A novel sample size formula for the weighted log-rank test under the proportional hazards cure model

Abstract Introduction: The association between classical Hodgkin's Lymphoma (cHL) and tumor Epstein-Barr virus (EBV) status is well established. However, the presence of EBV within Hodgkin/Reed-Sternberg (HRS) cells and its prognosis remains controversial, with conflicting findings from studies of various regions of the world. It is considered essential to deepen the understanding of the pathogenic role of EBV in cHL and its impact in prognosis. Methods: We assessed the correlation between EBV presence in HRS and outcomes in a cohort of Brazilian patients with cHL. EBV positivity was determined by in situ hybridization (ISH) for EBV-encoded RNA (EBER) and immunohistochemistry (IMH) for viral latent membrane protein (LMP-1). All cases were histologically confirmed by an expert hematopathologist who also performed the assays for EBV identification. We examined the prognostic impact of EBV status in 29 patients with cHL. The prognostic factors by IPS (International Prognostic Score) for patients with advanced stage and the risk factors by GHSG (German Hodgkin Study Group) for patients with limited stage were correlated with EBV status tumor cells. For associations between the presence of EBV and other categorical variables, we applied Chi-square or Fisher's exact tests. For describe the effect size (ES) measures for chi-square, we used Cramér's V (V) and odds ratios (OR) with the respective 95% Confidence Intervals (CIs). To evaluate the correlation between all methods of identification of EBV status and among evaluators in histological classification, we applied the Kappa test (K), which measures the degree of agreement these assessments. Differences in OS (overall survival) and EFS (event-free survival) Kaplan-Meier survival curves between EBV-positive and EBV-negative patients were compared statistically using the log-rank test. To evaluate the impact of EBV status on event-free survival controlling for prognostic factors and unfavorable risks, we applied Cox proportional hazards regression to determine hazards ratios (HR) and associated the respective 95% CIs. Multivariate analyses included variables significant at p ≤ 0.15 in univariate models. Results: The mean age at diagnosis was 33 years. Sixty-five percent of the patients had the Nodular Sclerosis histologic subtype and 62,1% had Ann Arbor stage I or II disease at diagnosis. According to GHSG, 88,3% of early-stage patients were classified with unfavorable risk (at least one risk factor) at diagnosis. Compared to advanced-stage patients, 81,9% were considered with favorable IPS (< 4 prognostic factors) at diagnosis. HRS cells were EBV-positive in 37.9% of cases. EBV-positive cHL cases were more frequent in patients ≥ 45 years (71,4% vs. 27,3%, p =0,07). Mixed cellularity (MC) histology subtype was more common in EBV-related tumor cells (p= 0,02) and its effect-size index was medium. The correlation between all methods of identification of EBV status was 96,5% (p< 0,001; K=0.93). The correlation among evaluators in histological classification was 89,6% (p< 0,001; K=0.79). In univariate analysis, age, stage, histologic subtype, nodal involvement, extranodal disease, sex, bulky disease, laboratory data were not associated with adverse EFS (p>0,05). EBV-positive HL seemed to have better EFS than EBV-negative HL (log-rank test, p = 0,07). Cox proportional hazards model confirmed that EBV-positive tumor status and prognosis factors did not impact HL outcome. Conclusions: Despite EBV status in HRS cells not being associated with adverse prognostic factors and not influencing the overall and event-free survivals, the presence of EBV was linked to MC subtype, showing possible implication in histological subtype and worse prognosis. Disclosures Costa: Sanofi: Honoraria, Research Funding.

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Pharmacogenetic analysis in metastatic colorectal cancer (mCRC) patients (pts) treated with second-line irinotecan (IR)+/− cetuximab (CB): The EPIC experience

Journal of Clinical Oncology ◽

10.1200/jco.2009.27.15_suppl.4022 ◽

2009 ◽

Vol 27 (15_suppl) ◽

pp. 4022-4022

Author(s):

D. Yang ◽

A. Pohl ◽

W. Zhang ◽

G. Lurje ◽

Y. Ning ◽

...

