Semiparametric inference for surrogate endpoints with bivariate censored data

Summary .   Considerable attention has been recently paid to the use of surrogate endpoints in clinical research. We deal with the situation where the two endpoints are both right censored. While proportional hazards analyses are typically used for this setting, their use leads to several complications. In this article, we propose the use of the accelerated failure time model for analysis of surrogate endpoints. Based on the model, we then describe estimation and inference procedures for several measures of surrogacy. A complication is that potentially both the independent and dependent variable are subject to censoring. We adapt the Theil–Sen estimator to this problem, develop the associated asymptotic results, and propose a novel resampling-based technique for calculating the variances of the proposed estimators. The finite-sample properties of the estimation methodology are assessed using simulation studies, and the proposed procedures are applied to data from an acute myelogenous leukemia clinical trial.     

On assessing surrogacy in a single trial setting using a semicompeting risks paradigm

Summary .  There has been a recent emphasis on the identification of biomarkers and other biologic measures that may be potentially used as surrogate endpoints in clinical trials. We focus on the setting of data from a single clinical trial. In this article, we consider a framework in which the surrogate must occur before the true endpoint. This suggests viewing the surrogate and true endpoints as semicompeting risks data; this approach is new to the literature on surrogate endpoints and leads to an asymmetrical treatment of the surrogate and true endpoints. However, such a data structure also conceptually complicates many of the previously considered measures of surrogacy in the literature. We propose novel estimation and inferential procedures for the relative effect and adjusted association quantities proposed by Buyse and Molenberghs (1998, Biometrics 54, 1014–1029). The proposed methodology is illustrated with application to simulated data, as well as to data from a leukemia study.     

Bayesian adaptive trial design for a newly validated surrogate endpoint

The evaluation of surrogate endpoints for primary use in future clinical trials is an increasingly important research area, due to demands for more efficient trials coupled with recent regulatory acceptance of some surrogates as 'valid.' However, little consideration has been given to how a trial that utilizes a newly validated surrogate endpoint as its primary endpoint might be appropriately designed. We propose a novel Bayesian adaptive trial design that allows the new surrogate endpoint to play a dominant role in assessing the effect of an intervention, while remaining realistically cautious about its use. By incorporating multitrial historical information on the validated relationship between the surrogate and clinical endpoints, then subsequently evaluating accumulating data against this relationship as the new trial progresses, we adaptively guard against an erroneous assessment of treatment based upon a truly invalid surrogate. When the joint outcomes in the new trial seem plausible given similar historical trials, we proceed with the surrogate endpoint as the primary endpoint, and do so adaptively-perhaps stopping the trial for early success or inferiority of the experimental treatment, or for futility. Otherwise, we discard the surrogate and switch adaptive determinations to the original primary endpoint. We use simulation to test the operating characteristics of this new design compared to a standard O'Brien-Fleming approach, as well as the ability of our design to discriminate trustworthy from untrustworthy surrogates in hypothetical future trials. Furthermore, we investigate possible benefits using patient-level data from 18 adjuvant therapy trials in colon cancer, where disease-free survival is considered a newly validated surrogate endpoint for overall survival.     

Comparing biomarkers as principal surrogate endpoints

Recently a new definition of surrogate endpoint, the "principal surrogate," was proposed based on causal associations between treatment effects on the biomarker and on the clinical endpoint. Despite its appealing interpretation, limited research has been conducted to evaluate principal surrogates, and existing methods focus on risk models that consider a single biomarker. How to compare principal surrogate value of biomarkers or general risk models that consider multiple biomarkers remains an open research question. We propose to characterize a marker or risk model's principal surrogate value based on the distribution of risk difference between interventions. In addition, we propose a novel summary measure (the standardized total gain) that can be used to compare markers and to assess the incremental value of a new marker. We develop a semiparametric estimated-likelihood method to estimate the joint surrogate value of multiple biomarkers. This method accommodates two-phase sampling of biomarkers and is more widely applicable than existing nonparametric methods by incorporating continuous baseline covariates to predict the biomarker(s), and is more robust than existing parametric methods by leaving the error distribution of markers unspecified. The methodology is illustrated using a simulated example set and a real data set in the context of HIV vaccine trials.     

The Use of Surrogate Endpoints in Regulating Medicines for Cardio-Renal Disease: Opinions of Stakeholders

Aim

There is discussion whether medicines can be authorized on the market based on evidence from surrogate endpoints. We assessed opinions of different stakeholders on this topic.

