A unified approach to power and sample size determination for log-rank tests under proportional and nonproportional hazards

2021 ◽  
pp. 096228022098857
Author(s):  
Yongqiang Tang
Keyword(s):  
Sample Size ◽  
Proportional Hazards ◽  
Sample Size Calculation ◽  
Unified Approach ◽  
Rank Tests ◽  
Trial Duration ◽  
Nonproportional Hazards ◽  
Equivalence Trials ◽  
Superiority Trials ◽  
Log Rank Tests

Log-rank tests have been widely used to compare two survival curves in biomedical research. We describe a unified approach to power and sample size calculation for the unweighted and weighted log-rank tests in superiority, noninferiority and equivalence trials. It is suitable for both time-driven and event-driven trials. A numerical algorithm is suggested. It allows flexible specification of the patient accrual distribution, baseline hazards, and proportional or nonproportional hazards patterns, and enables efficient sample size calculation when there are a range of choices for the patient accrual pattern and trial duration. A confidence interval method is proposed for the trial duration of an event-driven trial. We point out potential issues with several popular sample size formulae. Under proportional hazards, the power of a survival trial is commonly believed to be determined by the number of observed events. The belief is roughly valid for noninferiority and equivalence trials with similar survival and censoring distributions between two groups, and for superiority trials with balanced group sizes. In unbalanced superiority trials, the power depends also on other factors such as data maturity. Surprisingly, the log-rank test usually yields slightly higher power than the Wald test from the Cox model under proportional hazards in simulations. We consider various nonproportional hazards patterns induced by delayed effects, cure fractions, and/or treatment switching. Explicit power formulae are derived for the combination test that takes the maximum of two or more weighted log-rank tests to handle uncertain nonproportional hazards patterns. Numerical examples are presented for illustration.

Did the 2004 World Health Organization (WHO) histologic classification result in better prognostic categories for resected thymomas as compared to 1999 WHO classification scheme?

2013 ◽  
Vol 31 (15_suppl) ◽  
pp. e18552-e18552
Author(s):  
Yousif Yonan ◽  
Dani Zander ◽  
John M. Varlotto ◽  
Jennifer Toth ◽  
Michael Reed ◽  
...  
Keyword(s):  
Multivariate Analysis ◽  
Who Classification ◽  
Proportional Hazards ◽  
Wide Spectrum ◽  
World Health ◽  
Rank Tests ◽  
Histologic Classification ◽  
Time Periods ◽  
Log Rank Tests

e18552 Background: The classification of thymic epithelial neoplasms is subject of controversy. The purpose of our investigation is to see whether the 2004 histologic classification results in better prognostic categories than that of the 1999 classification. Methods: The SEER 18 database was used to investigate incidence and overall survival/cause-specific survival (OS/CSS) of resected thymomas during 2000-2009. Incidence was examined by frequency and trend analyses. Patients diagnosed with first primary localized thymoma/thymic carcinoma were selected in two time periods (2000-2003: N=201; 2005-2009: N = 497). The median follow up is 79 months and 27 months respectively. OS/CSS in two patients group were analyzed by Kaplan-Meier estimation, log-rank tests, and multivariate proportional hazards modeling. Results: The proportion of six histology categories (A, AB, B1-B3,C) did not change significantly during the two time periods. Compared to patients diagnosed in 2000-2003, OS was not significantly different in patients diagnosed in 2005-2009 in the log rank tests or multivariate analysis after accounting for treatment, tumor factors, and patient characteristics (OS, HR=0.737, p=0.1580; CSS, HR=0.731, p=0.3711). Histology as 6 categories is a significant predictor for OS in the multivariate analysis in 2005-2009, but not in 2000-2003. However, the predictive role of histology is similar in both time periods in the multivariate analysis of CSS. Complete resection, classification C, and tumor stage are significantly linked to OS and CSS. Conclusions: Patients diagnosed after 2004 did not have better survival outcomes than earlier patients. The WHO classification of 2004 may be a better predictor of OS than that of 1999 as shown by the wide-spectrum of pathologists reporting to SEER.

scholarly journals Association of Estrogen Receptor Alpha Expression With Survival in Oropharyngeal Cancer Following Chemoradiation Therapy

2019 ◽  
Vol 111 (9) ◽  
pp. 933-942 ◽  
Author(s):  
Maria B Koenigs ◽  
Armida Lefranc-Torres ◽  
Juliana Bonilla-Velez ◽  
Krupal B Patel ◽  
D Neil Hayes ◽  
...  
Keyword(s):  
Estrogen Receptor ◽  
Mrna Expression ◽  
Proportional Hazards ◽  
Hpv Infection ◽  
Cox Proportional Hazards ◽  
The Cancer Genome Atlas ◽  
Rank Tests ◽  
Potential Biomarker ◽  
Hpv Status ◽  
Log Rank Tests

Abstract Background Oropharyngeal squamous carcinoma (OPSC) continues to increase in incidence secondary to human papillomavirus (HPV) infection. Despite the good overall prognosis for these patients, treatment with chemoradiation is associated with morbidity and treatment failure. Better predictors for disease outcome are needed to guide de-intensification regimens. We hypothesized that estrogen receptor α (ERα), a prognostic biomarker in oncology with therapeutic implications, might have similar utility in OPSC. Methods To investigate associations among ERα and demographics, HPV status, and survival, we analyzed ERα mRNA expression of head and neck squamous carcinomas (HNSC) from The Cancer Genome Atlas (TCGA) and immunohistochemistry (IHC) of pretreatment biopsy specimens from an independent group of 215 OPSC patients subsequently treated with primary chemoradiation (OPSC-CR). Associations among variables were evaluated with Fisher exact tests and logistic regression; associations with survival were evaluated with log-rank tests and Cox proportional hazards regression. Results Among 515 patients in TCGA, ERα mRNA expression was highest in HPV-positive OPSC. High ERα mRNA expression was associated with improved survival among those receiving chemoradiation (hazard ratio adjusted for HPV status = 0.44, 95% confidence interval = 0.21 to 0.92). In OPSC-CR, ERα was positive by IHC in 51.6% of tumors and was associated with improved overall, disease-specific, progression-free, and relapse-free survival (log-rank tests: P < .001, P < .001, P = .002, P = .003, respectively); statistically significant associations of ERα positivity with improved survival were maintained after adjusting for clinical risk factors including HPV status. Conclusion In two independent cohorts, ERα is a potential biomarker for improved survival that also may represent a therapeutic target in OPSC.

scholarly journals Sample size calculation for the proportional hazards cure model

2012 ◽  
Vol 31 (29) ◽  
pp. 3959-3971 ◽  
Author(s):  
Songfeng Wang ◽  
Jiajia Zhang ◽  
Wenbin Lu
Keyword(s):  
Sample Size ◽  
Proportional Hazards ◽  
Sample Size Calculation ◽  
Cure Model

Sample size calculation for a proportional hazards mixture cure model with nonbinary covariates

2018 ◽  
Vol 46 (3) ◽  
pp. 468-483
Author(s):  
Yihong Zhan ◽  
Yanan Zhang ◽  
Jiajia Zhang ◽  
Bo Cai ◽  
James W. Hardin
Keyword(s):  
Sample Size ◽  
Proportional Hazards ◽  
Sample Size Calculation ◽  
Cure Model ◽  
Mixture Cure Model
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