Presence Of Non-proportional Hazards Research Articles

Bayesian pairwise meta-analysis of time-to-event outcomes in the presence of non-proportional hazards: A simulation study of flexible parametric, piecewise exponential and fractional polynomial models.

Traditionally, meta-analysis of time-to-event outcomes reports a single pooled hazard ratio assuming proportional hazards (PH). For health technology assessment evaluations, hazard ratios are frequently extrapolated across a lifetime horizon. However, when treatment effects vary over time, an assumption of PH is not always valid. The Royston-Parmar (RP), piecewise exponential (PE), and fractional polynomial (FP) models can accommodate non-PH and provide plausible extrapolations of survival curves beyond observed data. Simulation study to assess and compare the performance of RP, PE, and FP models in a Bayesian framework estimating restricted mean survival time difference (RMSTD) at 50 years from a pairwise meta-analysis with evidence of non-PH. Individual patient data were generated from a mixture Weibull distribution. Twelve scenarios were considered varying the amount of follow-up data, number of trials in a meta-analysis, non-PH interaction coefficient, and prior distributions. Performance was assessed through bias and mean squared error. Models were applied to a metastatic breast cancer example. FP models performed best when the non-PH interaction coefficient was 0.2. RP models performed best in scenarios with complete follow-up data. PE models performed well on average across all scenarios. In the metastatic breast cancer example, RMSTD at 50-years ranged from -14.6 to 8.48 months. Synthesis of time-to-event outcomes and estimation of RMSTD in the presence of non-PH can be challenging and computationally intensive. Different approaches make different assumptions regarding extrapolation and sensitivity analyses varying key assumptions are essential to check the robustness of conclusions to different assumptions for the underlying survival function.

A Comparison of Alternative Network Meta-Analysis Methods in the Presence of Nonproportional Hazards: A Case Study in First-Line Advanced or Metastatic Renal Cell Carcinoma

ObjectivesNetwork meta-analysis (NMA) of time-to-event outcomes based on constant hazard ratios can result in biased findings when the proportional hazards (PHs) assumption does not hold in a subset of trials. We aimed to summarize the published non-PH NMA methods for time-to-event outcomes, demonstrate their application, and compare their results. MethodsThe following non-PH NMA methods were compared through an illustrative case study in oncology of 4 randomized controlled trials in terms of progression-free survival and overall survival: (1) 1-step or (2) 2-step multivariate NMAs based on traditional survival distributions or fractional polynomials, (3) NMAs with restricted cubic splines for baseline hazard, and (4) restricted mean survival NMA. ResultsFor progression-free survival, the PH assumption did not hold across trials and non-PH NMA methods better reflected the relative treatment effects over time. The most flexible models (fractional polynomials and restricted cubic splines) fit better to the data than the other approaches. Estimated hazard ratios obtained with different non-PH NMA methods were similar at 5 years of follow-up but differed thereafter in the extrapolations. Although there was no strong evidence of PH violation for overall survival, non-PH NMA methods captured this uncertainty in the relative treatment effects over time. ConclusionsWhen the PH assumption is questionable in a subset of the randomized controlled trials, we recommend assessing alternative non-PH NMA methods to estimate relative treatment effects for time-to-event outcomes. We propose a transparent and explicit stepwise model selection process considering model fit, external constraints, and clinical validity. Given inherent uncertainty, sensitivity analyses are suggested.

Statistical methods of indirect comparison with real-world data for survival endpoint under non-proportional hazards

ABSTRACT In clinical studies that utilize real-world data, time-to-event outcomes are often germane to scientific questions of interest. Two main obstacles are the presence of non-proportional hazards and confounding bias. Existing methods that could adjust for NPH or confounding bias, but no previous work delineated the complexity of simultaneous adjustments for both. In this paper, a propensity score stratified MaxCombo and weighted Cox model is proposed. This model can adjust for confounding bias and NPH and can be pre-specified when NPH pattern is unknown in advance. The method has robust performance as demonstrated in simulation studies and in a case study.

Does osteoarthritis modify the association between NSAID use and risk of comorbidities and adverse events?