Methods

We conducted an online questionnaire that targeted various stakeholder groups (regulatory agencies, pharmaceutical industry, academia, relevant public sector organisations) and medical specialties (cardiology or nephrology vs. other). Participants were enrolled through purposeful sampling. We inquired for conditions under which surrogate endpoints can be used, the validity of various cardio-renal biomarkers and new approaches for biomarker use.

Results

Participants agreed that surrogate endpoints can be used when the surrogate is scientifically valid (5-point Likert response format, mean score: 4.3, SD: 0.9) or when there is an unmet clinical need (mean score: 3.8, SD: 1.2). Industry participants agreed to a greater extent than regulators and academics. However, out of four proposed surrogates (blood pressure (BP), HbA1c, albuminuria, CRP) for cardiovascular outcomes or end-stage renal disease, only use of BP for cardiovascular outcomes was deemed moderately accurate (mean: 3.6, SD: 1.1). Specialists in cardiology or nephrology tended to be more positive about the use of surrogate endpoints.

Conclusion

Stakeholders in drug development do not oppose to the use of surrogate endpoints in drug marketing authorization, but most surrogates are not considered valid. To solve this impasse, increased efforts are required to validate surrogate endpoints and to explore alternative ways to use them.     

Proportion of treatment effect mediated by surrogate endpoints

One of the central aims in randomized clinical trials is to find well‐validated surrogate endpoints to reduce the sample size and/or duration of trials. Clinical researchers and practitioners have proposed various surrogacy measures for assessing candidate surrogate endpoints. However, most existing surrogacy measures have the following shortcomings: (i) they often fall outside the range [0,1], (ii) they are imprecisely estimated, and (iii) they ignore the interaction associations between a treatment and candidate surrogate endpoints in the evaluation of the surrogacy level. To overcome these difficulties, we propose a new surrogacy measure, the proportion of treatment effect mediated by candidate surrogate endpoints (PMS), based on the decomposition of the treatment effect into direct, indirect, and interaction associations mediated by candidate surrogate endpoints. In addition, we validate the advantages of PMS through Monte Carlo simulations and the application to empirical data from ORIENT (the Olmesartan Reducing Incidence of Endstage Renal Disease in Diabetic Nephropathy Trial).     

A Bayesian platform trial design to simultaneously evaluate multiple drugs in multiple indications with mixed endpoints

In the era of targeted therapies and immunotherapies, the traditional drug development paradigm of testing one drug at a time in one indication has become increasingly inefficient. Motivated by a real-world application, we propose a master-protocol–based Bayesian platform trial design with mixed endpoints (PDME) to simultaneously evaluate multiple drugs in multiple indications, where different subsets of efficacy measures (eg, objective response and landmark progression-free survival) may be used by different indications as single or multiple endpoints. We propose a Bayesian hierarchical model to accommodate mixed endpoints and reflect the trial structure of indications that are nested within treatments. We develop a two-stage approach that first clusters the indications into homogeneous subgroups and then applies the Bayesian hierarchical model to each subgroup to achieve precision information borrowing. Patients are enrolled in a group-sequential way and adaptively assigned to treatments according to their efficacy estimates. At each interim analysis, the posterior probabilities that the treatment effect exceeds prespecified clinically relevant thresholds are used to drop ineffective treatments and “graduate” effective treatments. Simulations show that the PDME design has desirable operating characteristics compared to existing method.     

Robust approach to combining multiple markers to improve surrogacy

Identifying effective and valid surrogate markers to make inference about a treatment effect on long-term outcomes is an important step in improving the efficiency of clinical trials. Replacing a long-term outcome with short-term and/or cheaper surrogate markers can potentially shorten study duration and reduce trial costs. There is sizable statistical literature on methods to quantify the effectiveness of a single surrogate marker. Both parametric and nonparametric approaches have been well developed for different outcome types. However, when there are multiple markers available, methods for combining markers to construct a composite marker with improved surrogacy remain limited. In this paper, building on top of the optimal transformation framework of Wang et al. (2020), we propose a novel calibrated model fusion approach to optimally combine multiple markers to improve surrogacy. Specifically, we obtain two initial estimates of optimal composite scores of the markers based on two sets of models with one set approximating the underlying data distribution and the other directly approximating the optimal transformation function. We then estimate an optimal calibrated combination of the two estimated scores which ensures both validity of the final combined score and optimality with respect to the proportion of treatment effect explained by the final combined score. This approach is unique in that it identifies an optimal combination of the multiple surrogates without strictly relying on parametric assumptions while borrowing modeling strategies to avoid fully nonparametric estimation which is subject to the curse of dimensionality. Our identified optimal transformation can also be used to directly quantify the surrogacy of this identified combined score. Theoretical properties of the proposed estimators are derived, and the finite sample performance of the proposed method is evaluated through simulation studies. We further illustrate the proposed method using data from the Diabetes Prevention Program study.     

