Weighted log-rank test for time-to-event data in immunotherapy trials with random delayed treatment effect and cure rate

2018 ◽  
Author(s):  
Shufang Liu ◽  
Chenghao Chu ◽  
Alan Rong
Keyword(s):  
Treatment Effect ◽  
Rank Test ◽  
Event Data ◽  
Cure Rate ◽  
Time To Event ◽  
Delayed Treatment ◽  
Time To Event Data ◽  
Log Rank Test

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 Assessing Long-Term Survival Benefits of Immune Checkpoint Inhibitors Using the Net Survival Benefit

2019 ◽  
Vol 111 (11) ◽  
pp. 1186-1191 ◽  
Author(s):  
Julien Péron ◽  
Alexandre Lambert ◽  
Stephane Munier ◽  
Brice Ozenne ◽  
Joris Giai ◽  
...  
Keyword(s):  
Treatment Effect ◽  
Survival Benefit ◽  
Rank Test ◽  
Cure Rate ◽  
Term Survival ◽  
Long Term Survival ◽  
Delayed Treatment ◽  
Net Survival ◽  
Log Rank Test

Abstract Background The treatment effect in survival analysis is commonly quantified as the hazard ratio, and tested statistically using the standard log-rank test. Modern anticancer immunotherapies are successful in a proportion of patients who remain alive even after a long-term follow-up. This new phenomenon induces a nonproportionality of the underlying hazards of death. Methods The properties of the net survival benefit were illustrated using the dataset from a trial evaluating ipilimumab in metastatic melanoma. The net survival benefit was then investigated through simulated datasets under typical scenarios of proportional hazards, delayed treatment effect, and cure rate. The net survival benefit test was computed according to the value of the minimal survival difference considered clinically relevant. As comparators, the standard and the weighted log-rank tests were also performed. Results In the illustrative dataset, the net survival benefit favored ipilimumab [Δ(0) = 15.8%, 95% confidence interval = 4.6% to 27.3%, P = .006]. This favorable effect was maintained when the analysis was focused on long-term survival differences (eg, >12 months, Δ(12) = 12.5% (95% confidence interval = 4.4% to 20.6%, P = .002). Under the scenarios of a delayed treatment effect and cure rate, the power of the net survival benefit test compared favorably to the standard log-rank test power and was comparable to the power of the weighted log-rank test for large values of the threshold of clinical relevance. Conclusion The net long-term survival benefit is a measure of treatment effect that is meaningful whether or not hazards are proportional. The associated statistical test is more powerful than the standard log-rank test when a delayed treatment effect is anticipated.

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

2017 ◽  
Vol 17 (2) ◽  
pp. 405-421 ◽  
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.

Bayesian Phase II optimization for time-to-event data based on historical information

2017 ◽  
Vol 28 (4) ◽  
pp. 1272-1289
Author(s):  
Anja Bertsche ◽  
Frank Fleischer ◽  
Jan Beyersmann ◽  
Gerhard Nehmiz
Keyword(s):  
Phase Ii ◽  
Treatment Effect ◽  
Control Treatment ◽  
Design Parameters ◽  
Proof Of Concept ◽  
Event Data ◽  
Time To Event ◽  
Historical Information ◽  
Time To Event Data ◽  
The Right

After exploratory drug development, companies face the decision whether to initiate confirmatory trials based on limited efficacy information. This proof-of-concept decision is typically performed after a Phase II trial studying a novel treatment versus either placebo or an active comparator. The article aims to optimize the design of such a proof-of-concept trial with respect to decision making. We incorporate historical information and develop pre-specified decision criteria accounting for the uncertainty of the observed treatment effect. We optimize these criteria based on sensitivity and specificity, given the historical information. Specifically, time-to-event data are considered in a randomized 2-arm trial with additional prior information on the control treatment. The proof-of-concept criterion uses treatment effect size, rather than significance. Criteria are defined on the posterior distribution of the hazard ratio given the Phase II data and the historical control information. Event times are exponentially modeled within groups, allowing for group-specific conjugate prior-to-posterior calculation. While a non-informative prior is placed on the investigational treatment, the control prior is constructed via the meta-analytic-predictive approach. The design parameters including sample size and allocation ratio are then optimized, maximizing the probability of taking the right decision. The approach is illustrated with an example in lung cancer.

scholarly journals A new modeling and inference approach for the Systolic Blood Pressure Intervention Trial outcomes

2018 ◽  
Vol 15 (3) ◽  
pp. 305-312 ◽  
Author(s):  
Song Yang ◽  
Walter T Ambrosius ◽  
Lawrence J Fine ◽  
Adam P Bress ◽  
William C Cushman ◽  
...  
Keyword(s):  
Treatment Effect ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Rank Test ◽  
Time To Event ◽  
New Approach ◽  
New Methods ◽  
Log Rank Test ◽  
Hazards Model ◽  
Average Hazard Ratio

