A weighted log-rank test for comparing two survival curves

2020 ◽  
Vol 26 (3) ◽  
pp. 253-262
Author(s):  
Seung-Hwan Lee ◽  
Eun-Joo Lee
Keyword(s):  
Weight Function ◽  
Real World ◽  
Null Hypothesis ◽  
New Method ◽  
Rank Test ◽  
Survival Curves ◽  
Rank Tests ◽  
Asymptotically Normal ◽  
Real World Application ◽  
Log Rank Test

AbstractThis paper proposes a weighted log-rank test that maintains sensitivity to realistic alternatives of two survival curves, such as crossing curves, in the presence of heavy censoring. The new test incorporates a weight function that changes over the censoring level, increasing adaptivity and flexibility of the commonly used weighted log-rank tests. The new statistic is asymptotically normal under the null hypothesis that there is no difference in survival between two groups. The performances of the new test are evaluated via simulations under both proportional and non-proportional alternatives. We illustrate the new method with a real-world application.

scholarly journals Non-vitamin K Oral Anticoagulants and Anti-seizure Medications: A Retrospective Cohort Study

2021 ◽  
Vol 11 ◽  
Author(s):  
Chen-Jui Ho ◽  
Shih-Hsuan Chen ◽  
Chih-Hsiang Lin ◽  
Yan-Ting Lu ◽  
Che-Wei Hsu ◽  
...  
Keyword(s):  
Ischemic Stroke ◽  
Real World ◽  
Recurrent Stroke ◽  
Oral Anticoagulants ◽  
Rank Test ◽  
Potential Ddis ◽  
Survival Curves ◽  
Log Rank Test ◽  
Kaplan Meier ◽  
Real World Situation

Purpose: Concerns of drug–drug interactions (DDIs) between anti-seizure medications (ASMs) and non-vitamin K oral anticoagulants (NOACs) have emerged in recent case reports and guidelines. Theoretically, the induction of hepatic cytochrome P450 3A4 (CYP3A4) enzyme and permeability glycoprotein (P-GP) efflux transporter protein systems may reduce the effect of NOACs. We aimed to investigate whether such DDIs are clinically relevant in a real-world situation.Methods: We retrospectively reviewed 320 ischemic stroke patients with atrial fibrillation (Af) and grouped them according to different potential interactions with CYP3A4 and P-GP. Ischemic stroke events, transient ischemic attack (TIA) events, follow-up duration, baseline characteristics, concomitant ASMs, and stroke risk factors were collected. Statistical analysis included Kaplan–Meier survival curves and the log-rank test.Results: Overall, 320 ischemic stroke with Af patients received NOACs. Among the NOAC users, 75 also took ASMs, including 56 that have potential DDIs: 43 (13.4%) were categorized as potential CYP and P-GP DDIs and 13 (4.1%) as P-GP-only DDIs. The remaining 264 (82.5%) patients were used as controls including 19 exposed to nonsignificant DDI ASMs and 245 patients without ASM exposure. The incidence rates of recurrent stroke/TIA events in both CYP3A4 and P-GP DDIs, P-GP DDIs only, and no DDIs were 7.5, 2.1, and 8.4/100 person-years, respectively. Kaplan–Meier survival curves and the log-rank test did not show significant differences among the groups.Conclusions: The recurrent stroke rate of NOAC users with potential DDIs was not higher than in those without potential DDIs in this single-institute study. Our results suggest that theoretical interactions between ASMs and NOACs may not be as severe as previously thought in a real-world situation.

