Correcting for Noncompliance and Dependent Censoring in an AIDS Clinical Trial with Inverse Probability of Censoring Weighted (IPCW) 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.

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

Statistical Methods in Medical Research ◽

10.1177/0962280220988570 ◽

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.

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Targeted Minimum Loss-Based Estimation of Causal Effects in Right-Censored Survival Data with Time-Dependent Covariates: Warfarin, Stroke, and Death in Atrial Fibrillation

Journal of Causal Inference ◽

10.1515/jci-2013-0001 ◽

2013 ◽

Vol 1 (2) ◽

pp. 235-254 ◽

Cited By ~ 4

Author(s):

Jordan C. Brooks ◽

Mark J. van der Laan ◽

Daniel E. Singer ◽

Alan S. Go

Keyword(s):

Survival Data ◽

Causal Effect ◽

Estimating Equation ◽

Dependent Censoring ◽

Time Dependent ◽

Causal Effects ◽

Consistent Estimation ◽

Censored Survival Data ◽

Inverse Probability ◽

Time Dependent Covariates

AbstractCausal effects in right-censored survival data can be formally defined as the difference in the marginal cumulative event probabilities under particular interventions. Conventional estimators, such as the Kaplan-Meier (KM), fail to consistently estimate these marginal parameters under dependent treatment assignment or dependent censoring. Several modern estimators have been developed that reduce bias under both dependent treatment assignment and dependent censoring by incorporating information from baseline and time-dependent covariates. In the present article we describe a recently developed targeted minimum loss-based estimation (TMLE) algorithm for general longitudinal data structures and present in detail its application in right-censored survival data with time-dependent covariates. The treatment-specific marginal cumulative event probability is defined via a series of iterated conditional expectations in a time-dependent counting process framework. The TMLE involves an initial estimator of each conditional expectation and sequentially updates these such that the resulting estimator solves the efficient influence curve estimating equation in the nonparametric statistical model. We describe the assumptions required for consistent estimation of statistical parameters and additional assumptions required for consistent estimation of the causal effect parameter. Using simulated right-censored survival data, the mean squared error, bias, and 95% confidence interval coverage probability of the TMLE is compared with those of the conventional KM and the inverse probability of censoring weight estimating equation, conventional maximum likelihood substitution estimator, and the double robustaugmented inverse probability of censoring weighted estimating equation. We conclude the article with estimation of the causal effect of warfarin medical therapy on the probability of “stroke or death” within a 1-year time frame using data from the ATRIA-1 observational cohort of persons with atrial fibrillation. Our results suggest that a fixed policy of warfarin treatment for all patients would result in 2% fewer deaths or strokes within 1-year as compared with a policy of withholding warfarin from all patients.

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Nonparametric generalized fiducial inference for survival functions under censoring

Biometrika ◽

10.1093/biomet/asz016 ◽

2019 ◽

Vol 106 (3) ◽

pp. 501-518 ◽

Cited By ~ 2

Author(s):

Y Cui ◽

J Hannig

Keyword(s):

Confidence Intervals ◽

Average Length ◽

Asymptotic Methods ◽

Survival Function ◽

Right Censoring ◽

Rank Tests ◽

Fiducial Inference ◽

Fiducial Distribution ◽

Von Mises ◽

Log Rank Tests

Summary Since the introduction of fiducial inference by Fisher in the 1930s, its application has been largely confined to relatively simple, parametric problems. In this paper, we present what might be the first time fiducial inference is systematically applied to estimation of a nonparametric survival function under right censoring. We find that the resulting fiducial distribution gives rise to surprisingly good statistical procedures applicable to both one-sample and two-sample problems. In particular, we use the fiducial distribution of a survival function to construct pointwise and curvewise confidence intervals for the survival function, and propose tests based on the curvewise confidence interval. We establish a functional Bernstein–von Mises theorem, and perform thorough simulation studies in scenarios with different levels of censoring. The proposed fiducial-based confidence intervals maintain coverage in situations where asymptotic methods often have substantial coverage problems. Furthermore, the average length of the proposed confidence intervals is often shorter than the length of confidence intervals for competing methods that maintain coverage. Finally, the proposed fiducial test is more powerful than various types of log-rank tests and sup log-rank tests in some scenarios. We illustrate the proposed fiducial test by comparing chemotherapy against chemotherapy combined with radiotherapy, using data from the treatment of locally unresectable gastric cancer.

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Log-rank tests for censored clustered data under generalized randomized block design: Saddlepoint approximation

Journal of Biopharmaceutical Statistics ◽

10.1080/10543406.2020.1858310 ◽

2020 ◽

pp. 1-10

Author(s):

Abd El-Raheem M. Abd El-Raheem ◽

Ehab F. Abd-Elfattah

Keyword(s):

Clustered Data ◽

Block Design ◽

Saddlepoint Approximation ◽

Rank Tests ◽

Randomized Block Design ◽

Log Rank Tests

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Association of SPARC expression with metastatic progression and prostate cancer-specific mortality after radical prostatectomy.

Journal of Clinical Oncology ◽

10.1200/jco.2013.31.15_suppl.5071 ◽

2013 ◽

Vol 31 (15_suppl) ◽

pp. 5071-5071

Author(s):

Claudio Jeldres ◽

Richard Bruce Johnston ◽

Christopher R. Porter ◽

Peter Nelson

Keyword(s):

Prostate Cancer ◽

Radical Prostatectomy ◽

Cox Regression ◽

Metastatic Progression ◽

Rank Tests ◽

Cancer Specific Survival ◽

Cytoplasmic Staining ◽

Sparc Expression ◽

Log Rank Tests

5071 Background: We assessed the expression of the glycoprotein SPARC (secreted protein, acidic, rich in cysteine) in patients with prostate cancer (PCa) treated with radical prostatectomy (RP) and studied its association with adverse clinico-pathological features at RP and long-term clinical outcomes, such as metastatic progression after surgery and cancer-specific death. Methods: Tissues from 78 patients with PCa were used to quantify SPARC expression using tissue microarray (TMA) and immunohistochemistry techniques (IHC). Anti-SPARC mouse monoclonal antibody were use to target the protein and for each patients 4 samples of tissue were used for cytoplasmic staining. Staining of each core was reviewed by an uropathologist who assigned a score (score 0-3) to each core and a global score also assigned to each patient (score 0-3). Analyses of the data relied in cross tables, T-test analyses, survival plots and Cox regression models. Results: Higher expression of SPARC protein was recorded in patients who develop metastases during follow-up after RP (p=0.025) and in patients who died of PCa after RP (p=0.002). Median follow-up of the cohort was 9.3 years after RP. At 5 years, 95.5%, 92.0% and 89.3% of patients were metastases-free for SPARC expression score 1, 2 and 3 respectively. For the same categories, 10 years after RP, 82.2%, 77.0% and 69.9% were metastases-free (Log-rank tests all p≤0.05). Similarly, patients with high SPARC expression had worse cancer-specific survival at 5 and 10 years after RP compared to those with low SPARC expression (Log-rank tests all p≤0.01 when score 1 was compared to score 2 or score 3). Finally, advanced stage at RP (T3-T4) [p=0.04] and high Gleason sum (8-10) [p=0.02] were also associated with higher expression of SPARC. Conclusions: High SPARC expression was associated with worse outcomes in men with prostate cancer treated with radical prostatectomy. Men who developed metastatic disease and men who succumbed to prostate cancer had higher levels of SPARC at radical prostatectomy than their counterpart. SPARC may have an important role in the progression of the disease and may eventually help clinician to better ascertain the risk of progression of the disease.

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