The values of the parameter <i>θ</i> of the exponential distribution for various percentages of censoring and various values of parameters of the Weibull distribution.

The values of the parameter θ of the exponential distribution for various percentages of censoring and various values of parameters of the Weibull distribution.</p

Autocorrelation for different data simulation scenarios, include: The Weibull (b1_W, b2_W, Shape_W), the Birnbaum-Sanders (b1_BS, b2_BS, Shape_BS) distribution parameters, and the BC scenario parameters (the Weibull: Shape_BC_W, Scale_BC_W, the BS: Shape_BC_BS, Scale_BC_BS).

Autocorrelation for different data simulation scenarios, include: The Weibull (b1_W, b2_W, Shape_W), the Birnbaum-Sanders (b1_BS, b2_BS, Shape_BS) distribution parameters, and the BC scenario parameters (the Weibull: Shape_BC_W, Scale_BC_W, the BS: Shape_BC_BS, Scale_BC_BS).</p

Kaplan-Meier curves, Bayesian Approach(BA)(median of simulated times) curve under the Birnbaum-Saunders(BS) distribution, and failure times (Omitting-Censored) curve for each of the scenarios listed in S3 Table.

A) t~BS(0.5,4), c~Exp(0.01), 10% censoring, and 100 sample sizes. B) t~BS(0.5,4), c~exp(0.04), 20% censoring, and 100 sample sizes. C) t~BS(0.5,4), c~Exp(0.15), 50% censoring, and 100 sample sizes. D) t~BS(1,4), c~Exp(0.02), 10% censoring, and 100 sample sizes. E) t~BS(1,4), c~exp(0.04), 20% censoring, and 100 sample sizes. F) t~BS(1,4), c~Exp(0.15), 50% censoring, and 100 sample sizes. G) t~BS(2,4), c~Exp(0.01), 10% censoring, and 100 sample sizes. H) t~BS(2,4), c~exp(0.02), 20% censoring, and 100 sample sizes. I) t~BS(2,4), c~Exp(0.10), 50% censoring, and 100 sample sizes. (TIF)</p

Kaplan-Meier curves, Bayesian Approach(BA)(median of simulated times) curve under weibull distribution, and failure times (Omitting-Censored) curve for each of the scenarios listed in S1 Table.

A) t~weibull(0.5,4), c~Exp(0.02), 10% censoring, and 300 sample sizes. B) t~weibull(0.5,4), c~exp(0.04), 20% censoring, and 300 sample sizes. C) t~weibull(0.5,4), c~Exp(0.30), 50% censoring, and 300 sample sizes. D) t~weibull(1,4), c~Exp(0.04), 10% censoring, and 300 sample sizes. E) t~weibull(1,4), c~exp(0.08), 20% censoring, and 300 sample sizes. F) t~weibull(1,4), c~Exp(0.30), 50% censoring, and 300 sample sizes. G) t~weibull(2,4), c~Exp(0.02), 10% censoring, and 300 sample sizes. H) t~weibull(2,4), c~exp(0.06), 20% censoring, and 300 sample sizes. I) t~weibull(2,4), c~Exp(0.20), 50% censoring, and 300 sample sizes. (TIF)</p

Kaplan-Meier curves, Bayesian Approach(BA)(median of simulated times) curve under Birnbaum-Saunders(BS) distribution, and failure times (Omitting-Censored) curve for each of the scenarios listed in S3 Table.

A) t~BS(0.5,4), c~Exp(0.03), 10% censoring, and 300 sample sizes. B) t~BS(0.5,4), c~Exp(0.05), 20% censoring, and 300 sample sizes. C) t~BS(0.5,4), c~Exp(0.15), 50% censoring, and 300 sample sizes. D) t~BS(1,4), c~Exp(0.02), 10% censoring, and 300 sample sizes. E) t~BS(1,4), c~Exp(0.04), 20% censoring, and 300 sample sizes. F) t~BS(1,4), c~Exp(0.15), 50% censoring, and 300 sample sizes. G) t~BS(2,4), c~Exp(0.01), 10% censoring, and 300 sample sizes. H) t~BS(2,4), c~Exp(0.02), 20% censoring, and 300 sample sizes. I) t~BS(2,4), c~Exp(0.15), 50% censoring, and 300 sample sizes. (TIF)</p

Values of the parameter <i>θ</i> of the exponential distribution for different percentages of censoring and different values of the BS distribution (BS) shape parameter.

Values of the parameter θ of the exponential distribution for different percentages of censoring and different values of the BS distribution (BS) shape parameter.</p

Kaplan-Meier curves, BA (median of simulated times), and observed times (omitting censored) for each of the scenarios listed in Table 1.

Kaplan-Meier curves, BA (median of simulated times), and observed times (omitting censored) for each of the scenarios listed in Table 1.</p

WibBUGS and R codes.

Almost all survival data is censored, and censor imputation is necessary. This study aimed to investigate the performance of the Bayesian Approach (BA) in the imputation of censored records in simulated and Breast Cancer (BC) data. Due to the difference in the distribution of time to event in survival analysis, two well-known the Weibull and Birnbaum-Saunders (BS) distributions have been used to test the performance of the BA. For each of the censored, 10,000 times were simulated using the BA in R and BUGS software, and their median or mean was imputed instead of each censor. The eligibility of both imputation methods was investigated using different curves, different censoring percentages, and sample sizes, as well as the Deviance Information Criteria (DIC), Effective Sample Size, and the Geweke diagnostic in simulated and especially real BC data. The BC data, which contains 220 patients who were identified and followed up between 2015 and 2023, was made accessible on February 1, 2023. The Kaplan-Meier, the BA, and other survival curves were drawn for the observed times. Findings indicated that the performance of the BA under the Weibull and BS distributions in simulated data is similar. The DIC index in the BC data under the BS distribution (1510) is less than the Weibull distribution (1698). Therefore, the BS distribution is preferred over the Weibull for imputation of censoring times in real BC data.</div

Kaplan-Meier curves, observed times, mean, and median of simulated times with Weibull distribution under BA.

Kaplan-Meier curves, observed times, mean, and median of simulated times with Weibull distribution under BA.</p

The values of regression coefficients for different values of the Weibull distribution shape parameter.

The values of regression coefficients for different values of the Weibull distribution shape parameter.</p