Causal assessment of surrogacy in a meta-analysis of colorectal cancer trials

When the true end points (T) are difficult or costly to measure, surrogate markers (S) are often collected in clinical trials to help predict the effect of the treatment (Z). There is great interest in understanding the relationship among S, T, and Z. A principal stratification (PS) framework has been proposed by Frangakis and Rubin (2002) to study their causal associations. In this paper, we extend the framework to a multiple trial setting and propose a Bayesian hierarchical PS model to assess surrogacy. We apply the method to data from a large collection of colon cancer trials in which S and T are binary. We obtain the trial-specific causal measures among S, T, and Z, as well as their overall population-level counterparts that are invariant across trials. The method allows for information sharing across trials and reduces the nonidentifiability problem. We examine the frequentist properties of our model estimates and the impact of the monotonicity assumption using simulations. We also illustrate the challenges in evaluating surrogacy in the counterfactual framework that result from nonidentifiability.     

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.     

Gestational surrogacy and the role of routine embryo screening: Current challenges and future directions for preimplantation genetic testing

Preimplantation genetic screening (PGS) is a component of IVF entailing selection of an embryo for transfer on the basis of chromosomal normalcy. If PGS were integrated with single embryo transfer (SET) in a surrogacy setting, this approach could improve pregnancy rates, minimize miscarriage risk, and limit multiple gestations. Even without PGS, pregnancy rates for IVF surrogacy cases are generally satisfactory, especially when treatment utilizes embryos derived from young oocytes and transferred to a healthy surrogate. However, there could be a more general role for PGS in surrogacy, since background aneuploidy in embryos remains a major factor driving implantation failure and miscarriage for all infertility patients. At present, the proportion of IVF cases involving GS is limited, while the number of IVF patients requesting PGS appears to be increasing. In this report, the relevance of PGS for surrogacy in the rapidly changing field of assisted fertility medicine is discussed. Birth Defects Research (Part C) 108:98–102, 2016. © 2015 Wiley Periodicals, Inc.     

Commentary on "Principal stratification - a goal or a tool?" by Judea Pearl

This commentary takes up Pearl's welcome challenge to clearly articulate the scientific value of principal stratification estimands that we and colleagues have investigated, in the area of randomized placebo-controlled preventive vaccine efficacy trials, especially trials of HIV vaccines. After briefly arguing that certain principal stratification estimands for studying vaccine effects on post-infection outcomes are of genuine scientific interest, the bulk of our commentary argues that the "causal effect predictiveness" (CEP) principal stratification estimand for evaluating immune biomarkers as surrogate endpoints is not of ultimate scientific interest, because it evaluates surrogacy restricted to the setting of a particular vaccine efficacy trial, but is nevertheless useful for guiding the selection of primary immune biomarker endpoints in Phase I/II vaccine trials and for facilitating assessment of transportability/bridging surrogacy.     

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.     

Validation of surrogate markers in multiple randomized clinical trials with repeated measurements: canonical correlation approach

Part of the recent literature on the evaluation of biomarkers as surrogate endpoints starts from a multitrial context, which leads to a definition of validity in terms of the quality of both trial-level and individual-level association between the surrogate and true endpoints (Buyse et al., 2000, Biostatistics1, 49-67). These authors concentrated on cross-sectional continuous responses. However, in many randomized clinical studies, repeated measurements are encountered on either or both endpoints. A challenge in this setting is the formulation of a simple and meaningful concept of "surrogacy."Alonso et al. (2003, Biometrical Journal45, 931-945) proposed the variance reduction factor (VRF) to evaluate surrogacy at the individual level. They also showed how and when this concept should be extended to study surrogacy at the trial level. Here, we approach the problem from the natural canonical correlation perspective. We define a class of canonical correlation functions that can be used to study surrogacy at the trial and individual level. We show that the VRF and the R2 measure defined by Buyse et al. (2000) follow as special cases. Simulations are conducted to evaluate the performance of different members of this family. The methodology is illustrated on data from a meta-analysis of five clinical trials comparing antipsychotic agents for the treatment of chronic schizophrenia.     