Carotid intimal-media thickness as a surrogate for cardiovascular disease events in trials of HMG-CoA reductase inhibitors

BACKGROUND: Surrogate measures for cardiovascular disease events have the potential to increase greatly the efficiency of clinical trials. A leading candidate for such a surrogate is the progression of intima-media thickness (IMT) of the carotid artery; much experience has been gained with this endpoint in trials of HMG-CoA reductase inhibitors (statins). METHODS AND RESULTS: We examine two separate systems of criteria that have been proposed to define surrogate endpoints, based on clinical and statistical arguments. We use published results and a formal meta-analysis to evaluate whether progression of carotid IMT meets these criteria for HMG-CoA reductase inhibitors (statins).IMT meets clinical-based criteria to serve as a surrogate endpoint for cardiovascular events in statin trials, based on relative efficiency, linkage to endpoints, and congruency of effects. Results from a meta-analysis and post-trial follow-up from a single published study suggest that IMT meets established statistical criteria by accounting for intervention effects in regression models. CONCLUSION: Carotid IMT progression meets accepted definitions of a surrogate for cardiovascular disease endpoints in statin trials. This does not, however, establish that it may serve universally as a surrogate marker in trials of other agents.     

Meta-analysis for surrogacy: accelerated failure time models and semicompeting risks modeling

There has been great recent interest in the medical and statistical literature in the assessment and validation of surrogate endpoints as proxies for clinical endpoints in medical studies. More recently, authors have focused on using metaanalytical methods for quantification of surrogacy. In this article, we extend existing procedures for analysis based on the accelerated failure time model to this setting. An advantage of this approach relative to proportional hazards model is that it allows for analysis in the semicompeting risks setting, where we model the region where the surrogate endpoint occurs before the true endpoint. Several estimation methods and attendant inferential procedures are presented. In addition, between- and within-trial methods for evaluating surrogacy are developed; a novel principal components procedure is developed for quantifying trial-level surrogacy. The methods are illustrated by application to data from several studies in colorectal cancer.     

Solutions for surrogacy validation with longitudinal outcomes for a gene therapy

Valid surrogate endpoints S can be used as a substitute for a true outcome of interest T to measure treatment efficacy in a clinical trial. We propose a causal inference approach to validate a surrogate by incorporating longitudinal measurements of the true outcomes using a mixed modeling approach, and we define models and quantities for validation that may vary across the study period using principal surrogacy criteria. We consider a surrogate-dependent treatment efficacy curve that allows us to validate the surrogate at different time points. We extend these methods to accommodate a delayed-start treatment design where all patients eventually receive the treatment. Not all parameters are identified in the general setting. We apply a Bayesian approach for estimation and inference, utilizing more informative prior distributions for selected parameters. We consider the sensitivity of these prior assumptions as well as assumptions of independence among certain counterfactual quantities conditional on pretreatment covariates to improve identifiability. We examine the frequentist properties (bias of point and variance estimates, credible interval coverage) of a Bayesian imputation method. Our work is motivated by a clinical trial of a gene therapy where the functional outcomes are measured repeatedly throughout the trial.     

A Systems Model Approach to Determining Resilience Surrogates for Case Studies

Resilience theory offers a framework for understanding the dynamics of complex systems. However, operationalizing resilience theory to develop and test empirical hypotheses can be difficult. We present a method in which simple systems models are used as a framework to identify resilience surrogates for case studies. The process of constructing a systems model for a particular case offers a path for identifying important variables related to system resilience, including the slowly-changing variables and thresholds that often are keys to understanding the resilience of a system. We develop a four-step process for identifying resilience surrogates through development of systems models. Because systems model development is often a difficult step, we summarize four basic existing systems models and give examples of how each may be used to identify resilience surrogates. The construction and analysis of simple systems models provides a useful basis for guiding and directing the selection of surrogate variables that will offer appropriate empirical measures of resilience.     

