Comparing two hazard curves when there is a treatment time-lag effect.

In cancer and other medical studies, time-to-event (eg, death) data are common. One major task to analyze time-to-event (or survival) data is usually to compare two medical interventions (eg, a treatment and a control) regarding their effect on patients' hazard to have the event in concern. In such cases, we need to compare two hazard curves of the two related patient groups. In practice, a medical treatment often has a time-lag effect, that is, the treatment effect can only be observed after a time period since the treatment is applied. In such cases, the two hazard curves would be similar in an initial time period, and the traditional testing procedures, such as the log-rank test, would be ineffective in detecting the treatment effect because the similarity between the two hazard curves in the initial time period would attenuate the difference between the two hazard curves that is reflected in the related testing statistics. In this paper, we suggest a new method for comparing two hazard curves when there is a potential treatment time-lag effect based on a weighted log-rank test with a flexible weighting scheme. The new method is shown to be more effective than some representative existing methods in various cases when a treatment time-lag effect is present.

Beyond hazard ratios: appropriate statistical methods for quantifying the clinical effectiveness of immune-oncology therapies - the example of the Netherlands.

BACKGROUND: The Dutch Committee for the Evaluation of Oncological Drugs evaluates the effectiveness of new oncological treatments. The committee compares survival endpoints to the so-called PASKWIL-2023 criteria for palliative treatments, which define if treatment effects are considered clinically relevant. A positive recommendation depends on whether the median overall survival (OS) is below or above 12 months in the comparator arm. If the former applies, an OS benefit of at least 12 weeks, and a hazard ratio (HR) smaller than 0.7 are required. If the latter applies, an OS or progression free survival (PFS) benefit of at least 16 weeks, and an HR smaller than 0.7 are required. Nonetheless, the median survival time may not be reached and the proportional hazards (PH) assumption, quantified by the HR, is likely violated for immuno-oncology (IO) therapies, deeming these criteria inappropriate. METHODS: We conducted a systematic literature review to identify statistical methods used to represent the clinical effectiveness of IO therapies based on trial data. We searched MEDLINE and EMBASE databases from inception to August 31, 2022, limited to English papers. Methodological studies, randomized controlled trials, and discussion papers recognising key issues of survival data analysis of IO therapies were eligible for inclusion. RESULTS: A total of 1,035 unique references were identified. After full paper screening, 17 publications were included in the review. Additionally, 43 papers were identified through 'snowballing'. We conclude that the current PASKWIL-2023 criteria are methodologically incorrect under non-PH. In that case, single summary statistics fail to capture the treatment effect and any measure should be interpreted in combination with the Kaplan-Meier curves. We recommend 'parameter-free' measures, such as the difference in restricted mean survival time, avoiding assumptions on the underlying survival. CONCLUSIONS: The HR is commonly used to assess treatment effectiveness, without investigating the validity of the PH assumption. This happens with the application of the PASKWIL-2023 criteria for palliative oncology treatments, which can only be valid under a PH setting. Under non-PH, alternative treatment effect measures are suggested. We propose a step-by-step approach supporting the choice of the most appropriate methods to quantify treatment effectiveness that can be used to redefine the PASKWIL-2023 criteria, or similar criteria in other clinical areas.

Comparison between asymptotic and re-randomisation tests under non-proportional hazards in a randomised controlled trial using the minimisation method.