Keyword(s):

Proportional Hazards ◽

Progression Free Survival ◽

Cox Proportional Hazards ◽

Phase Iii ◽

Rank Test ◽

Second Line ◽

Ca Repeat ◽

Ras Mutation ◽

Mutation Status ◽

Log Rank Test

4022 Background: EPIC, a multinational phase III clinical trial with IR + CB vs IR alone in mCRC pts in the second-line setting after failure of FOLFOX demonstrated a benefit for IR+CB in progression-free survival (PFS) and response rate (RR). We evaluated functional germline polymorphisms involved in the EGFR- (EGF, EGFR), angiogenesis- (VEGF, IL-8, CXCR-2) - and drug- metabolism related genes (UGT1A1, MTHFR) for their potential role as molecular predictors for clinical outcome in pts treated with CB/IR vs. IR alone. Methods: DNA was extracted from all available formalin-fixed paraffin-embedded tumor samples from the phase III EPIC trial (US sites only). Genotyping was performed using PCR-RFLP assays and 5’ -end [g-33P] ATP’ labeled PCR-protocols. Results: 186 pts were treated either with IR/CB (arm A, 84 pts) or IR (arm B, 102 pts) only. In arm A, 11/84 pts (13%) showed CR or PR, whereas 73/84 (87%) pts had SD or PD. For arm B, 6/102 pts (6%) showed CR or PR, whereas 96/102 pts (94%) had SD or PD. Median PFS in arm A was 3.0 months (95%CI: 2.4- 4.1 months) vs 2.7 months (95%CI: 2.2–2.9 months) in arm B; median overall survival (OS) was 9.3 months (95%CI: 7.1–12.1 months) in arm A vs. 12.3 months (95%CI: 10.4- 17.9 months) in arm B. K-ras mutation status was not significantly associated with PFS or response to CB/IR in the subgroup of 186 patients. We found an EGFR-CA- repeat in intron 1 in arm A to be associated with PFS (p=0.031, log-rank test). In arm B, we found a significant association with RR (p=0.0103, Fisher's exact test) for MTHFR1298. Furthermore, MTHFR 677 (p =0.0048, log-rank test) and MTHFR 1298 (p=0.038, log-rank test) were also found to be associated with OS in arm B. In multivariate analysis, EGFR-CA-repeat was significantly associated with PFS (adjusted p= 0.023). Furthermore, MTHFR 677 and MTHFR 1298 was associated with OS (adjusted p=0.028 and 0.026, respectively, Cox-proportional hazards models), independent from K-ras mutation status, race and number of disease sites. Conclusions: Our study demonstrates the potential predictive value of polymorphisms in the EGFR- and MTHFR- gene in mCRC pts treated with IR+ CB. Further validation in additional clinical trials is necessary. [Table: see text]

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Tumor IGF-1 expression as a predictive biomarker for IGF1R-directed therapy in advanced pancreatic cancer (APC).

Journal of Clinical Oncology ◽

10.1200/jco.2012.30.15_suppl.4054 ◽

2012 ◽

Vol 30 (15_suppl) ◽

pp. 4054-4054 ◽

Cited By ~ 3

Author(s):

Milind M. Javle ◽

Rachna T. Shroff ◽

Gauri R. Varadhachary ◽

Robert A. Wolff ◽

David R. Fogelman ◽

...

Keyword(s):

Proportional Hazards ◽

Proportional Hazards Model ◽

Predictive Biomarker ◽

Cox Proportional Hazards ◽

Cox Proportional Hazards Model ◽

Rank Test ◽

Primary Study ◽

Study Objective ◽

Log Rank Test ◽

Hazards Model

4054 Background: IGF-1 up-regulates PC proliferation and invasiveness through activation of PI3K/Akt signaling pathway and down-regulates PTEN. We investigated IGF-1 expression in tissue and blood as potential predictive markers in phase II study of IGF1R-directed monoclonal antibody, MK-0646 in APC. Prior phase I established the MTD of MK0646 at 5 mg/kg with gemcitabine (G) and erlotinib (E) and 10 mg/kg with G alone. Methods: Patients (pts) with stage IV, previously untreated APC, ECOG PS 0-1, adequate hematologic and organ function were enrolled. Arm A: G 1,000 mg/m2 over 100 min, weekly x 3, MK-0646 weekly x 4; Arm B: G 1000 mg/m2 and MK-0646 + E 100 mg daily. Arm C (control) was G 1,000 mg/m2 + E 100 mg. Cycles were repeated every 4 weeks. Pts were equally randomized in the 3 arms. Primary study objective was progression-free survival (PFS). Pre-treatment peripheral blood samples were measured for IGF-1 level by ELISA; archival core biopsies were analyzed for IGF-1 mRNA expression. RNA extraction from FFPE samples used Roche Transcriptor First Strand cDNA Synthesis Kit. TaqMan PreAmp technique was used to amplify target cDNA prior to TaqMan RT-PCR analysis. Cox proportional hazards model for PFS analyzed the interaction between tissue IGF-1 expression and treatment. Results: 50 pts were enrolled (A=15, B=16,C=16 pts, 3 ineligible). Median PFS of arms A, B and C were 5.5 months (95% CI: 3.9 – NA), 3.0 months (95% CI:1.8 – 5.6) and 2.0 months (95% CI: 1.8 – NA), respectively (log-rank test; p = 0.17). Median OS of A was 11.3 months (95% CI: 8.9 – NA), B 8.9 months (95% CI: 5.3 – NA) and C 5.7 months (95% CI: 2.0 – NA) (log-rank test; p = 0.44). 35 archival core biopsies were analyzed, 21 had adequate tissue for analysis. Using a Multivariable Cox proportional hazards model for PFS, where IGF-1 was dichotomized at the median, there was a 76% reduction in the risk of disease progression or death in arm A as compared with the control (arm C) at high IGF-1 level (p = 0.16). When IGF-1 was fitted as a continuous variable, this reduction was 96% (p = 0.08). There was no correlation between tissue and serum IGF-1. Conclusions: Tissue expression of IGF-1 level may represent a promising predictive biomarker for IGF1R-directed therapy in APC.