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).     

Best Practicable Aggregation of Species: a step forward for species surrogacy in environmental assessment and monitoring

The available taxonomic expertise and knowledge of species is still inadequate to cope with the urgent need for cost‐effective methods to quantifying community response to natural and anthropogenic drivers of change. So far, the mainstream approach to overcome these impediments has focused on using higher taxa as surrogates for species. However, the use of such taxonomic surrogates often limits inferences about the causality of community patterns, which in turn is essential for effective environmental management strategies. Here, we propose an alternative approach to species surrogacy, the “Best Practicable Aggregation of Species” (BestAgg), in which surrogates exulate from fixed taxonomic schemes. The approach uses null models from random aggregations of species to minimizing the number of surrogates without causing significant losses of information on community patterns. Surrogate types are then selected in order to maximize ecological information. We applied the approach to real case studies on natural and human‐driven gradients from marine benthic communities. Outcomes from BestAgg were also compared with those obtained using classic taxonomic surrogates. Results showed that BestAgg surrogates are effective in detecting community changes. In contrast to classic taxonomic surrogates, BestAgg surrogates allow retaining significantly higher information on species‐level community patterns than what is expected to occur by chance and a potential time saving during sample processing up to 25% higher. Our findings showed that BestAgg surrogates from a pilot study could be used successfully in similar environmental investigations in the same area, or for subsequent long‐term monitoring programs. BestAgg is virtually applicable to any environmental context, allowing exploiting multiple surrogacy schemes beyond stagnant perspectives strictly relying on taxonomic relatedness among species. This prerogative is crucial to extend the concept of species surrogacy to ecological traits of species, thus leading to ecologically meaningful surrogates that, while cost effective in reflecting community patterns, may also contribute to unveil underlying processes. A specific R code for BestAgg is provided.     

Little loss of information due to unknown phase for fine-scale linkage-disequilibrium mapping with single-nucleotide-polymorphism genotype data

We present the results of a simulation study that indicate that true haplotypes at multiple, tightly linked loci often provide little extra information for linkage-disequilibrium fine mapping, compared with the information provided by corresponding genotypes, provided that an appropriate statistical analysis method is used. In contrast, a two-stage approach to analyzing genotype data, in which haplotypes are inferred and then analyzed as if they were true haplotypes, can lead to a substantial loss of information. The study uses our COLDMAP software for fine mapping, which implements a Markov chain-Monte Carlo algorithm that is based on the shattered coalescent model of genetic heterogeneity at a disease locus. We applied COLDMAP to 100 replicate data sets simulated under each of 18 disease models. Each data set consists of haplotype pairs (diplotypes) for 20 SNPs typed at equal 50-kb intervals in a 950-kb candidate region that includes a single disease locus located at random. The data sets were analyzed in three formats: (1). as true haplotypes; (2). as haplotypes inferred from genotypes using an expectation-maximization algorithm; and (3). as unphased genotypes. On average, true haplotypes gave a 6% gain in efficiency compared with the unphased genotypes, whereas inferring haplotypes from genotypes led to a 20% loss of efficiency, where efficiency is defined in terms of root mean integrated square error of the location of the disease locus. Furthermore, treating inferred haplotypes as if they were true haplotypes leads to considerable overconfidence in estimates, with nominal 50% credibility intervals achieving, on average, only 19% coverage. We conclude that (1). given appropriate statistical analyses, the costs of directly measuring haplotypes will rarely be justified by a gain in the efficiency of fine mapping and that (2). a two-stage approach of inferring haplotypes followed by a haplotype-based analysis can be very inefficient for fine mapping, compared with an analysis based directly on the genotypes.     