ObjectivesTo investigate the role of osteoarthritis (OA) in the incidence of musculoskeletal, metabolic, cardiovascular, digestive, neuro-psychological, kidney and other comorbidities/adverse events after (i) incident non-steroidal anti-inflammatory drug (NSAID) initiation and (ii) NSAID discontinuation. MethodsWe used register data for the population of Skåne, Sweden. For (i), we analysed the association between starting NSAIDs and the risk of incident outcome events in the 6 years following NSAID dispensation among people with prevalent OA vs no OA. For (ii) we studied the effect of discontinuing NSAIDs among people with and without OA up to 120 days. We used flexible parametric models to estimate adjusted differences in cumulative incidence with NSAIDs as time-varying exposure in the presence of non-proportional hazards. ResultsFor (i) we included between 243,832 and 409,749 persons. In the whole cohort, over the 6 years of follow-up, NSAID initiation was associated with a 3% (metabolic) to 16% (musculoskeletal) higher cumulative incidence of outcomes compared to non-users. The difference between those initiating NSAIDs vs non-users was similar in those with and without OA for most outcomes, but in those with OA the increase was lower for neuro-psychological (95%CI: 3.7%–4.6% vs 7.1%–7.9%) and musculoskeletal comorbidities (12%–14.5% vs 16.2%–17.2%).In (ii), we found no interaction between OA and NSAID discontinuation. NSAID discontinuation was associated with decreased risks for most of the outcomes, from −1.3% for musculoskeletal to −0.4% for cardiovascular comorbidities. ConclusionsOA appears to have little influence on the increased risk of comorbidities observed after NSAID initiation or decrease after discontinuation.

Which test for crossing survival curves? A user\u2019s guideline

BackgroundThe exchange of knowledge between statisticians developing new methodology and clinicians, reviewers or authors applying them is fundamental. This is specifically true for clinical trials with time-to-event endpoints. Thereby, one of the most commonly arising questions is that of equal survival distributions in two-armed trial. The log-rank test is still the gold-standard to infer this question. However, in case of non-proportional hazards, its power can become poor and multiple extensions have been developed to overcome this issue. We aim to facilitate the choice of a test for the detection of survival differences in the case of crossing hazards.MethodsWe restricted the review to the most recent two-armed clinical oncology trials with crossing survival curves. Each data set was reconstructed using a state-of-the-art reconstruction algorithm. To ensure reproduction quality, only publications with published number at risk at multiple time points, sufficient printing quality and a non-informative censoring pattern were included. This article depicts the p-values of the log-rank and Peto-Peto test as references and compares them with nine different tests developed for detection of survival differences in the presence of non-proportional or crossing hazards.ResultsWe reviewed 1400 recent phase III clinical oncology trials and selected fifteen studies that met our eligibility criteria for data reconstruction. After including further three individual patient data sets, for nine out of eighteen studies significant differences in survival were found using the investigated tests. An important point that reviewers should pay attention to is that 28% of the studies with published survival curves did not report the number at risk. This makes reconstruction and plausibility checks almost impossible.ConclusionsThe evaluation shows that inference methods constructed to detect differences in survival in presence of non-proportional hazards are beneficial and help to provide guidance in choosing a sensible alternative to the standard log-rank test.

Comparison of statistical methods for the analysis of recurrent adverse events in the presence of non-proportional hazards and unobserved heterogeneity: a simulation study