Histologic Grade Predicts Recurrence for Marginally Excised Canine Subcutaneous Soft Tissue Sarcomas

2009 ◽  
Vol 46 (5) ◽  
pp. 928-933 ◽  
Author(s):  
K. D. McSporran
Keyword(s):  
Soft Tissue ◽  
Local Recurrence ◽  
Tumor Recurrence ◽  
Soft Tissue Sarcomas ◽  
Rank Test ◽  
Survival Curves ◽  
Marginal Excision ◽  
Log Rank Test ◽  
Kaplan Meier ◽  
Grade 3

Local recurrence of marginally excised subcutaneous soft tissue sarcomas is variable and difficult to predict. This study aimed to identify predictors of local recurrence after excisional biopsy. Medical records of 236 dogs from which tumors had been received between 2004 and 2007 were analyzed. Medium- to large-breed dogs, median age 10 years, were most commonly affected. A total of 139 tumors were graded histologically: 71 were grade 1 (51%); 59, grade 2 (42%); and 9, grade 3 (7%). Of these, 34 tumors (25%) were completely excised, and 104 (75%) were marginally excised. None of 30 completely excised tumors with follow-up information recurred. Three of 41 grade 1 tumors (7%), 14 of 41 grade 2 tumors (34%), and 3 out of 4 grade 3 tumors recurred after marginal excision. Kaplan-Meier survival curves were generated to evaluate survival and the tumor-free interval. The log-rank test and log-rank test for trend were used for comparisons. Tumor recurrence-free intervals for dogs with grade 1 and 2 tumors and for those with grade 1 and 3 tumors differed significantly ( P = .0027 and .0001, respectively) and overall were inversely related to tumor grade ( P = .0007). Kaplan-Meier survival curves, regardless of recurrence, for patients with grade 1, 2, or 3 tumors treated by marginal excision did not differ significantly, and none differed from the survival curves of patients treated by complete excision. In conclusion, histologic grade is a strong predictor for recurrence of marginally excised subcutaneous soft tissue sarcomas. Clean margins predict nonrecurrence. Tumor recurrence did not significantly reduce survival time.

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

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.

scholarly journals Crossing survival curves: alternatives to the log-rank test

Trials ◽  
2011 ◽  
Vol 12 (S1) ◽  
Author(s):  
George Bouliotis ◽  
Lucinda Billingham
Keyword(s):  
Rank Test ◽  
Survival Curves ◽  
Log Rank Test

scholarly journals Real-world survival outcomes with immune checkpoint inhibitors in large-cell neuroendocrine tumors of lung

2021 ◽  
Vol 9 (2) ◽  
pp. e001999
Author(s):  
Elizabeth Dudnik ◽  
Samuel Kareff ◽  
Mor Moskovitz ◽  
Chul Kim ◽  
Stephen V Liu ◽  
...  
Keyword(s):  
Real World ◽  
Immune Checkpoint ◽  
Immune Checkpoint Inhibitors ◽  
Checkpoint Inhibitors ◽  
Eastern Cooperative Oncology Group ◽  
Large Cell ◽  
Disease Diagnosis ◽  
Small Sample ◽  
Rank Test ◽  
Log Rank Test

BackgroundLittle is known regarding the efficacy of immune checkpoint inhibitors (ICI) in patients with advanced large-cell neuroendocrine lung carcinoma (aLCNEC).Methods125 consecutive patients with aLCNEC were identified in the electronic databases of 4 participating cancer centers. The patients were divided into group A (patients who received ICI, n=41) and group B (patients who did not receive ICI, n=84). Overall survival since advanced disease diagnosis (OS DX) and OS since ICI initiation (OS ICI) were captured.ResultsWith a median follow-up of 11.8 months (mo) (IQR 7.5–17.9) and 6.0mo (IQR 3.1–10.9), 66% and 76% of patients died in groups A and B, respectively. Median OS DX was 12.4mo (95% CI 10.7 to 23.4) and 6.0mo (95% CI 4.7 to 9.4) in groups A and B, respectively (log-rank test, p=0.02). For ICI administration, HR for OS DX was 0.59 (95% CI 0.38 to 0.93, p=0.02—unadjusted), and 0.58 (95% CI 0.34 to 0.98, p=0.04—adjusted for age, Eastern Cooperative Oncology Group (ECOG) performance status (PS), presence of liver metastases and chemotherapy administration). In a propensity score matching analysis (n=74; 37 patients in each group matched for age and ECOG PS), median OS DX was 12.5 mo (95% CI 10.6 to 25.2) and 8.4 mo (95% CI 5.4 to 16.9) in matched groups A and B, respectively (log-rank test, p=0.046). OS ICI for patients receiving ICI as monotherapy (n=36) was 11.0 mo (95% CI 6.1 to 19.4).ConclusionsWith the limitations of retrospective design and small sample size, the results of this real-world cohort analysis suggest a positive impact of ICI on OS in aLCNEC.