BACKGROUND: Pocock-Simon's minimisation method has been widely used to balance treatment assignments across prognostic factors in randomised controlled trials (RCTs). Previous studies focusing on the survival outcomes have demonstrated that the conservativeness of asymptotic tests without adjusting for stratification factors, as well as the inflated type I error rate of adjusted asymptotic tests conducted in a small sample of patients, can be relaxed using re-randomisation tests. Although several RCTs using minimisation have suggested the presence of non-proportional hazards (non-PH) effects, the application of re-randomisation tests has been limited to the log-rank test and Cox PH models, which may result in diminished statistical power when confronted with non-PH scenarios. To address this issue, we proposed two re-randomisation tests based on a maximum combination of weighted log-rank tests (MaxCombo test) and the difference in restricted mean survival time (dRMST) up to a fixed time point τ , both of which can be extended to adjust for randomisation stratification factors. METHODS: We compared the performance of asymptotic and re-randomisation tests using the MaxCombo test, dRMST, log-rank test, and Cox PH models, assuming various non-PH situations for RCTs using minimisation, with total sample sizes of 50, 100, and 500 at a 1:1 allocation ratio. We mainly considered null, and alternative scenarios featuring delayed, crossing, and diminishing treatment effects. RESULTS: Across all examined null scenarios, re-randomisation tests maintained the type I error rates at the nominal level. Conversely, unadjusted asymptotic tests indicated excessive conservatism, while adjusted asymptotic tests in both the Cox PH models and dRMST indicated inflated type I error rates for total sample sizes of 50. The stratified MaxCombo-based re-randomisation test consistently exhibited robust power across all examined scenarios. CONCLUSIONS: The re-randomisation test is a useful alternative in non-PH situations for RCTs with minimisation using the stratified MaxCombo test, suggesting its robust power in various scenarios.

Incidence of recurrent ischemic stroke and its associated factors in a tertiary care center in Thailand: a retrospective cohort study.

BACKGROUND: Ischemic stroke (IS) is one of the leading causes of death among non-communicable diseases in Thailand. Patients who have survived an IS are at an increased risk of developing recurrent IS, which can result in worse outcomes and post-stroke complications. OBJECTIVES: The study aimed to investigate the incidence of recurrent IS among patients with first-ever IS during a one-year follow-up period and to determine its associated risk factors. METHODS: Adult patients (aged ≥ 18 years) who were hospitalized at the Stroke Center, King Chulalongkorn Memorial Hospital (KCMH) in Bangkok, Thailand, due to first-ever IS between January and December 2019 and had at least one follow-up visit during the one-year follow-up period were included in this retrospective cohort study. IS diagnosis was confirmed by neurologists and imaging. The log-rank test was used to determine the event-free survival probabilities of recurrent IS in each risk factor. RESULTS: Of 418 patients hospitalized due to first-ever IS in 2019, 366 (87.6%) were included in the analysis. During a total of 327.2 person-years of follow-up, 25 (6.8%) patients developed recurrent IS, accounting for an incidence rate of 7.7 per 100 person-year (95% confidence interval [CI] 5.2-11.3). The median (interquartile range) time of recurrence was 35 (16-73) days. None of the 47 patients with atrial fibrillation developed recurrent IS. The highest incidence rate of recurrent IS occurred within 1 month after the first episode (34 per 100 person-years) compared to other follow-up periods. Patients with small vessel occlusion and large-artery atherosclerosis (LAA) constituted the majority of patients in the recurrent IS episode (48% and 40%, respectively), with LAA exhibiting a higher recurrence rate (13.5%). Additionally, smoking status was found to be associated with an increased risk of recurrence. CONCLUSION: The incidence rate of the recurrence was moderate in our tertiary care setting, with a decreasing trend over time after the first episode. The various subtypes of IS and smoking status can lead to differences in event-free survival probabilities.

Group sequential designs for cancer immunotherapy trial with delayed treatment effect.

Cancer immunotherapy trials are frequently characterized by delayed treatment effects such that the proportional hazards assumption is violated and the log-rank test suffers a substantial loss of statistical power. To increase the efficacy of the trial design, a variety of weighted log-rank tests have been proposed for fixed sample and group sequential trial designs. However, in such a group sequential design, it is often not recommended for futility interim monitoring due to possible delayed treatment effect which could result a high false-negative rate. To resolve this problem, we propose a group sequential design using a piecewise weighted log-rank test which provides an event-driven approach based on number of events after the delayed time. That is, the interim looks will not be conducted until the planned number of events observed after the delay time. Thus, it avoids the possibility of false-negative rate due to the delayed treatment effect. Furthermore, with an event-driven approach, the proposed group sequential design is robust against the underlying survival, accrual and censoring distributions. The group sequential designs using Fleming-Harrington-(ρ,γ) weighted log-rank test and a new weighted log-rank test are also discussed.