BackgroundIn preventive drug trials such as intermittent preventive treatment for malaria prevention during pregnancy (IPTp), where there is repeated treatment administration, recurrence of adverse events (AEs) is expected. Challenges in modelling the risk of the AEs include accounting for time-to-AE and within-patient-correlation, beyond the conventional methods. The correlation comes from two sources; (a) individual patient unobserved heterogeneity (i.e. frailty) and (b) the dependence between AEs characterised by time-dependent treatment effects. Potential AE-dependence can be modelled via time-dependent treatment effects, event-specific baseline and event-specific random effect, while heterogeneity can be modelled via subject-specific random effect. Methods that can improve the estimation of both the unobserved heterogeneity and treatment effects can be useful in understanding the evolution of risk of AEs, especially in preventive trials where time-dependent treatment effect is expected.MethodsUsing both a simulation study and the Chloroquine for Malaria in Pregnancy (NCT01443130) trial data to demonstrate the application of the models, we investigated whether the lognormal shared frailty models with restricted cubic splines and non-proportional hazards (LSF-NPH) assumption can improve estimates for both frailty variance and treatment effect compared to the conventional inverse Gaussian shared frailty model with proportional hazard (ISF-PH), in the presence of time-dependent treatment effects and unobserved patient heterogeneity. We assessed the bias, precision gain and coverage probability of 95% confidence interval of the frailty variance estimates for the models under varying known unobserved heterogeneity, sample sizes and time-dependent effects.ResultsThe ISF-PH model provided a better coverage probability of 95% confidence interval, less bias and less precise frailty variance estimates compared to the LSF-NPH models. The LSF-NPH models yielded unbiased hazard ratio estimates at the expense of imprecision and high mean square error compared to the ISF-PH model.ConclusionThe choice of the shared frailty model for the recurrent AEs analysis should be driven by the study objective. Using the LSF-NPH models is appropriate if unbiased hazard ratio estimation is of primary interest in the presence of time-dependent treatment effects. However, ISF-PH model is appropriate if unbiased frailty variance estimation is of primary interest.Trial registrationClinicalTrials.gov; NCT01443130

OP236 Evidence Synthesis Of Time-To-Event Outcomes In The Presence Of Non-Proportional Hazards

IntroductionSynthesis of clinical effectiveness is a well-established component of health technology assessment (HTA) combining data from multiple trials to obtain an overall pooled estimate of clinical effectiveness, which may inform an associated economic evaluation. Time-to-event outcomes are often synthesized using effect measures from Cox proportional hazards models assuming a constant hazard ratio over time. However, where treatment effects vary over time an assumption of proportional hazards is not always valid. Several methods have been proposed for synthesizing time-to-event outcomes in the presence of non-proportional hazards. However, guidance on choosing between these methods and the implications for HTA is lacking.MethodsWe applied five methods for estimating treatment effects from time-to-event outcomes, which relax the proportional hazards assumption to a network of melanoma trials, reporting overall survival: restricted mean survival time, an accelerated failure time generalized gamma model, piecewise exponential, fractional polynomial and Royston-Parmar models. We conducted a simulation study to compare these five methods. Simulated individual patient data was generated from a mixture Weibull distribution assuming a treatment-time interaction. Each simulated meta-analysis consisted of five trials with varying numbers of patients and length of follow-up across trials. For each model fitted to each dataset, we calculated the restricted mean survival time at the end of observed follow-up and following extrapolation to a 20-year time horizon.ResultsAll models fitted the melanoma data reasonably well with some variation in the treatment rankings and differences in the survival curves. The simulation study demonstrated the potential for different conclusions from different modelling approaches.ConclusionsThe restricted mean survival time, generalized gamma, piecewise exponential, fractional polynomial and Royston-Parmar models can all accommodate non-proportional hazards and differing lengths of trial follow-up within an evidence synthesis of time-to-event outcomes. Further work is needed in this area to extend the simulation study to the network meta-analysis setting and provide guidance on the key considerations for informing model choice for the purposes of HTA.

PCN202 Use of Restricted Mean Survival Time in the Presence of Non-Proportional Hazards As an Alternative Measure of Treatment Benefit in Cost-Effectiveness Analyses