Doubly robust weighted log-rank tests and Renyi-type tests under non-random treatment assignment and dependent censoring

2018 ◽  
Vol 28 (9) ◽  
pp. 2649-2664
Author(s):  
Chenxi Li
Keyword(s):  
Dependent Censoring ◽  
Rank Test ◽  
Rank Tests ◽  
Data Set ◽  
Treatment Assignment ◽  
Treatment Groups ◽  
Event Time ◽  
Log Rank Test ◽  
Doubly Robust ◽  
Log Rank Tests

The log-rank test is widely used to test difference in event time distribution between treatment groups. However, if subjects are not randomly assigned to treatment groups, which is often the case in observation studies, the log-rank test is not asymptotically correct for detecting group survival difference due to the imbalance of confounding variables between groups. We develop a class of modified weighted log-rank tests and Renyi-type tests for two-sample survival comparison under non-random treatment assignment. The new tests can also account for non-random censoring that depends on baseline covariates. The proposed methods involve building working models for treatment assignment, cause-specific hazard of dependent censoring, and the time to event. We prove that, when either the models for treatment assignment and dependent censoring or the model for the event time is true, the new tests are asymptotically correct, i.e. being doubly robust. Numerical experiments demonstrate the tests’ double-robustness property in finite samples of realistic sizes, and also show that the doubly robust log-rank test is at least as powerful as the regular log-rank test when the treatment assignment is random and there is no dependent censoring. An application to a kidney transplant data set illustrates the utility of the proposed methods.

scholarly journals Survival Comparability Between Thalassemia Major Versus Thalassemia Intermedia

Blood ◽  
2015 ◽  
Vol 126 (23) ◽  
pp. 2141-2141
Author(s):  
Angela Vitrano ◽  
Giuseppina Calvaruso ◽  
Eliana Lai ◽  
Grazia Colletta ◽  
Alessandra Quota ◽  
...  
Keyword(s):  
Causes Of Death ◽  
Thalassemia Major ◽  
Rank Test ◽  
P Value ◽  
Thalassemia Intermedia ◽  
Survival Curves ◽  
Risk Of Death ◽  
Log Rank Test ◽  
Kaplan Meier ◽  
Before And After