A unified procedure for meta-analytic evaluation of surrogate end points in randomized clinical trials

The meta-analytic approach to evaluating surrogate end points assesses the predictiveness of treatment effect on the surrogate toward treatment effect on the clinical end point based on multiple clinical trials. Definition and estimation of the correlation of treatment effects were developed in linear mixed models and later extended to binary or failure time outcomes on a case-by-case basis. In a general regression setting that covers nonnormal outcomes, we discuss in this paper several metrics that are useful in the meta-analytic evaluation of surrogacy. We propose a unified 3-step procedure to assess these metrics in settings with binary end points, time-to-event outcomes, or repeated measures. First, the joint distribution of estimated treatment effects is ascertained by an estimating equation approach; second, the restricted maximum likelihood method is used to estimate the means and the variance components of the random treatment effects; finally, confidence intervals are constructed by a parametric bootstrap procedure. The proposed method is evaluated by simulations and applications to 2 clinical trials.     

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.     

Enhancing autonomy in paid surrogacy

The gestational surrogate – and her economic and educational vulnerability in particular – is the focus of many of the most persistent worries about paid surrogacy. Those who employ her, and those who broker and organize her services, usually have an advantage over her in resources and information. That asymmetry exposes her to the possibility of exploitation and abuse. Accordingly, some argue for banning paid surrogacy. Others defend legal permission on grounds of surrogate autonomy, but often retain concerns about the surrogate. In response to the dilemma of a ban versus bald permission, we propose a 'soft law' approach: states should require several hours of education of surrogates – education aimed at informing and enhancing surrogate autonomy.     

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.     

Design and Analysis of Multiple Events Case–Control Studies

Summary In case–control research where there are multiple case groups, standard analyses fail to make use of all available information. Multiple events case–control (MECC) studies provide a new approach to sampling from a cohort and are useful when it is desired to study multiple types of events in the cohort. In this design, subjects in the cohort who develop any event of interest are sampled, as well as a fraction of the remaining subjects. We show that a simple case–control analysis of data arising from MECC studies is biased and develop three general estimating‐equation‐based approaches to analyzing data from these studies. We conduct simulation studies to compare the efficiency of the various MECC analyses with each other and with the corresponding conventional analyses. It is shown that the gain in efficiency by using the new design is substantial in many situations. We demonstrate the application of our approach to a nested case–control study of the effect of oral sodium phosphate use on chronic kidney injury with multiple case definitions.     

A Bayesian Approach to Surrogacy Assessment Using Principal Stratification in Clinical Trials

Summary A surrogate marker (S) is a variable that can be measured earlier and often more easily than the true endpoint (T) in a clinical trial. Most previous research has been devoted to developing surrogacy measures to quantify how well S can replace T or examining the use of S in predicting the effect of a treatment (Z). However, the research often requires one to fit models for the distribution of T given S and Z. It is well known that such models do not have causal interpretations because the models condition on a postrandomization variable S. In this article, we directly model the relationship among T, S, and Z using a potential outcomes framework introduced by Frangakis and Rubin (2002, Biometrics 58 , 21–29). We propose a Bayesian estimation method to evaluate the causal probabilities associated with the cross‐classification of the potential outcomes of S and T when S and T are both binary. We use a log‐linear model to directly model the association between the potential outcomes of S and T through the odds ratios. The quantities derived from this approach always have causal interpretations. However, this causal model is not identifiable from the data without additional assumptions. To reduce the nonidentifiability problem and increase the precision of statistical inferences, we assume monotonicity and incorporate prior belief that is plausible in the surrogate context by using prior distributions. We also explore the relationship among the surrogacy measures based on traditional models and this counterfactual model. The method is applied to the data from a glaucoma treatment study.     