The restricted mean survival time (rmst) is a well-established measure of treatment benefit, that is defined as the average event-free survival time up to a pre-specified time point. The rmst difference (rmstD) between two treatments corresponds to the area between their respective Kaplan Meier curves. This empirical study aimed to explore how to use the rmstD in cost-effectiveness models (CEM). The case study was based on a network of three studies related to lung cancer. Two analyses were conducted: the first considered the pooled Kaplan-Meier estimates (time horizon t* of 25 months) and the second was based on extrapolated mean survival time estimators (t* of 15 years). Distributions minimizing the Akaike Information Criteria were considered for the extrapolations of both the Progression-Free survival (Log-Logistic) and the Overall survival (Weibull), separately. The CEM was designed to allow for the use of the rmstD resulting from a random effect network meta-analysis (NMA). Discounted and undiscounted results were generated. The NMA estimates were highly sensitive to t*. The use of restricted or extrapolated estimates, with or without applying the discount rate led to similar conclusions in the cost-effectiveness assessments. The extrapolated mean survival time estimates allowed to capture all treatment benefit although it relied on a larger set of assumptions. This study demonstrates that the rmstD can be used to develop CEM in oncology, which provides a relevant method in a context of non-proportional hazards. The method is sensitive to the selection of the time horizon. Alternative computational methods of the rmstD need to be further explored to better understand the implications on the results. In practice, extrapolations should be based on real world evidence and expert opinions to better reflect expected long-term outcomes.

A simulation-free group sequential design with max-combo tests in the presence of non-proportional hazards.

Non-proportional hazards (NPH) have been observed in many immuno-oncology clinical trials. Weighted log-rank tests (WLRT) with suitable weights can be used to improve the power of detecting the difference between survival curves in the presence of NPH. However, it is not easy to choose a proper WLRT in practice. A versatile max-combo test was proposed to achieve the balance of robustness and efficiency, and has received increasing attention recently. Survival trials often warrant interim analyses due to their high cost and long durations. The integration and implementation of max-combo tests in interim analyses often require extensive simulation studies. In this report, we propose a simulation-free approach for group sequential designs with the max-combo test in survival trials. The simulation results support that the proposed method can successfully control the type I error rate and offer excellent accuracy and flexibility in estimating sample sizes, with light computation burden. Notably, our method displays strong robustness towards various model misspecifications and has been implemented in an R package.

Optimality of testing procedures for survival data in the nonproportional hazards setting.

Most statistical tests for treatment effects used in randomized clinical trials with survival outcomes are based on the proportional hazards assumption, which often fails in practice. Data from early exploratory studies may provide evidence of nonproportional hazards, which can guide the choice of alternative tests in the design of practice-changing confirmatory trials. We developed a test to detect treatment effects in a late-stage trial, which accounts for the deviations from proportional hazards suggested by early-stage data. Conditional on early-stage data, among all tests that control the frequentist Type I error rate at a fixed α level, our testing procedure maximizes the Bayesian predictive probability that the study will demonstrate the efficacy of the experimental treatment. Hence, the proposed test provides a useful benchmark for other tests commonly used in the presence of nonproportional hazards, for example, weighted log-rank tests. We illustrate this approach in simulations based on data from a published cancer immunotherapy phase III trial.

On Weighted Log-Rank Combination Tests and Companion Cox Model Estimators

In randomized clinical trials, the log-rank test and Cox proportional hazards model are the gold standard in survival data analyses. While the log-rank test is generally valid, in the presence of non-proportional hazards, the power can be substantially decreased relative to the proportional hazards assumptions under which studies are usually designed. In contrast, weighted log-rank tests can be more powerful for specific treatment differences under non-proportional hazards scenarios. However, a poor choice of the weighting form can be detrimental. Recent work on combining various weighted log-rank tests allows for tests that are capable of detecting treatment effects across a broad range of non-proportional hazards scenarios. In this paper, we expand on these ideas with a framework based on a flexible resampling approach [5] which allows for the combination of various testing procedures in addition to weighted log-rank tests. In particular, we describe how tests based on restricted mean survival time (RMST) comparisons can be included within combinations of weighted log-rank tests as well as other test statistics such as Tarone-Ware and Renyi-type supremum families. For estimation, we propose companion weighted Cox model estimators [14, 21, 22] which utilize the weighting form that is “selected” through the combination test and provide simultaneous confidence intervals. The performance of various combinations and their companion Cox estimators as well as RMST are evaluated in simulation studies under null, proportional hazards, late-separation, and early-separation scenarios. We find the combination tests perform quite well in controlling type-1 error rates and in achieving higher power than individual tests across the scenarios considered here. We suggest the companion Cox estimators are a natural link to the testing procedures and can be a useful complementary summary of treatment effects with careful interpretation. For illustration, we apply the proposals to a randomized clinical trial study of the PD-L1-targeted therapy atezolizumab in comparison with docetaxel in previously treated non-small-cell lung cancer patients. R code can be found at https://github.com/larryleon/combination-tests-and-estimators.