Abstract Introduction. In the last few decades, the life expectancy of Thalassemia Major (TM) patients has progressively been increasing. The improvement can be due to several factors, including introduction of chelation treatment (Deferoxamine 1965, Deferiprone 1987, Deferasirox 2006), screening of blood for the most common viral agents, aggressive treatment of infection and improved treatment of cardiac complications. However, no comparative survival curves between TM versus Thalassemia Intermedia (TI) have been so far reported. Moreover, no data on life expectancy, after introduction of chelation treatment have been described. Methods. Data coming from several randomized clinical trials, carried ahead by Campus of Hematology Franco and Piera Cutino-A.O.O.R Villa Sofia-V. Cervello, Palermo (Italy), were retrospectively considered for this study. Primary goal of the study was to provide evidence of possible differences in survival curves between TM versus TI. Survival curves in TM versus TI patients were compared using Kaplan-Meier method and the log-rank test before and after the introduction of Deferoxamine (DFO) (1965). Moreover, Cox regression model was even used to explore risk of death between the two diagnoses. Each dead patient was observed from its birth to its death, and each alive patient was observed from its birth to June 30, 2015. Results. Three hundred seventy-nine patients with TM (n=284, dead 40) and TI (n=95, dead 13) entered into the study. Males were 50.7% of this cohort of patients. Among the cohort of dead patients, 15% (6/40) TM and 76.9% (10/13) TI patients were born before introduction of DFO (1965) . The mean age survival was 50.6 (SE 0.9) and 70.6 (SE 1.7) for TM and TI, respectively. Table 1 shows the main causes of death. In TM patients the most common causes of death were heart damage (16 cases, 40%, Tab. 1), followed by cancer (3 cases, 7.5%, Tab. 1), liver cirrhosis (3 cases, 7.5%, Tab. 1) and infections (3 cases, 7.5%, Tab. 1). In TI patients the most common causes of death were cancer (2 cases, 38.5%, Tab. 1), followed by infections (3 cases, 23.1% , Tab. 1), heart damage (2 case, 15.4%, Tab. 1). Kaplan-Meir curves showed statistically significant difference in TM versus TI survival (log-rank test, p- value<0.0001; Figure 1A). Survival was higher for TI subjects (median age was 73.6 years). Cox regression models of TM versus TI suggested that risk of death for TM patients was 6.8 times higher than TI patients (HR 6.8 (3.3), p- value<0.0001). However, the introduction of chelation treatment (DFO, 1965), changed the Kaplan-Meier curves showing that there was not statistically significant difference between TM versus TI patients in life expectancy ( log-rank test, p- value=0.086; Fig. 1B). Conclusion. These results suggest as TM survival, after the introduction of chelation treatment, improved so much that nowadays it is not different in comparison with TI one's. Moreover, the TM risk of death has been decreased from 6.8 to 2.8 (Cox Model HR 2.8 (1.7), p- value=0.099). These findings, if further confirmed, suggest as, in Western countries, our approach for genetic counselling of "at risk couples" for TM should be reconsidered. Table 1. Causes of death in Thalassemia Major and Thalassemia Intermedia patients. Diagnosis Causes of Death TM n (%) TI n (%) Cancer 3 (7,5) 5 (38,5) Heart Damage 16 (40,0) 2 (15,4) Infection 3 (7,5) 3 (23,1) Multi Organ Failure 1 (2,5) 0 (0,0) Stroke 1 (2,5) 0 (0,0) Liver Failure 3 (7,5) 1 (7,7) Not Available 11 (27,5) 1 (7,7) Other complications not related to Thalassemia 2 (5,0) 1 (7,7) Total 13 40 Figure 1. Kaplan-Meier Survival curves of Thalassemia Major versus Thalassemia Intermedia patients before and after the introduction of chelation treatment (DFO, 1965). Figure 1. Kaplan-Meier Survival curves of Thalassemia Major versus Thalassemia Intermedia patients before and after the introduction of chelation treatment (DFO, 1965). Disclosures Pepe: Chiesi: Speakers Bureau; ApoPharma Inc: Speakers Bureau; Novartis: Speakers Bureau.

Event-specific win ratios and testing with terminal and non-terminal events

2020 ◽  
pp. 174077452097240
Author(s):  
Song Yang ◽  
James Troendle
Keyword(s):  
Clinical Trials ◽  
Treatment Effect ◽  
Null Hypothesis ◽  
Rank Test ◽  
Terminal Event ◽  
Log Rank Test ◽  
Maximum Test ◽  
Terminal Events ◽  
Different Types ◽  
Ratio Approach