Multi-arm multi-stage survival trial design with arm-specific stopping rule.

Traditional two-arm randomized trial designs have played a pivotal role in establishing the efficacy of medical interventions. However, their efficiency is often compromised when confronted with multiple experimental treatments or limited resources. In response to these challenges, the multi-arm multi-stage designs have emerged, enabling the simultaneous evaluation of multiple treatments within a single trial. In such an approach, if an arm meets efficacy success criteria at an interim stage, the whole trial stops and the arm is selected for further study. However when multiple treatment arms are active, stopping the trial at the moment one arm achieves success diminishes the probability of selecting the best arm. To address this issue, we have developed a group sequential multi-arm multi-stage survival trial design with an arm-specific stopping rule. The proposed method controls the familywise type I error in a strong sense and selects the best promising treatment arm with a high probability.

Post-surgery survival and associated factors for cardiac patients in Ethiopia: applications of machine learning, semi-parametric and parametric modelling.

INTRODUCTION: Living in poverty, especially in low-income countries, are more affected by cardiovascular disease. Unlike the developed countries, it remains a significant cause of preventable heart disease in the Sub-Saharan region, including Ethiopia. According to the Ethiopian Ministry of Health statement, around 40,000 cardiac patients have been waiting for surgery in Ethiopia since September 2020. There is insufficient information about long-term cardiac patients' post-survival after cardiac surgery in Ethiopia. Therefore, the main objective of the current study was to determine the long-term post-cardiac surgery patients' survival status in Ethiopia. METHODS: All patients attended from 2012 to 2023 throughout the country were included in the current study. The total number of participants was 1520 heart disease patients. The data collection procedure was conducted from February 2022- January 2023. Machine learning algorithms were applied. Gompertz regression was used also for the multivariable analysis report. RESULTS: From possible machine learning models, random survival forest were preferred. It emphasizes, the most important variable for clinical prediction was SPO2, Age, time to surgery waiting time, and creatinine value and it accounts, 42.55%, 25.17%,11.82%, and 12.19% respectively. From the Gompertz regression, lower saturated oxygen, higher age, lower ejection fraction, short period of cardiac center stays after surgery, prolonged waiting time to surgery, and creating value were statistically significant predictors of death outcome for post-cardiac surgery patients' survival in Ethiopia. CONCLUSION: Some of the risk factors for the death of post-cardiac surgery patients are identified in the current investigation. Particular attention should be given to patients with prolonged waiting times and aged patients. Since there were only two fully active cardiac centers in Ethiopia it is far from an adequate number of centers for more than 120 million population, therefore, the study highly recommended to increase the number of cardiac centers that serve as cardiac surgery in Ethiopia.

A propensity score-integrated approach for leveraging external data in a randomized controlled trial with time-to-event endpoints.

In a randomized controlled trial with time-to-event endpoint, some commonly used statistical tests to test for various aspects of survival differences, such as survival probability at a fixed time point, survival function up to a specific time point, and restricted mean survival time, may not be directly applicable when external data are leveraged to augment an arm (or both arms) of an RCT. In this paper, we propose a propensity score-integrated approach to extend such tests when external data are leveraged. Simulation studies are conducted to evaluate the operating characteristics of three propensity score-integrated statistical tests, and an illustrative example is given to demonstrate how these proposed procedures can be implemented.

Sample size calculation for mixture model based on geometric average hazard ratio and its applications to nonproportional hazard.