Measuring Survival Benefit in Health Technology Assessment in the Presence of Nonproportional Hazards

BackgroundProportional hazards (PH) is an assumption often made by researchers, despite evidence of nonproportionality in a significant proportion of clinical trials. In the presence of non-PH, the interpretation of hazard ratios, medians, and landmark survival as summary measures of treatment effect can become problematic. Several recent studies have recommended restricted mean survival time (RMST) as an alternative metric for survival analysis, particularly where non-PH may apply. ObjectivesTo determine the current approaches of health technology assessment (HTA) agencies to value assessment in the presence of non-PH, and the extent to which RMST is accepted as an alternative measure of treatment benefit. MethodsMethodological guidelines published by 10 HTA agencies were reviewed to establish recommended approaches for presenting survival benefit from clinical trials. Published HTA reports for 23 oncology agents approved by the US Food and Drug Administration and the European Medicines Agency since 2014 were reviewed to determine how guidelines are implemented in practice and identify instances where the PH assumption was tested and RMST analyses reported. ResultsTesting for non-PH is not widely incorporated into HTA except by the UK National Institute for Health and Care Excellence. RMST is used infrequently but has been used in a number of countries, particularly by agencies that focus on cost effectiveness. ConclusionsHTA agencies vary in their approaches to non-PH. Most do not routinely check the PH assumption. RMST has played a role in assessing clinical benefit within HTA, although not consistently within countries (across drugs) or across countries (for the same drug).

Weighted Cox Regression Using the R Package coxphw

Cox's regression model for the analysis of survival data relies on the proportional hazards assumption. However, this assumption is often violated in practice and as a consequence the average relative risk may be under- or overestimated. Weighted estimation of Cox regression is a parsimonious alternative which supplies well interpretable average effects also in case of non-proportional hazards. We provide the R package coxphw implementing weighted Cox regression. By means of two biomedical examples appropriate analyses in the presence of non-proportional hazards are exemplified and advantages of weighted Cox regression are discussed. Moreover, using package coxphw, time-dependent effects can be conveniently estimated by including interactions of covariates with arbitrary functions of time.

Analysis techniques in the presence of non-proportional hazards (PH); application to an ovarian cancer RCT with long-term follow-up

AHT was an international, non-blinded phase III RCT designed to assess whether administering adjuvant hormone therapy (AHT) after ovarian cancer affects overall survival (OS). Between 1990-1995, 150 patients were randomised to receive AHT (n=75) or no AHT (Control, n=75). Death data for UK patients (83% of total) provided by the Health and Social Care Information Centre (HSCIC) has allowed long-term follow-up and therefore detailed investigation into the pattern of events over time. At time of data snapshot, median follow-up was 19yrs.

Authors' Reply to 'Pyogenic Liver Abscess and Risk of Acute Pancreatitis'.

Dear Dr. Shen, We sincerely thank you for your interest in our study, which was recently published in the Journal of Epidemiology.1 First, we agree that, in the presence of non-proportional hazards, presenting an average hazard ratio (HR) over the entire follow-up period might not be informative because the magnitude of effect changes over time. However, a methodology report has shown that period-specific HRs (ie, HRs estimated in time-partitioned periods) may have built-in selection bias.2 Therefore, instead of time-partitioned estimations, we presented a series of average HRs with increasingly longer follow-up time, with findings showing that the elevated risk of acute pancreatitis associated with pyogenic liver abscess steadily decreased over time and that the association persisted for 5 years (Table 2 of our paper). Second, we agree that the strength of interaction effects of pyogenic liver abscess and comorbidities on risk of acute pancreatitis (Table 3 of our paper) may differ among time-partitioned periods. If possible, we will analyze this effect for each time-partitioned period in further research. We appreciate your helpful comments.

