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. 2023 Jul 20;51(5):1007-1022.
doi: 10.1080/02664763.2023.2229973. eCollection 2024.

Alternative statistical modeling for radical prostatectomy data

Julio C S Vasconcelos  1 , Thiago da Costa Travassos  2 , Edwin M M Ortega  3 , Gauss M Cordeiro  4 , Leonardo Oliveira Reis  5
Affiliations

Alternative statistical modeling for radical prostatectomy data

Julio C S Vasconcelos et al. J Appl Stat. .

Abstract

Several statistical models have been proposed in recent years, among them is the semiparametric regression. In medicine, there are several situations in which it is impracticable to consider a linear regression for statistical modeling, especially when the data contain explanatory variables that present a nonlinear relationship with the response variable. Another common situation is when the response variable does not have a unimodal shape, and it is not possible to adopt distributions belonging to the symmetric or asymmetric classes. In this context, a semiparametric heteroskedastic regression is proposed based on an extension of the normal distribution. Then, we show the usefulness of this model to analyze the cost of prostate cancer surgery. The predictor variables refer to two groups of patients such that one group receives a multimodal local anesthetic solution (Preemptive Target Anesthetic Solution) and the second group is treated with neuraxial blockade (spinal anesthesia/traditional standard). The other relevant predictor variables are also evaluated, thus allowing for the in-depth interpretation of the predictor variables with a nonlinear effect on the dependent variable cost. The penalized maximum likelihood method is adopted to estimate the model parameters. The new regression is a useful statistical tool for analyzing medical data.

Keywords: 62-08; 62-11; 62P10; Cubic smoothing splines; Marshall-Olkin family; local anesthetic; prostate cancer; quantile residuals.

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Conflict of interest statement

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

Figures

Figure 1.
Figure 1.
(a) Histogram of the cost of open radical prostatectomy (divided by 1000). (b) Dispersion plot of the cost of open radical prostatectomy versus patient age (in years). (c) Dispersion plot of the cost of open radical prostatectomy versus duration (in minutes) of the operation.
Figure 2.
Figure 2.
True and estimated curves for the smooth function h(ti1): (a) n = 60, (b) n = 180, (c) 360 and (d) 540.
Figure 3.
Figure 3.
Normal probability plots for the qrs with sample sizes: (a) n = 60, (b) n = 180, (c) 360 and(d) 540.
Figure 4.
Figure 4.
(a) Estimated densities to prostatectomy data. (b) Estimated cdfs.
Figure 5.
Figure 5.
(a) Plot of the qrs versus the index. (b) Normal probability plot for the qrs with envelope.
Figure 6.
Figure 6.
Estimated smooth curve. (a) Age (in years). (b) Surgical time (in minutes).
Figure A1.
Figure A1.
(a) Plots of the Bowleys skewness as function of ν and τ for μ=0.01 and σ=1. (b) Plots of the Moors' kurtosis as function of ν and τ for μ=0.5 and σ=3.
See this image and copyright information in PMC

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