Which test for crossing survival curves? A user’s guideline

The use and abuse of survival analysis and Kaplan-Meier curves in surgical trials

BACKGROUND

Survival analysis based on Cox regression and Kaplan-Meier curves, initially devised for oncology trials, have frequently been used in other contexts where fundamental statistical assumptions (such as a constant hazard ratio) are not satisfied. This is almost always the case in trials that compare surgery with medical management.

METHODS

We review a trial that compared extracranial-intracranial bypass surgery (EC-IC bypass) with medical management (MM) of patients with symptomatic occlusion of the carotid or middle cerebral artery, where it was claimed that surgery was of no benefit. We discuss a hypothetical study and review other neurovascular trials which have also used survival analysis to compare results.

RESULTS

The trial comparing EC-IC bypass and MM did not satisfy the fundamental proportional hazard assumption necessary for valid analyses. This was also the case for two prior EC-IC bypass trials, as well as for other landmark neurovascular studies, such as the trials comparing endarterectomy with MM for carotid stenoses, or for the trial that compared intervention and MM for unruptured brain arteriovenous malformations. While minor deviations may have little effect on large trials, it may be impossible to show the benefits of surgery when trial size is small and deviations large.

CONCLUSION

Survival analyses are inappropriate in RCTs comparing surgery with conservative management, unless survival is calculated after the postoperative period. Alternative ways to compare final clinical outcomes, using for example a fixed follow-up period, should be planned for preventive surgical trials that compare intervention with conservative management.

Indolent cancer and pattern of progression: Two missing parameters in trial design for hepatology

The indolent and aggressive behaviors of HCC might have a role in clinical trial (CT) results; however, the indolent HCC is less analyzed compared to others cancer. Indolent profile could be characterized as follows: (1) patients with low risk of progression itself due to the HCC molecular profile and/or due to the interaction between cancer cell their microenvironment; (2) patients who achieve objective response or present spontaneous regression; and (3) patients who develop radiological progression with no consequence on either the liver function or general status, and without trigger a change in the tumor stage. Patients with "indolent HCC" generally never develop cancer-related symptoms neither die for HCC-related causes. Thus, we hypothesize that the imbalance in the proportion of "indolent" versus "aggressive HCC" between arms or the underestimation/overestimation of HCC behavior at baseline in single-arm CT could be associated with CT failure or under-overestimation of trial results. The "indolent progression" may also explain the discrepancy between radiological progression-based end points and survival. Moreover, we discuss the related causes that explain the indolent profile of HCC and propose (1) refining the progression-related end point by the pattern of progression to minimize the limitations of the current end points; (2) considering alternative statistical tools for survival analysis such as milestone survival, or restricted mean survival time to capture the value of indolent HCC. According to these considerations, we propose incorporating novel end points into the single arm of phase I/II CT as exploratory analysis or as a secondary end point in phase III CT.

Methods for non-proportional hazards in clinical trials: A systematic review

For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under non-proportional hazard. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific non-proportional hazard situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles.

A study combining microbubble-mediated focused ultrasound and radiation therapy in the healthy rat brain and a F98 glioma model

Focused Ultrasound (FUS) has been shown to sensitize tumors outside the brain to Radiotherapy (RT) through increased ceramide-mediated apoptosis. This study investigated the effects of FUS + RT in healthy rodent brains and F98 gliomas. Tumors, or striata in healthy rats, were targeted with microbubble-mediated, pulsed FUS (220 kHz, 102-444 kPa), followed by RT (4, 8, 15 Gy). FUS + RT (8, 15 Gy) resulted in ablative lesions, not observed with FUS or RT only, in healthy tissue. Lesions were visible using Magnetic Resonance Imaging (MRI) within 72 h and persisted until 21 days post-treatment, indicating potential applications in ablative neurosurgery. In F98 tumors, at 8 and 15 Gy, where RT only had significant effects, FUS + RT offered limited improvements. At 4 Gy, where RT had limited effects compared with untreated controls, FUS + RT reduced tumor volumes observed on MRI by 45-57%. However, survival benefits were minimal (controls: 27 days, RT: 27 days, FUS + RT: 28 days). Histological analyses of tumors 72 h after FUS + RT (4 Gy) showed 93% and 396% increases in apoptosis, and 320% and 336% increases in vessel-associated ceramide, compared to FUS and RT only. Preliminary evidence shows that FUS + RT may improve treatment of glioma, but additional studies are required to optimize effect size.