Individual patient data meta-analysis of survival data using Poisson regression models

BackgroundAn Individual Patient Data (IPD) meta-analysis is often considered the gold-standard for synthesising survival data from clinical trials. An IPD meta-analysis can be achieved by either a two-stage or a one-stage approach, depending on whether the trials are analysed separately or simultaneously. A range of one-stage hierarchical Cox models have been previously proposed, but these are known to be computationally intensive and are not currently available in all standard statistical software. We describe an alternative approach using Poisson based Generalised Linear Models (GLMs).MethodsWe illustrate, through application and simulation, the Poisson approach both classically and in a Bayesian framework, in two-stage and one-stage approaches. We outline the benefits of our one-stage approach through extension to modelling treatment-covariate interactions and non-proportional hazards. Ten trials of hypertension treatment, with all-cause death the outcome of interest, are used to apply and assess the approach.ResultsWe show that the Poisson approach obtains almost identical estimates to the Cox model, is additionally computationally efficient and directly estimates the baseline hazard. Some downward bias is observed in classical estimates of the heterogeneity in the treatment effect, with improved performance from the Bayesian approach.ConclusionOur approach provides a highly flexible and computationally efficient framework, available in all standard statistical software, to the investigation of not only heterogeneity, but the presence of non-proportional hazards and treatment effect modifiers.

Double Inverse-Weighted Estimation of Cumulative Treatment Effects Under Nonproportional Hazards and Dependent Censoring

In medical studies of time-to-event data, nonproportional hazards and dependent censoring are very common issues when estimating the treatment effect. A traditional method for dealing with time-dependent treatment effects is to model the time-dependence parametrically. Limitations of this approach include the difficulty to verify the correctness of the specified functional form and the fact that, in the presence of a treatment effect that varies over time, investigators are usually interested in the cumulative as opposed to instantaneous treatment effect. In many applications, censoring time is not independent of event time. Therefore, we propose methods for estimating the cumulative treatment effect in the presence of nonproportional hazards and dependent censoring. Three measures are proposed, including the ratio of cumulative hazards, relative risk, and difference in restricted mean lifetime. For each measure, we propose a double inverse-weighted estimator, constructed by first using inverse probability of treatment weighting (IPTW) to balance the treatment-specific covariate distributions, then using inverse probability of censoring weighting (IPCW) to overcome the dependent censoring. The proposed estimators are shown to be consistent and asymptotically normal. We study their finite-sample properties through simulation. The proposed methods are used to compare kidney wait-list mortality by race.

Estimating Cumulative Treatment Effects in the Presence of Nonproportional Hazards

Often in medical studies of time to an event, the treatment effect is not constant over time. In the context of Cox regression modeling, the most frequent solution is to apply a model that assumes the treatment effect is either piecewise constant or varies smoothly over time, i.e., the Cox nonproportional hazards model. This approach has at least two major limitations. First, it is generally difficult to assess whether the parametric form chosen for the treatment effect is correct. Second, in the presence of nonproportional hazards, investigators are usually more interested in the cumulative than the instantaneous treatment effect (e.g., determining if and when the survival functions cross). Therefore, we propose an estimator for the aggregate treatment effect in the presence of nonproportional hazards. Our estimator is based on the treatment-specific baseline cumulative hazards estimated under a stratified Cox model. No functional form for the nonproportionality need be assumed. Asymptotic properties of the proposed estimators are derived, and the finite-sample properties are assessed in simulation studies. Pointwise and simultaneous confidence bands of the estimator can be computed. The proposed method is applied to data from a national organ failure registry.

Sample size determination in complex clinical trials comparing more than two groups for survival endpoints.

This paper presents a sample size formula for testing the equality of kappa (> or = 2) survival distributions using the Tarone-Ware class of test statistics in the presence of non-proportional hazards, time dependent losses, non-compliance and drop-in. This method extends the derivation by Lakatos of a sample size formula for comparing two survival distributions. A sample size formula is also presented for the stratified logrank test. We describe how one can utilize these generalized formulae in calculating sample sizes and assessing power in complex multi-arm clinical trials.