Background/aims In clinical trials with time-to-event outcomes, usually the significance tests and confidence intervals are based on a proportional hazards model. Thus, the temporal pattern of the treatment effect is not directly considered. This could be problematic if the proportional hazards assumption is violated, as such violation could impact both interim and final estimates of the treatment effect. Methods We describe the application of inference procedures developed recently in the literature for time-to-event outcomes when the treatment effect may or may not be time-dependent. The inference procedures are based on a new model which contains the proportional hazards model as a sub-model. The temporal pattern of the treatment effect can then be expressed and displayed. The average hazard ratio is used as the summary measure of the treatment effect. The test of the null hypothesis uses adaptive weights that often lead to improvement in power over the log-rank test. Results Without needing to assume proportional hazards, the new approach yields results consistent with previously published findings in the Systolic Blood Pressure Intervention Trial. It provides a visual display of the time course of the treatment effect. At four of the five scheduled interim looks, the new approach yields smaller p values than the log-rank test. The average hazard ratio and its confidence interval indicates a treatment effect nearly a year earlier than a restricted mean survival time–based approach. Conclusion When the hazards are proportional between the comparison groups, the new methods yield results very close to the traditional approaches. When the proportional hazards assumption is violated, the new methods continue to be applicable and can potentially be more sensitive to departure from the null hypothesis.

scholarly journals Power and sample-size analysis for the Royston–Parmar combined test in clinical trials with a time-to-event outcome

2018 ◽  
Vol 18 (1) ◽  
pp. 3-21 ◽  
Author(s):  
Patrick Royston
Keyword(s):  
Sample Size ◽  
Treatment Effect ◽  
Null Hypothesis ◽  
Sample Size Calculation ◽  
Rank Test ◽  
Size Analysis ◽  
Time To Event ◽  
Log Rank Test ◽  
Sample Size Calculations ◽  
Combined Test

Randomized controlled trials with a time-to-event outcome are usually designed and analyzed assuming proportional hazards (PH) of the treatment effect. The sample-size calculation is based on a log-rank test or the nearly identical Cox test, henceforth called the Cox/log-rank test. Nonproportional hazards (non-PH) has become more common in trials and is recognized as a potential threat to interpreting the trial treatment effect and the power of the log-rank test—hence to the success of the trial. To address the issue, in 2016, Royston and Parmar ( BMC Medical Research Methodology 16: 16) proposed a “combined test” of the global null hypothesis of identical survival curves in each trial arm. The Cox/log-rank test is combined with a new test derived from the maximal standardized difference in restricted mean survival time (RMST) between the trial arms. The test statistic is based on evaluations of the between-arm difference in RMST over several preselected time points. The combined test involves the minimum p-value across the Cox/log-rank and RMST-based tests, appropriately standardized to have the correct distribution under the global null hypothesis. In this article, I introduce a new command, power_ct, that uses simulation to implement power and sample-size calculations for the combined test. power_ct supports designs with PH or non-PH of the treatment effect. I provide examples in which the power of the combined test is compared with that of the Cox/log-rank test under PH and non-PH scenarios. I conclude by offering guidance for sample-size calculations in time-to-event trials to allow for possible non-PH.

Approximate Bayesian inference for joint linear and partially linear modeling of longitudinal zero-inflated count and time to event data

2021 ◽  
pp. 096228022110028
Author(s):  
T Baghfalaki ◽  
M Ganjali
Keyword(s):  
Linear Model ◽  
Joint Modeling ◽  
Partially Linear Model ◽  
Event Data ◽  
Time To Event ◽  
Data Set ◽  
Partially Linear ◽  
Time To Event Data ◽  
Count Response ◽  
Approximate Bayesian

Joint modeling of zero-inflated count and time-to-event data is usually performed by applying the shared random effect model. This kind of joint modeling can be considered as a latent Gaussian model. In this paper, the approach of integrated nested Laplace approximation (INLA) is used to perform approximate Bayesian approach for the joint modeling. We propose a zero-inflated hurdle model under Poisson or negative binomial distributional assumption as sub-model for count data. Also, a Weibull model is used as survival time sub-model. In addition to the usual joint linear model, a joint partially linear model is also considered to take into account the non-linear effect of time on the longitudinal count response. The performance of the method is investigated using some simulation studies and its achievement is compared with the usual approach via the Bayesian paradigm of Monte Carlo Markov Chain (MCMC). Also, we apply the proposed method to analyze two real data sets. The first one is the data about a longitudinal study of pregnancy and the second one is a data set obtained of a HIV study.

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