With the advent of cancer immunotherapy, some special features including delayed treatment effect, cure rate, diminishing treatment effect and crossing survival are often observed in survival analysis. They violate the proportional hazard model assumption and pose a unique challenge for the conventional trial design and analysis strategies. Many methods like cure rate model have been developed based on mixture model to incorporate some of these features. In this work, we extend the mixture model to deal with multiple non-proportional patterns and develop its geometric average hazard ratio (gAHR) to quantify the treatment effect. We further derive a sample size and power formula based on the non-centrality parameter of the log-rank test and conduct a thorough analysis of the impact of each parameter on performance. Simulation studies showed a clear advantage of our new method over the proportional hazard based calculation across different non-proportional hazard scenarios. Moreover, the mixture modeling of two real trials demonstrates how to use the prior information on the survival distribution among patients with different biomarker and early efficacy results in practice. By comparison with a simulation-based design, the new method provided a more efficient way to compute the power and sample size with high accuracy of estimation. Overall, both theoretical derivation and empirical studies demonstrate the promise of the proposed method in powering future innovative trial designs.

Confirmatory Adaptive Designs for Clinical Trials With Multiple Time-to-Event Outcomes in Multi-state Markov Models.

The analysis of multiple time-to-event outcomes in a randomized controlled clinical trial can be accomplished with existing methods. However, depending on the characteristics of the disease under investigation and the circumstances in which the study is planned, it may be of interest to conduct interim analyses and adapt the study design if necessary. Due to the expected dependency of the endpoints, the full available information on the involved endpoints may not be used for this purpose. We suggest a solution to this problem by embedding the endpoints in a multistate model. If this model is Markovian, it is possible to take the disease history of the patients into account and allow for data-dependent design adaptations. To this end, we introduce a flexible test procedure for a variety of applications, but are particularly concerned with the simultaneous consideration of progression-free survival (PFS) and overall survival (OS). This setting is of key interest in oncological trials. We conduct simulation studies to determine the properties for small sample sizes and demonstrate an application based on data from the NB2004-HR study.

Sample Size Calculation Under Nonproportional Hazards Using Average Hazard Ratios.

Many clinical trials assess time-to-event endpoints. To describe the difference between groups in terms of time to event, we often employ hazard ratios. However, the hazard ratio is only informative in the case of proportional hazards (PHs) over time. There exist many other effect measures that do not require PHs. One of them is the average hazard ratio (AHR). Its core idea is to utilize a time-dependent weighting function that accounts for time variation. Though propagated in methodological research papers, the AHR is rarely used in practice. To facilitate its application, we unfold approaches for sample size calculation of an AHR test. We assess the reliability of the sample size calculation by extensive simulation studies covering various survival and censoring distributions with proportional as well as nonproportional hazards (N-PHs). The findings suggest that a simulation-based sample size calculation approach can be useful for designing clinical trials with N-PHs. Using the AHR can result in increased statistical power to detect differences between groups with more efficient sample sizes.

Model-based hypothesis tests for the causal mediation of semi-competing risks.

Analyzing the causal mediation of semi-competing risks has become important in medical research. Semi-competing risks refers to a scenario wherein an intermediate event may be censored by a primary event but not vice versa. Causal mediation analyses decompose the effect of an exposure on the primary outcome into an indirect (mediation) effect: an effect mediated through a mediator, and a direct effect: an effect not through the mediator. Here we proposed a model-based testing procedure to examine the indirect effect of the exposure on the primary event through the intermediate event. Under the counterfactual outcome framework, we defined a causal mediation effect using counting process. To assess statistical evidence for the mediation effect, we proposed two tests: an intersection-union test (IUT) and a weighted log-rank test (WLR). The test statistic was developed from a semi-parametric estimator of the mediation effect using a Cox proportional hazards model for the primary event and a series of logistic regression models for the intermediate event. We built a connection between the IUT and WLR. Asymptotic properties of the two tests were derived, and the IUT was determined to be a size [Formula: see text] test and statistically more powerful than the WLR. In numerical simulations, both the model-based IUT and WLR can properly adjust for confounding covariates, and the Type I error rates of the proposed methods are well protected, with the IUT being more powerful than the WLR. Our methods demonstrate the strongly significant effects of hepatitis B or C on the risk of liver cancer mediated through liver cirrhosis incidence in a prospective cohort study. The proposed method is also applicable to surrogate endpoint analyses in clinical trials.

A win ratio approach for comparing crossing survival curves in clinical trials.