Optimal selection of epitopes for TXP-immunoaffinity mass spectrometry

Background  

Mass spectrometry (MS) based protein profiling has become one of the key technologies in biomedical research and biomarker discovery. One bottleneck in MS-based protein analysis is sample preparation and an efficient fractionation step to reduce the complexity of the biological samples, which are too complex to be analyzed directly with MS. Sample preparation strategies that reduce the complexity of tryptic digests by using immunoaffinity based methods have shown to lead to a substantial increase in throughput and sensitivity in the proteomic mass spectrometry approach. The limitation of using such immunoaffinity-based approaches is the availability of the appropriate peptide specific capture antibodies. Recent developments in these approaches, where subsets of peptides with short identical terminal sequences can be enriched using antibodies directed against short terminal epitopes, promise a significant gain in efficiency.     

Statistical considerations of optimal study design for human plasma proteomics and biomarker discovery

A mass spectrometry-based plasma biomarker discovery workflow was developed to facilitate biomarker discovery. Plasma from either healthy volunteers or patients with pancreatic cancer was 8-plex iTRAQ labeled, fractionated by 2-dimensional reversed phase chromatography and subjected to MALDI ToF/ToF mass spectrometry. Data were processed using a q-value based statistical approach to maximize protein quantification and identification. Technical (between duplicate samples) and biological variance (between and within individuals) were calculated and power analysis was thereby enabled. An a priori power analysis was carried out using samples from healthy volunteers to define sample sizes required for robust biomarker identification. The result was subsequently validated with a post hoc power analysis using a real clinical setting involving pancreatic cancer patients. This demonstrated that six samples per group (e.g., pre- vs post-treatment) may provide sufficient statistical power for most proteins with changes>2 fold. A reference standard allowed direct comparison of protein expression changes between multiple experiments. Analysis of patient plasma prior to treatment identified 29 proteins with significant changes within individual patient. Changes in Peroxiredoxin II levels were confirmed by Western blot. This q-value based statistical approach in combination with reference standard samples can be applied with confidence in the design and execution of clinical studies for predictive, prognostic, and/or pharmacodynamic biomarker discovery. The power analysis provides information required prior to study initiation.     

On meta-analytic assessment of surrogate outcomes

We discuss the strengths and weaknesses of the meta-analytic approach to estimating the effect of a new treatment on a true clinical outcome measure, T, from the effect of treatment on a surrogate response, S. The meta-analytic approach (see Daniels and Hughes (1997) 16, 1965-1982) uses data from a series of previous studies of interventions similar to the new treatment. The data are used to estimate relationships between summary measures of treatment effects on T and S that can be used to infer the magnitude of the effect of the new treatment on T from its effects on S. We extend the class of models to cover a broad range of applications in which the parameters define features of the marginal distribution of (T, S). We present a new bootstrap procedure to allow for the variability in estimating the distribution that governs the between-study variation. Ignoring this variability can lead to confidence intervals that are much too narrow. The meta-analytic approach relies on quite different data and assumptions than procedures that depend, for example, on the conditional independence, at the individual level, of treatment and T, given S (see Prentice (1989) 8, 431-440). Meta-analytic calculations in this paper can be used to determine whether a new study, based only on S, will yield estimates of the treatment effect on T that are precise enough to be useful. Compared to direct measurement on T, the meta-analytic approach has a number of limitations, including likely serious loss of precision and difficulties in defining the class of previous studies to be used to predict the effects on T for a new intervention.     

Personalized Evaluation of Biomarker Value: A Cost-Benefit Perspective

For a patient who is facing a treatment decision, the added value of information provided by a biomarker depends on the individual patient’s expected response to treatment with and without the biomarker, as well as his/her tolerance of disease and treatment harm. However, individualized estimators of the value of a biomarker are lacking. We propose a new graphical tool named the subject-specific expected benefit curve for quantifying the personalized value of a biomarker in aiding a treatment decision. We develop semiparametric estimators for two general settings: (i) when biomarker data are available from a randomized trial; and (ii) when biomarker data are available from a cohort or a cross-sectional study, together with external information about a multiplicative treatment effect. We also develop adaptive bootstrap confidence intervals for consistent inference in the presence of nonregularity. The proposed method is used to evaluate the individualized value of the serum creatinine marker in informing treatment decisions for the prevention of renal artery stenosis.