Advanced considerations in survival analysis

Investigation of survival during the follow-up period is common in cardiovascular research and has intrinsic issues that require precise knowledge, such as survival or censoring. Besides, as the follow-up period lengthens and events other than mortality are studied, the analysis becomes more complex, so Kaplan-Meier analyses or Cox models are not always sufficient. In this primer, we provide the reader with detailed information on the interpretation of the most common survival analyses and delve into methods to analyse competing risks or alternatives to the conventional methods when the proportional hazards assumption is not met.

On the role of benchmarking data sets and simulations in method comparison studies

Method comparisons are essential to provide recommendations and guidance for applied researchers, who often have to choose from a plethora of available approaches. While many comparisons exist in the literature, these are often not neutral but favor a novel method. Apart from the choice of design and a proper reporting of the findings, there are different approaches concerning the underlying data for such method comparison studies. Most manuscripts on statistical methodology rely on simulation studies and provide a single real-world data set as an example to motivate and illustrate the methodology investigated. In the context of supervised learning, in contrast, methods are often evaluated using so-called benchmarking data sets, that is, real-world data that serve as gold standard in the community. Simulation studies, on the other hand, are much less common in this context. The aim of this paper is to investigate differences and similarities between these approaches, to discuss their advantages and disadvantages, and ultimately to develop new approaches to the evaluation of methods picking the best of both worlds. To this aim, we borrow ideas from different contexts such as mixed methods research and Clinical Scenario Evaluation.

Ball divergence for the equality test of crossing survival curves

It is a very common problem to test survival equality using the right-censored time-to-event data in clinical research. Although the log-rank test is popularly used in various studies, it may become insensitive when the proportional hazards assumption is violated. As follows, there have a variety of statistical methods being proposed to identify the discrepancy between crossing survival curves or hazard functions. The omnibus tests against general alternatives are usually preferred due to their wide applicability to complicated scenarios in real applications. In this paper, we propose two novel statistics to estimate the ball divergence using the right-censored survival data, and then implement them in the equality test on survival time in two independent groups. The simulation analysis demonstrates their efficiency in identifying the survival discrepancy. Compared to the existing methods, our proposed methods present higher power in situations with complex distributions, especially when there is a scale shift between groups. Real examples illustrate its advantage in practical applications.

The Inverse Log-Rank Test: A Versatile Procedure for Late Separating Survival Curves

Often in the planning phase of a clinical trial, a researcher will need to choose between a standard versus weighted log-rank test (LRT) for investigating right-censored survival data. While a standard LRT is optimal for analyzing evenly distributed but distinct survival events (proportional hazards), an appropriately weighted LRT test may be better suited for handling non-proportional, delayed treatment effects. The "a priori" misspecification of this alternative may result in a substantial loss of power when determining the effectiveness of an experimental drug. In this paper, the standard unweighted and inverse log-rank tests (iLRTs) are compared with the multiple weight, default Max-Combo procedure for analyzing differential late survival outcomes. Unlike combination LRTs that depend on the arbitrary selection of weights, the iLRT by definition is a single weight test and does not require implicit multiplicity correction. Empirically, both weighted methods have reasonable flexibility for assessing continuous survival curve differences from the onset of a study. However, the iLRT may be preferable for accommodating delayed separating survival curves, especially when one arm finishes first. Using standard large-sample methods, the power and sample size for the iLRT are easily estimated without resorting to complex and timely simulations.

Carfilzomib, lenalidomide and dexamethasone followed by a second ASCT is an effective strategy in first relapse multiple myeloma: a study on behalf of the Chronic malignancies working party of the EBMT

In the setting of a first relapse of multiple myeloma (MM), a second autologous stem cell transplant (ASCT) following carfilzomib-lenalidomide-dexamethasone (KRd) is an option, although there is scarce data concerning this approach. We performed a retrospective study involving 22 EBMT-affiliated centers. Eligible MM patients had received a second-line treatment with KRd induction followed by a second ASCT between 2016 and 2018. Primary objective was to estimate progression-free survival (PFS) and overall survival (OS). Secondary objectives were to assess the response rate and identify significant variables affecting PFS and OS. Fifty-one patients were identified, with a median age of 62 years. Median PFS after ASCT was 29.5 months while 24- and 36-months OS rates were 92.1% and 84.5%, respectively. Variables affecting PFS were an interval over four years between transplants and the achievement of a very good partial response (VGPR) or better before the relapse ASCT. Our study suggests that a relapse treatment with ASCT after KRd induction is an effective strategy for patients with a lenalidomide-sensitive first relapse. Patients with at least four years of remission after a frontline ASCT and who achieved at least a VGPR after KRd induction appear to benefit the most from this approach.