Background/aims In clinical trials, the primary outcome is often a composite endpoint defined as time to the first occurrence of either death or certain non-fatal events. Thus, a portion of available data would be omitted. In the win ratio approach, priorities are given to the clinically more important events, and more data are used. However, its power may be low if the treatment effect is predominantly on the non-terminal event. Methods We propose event-specific win ratios obtained separately on the terminal and non-terminal events. They can then be used to form global tests such as a linear combination test, the maximum test, or a [Formula: see text] test. Results In simulations, these tests often improve the power of the original win ratio test. Furthermore, when the terminal and non-terminal events experience differential treatment effects, the new tests are often more powerful than the log-rank test for the composite outcome. Whether the treatment effect is primarily on the terminal events or not, the new tests based on the event-specific win ratios can be useful when different types of events are present. The new tests can reject the null hypothesis of no difference in the event distributions in the two treatment arms with the terminal event showing detrimental effect and the non-terminal event showing beneficial effect. The maximum test and the [Formula: see text] test do not have test-estimation coherency, but the maximum test has the coherency that the global null is rejected if and only if the null for one of the event types is rejected. When applied to data from the trial Aldosterone Antagonist Therapy for Adults With Heart Failure and Preserved Systolic Function (TOPCAT), the new tests all reject the null hypothesis of no treatment effect while both the log-rank test used in TOPCAT and the original win ratio approach show non-significant p-values. Conclusion Whether the treatment effect is primarily on the terminal events or the non-terminal events, the maximum test based on the event-specific win ratios can be a useful alternative for testing treatment effect in clinical trials with time-to-event outcomes when different types of events are present.

The prognostic significance of lymphatic invasion in primary melanoma

2009 ◽  
Vol 27 (15_suppl) ◽  
pp. 9050-9050
Author(s):  
X. Xu ◽  
L. Chen ◽  
W. Hwang ◽  
P. Dawson ◽  
D. Guerry ◽  
...  
Keyword(s):  
Prognostic Factor ◽  
Prognostic Significance ◽  
Primary Melanoma ◽  
Risk Groups ◽  
Lymphatic Invasion ◽  
Independent Prognostic Factor ◽  
Rank Test ◽  
Survival Curves ◽  
Cox Models ◽  
Log Rank Test

9050 Background: Lymphatic invasion (LI) is an under-observed phenomenon in primary malignancies that can be better detected by immunostaining and that may associate with prognosis. In this study we sought to test the hypothesis that LI was associated with melanoma-specific survival (MSS) and was an independent prognostic factor. Methods: This study included 277 patients with stage I/II melanomas in vertical growth phase (VGP) who had at least 10 years of follow up. The log-rank test was used to test the study hypothesis - 72 melanoma-specific deaths were needed for 80% power to detect an odds ratio of 2.1. Paraffin sections were stained with antibodies to podoplanin (lymphatic vessels) and S-100 (melanoma cells) to identify LI. Univariate and multivariate Cox models were used to evaluate the prognostic significance of LI. An independent cohort of 106 similar patients was used for validation of the 10-year MSS rates. Results: LI was observed in 44.5% (95% CI: 38.6% - 50.4%) of the melanomas and its presence was significantly associated with thickness, mitotic rate, gender, age, and ulceration (U). The Kaplan-Meier survival curves for those with and without LI were significantly different (log-rank test p=0.022). The final multivariate model for time to MSD identified 4 independent prognostic factors: thickness (HR=1.5, p<0.001), U (HR=2.2 p=0.013), site (HR=3.9, p<0.001) and LI (HR=1.9, p=0.015). These factors were used to define a prognostic tree with 5 risk groups defined by melanomas that were thin (≤1.0mm) with no LI or U; thin with LI but no U; 1–3mm with no U; 1–3mm with U; and >3mm. Respectively, MSS rates were 100%, 88.6%, 77%, 48% and 42%. In the validation set, observed 10-year MSS rates in each risk group were not significantly different from those predicted from the survival curves for the tree-based risk groups. Conclusions: LI is an independent prognostic factor for MSS. Among patients with thin melanomas without U the 10-year MSS was lower for those patients with LI (89%, 95% CI=78% - 99%; n=41) compared to those without (100%, n=78). LI is an important prognostic factor that needs further validation in a population of patients from the sentinel node biopsy era. No significant financial relationships to disclose.

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