Many clinical trials include time-to-event or survival data as an outcome. To compare two survival distributions, the log-rank test is often used to produce a P-value for a statistical test of the null hypothesis that the two survival curves are identical. However, such a P-value does not provide the magnitude of the difference between the curves regarding the treatment effect. As a result, the P-value is often accompanied by an estimate of the hazard ratio from the proportional hazards model or Cox model as a measurement of treatment difference. However, one of the most important assumptions for Cox model is that the hazard functions for the two treatment groups are proportional. When the hazard curves cross, the Cox model could lead to misleading results and the log-rank test could also perform poorly. To address the problem of crossing curves in survival analysis, we propose the use of the win ratio method put forward by Pocock et al. as an estimand for analysing such data. The subjects in the test and control treatment groups are formed into all possible pairs. For each pair, the test treatment subject is labelled a winner or a loser if it is known who had the event of interest such as death. The win ratio is the total number of winners divided by the total number of losers and its standard error can be estimated using Bebu and Lachin method. Using real trial datasets and Monte Carlo simulations, this study investigates the power and type I error and compares the win ratio method with the log-rank test and Cox model under various scenarios of crossing survival curves with different censoring rates and distribution parameters. The results show that the win ratio method has similar power as the log-rank test and Cox model to detect the treatment difference when the assumption of proportional hazards holds true, and that the win ratio method outperforms log-rank test and Cox model in terms of power to detect the treatment difference when the survival curves cross.

Determining the late effect parameter in the Fleming-Harrington test using asymptotic relative efficiency in cancer immunotherapy clinical trials.

The delayed treatment effect, which manifests as a separation of survival curves after a change point, has often been observed in immunotherapy clinical trials. A late effect of this kind may violate the proportional hazards assumption, resulting in the non-negligible loss of statistical power of an ordinary log-rank test when comparing survival curves. The Fleming-Harrington (FH) test, a weighted log-rank test, is configured to mitigate the loss of power by incorporating a weight function with two parameters, one each for early and late treatment effects. The two parameters need to be appropriately determined, but no helpful guides have been fully established. Since the late effect is expected in immunotherapy trials, we focus on the late effect parameter in this study. We consider parameterizing the late effect in a readily interpretable fashion and determining the optimal late effect parameter in the FH test to maintain statistical power in reference to the asymptotic relative efficiency (ARE). The optimization is carried out under three lag models (i.e. linear, threshold, and generalized linear lag), where the optimal weights are proportional to the lag functions characterized by the change points. Extensive simulation studies showed that the FH test with the selected late parameter reliably provided sufficient power even when the change points in the lag models were misspecified. This finding suggests that the FH test with the ARE-guided late parameter may be a reasonable and practical choice for the primary analysis in immunotherapy clinical trials.

Sequential monitoring of cancer immunotherapy trial with random delayed treatment effect.

Cancer immunotherapy trials are frequently characterized by a delayed treatment effect that violates the proportional hazards assumption. The log-rank test (LRT) suffers a substantial loss of statistical power under the nonproportional hazards model. Various group sequential designs using weighted LRTs (WLRTs) have been proposed under the fixed delayed treatment effect model. However, patients enrolled in immunotherapy trials are often heterogeneous, and the duration of the delayed treatment effect is a random variable. Therefore, we propose group sequential designs under the random delayed effect model using the random delayed distribution WLRT. The proposed group sequential designs are developed for monitoring the efficacy of the trial using the method of Lan-DeMets alpha-spending function with O'Brien-Fleming stopping boundaries or a gamma family alpha-spending function. The maximum sample size for the group sequential design is obtained by multiplying an inflation factor with the sample size for the fixed sample design. Simulations are conducted to study the operating characteristics of the proposed group sequential designs. The robustness of the proposed group sequential designs for misspecifying random delay time distribution and domain is studied via simulations.

Group sequential multi-arm multi-stage survival trial design with treatment selection.