Dealing With Nonproportional Hazards in Coronary Revascularisation Studies

The Cox proportional hazards model is one of the most popular statistical tools to model time to event outcomes without the need for specifying the hazards or survival time distributions. The Cox model requires that the ratio of the hazards of the occurrence of the outcome for any 2 individuals remains constant during the entire follow-up. Studies comparing coronary revascularisation strategies, however, might be prone to violations of proportionality by the crossing of the hazard functions over time. Early increases in the risk of cardiovascular outcomes are commonly observed when comparing coronary artery bypass grafting vs percutaneous coronary intervention, whereas decreased risk might be observed later during the follow-up. The same is valid for comparisons between invasive vs conservative coronary revascularisation strategies. In these situations, the statistical power of the Cox model is reduced, and hazard ratios might not be an informative summary measure of treatment effect. In this article, we discuss methods to identify and account for nonproportionality. We illustrate the use of these methods in a case study based on reconstructed data from a coronary revascularisation clinical trial. And finally, we review the cardiovascular literature to estimate how the proportionality assumption has been reported in coronary revascularisation studies recently.

Avelumab vs Standard Second-Line Chemotherapy in Patients With Metastatic Colorectal Cancer and Microsatellite Instability: A Randomized Clinical Trial

Importance

Only 1 randomized clinical trial has shown the superiority of immune checkpoint inhibitors in patients with deficient mismatch repair and/or microsatellite instability (dMMR/MSI) metastatic colorectal cancer (mCRC) in the first-line setting.

Objectives

To determine whether avelumab (an anti-programmed cell death ligand 1 antibody) improves progression-free survival (PFS) compared with standard second-line chemotherapy in patients with dMMR/MSI mCRC.

Design, Setting, and Participants

The SAMCO-PRODIGE 54 trial is a national open-label phase 2 randomized clinical trial that was conducted from April 24, 2018, to April 29, 2021, at 49 French sites. Patients with dMMR/MSI mCRC who experienced progression while receiving standard first-line therapy were included in the analysis.

Interventions

Patients were randomized to receive standard second-line therapy or avelumab every 2 weeks until progression, unacceptable toxic effects, or patient refusal.

Main Outcome and Measures

The primary end point was PFS according to RECIST (Response Evaluation Criteria in Solid Tumours), version 1.1, evaluated by investigators in patients with mCRC and confirmed dMMR and MSI status who received at least 1 dose of treatment (modified intention-to-treat [mITT] population).

Results

A total of 122 patients were enrolled in the mITT population. Median age was 66 (IQR, 56-76) years, 65 patients (53.3%) were women, 100 (82.0%) had a right-sided tumor, and 52 (42.6%) had BRAF V600E-mutated tumors. There was no difference in patients and tumor characteristics between treatment groups. No new safety concerns in either group were detected, with fewer treatment-related adverse events of at least grade 3 in the avelumab group than in the chemotherapy group (20 [31.7%] vs 34 [53.1%]; P = .02). After a median follow-up of 33.3 (95% CI, 28.3-34.8) months, avelumab was superior to chemotherapy with or without targeted agents with respect to PFS (15 [24.6%] vs 5 [8.2%] among patients without progression; P = .03). Rates of PFS rates at 12 months were 31.2% (95% CI, 20.1%-42.9%) and 19.4% (95% CI, 10.6%-30.2%) in the avelumab and control groups, respectively, and 27.4% (95% CI, 16.8%-39.0%) and 9.1% (95% CI, 3.2%-18.8%) at 18 months. Objective response rates were similar in both groups (18 [29.5%] vs 16 [26.2%]; P = .45). Among patients with disease control, 18 (75.7%) in the avelumab group compared with 9 (19.1%) in the control group had ongoing disease control at 18 months.

Conclusions

The SAMCO-PRODIGE 54 phase 2 randomized clinical trial showed, in patients with dMMR/MSI mCRC, better PFS and disease control duration with avelumab over standard second-line treatment, with a favorable safety profile.

