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. 2024 Apr 2;51(15):3248-3265.
doi: 10.1080/02664763.2024.2337086. eCollection 2024.

Reparametrized generalized gamma partially linear regression with application to breast cancer data

Cleanderson R Fidelis  1 , Edwin M M Ortega  1 , Fábio Prataviera  1 , Roberto Vila  2 , Gauss M Cordeiro  3
Affiliations

Reparametrized generalized gamma partially linear regression with application to breast cancer data

Cleanderson R Fidelis et al. J Appl Stat. .

Abstract

We construct a new partially linear regression based on a reparametrized generalized gamma distribution with two systematic components that can be easily interpreted. Its parameters are estimated by penalized maximum likelihood. For different parameter settings, sample sizes, and censoring percentages, some simulations are performed to examine the accuracy of the maximum likelihood estimators, and the empirical distribution of the residuals compared with the standard normal distribution. The methodology is applied to breast cancer data in the city of João Pessoa in the state of Paraíba in Brazil.

Keywords: Breast cancer data; gamma generalized distribution; partially linear regressions; penalized maximum likelihood; stochastic representation.

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Conflict of interest statement

No potential conflict of interest was reported by the author(s).

Figures

Figure 1.
Figure 1.
Unadjusted mortality rate per year of breast cancer cases between 2000 and 2020.
Figure 2.
Figure 2.
Breast cancer data. (a) Empirical survival function. (b) Empirical failure rate function. (c) Smooth function.
Figure 3.
Figure 3.
Fitted RGG semi-regression model under scenario A with n=100,250and500 (left to right).
Figure 4.
Figure 4.
Fitted RGG semi-regression model under scenario B with n=100,250and500 (left to right).
Figure 5.
Figure 5.
Normal probability plots for the qrs in the fitted RGG semi-regression model under scenario A with n=100,250and500 (left to right).
Figure 6.
Figure 6.
Normal probability plots for the qrs in the fitted RGG semi-regression model under scenario B with n=100,250and500 (left to right).
Figure 7.
Figure 7.
(a) Empirical and estimated survival functions. (b) Estimated hrf.
Figure 8.
Figure 8.
(a) Empirical and estimated survival functions. (b) Estimated hrf.
Figure 9.
Figure 9.
Fitted percentile curves for q×100=(5,25,50,75,90,95,99) for time versus age.
Figure 10.
Figure 10.
Estimated risk function considering ages (25, 45, 60, 85). Left carcinoma, middle Adenocarcinoma, and right malignant neoplasm.
See this image and copyright information in PMC

References

    1. Abadi A., Amanpour F., Bajdik C., and Yavari P., Breast cancer survival analysis: Applying the generalized gamma distribution under different conditions of the proportional hazards and accelerated failure time assumptions, Int. J. Prev. Med. 3 (2012), p. 644. - PMC - PubMed
    1. Atkinson A.C., Two graphical displays for outlying and influential observations in regression, Biometrika 68 (1981), pp. 13–20.
    1. Atkinson E.N. and Brown B.W., Confidence limits for probability of response in multistage phase ii clinical trials, Biometrics 41 (1985), pp. 741–744. - PubMed
    1. Bakery A.A, Zakaria W., Kalthum O.M., and Mohamed S.K., A new double truncated generalized gamma model with some applications, J. Math. 2021 (2021), pp. 1–27.
    1. Cardozo C.A., Paula G.A., and Vanegas L.H., Generalized log-gamma additive partial linear models with p-spline smoothing, Statist. Papers 63 (2022), pp. 1953–1978.

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