Multi-arm trials are increasingly of interest because for many diseases; there are multiple experimental treatments available for testing efficacy. Several novel multi-arm multi-stage (MAMS) clinical trial designs have been proposed. However, a major hurdle to adopting the group sequential MAMS routinely is the computational effort of obtaining stopping boundaries. For example, the method of Jaki and Magirr for time-to-event endpoint, implemented in R package MAMS, requires complicated computational efforts to obtain stopping boundaries. In this study, we develop a group sequential MAMS survival trial design based on the sequential conditional probability ratio test. The proposed method is an improvement of the Jaki and Magirr's method in the following three directions. First, the proposed method provides explicit solutions for both futility and efficacy boundaries to an arbitrary number of stages and arms. Thus, it avoids complicated computational efforts for the trial design. Second, the proposed method provides an accurate number of events for the fixed sample and group sequential designs. Third, the proposed method uses a new procedure for interim analysis which preserves the study power.

Stratified modestly weighted log-rank tests in settings with an anticipated delayed separation of survival curves.

Delayed separation of survival curves is a common occurrence in confirmatory studies in immuno-oncology. Many novel statistical methods that aim to efficiently capture potential long-term survival improvements have been proposed in recent years. However, the vast majority do not consider stratification, which is a major limitation considering that most large confirmatory studies currently employ a stratified primary analysis. In this article, we combine recently proposed weighted log-rank tests that have been designed to work well under a delayed separation of survival curves, with stratification by a baseline variable. The aim is to increase the efficiency of the test when the stratifying variable is highly prognostic for survival. As there are many potential ways to combine the two techniques, we compare several possibilities in an extensive simulation study. We also apply the techniques retrospectively to two recent randomized clinical trials.

Survival-related genes are diversified across cancers but generally enriched in cancer hallmark pathways.

BACKGROUND: Pan-cancer studies have disclosed many commonalities and differences in mutations, copy number variations, and gene expression alterations among cancers. Some of these features are significantly associated with clinical outcomes, and many prognosis-predictive biomarkers or biosignatures have been proposed for specific cancer types. Here, we systematically explored the biological functions and the distribution of survival-related genes (SRGs) across cancers. RESULTS: We carried out two different statistical survival models on the mRNA expression profiles in 33 cancer types from TCGA. We identified SRGs in each cancer type based on the Cox proportional hazards model and the log-rank test. We found a large difference in the number of SRGs among different cancer types, and most of the identified SRGs were specific to a particular cancer type. While these SRGs were unique to each cancer type, they were found mostly enriched in cancer hallmark pathways, e.g., cell proliferation, cell differentiation, DNA metabolism, and RNA metabolism. We also analyzed the association between cancer driver genes and SRGs and did not find significant over-representation amongst most cancers. CONCLUSIONS: In summary, our work identified all the SRGs for 33 cancer types from TCGA. In addition, the pan-cancer analysis revealed the similarities and the differences in the biological functions of SRGs across cancers. Given the potential of SRGs in clinical utility, our results can serve as a resource for basic research and biotech applications.

Group sequential testing for cluster randomized trials with time-to-event endpoint.

We propose group sequential methods for cluster randomized trials (CRTs) with time-to-event endpoint. The alpha spending function approach is used for sequential data monitoring. The key to this approach is determining the joint distribution of test statistics and the information fraction at the time of interim analysis. We prove that the sequentially computed log-rank statistics in CRTs do not have independent increment property. We also propose an information fraction for group sequential trials with clustered survival data and a corresponding sample size determination approach. Extensive simulation studies are conducted to evaluate the performance of our proposed testing procedure using some existing alpha spending functions in terms of expected sample size and maximal sample size. Real study examples are taken to demonstrate our method.

Cancer immunotherapy trial design with random delayed treatment effect and cure rate.

Immunotherapies are increasingly used for treating patients with advanced-stage cancers. However, cancer immunotherapy trials often present delayed treatment effects and long-term survivors which result nonproportional hazard models and challenge the immunotherapy trial designs. In this article, we proposed a general random delayed cure rate model for designing cancer immunotherapy trials. A sample size formula is derived for a weighted log-rank test. The accuracy of sample size estimation is assessed and compared with the existing methods via simulation studies. The sensitivities for misspecifying the random delay time are also studied through simulations.