Trial Registration

ClinicalTrials.gov Identifier: NCT03186326.

Randomized controlled trials and alternative study designs in surgical oncology

Surgery is central to the cure of most solid cancers and an integral part of modern multimodal cancer management for early and advanced stage cancers. Decisions made by surgeons and multidisciplinary team members are based on best available knowledge for the defined clinical situation at hand. While surgery is both an art and a science, good decision-making requires data that are robust, valid, representative and, applicable to most if not all patients with a specific cancer. Such data largely comes from clinical observations and registries, and more preferably from trials conducted with the specific purpose of arriving at new answers. As part of the ESSO core curriculum development an increased focus has been put on the need to enhance research literacy among surgical candidates. As an expansion of the curriculum catalogue list and to enhance the educational value, we here present a set of principles and emerging concepts which applies to surgical oncologist for reading, understanding, planning and contributing to future surgeon-led cancer trials.

Quantification of follow-up time in oncology clinical trials with a time-to-event endpoint: Asking the right questions

For the analysis of a time-to-event endpoint in a single-arm or randomized clinical trial it is generally perceived that interpretation of a given estimate of the survival function, or the comparison between two groups, hinges on some quantification of the amount of follow-up. Typically, a median of some loosely defined quantity is reported. However, whatever median is reported, is typically not answering the question(s) trialists actually have in terms of follow-up quantification. In this paper, inspired by the estimand framework, we formulate a comprehensive list of relevant scientific questions that trialists have when reporting time-to-event data. We illustrate how these questions should be answered, and that reference to an unclearly defined follow-up quantity is not needed at all. In drug development, key decisions are made based on randomized controlled trials, and we therefore also discuss relevant scientific questions not only when looking at a time-to-event endpoint in one group, but also for comparisons. We find that different thinking about some of the relevant scientific questions around follow-up is required depending on whether a proportional hazards assumption can be made or other patterns of survival functions are anticipated, for example, delayed separation, crossing survival functions, or the potential for cure. We conclude the paper with practical recommendations.

Investigating non-inferiority or equivalence in time-to-event data under non-proportional hazards

The classical approach to analyze time-to-event data, e.g. in clinical trials, is to fit Kaplan-Meier curves yielding the treatment effect as the hazard ratio between treatment groups. Afterwards, a log-rank test is commonly performed to investigate whether there is a difference in survival or, depending on additional covariates, a Cox proportional hazard model is used. However, in numerous trials these approaches fail due to the presence of non-proportional hazards, resulting in difficulties of interpreting the hazard ratio and a loss of power. When considering equivalence or non-inferiority trials, the commonly performed log-rank based tests are similarly affected by a violation of this assumption. Here we propose a parametric framework to assess equivalence or non-inferiority for survival data. We derive pointwise confidence bands for both, the hazard ratio and the difference of the survival curves. Further we propose a test procedure addressing non-inferiority and equivalence by directly comparing the survival functions at certain time points or over an entire range of time. Once the model's suitability is proven the method provides a noticeable power benefit, irrespectively of the shape of the hazard ratio. On the other hand, model selection should be carried out carefully as misspecification may cause type I error inflation in some situations. We investigate the robustness and demonstrate the advantages and disadvantages of the proposed methods by means of a simulation study. Finally, we demonstrate the validity of the methods by a clinical trial example.

In-hospital cost-effectiveness analysis of open versus staged fenestrated/branched endovascular elective repair of thoracoabdominal aneurysms

OBJECTIVE

To compare costs and effectiveness of elective open (OR) versus fenestrated/branched endovascular (ER) repair of thoracoabdominal aneurysms (TAAA) in a high-volume center.

METHODS

This single-center retrospective observational study (PRO-ENDO TAAA Study, NCT05266781) was designed as part of a larger Health Technology Assessment analysis. All electively treated TAAAs between 2013 and 2021 were analyzed and propensity-matched. Endpoints were clinical success, major adverse events (MAE), hospital direct costs, and freedom from all causes and aneurysm-related mortality and reinterventions. Risk factors and outcomes were homogeneously classified according to the Society of Vascular Surgery reporting standards. Cost-effectiveness value (CEV) and Incremental Cost-Effectiveness Ratio (ICER) were calculated, considering the absence of MAEs as a measure of effectiveness.