Learning from clinical medicine to improve the use of surrogates in ecology

Surrogates are used widely in ecology to detect or monitor changes in the environment that are too difficult or costly to assess directly. Yet most work on surrogates to date has been correlative, with little work on their predictive capacity or the circumstances under which they work. Our suggestion is to revisit and learn from research in the clinical medical sciences, including the causal statistical frameworks available to validate relationships between treatments, surrogate variables, and the outcome of interest. We adapt this medical thinking to ecology by providing a new framework that involves specification of the surrogate model, statistical validation, and subsequent evaluation in a range of spatial and temporal contexts. An inter‐disciplinary surrogate concept will allow for a more rigorous approach to validating and evaluating proxy variables, thus advancing the selection and application of surrogates in ecology. Synthesis We draw together ideas from the medical sciences to define an explicit surrogate concept that has not previously been used in ecology. We present a new framework for specifying surrogate models involving validation using a causal framework, and subsequent re‐evaluation in different spatial and temporal contexts – an approach closely aligned with that used by researchers in the clinical medical sciences. This rigorous method can advance the science underpinning the application of surrogates in ecology by shifting the focus away from correlative understanding to one that focuses instead on causation and prediction. An improved use of surrogates is imperative if we are to meet the challenge of properly measuring and understanding the multifarious and complex problems in contemporary ecology.     

Statistical validation of surrogate endpoints: is bone density a valid surrogate for fracture?

In the treatment of osteoporosis using anti-resorptive agents there has been increasing interest in quantifying the relationship between fracture endpoints and surrogates such as bone mineral density (BMD) or bone turnover markers. Statistical methodology constitutes a critical component of assessing surrogate validity. Depending on study designs, data resources, and statistical methods used for analyses, one has to use caution when interpreting results from different analyses, especially when results are disparate. For example, analyses based on individual patient data reported that only a limited proportion of the anti-fracture efficacy was explained by BMD increases for agents such as alendronate, risedronate and raloxifene. Analyses employing meta-regression based on summary statistics, however, indicated that most of the anti-fracture benefits were due to improvements in BMD. In this paper, we review definitions of surrogate endpoints and requirements for their statistical validation. We evaluate whether BMD meets these requirements as a possible surrogate for fracture. Our review indicates that the actual BMD value is correlated with fracture risk and thus BMD is useful in identifying patients that might need treatment. There is limited evidence to support BMD increase with anti-resorptive agents as a reliable substitute for fracture risk reduction. Strengths and limitations for various statistical methods are discussed.     

Counterfactual links to the proportion of treatment effect explained by a surrogate marker

In a randomized clinical trial, a statistic that measures the proportion of treatment effect on the primary clinical outcome that is explained by the treatment effect on a surrogate outcome is a useful concept. We investigate whether a statistic proposed to estimate this proportion can be given a causal interpretation as defined by models of counterfactual variables. For the situation of binary surrogate and outcome variables, two counterfactual models are considered, both of which include the concept of the proportion of the treatment effect, which acts through the surrogate. In general, the statistic does not equal either of the two proportions from the counterfactual models, and can be substantially different. Conditions are given for which the statistic does equal the counterfactual model proportions. A randomized clinical trial with potential surrogate endpoints is undertaken in a scientific context; this context will naturally place constraints on the parameters of the counterfactual model. We conducted a simulation experiment to investigate what impact these constraints had on the relationship between the proportion explained (PE) statistic and the counterfactual model proportions. We found that observable constraints had very little impact on the agreement between the statistic and the counterfactual model proportions, whereas unobservable constraints could lead to more agreement.     

Joint regression analysis for survival data in the presence of two sets of semi‐competing risks

In many clinical trials, multiple time‐to‐event endpoints including the primary endpoint (e.g., time to death) and secondary endpoints (e.g., progression‐related endpoints) are commonly used to determine treatment efficacy. These endpoints are often biologically related. This work is motivated by a study of bone marrow transplant (BMT) for leukemia patients, who may experience the acute graft‐versus‐host disease (GVHD), relapse of leukemia, and death after an allogeneic BMT. The acute GVHD is associated with the relapse free survival, and both the acute GVHD and relapse of leukemia are intermediate nonterminal events subject to dependent censoring by the informative terminal event death, but not vice versa, giving rise to survival data that are subject to two sets of semi‐competing risks. It is important to assess the impacts of prognostic factors on these three time‐to‐event endpoints. We propose a novel statistical approach that jointly models such data via a pair of copulas to account for multiple dependence structures, while the marginal distribution of each endpoint is formulated by a Cox proportional hazards model. We develop an estimation procedure based on pseudo‐likelihood and carry out simulation studies to examine the performance of the proposed method in finite samples. The practical utility of the proposed method is further illustrated with data from the motivating example.     

