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Application of Parametric Shared Frailty Models to Analyze Time-to-Death of Gastric Cancer Patients

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Abstract

Background

Despite its declining incidence, gastric cancer (GC) is one of the world’s leading malignancies and a major global health concern due to its high prevalence and fatality rate. Furthermore, it is the world’s fourth most common cancer and the second leading cause of cancer death. Studying the determinants of time to death of gastric cancer patients will give clinicians more information to develop specific treatment plans, forecast prognosis, and track the progress of death cases. The application of the frailty model can help account for random variation in survival that may exist due to unobserved factors, as well as show the impact of latent factors on death risk. As a result, the purpose of this study was to assess the determinants of time to death of GC patients’ by applying the parametric shared frailty models.

Methods

The data for this study were obtained from gastric cancer patients admitted to the Tikur Anbesa Specialized Hospital, Addis Ababa, from January 1, 2015, to February 29, 2020. With the aim of coming up with an appropriate survival model that determines factors that affect the time to death of gastric cancer patients, various parametric shared frailty models were compared. In all of the frailty models, patient regions were used as a clustering variable. The current study implemented exponential, Weibull, log-logistic, and lognormal distributions for baseline hazard functions with gamma and inverse Gaussian’s frailty distributions. The performance of all models was compared using the AIC and BIC criteria. R statistical software was used to conduct the analysis.

Results

A retrospective study was undertaken on a total of 407 gastric cancer patients under follow-up at Tikur Anbesa Specialized Hospital. Of all 407 GC patients, 56.3% died while the remaining 43.7% were censored. The patients’ median time to death was 21.9 months, with a maximum survival time of 49.6 months. In the current study, the clustering effect was significant in modeling the time to death from gastric cancer. The Weibull model with inverse Gaussian frailty has the minimum AIC and BIC value among the candidate models compared. The dependency within the clusters for the Weibull–inverse Gaussian frailty model was \(kendal{l}^{^{\prime}}s tau(\tau )=0.134\) (13.4%). According to the results of our best model (Weibull–inverse Gaussian), the sex of the patient, the smoking status, the tumor size, the treatment taken, the vascular invasion, and the disease stage was found to be statistically significant at an alpha = 0.05 significance level.

Conclusion

Time to death of GC patient’s data set was well described by the Weibull–inverse Gaussian shared frailty. Furthermore, Weibull baseline distribution best fits the GC data set as it enables proportional hazard and accelerated failure time model, for time to failure data. There is unobserved heterogeneity between clusters (patient regions), indicating the need to account for this clustering effect. In this study, survival time to death among GC patients was discovered to be small. Covariates like older age, being male, having higher (advanced) stage of GC disease (stage three and stage four), advanced tumor size, being smoker, infected by Helicobacter pylori, and existence of vascular invasion significantly accelerate the time to death of GC patients. In contrast, talking combination of more treatments prolongs the time to death of patients. To improve the health of patients, interventions should be taken based on significant prognostic factors, with special attention dedicated to patients with such factors to prevent GC death.

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Data Availability

The datasets used in this study are available from the corresponding author on reasonable request.

Abbreviations

AA:

Addis Ababa

AFT:

Acceleration failure time

AIC:

Akanke’s Information Criteria

BIC:

Bayesian Information Criteria

CI:

Confidence interval for acceleration factor

GC:

Gastric cancer

GI:

Gastrointestinal

LRT:

The likelihood ratio test

N.G.I:

Non-gastrointestinal

P.D.T:

Poorly differentiated tumor

S.R.C:

Signet ring cell

TASH:

Tikur Anbesa Specialized Hospital

WDT:

Well-differentiated tumor

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Acknowledgements

We would like to thank Tikur Anbesa Specialized Hospital for allowing this data to be collected from patients’ cards. We would also like to thank Jimma University for assisting us in collecting data and conducting this crucial study.

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Authors and Affiliations

  1. Department of Statistics, College of Natural and Computational Science, Mizan-Tepi University, Tepi, Ethiopia

    Mesfin Esayas Lelisho, Solomon Abebaw Andargie & Seid Ali Tareke

  2. Department of Statistics, College of Natural Science, Jimma University, Jimma, Ethiopia

    Geremew Muleta Akessa, Demeke Kifle Demissie & Samuel Fikadu Yermosa

  3. Department of Technical Education, IET, Dr. A.P.J.Abdul Kalam Technical University Uttar Pradesh, Lucknow, 226021, India

    Digvijay Pandey

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  1. Mesfin Esayas Lelisho
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Contributions

MEL: Study conception and design, data collection, analysis and interpretation of results, and manuscript preparation. GMA: Main supervision, guide data analysis and writing the manuscript draft, and review the final manuscript. DK: Co-supervision and advising. SAT: Manuscript revision. Finally, the manuscript was read and approved by all authors.

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Correspondence to Mesfin Esayas Lelisho or Digvijay Pandey.

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The Jimma University Institute of Research Review Board provided ethical approval for this study. The author requested and was granted access to the data from Tikur Anbesa specialized hospital for the purpose of this study.

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Esayas Lelisho, M., Akessa, G.M., Kifle Demissie, D. et al. Application of Parametric Shared Frailty Models to Analyze Time-to-Death of Gastric Cancer Patients. J Gastrointest Canc 54, 104–116 (2023). https://doi.org/10.1007/s12029-021-00775-y

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