RESULTS

Propensity matching identified 102 pairs of patients out of 789 TAAAs. Mortality, MAE, permanent spinal cord ischemia rates, respiratory complications, cardiac complications, and renal injury were higher for OR (13% vs 5%, p=.048; 60% vs 17%, p<.001; 10% vs 3%, p=.045; 91% vs 18%, p<.001; 16% vs 6%, p=.024; 27% vs 6%, p<.001; respectively). Access complication rate (6% vs 27%; p<.001) was higher in the ER group. Intensive Care Unit stay was longer (p<.001) for OR and ER patients were discharged home more frequently (3% vs 94%; p<.001). No differences in mid-term endpoints were observed at 2 years. Despite ER reducing all the hospital cost items (-42% to -88%, p<.001), the higher expenses (p<.001) of the endovascular devices increased the overall cost of ER by 80%. CEV for ER was favorable to OR (56 365 vs 64 903 €/patient) with an ICER of 48 409 € per MAE saved.

CONCLUSIONS

ER of TAAA reduces perioperative mortality and morbidity compared to OR, with no differences in reinterventions and survival rates at midterm follow-up. Despite the expenses for endovascular grafts, ER resulted more cost-effective in preventing MAEs.

A comparative study to alternatives to the log-rank test

BACKGROUND

Studies to compare the survival of two or more groups using time-to-event data are of high importance in medical research. The gold standard is the log-rank test, which is optimal under proportional hazards. As the latter is no simple regularity assumption, we are interested in evaluating the power of various statistical tests under different settings including proportional and non-proportional hazards with a special emphasis on crossing hazards. This challenge has been going on for many years now and multiple methods have already been investigated in extensive simulation studies. However, in recent years new omnibus tests and methods based on the restricted mean survival time appeared that have been strongly recommended in biometric literature.

METHODS

Thus, to give updated recommendations, we perform a vast simulation study to compare tests that showed high power in previous studies with these more recent approaches. We thereby analyze various simulation settings with varying survival and censoring distributions, unequal censoring between groups, small sample sizes and unbalanced group sizes.

RESULTS

Overall, omnibus tests are more robust in terms of power against deviations from the proportional hazards assumption.

CONCLUSION

We recommend considering the more robust omnibus approaches for group comparison in case of uncertainty about the underlying survival time distributions.

Identification and development of TP53 mutation-associated Long non-coding RNAs signature for optimized prognosis assessment and treatment selection in hepatocellular carcinoma

BACKGROUND

The TP53 gene is estimated to be mutated in over 50% of tumors, with the majority of tumors exhibiting abnormal TP53 signaling pathways. However, the exploration of TP53 mutation-related LncRNAs in Hepatocellular carcinoma (HCC) remains incomplete. This study aims to identify such LncRNAs and enhance the prognostic accuracy for Hepatoma patients.

MATERIAL AND METHODS

Differential gene expression was identified using the "limma" package in R. Prognosis-related LncRNAs were identified via univariate Cox regression analysis, while a prognostic model was crafted using multivariate Cox regression analysis. Survival analysis was conducted using Kaplan-Meier curves. The precision of the prognostic model was assessed through ROC analysis. Subsequently, the Tumor Immune Dysfunction and Exclusion (TIDE) algorithm were executed on the TCGA dataset via the TIDE database. Fractions of 24 types of immune cell infiltration were obtained from NCI Cancer Research Data Commons using deconvolution techniques. The protein expression levels encoded by specific genes were obtained through the TPCA database.

RESULTS

In this research, we have identified 85 LncRNAs associated with TP53 mutations and developed a corresponding signature referred to as TP53MLncSig. Kaplan-Meier analysis revealed a lower 3-year survival rate in high-risk patients (46.9%) compared to low-risk patients (74.2%). The accuracy of the prognostic TP53MLncSig was further evaluated by calculating the area under the ROC curve. The analysis yielded a 5-year ROC score of 0.793, confirming its effectiveness. Furthermore, a higher score for TP53MLncSig was found to be associated with an increased response rate to immune checkpoint blocker (ICB) therapy (p = .005). Patients possessing high-risk classification exhibited lower levels of P53 protein expression and higher levels of genomic instability.

CONCLUSION

The present study aimed to identify and validate LncRNAs associated with TP53 mutations. We constructed a prognostic model that can predict chemosensitivity and response to ICB therapy in HCC patients. This novel approach sheds light on the role of LncRNAs in TP53 mutation and provides valuable resources for analyzing patient prognosis and treatment selection.