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Sample size calculation for testing differences between cure rates with the optimal log-rank test

Journal of Biopharmaceutical Statistics ◽

10.1080/10543406.2016.1148711 ◽

2016 ◽

Vol 27 (1) ◽

pp. 124-134 ◽

Cited By ~ 3

Author(s):

Jianrong Wu

Keyword(s):

Sample Size ◽

Sample Size Calculation ◽

Rank Test ◽

Log Rank Test ◽

Cure Rates

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Progression-Free Survival Prediction in Patients with Nasopharyngeal Carcinoma after Intensity-Modulated Radiotherapy: Machine Learning versus Traditional Statistics

Journal of Personalized Medicine ◽

10.3390/jpm11080787 ◽

2021 ◽

Vol 11 (8) ◽

pp. 787

Author(s):

Ronald Wihal Oei ◽

Yingchen Lyu ◽

Lulu Ye ◽

Fangfang Kong ◽

Chengrun Du ◽

...

Keyword(s):

Machine Learning ◽

Nasopharyngeal Carcinoma ◽

Proportional Hazards ◽

Progression Free Survival ◽

Cox Proportional Hazards ◽

Brier Score ◽

Rank Test ◽

Survival Prediction ◽

Free Survival ◽

Log Rank Test

Background: The Cox proportional hazards (CPH) model is the most commonly used statistical method for nasopharyngeal carcinoma (NPC) prognostication. Recently, machine learning (ML) models are increasingly adopted for this purpose. However, only a few studies have compared the performances between CPH and ML models. This study aimed at comparing CPH with two state-of-the-art ML algorithms, namely, conditional survival forest (CSF) and DeepSurv for disease progression prediction in NPC. Methods: From January 2010 to March 2013, 412 eligible NPC patients were reviewed. The entire dataset was split into training cohort and testing cohort in a ratio of 90%:10%. Ten features from patient-related, disease-related, and treatment-related data were used to train the models for progression-free survival (PFS) prediction. The model performance was compared using the concordance index (c-index), Brier score, and log-rank test based on the risk stratification results. Results: DeepSurv (c-index = 0.68, Brier score = 0.13, log-rank test p = 0.02) achieved the best performance compared to CSF (c-index = 0.63, Brier score = 0.14, log-rank test p = 0.38) and CPH (c-index = 0.57, Brier score = 0.15, log-rank test p = 0.81). Conclusions: Both CSF and DeepSurv outperformed CPH in our relatively small dataset. ML-based survival prediction may guide physicians in choosing the most suitable treatment strategy for NPC patients.

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Group sequential monitoring based on the maximum of weighted log-rank statistics with the Fleming–Harrington class of weights in oncology clinical trials

Statistical Methods in Medical Research ◽

10.1177/0962280220931560 ◽

2020 ◽

Vol 29 (12) ◽

pp. 3525-3532

Author(s):

Thomas J Prior

Keyword(s):

Clinical Trials ◽

Treatment Effect ◽

Proportional Hazards ◽

Rank Test ◽

Event Data ◽

Time To Event ◽

Survival Curves ◽

Delayed Treatment ◽

Time To Event Data ◽

Log Rank Test

Clinical trials in oncology often involve the statistical analysis of time-to-event data such as progression-free survival or overall survival to determine the benefit of a treatment or therapy. The log-rank test is commonly used to compare time-to-event data from two groups. The log-rank test is especially powerful when the two groups have proportional hazards. However, survival curves encountered in oncology studies that differ from one another do not always differ by having proportional hazards; in such instances, the log-rank test loses power, and the survival curves are said to have “non-proportional hazards”. This non-proportional hazards situation occurs for immunotherapies in oncology; immunotherapies often have a delayed treatment effect when compared to chemotherapy or radiation therapy. To correctly identify and deliver efficacious treatments to patients, it is important in oncology studies to have available a statistical test that can detect the difference in survival curves even in a non-proportional hazards situation such as one caused by delayed treatment effect. An attempt to address this need was the “max-combo” test, which was originally described only for a single analysis timepoint; this article generalizes that test to preserve type I error when there are one or more interim analyses, enabling efficacious treatments to be identified and made available to patients more rapidly.

