003). Empirical likelihood regression analysis for right censored data. Statistica Sinica, 13, no. 1, pp. 51–68.

A. OWEN (1990). Empirical likelihood ratio confidence regions. The Annals of Statistics, 18, no. 1, pp. 90–120.

A. B.OWEN (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika, 75, no. 2, pp. 237–249.

R. L. PRENTICE, J. D. KALBFLEISCH, A. V. PETERSON JR, N. FLOURNOY, V. T. FAREWELL, N. E. BRESLOW (1978). The analysis of failure times in the presence of competing risks. Biometrics, 34, no. 4, pp. 541–554.

P. SANKARAN, I.DEWAN, E. SREEDEVI (2017). Amartingale-based test for independence of time to failure and cause of failure for competing risks models. Communications in Statistics-Theory and Methods, 46, no. 16, pp. 8178–8186.

G. SCHULGEN, M. OLSCHEWSKI, V. KRANE, C. WANNER, G. RUF, M. SCHUMACHER (2005). Sample sizes for clinical trials with time-to-event endpoints and competing risks. Contemporary Clinical Trials, 26, no. 3, pp. 386–396.

D. R. THOMAS, G. L.GRUNKEMEIER (1975). Confidence interval estimation of survival probabilities for censored data. Journal of the American Statistical Association, 70, no. 352, pp. 865–871.

A. M. VARIYATH, P. SANKARAN (2020). Empirical likelihood based test for equality of cumulative incidence functions. Journal of the Indian Society for Probability and Statistics, 21, no. 2, pp. 427–436.

Q.-H.WANG, B.-Y. JING (2001). Empirical likelihood for a class of functionals of survival distribution with censored data. Annals of the Institute of Statistical Mathematics, 53, no. 3, pp. 517–527.

X. YU, Y. ZHAO (2019). Jackknife empirical likelihood inference for the accelerated failure time model. Test, 28, no. 1, pp. 269–288.

M. ZHOU (2015). Empirical Likelihood in Survival Analysis, vol. 79. CRC Press, Boca Raton.

## Downloads

## Published

## How to Cite

*Statistica*,

*83*(1), 27–39. https://doi.org/10.6092/issn.1973-2201/13836

## Issue

## Section

## License

Copyright (c) 2023 Statistica

This work is licensed under a Creative Commons Attribution 3.0 Unported License.