Evaluation of five clustering algorithms for biodiversity surrogates

Conservation planning requires knowledge of the distribution of all species in the area of interest. Surrogates for biodiversity are considered as a possible solution. The two major types are biological and environmental surrogates. Here, we evaluate four different methods of hierarchical clustering, as well as one non-hierarchical method, in the context of producing surrogates for biodiversity. Each clustering method was used to produce maps of both surrogate types. We evaluated the representativeness of each clustering method by finding the average number of species represented in a set of sites, one site of each domain, which was carried out with Monte-Carlo permutations procedure. We propose an additional measure of surrogate performance, which is the degree of evenness of the different domains, e.g., by calculating Simpson's diversity index. Surrogates with low evenness leave little flexibility in site selection since often some of the domains may be represented by a single or very few sites, and thus surrogate maps with a high Simpson's index value may be more relevant for actual decision making. We found that there is a trade-off between species representativeness and evenness. Centroid clustering represented the most species, but had very low values of evenness. Ward's method of minimum variance represented more species than a random choice, and had high evenness values. Using the typical evaluation measures, the Centroid clustering method was most efficient for surrogate production. However, when Simpson's index is also considered, Ward's method of minimum variance is more appropriate for managers.     

A measure of the proportion of treatment effect explained by a surrogate marker

Randomized clinical trials with rare primary endpoints or long duration times are costly. Because of this, there has been increasing interest in replacing the true endpoint with an earlier measured marker. However, surrogate markers must be appropriately validated. A quantitative measure for the proportion of treatment effect explained by the marker in a specific trial is a useful concept. Freedman, Graubard, and Schatzkin (1992, Statistics in Medicine 11, 167-178) suggested such a measure of surrogacy by the ratio of regression coefficients for the treatment indicator from two separate models with or without adjusting for the surrogate marker. However, it has been shown that this measure is very variable and there is no guarantee that the two models both fit. In this article, we propose alternative measures of the proportion explained that adapts an idea in Tsiatis, DeGruttola, and Wulfsohn (1995, Journal of the American Statistical Association 90, 27-37). The new measures require fewer assumptions in estimation and allow more flexibility in modeling. The estimates of these different measures are compared using data from an ophthalmology clinical trial and a series of simulation studies. The results suggest that the new measures are less variable.     

Two roles for ecological surrogacy: Indicator surrogates and management surrogates

Ecological surrogacy – here defined as using a process or element (e.g., species, ecosystem, or abiotic factor) to represent another aspect of an ecological system – is a widely used concept, but many applications of the surrogate concept have been controversial. We argue that some of this controversy reflects differences among users with different goals, a distinction that can be crystalized by recognizing two basic types of surrogate. First, many ecologists and natural resource managers measure “indicator surrogates” to provide information about ecological systems. Second, and often overlooked, are “management surrogates” (e.g., umbrella species) that are primarily used to facilitate achieving management goals, especially broad goals such as “maintain biodiversity” or “increase ecosystem resilience.” We propose that distinguishing these two overarching roles for surrogacy may facilitate better communication about project goals. This is critical when evaluating the usefulness of different surrogates, especially where a potential surrogate might be useful in one role but not another. Our classification for ecological surrogacy applies to species, ecosystems, ecological processes, abiotic factors, and genetics, and thus can provide coherence across a broad range of uses.     

The use of coarser taxonomic resolution in studies of predation on marine sedimentary fauna

Given the logistical difficulties, cost, and time involved in species-level identifications, several authors have proposed the use of coarser taxonomic resolution (e.g. family, order) in studies of pollution. The use of surrogates instead of species relies on their sufficiency to detect community responses to the pollution gradient without appreciable loss of information. No studies, however, have applied this approach to experimental studies such as community responses to predation disturbance and evaluated the performance of surrogates at the spatial scales typical of experiments. We addressed both problems by analyzing the results of three predation experiments carried out in Bonne Bay, Newfoundland. We pooled species data into coarser taxonomic categories (family to class) and determined whether effects of predation that were evident at the species level were also evident with the use of each coarser surrogate and increasing data transformation. Our results indicate that non-transformed data at the family level represent a reasonable surrogate of species; however, the ability to discriminate between ambient and (predator) manipulated sediments is gradually lost with data transformation and with the pooling of species into coarser taxonomic categories. Successive data transformation indicates that in this system predation plays a strong role on dominant but not necessarily rare species. Moreover, our results suggest that varying reliability of surrogates precludes the identification of a single general level of taxonomic sufficiency to be used in experimental studies. The use of surrogates, therefore, is suggested only after scrutiny and evaluation, and should be limited to preliminary studies where biodiversity has been well described.