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From the Log-Rank Test to the Cox Proportional Hazards Model

Understanding Biostatistics ◽

10.1002/9781119992677.ch12 ◽

2011 ◽

pp. 317-342

Keyword(s):

Proportional Hazards ◽

Proportional Hazards Model ◽

Cox Proportional Hazards ◽

Cox Proportional Hazards Model ◽

Rank Test ◽

Log Rank Test ◽

Hazards Model

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Systemic Sclerosis is Linked to Psoriasis and May Impact on Patients’ Survival: A Large Cohort Study

Journal of Clinical Medicine ◽

10.3390/jcm8040521 ◽

2019 ◽

Vol 8 (4) ◽

pp. 521 ◽

Cited By ~ 13

Author(s):

Watad ◽

Bragazzi ◽

McGonagle ◽

Damiani ◽

Comaneshter ◽

...

Keyword(s):

Cohort Study ◽

Systemic Sclerosis ◽

Proportional Hazards ◽

Cox Proportional Hazards ◽

Rank Test ◽

Medical Database ◽

Log Rank Test ◽

Kaplan Meier ◽

Large Cohort Study ◽

And Gender

Although skin manifestations are quite common in systemic sclerosis (SSc), a link between SSc and psoriasis (PsO) has been poorly investigated. We assessed the Clalit medical database in a cohort study to compare the prevalence of PsO between SSc-patients and SSc-free controls. We also evaluated the SSc-related autoantibodies’ role in the co-existence of the two conditions. Survival analysis was performed using both univariate (Kaplan–Meier, log-rank test) and multivariate (Cox proportional-hazards technique) analyses. Our cohort of 2,431 SSc-patients was age- and gender-matched with 12,710 controls (case-control match 1:5.2). There were 150 (1.2%) cases of PsO among controls and 47 (1.9%) among SSc-patients (p = 0.0027). A SSc diagnosis was an independent risk factor for PsO with an odds ratio (OR) of 2.16 (95%CI 1.38–3.39, p = 0.0008). Among SSc-patients, 98.6% with PsO were antinuclear antibodies (ANA)-negative. In terms of survival, the mortality rate in SSc-patients with PsO was lower than SSc without PsO (14.9% vs. 26%, p < 0.0001). At the multivariate-analysis, SSc-patients with PsO compared to SSc-patients without PsO had an OR for death of 0.44 (95%CI 0.19–0.99, p < 0.05). SSc is independently associated with PsO. The cases with concurrent PsO and SSc are almost exclusively ANA-negative and may exhibit a better survival.

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A Combined Test for a Generalized Treatment Effect in Clinical Trials with a Time-to-event Outcome

The Stata Journal Promoting communications on statistics and Stata ◽

10.1177/1536867x1701700209 ◽

2017 ◽

Vol 17 (2) ◽

pp. 405-421 ◽

Cited By ~ 4

Author(s):

Patrick Royston

Keyword(s):

Sample Size ◽

Treatment Effect ◽

Sample Size Calculation ◽

Rank Test ◽

P Value ◽

Time To Event ◽

Test Statistic ◽

Potential Threat ◽

Log Rank Test ◽

Combined Test

Most randomized controlled trials with a time-to-event outcome are designed and analyzed assuming proportional hazards of the treatment effect. The sample-size calculation is based on a log-rank test or the equivalent Cox test. Nonproportional hazards are seen increasingly in trials and are recognized as a potential threat to the power of the log-rank test. To address the issue, Royston and Parmar (2016, BMC Medical Research Methodology 16: 16) devised a new “combined test” of the global null hypothesis of identical survival curves in each trial arm. The test, which combines the conventional Cox test with a new formulation, is based on the maximal standardized difference in restricted mean survival time (RMST) between the arms. The test statistic is based on evaluations of RMST over several preselected time points. The combined test involves the minimum p-value across the Cox and RMST-based tests, appropriately standardized to have the correct null distribution. In this article, I outline the combined test and introduce a command, stctest, that implements the combined test. I point the way to additional tools currently under development for power and sample-size calculation for the combined test.

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