Statistical challenges in the evaluation of surrogate endpoints in randomized trials

Multiparameter evidence synthesis in epidemiology and medical decision-making

Meta-analysis has been well-established for many years, but has been largely confined to pooling evidence on pair-wise contrasts. Broader forms of synthesis have also been described, apparently re-invented in disparate fields, each time taking different computational approaches. The potential value of Bayesian estimation of a joint posterior parameter distribution and simultaneously sampling from it for decision analysis has also been appreciated. However, applications have been relatively few in number, sometimes stylized, and presented mainly to a statistical methods audience. As a result, the potential for multiparameter evidence synthesis in both epidemiology and health technology assessment has remained largely unrecognized. The advent of flexible software for Bayesian Markov chain Monte Carlo in the shape of WinBUGS has the made these earlier strands of work more widely available. Researchers can now carry out synthesis at a realistic level of complexity. The Bristol programme has not only contributed to a growing body of literature on how to synthesize different evidence structures, but also on how to check the consistency of multiple information sources and how to use the resulting models to prioritize future research.

LDL-cholesterol differences predicted survival benefit in statin trials by the surrogate threshold effect (STE)

OBJECTIVE

We describe a new statistical method called the surrogate threshold effect (STE) that estimates the threshold level of a surrogate needed in a clinical trial to predict a benefit in the target clinical outcome. In this article, we apply this method to the LDL-cholesterol biomarker surrogate and survival benefit-target outcome in statin trials.

STUDY DESIGN AND SETTING

We identified randomized trials comparing statin treatment to placebo treatment or no treatment and reporting all-cause and cardiovascular mortality. Trials with fewer than five all-cause deaths in at least one arm were excluded. Multiple regression modeled the reduction in all-cause and cardiovascular mortality as a function of LDL-cholesterol difference. The 95% confidence and 95% prediction bands were calculated and graphed to determine the minimum LDL-cholesterol difference (the surrogate threshold) below which there would be no predicted survival benefit.

RESULTS

In 16 qualifying trials, regression analysis yielded an all-cause mortality model whose prediction bands demonstrated no overall survival gain with LDL-cholesterol difference values below 1.5 mmol/L. The cardiovascular mortality model yielded prediction bands that demonstrated no cardiovascular survival benefit with LDL-cholesterol difference values below 1.4 mmol/L.

CONCLUSIONS

In a multitrial setting, the STE approach is a promising yet straightforward statistical method for evaluating the surrogate validity of biomarkers.

Does the decision in a validation process of a surrogate endpoint change with level of significance of treatment effect? A proposal on validation of surrogate endpoints

BACKGROUND

In recent years the use of surrogate end points (S) has become an interesting issue. In clinical trials, it is important to get treatment outcomes as early as possible. For this reason there is a need for surrogate endpoints (S) which are measured earlier than the true endpoint (T). However, before a surrogate endpoint can be used it must be validated. For a candidate surrogate endpoint, for example time to recurrence, the validation result may change dramatically between clinical trials. The aim of this study is to show how the validation criterion (R(2)(trial)) proposed by Buyse et al. are influenced by the magnitude of treatment effect with an application using real data.

METHODS

The criterion R(2)(trial) proposed by Buyse et al. (2000) is applied to the four data sets from colon cancer clinical trials (C-01, C-02, C-03 and C-04). Each clinical trial is analyzed separately for treatment effect on survival (true endpoint) and recurrence free survival (surrogate endpoint) and this analysis is done also for each center in each trial. Results are used for standard validation analysis. The centers were grouped by the Wald statistic in 3 equal groups.

RESULTS

Validation criteria R(2)(trial) were 0.641 95% CI (0.432-0.782), 0.223 95% CI (0.008-0.503), 0.761 95% CI (0.550-0.872) and 0.560 95% CI (0.404-0.687) for C-01, C-02, C-03 and C-04 respectively. The R(2)(trial) criteria changed by the Wald statistics observed for the centers used in the validation process. Higher the Wald statistic groups are higher the R(2)(trial) values observed.

CONCLUSION

The recurrence free survival is not a good surrogate for overall survival in clinical trials with non significant treatment effects and moderate for significant treatment effects. This shows that the level of significance of treatment effect should be taken into account in validation process of surrogate endpoints.

ASSESSING SURROGATE ENDPOINTS IN VACCINE TRIALS WITH CASE-COHORT SAMPLING AND THE COX MODEL

Assessing immune responses to study vaccines as surrogates of protection plays a central role in vaccine clinical trials. Motivated by three ongoing or pending HIV vaccine efficacy trials, we consider such surrogate endpoint assessment in a randomized placebo-controlled trial with case-cohort sampling of immune responses and a time to event endpoint. Based on the principal surrogate definition under the principal stratification framework proposed by Frangakis and Rubin [Biometrics58 (2002) 21-29] and adapted by Gilbert and Hudgens (2006), we introduce estimands that measure the value of an immune response as a surrogate of protection in the context of the Cox proportional hazards model. The estimands are not identified because the immune response to vaccine is not measured in placebo recipients. We formulate the problem as a Cox model with missing covariates, and employ novel trial designs for predicting the missing immune responses and thereby identifying the estimands. The first design utilizes information from baseline predictors of the immune response, and bridges their relationship in the vaccine recipients to the placebo recipients. The second design provides a validation set for the unmeasured immune responses of uninfected placebo recipients by immunizing them with the study vaccine after trial closeout. A maximum estimated likelihood approach is proposed for estimation of the parameters. Simulated data examples are given to evaluate the proposed designs and study their properties.

The intermediate endpoint effect in logistic and probit regression

BACKGROUND

An intermediate endpoint is hypothesized to be in the middle of the causal sequence relating an independent variable to a dependent variable. The intermediate variable is also called a surrogate or mediating variable and the corresponding effect is called the mediated, surrogate endpoint, or intermediate endpoint effect. Clinical studies are often designed to change an intermediate or surrogate endpoint and through this intermediate change influence the ultimate endpoint. In many intermediate endpoint clinical studies the dependent variable is binary, and logistic or probit regression is used.

PURPOSE

The purpose of this study is to describe a limitation of a widely used approach to assessing intermediate endpoint effects and to propose an alternative method, based on products of coefficients, that yields more accurate results.

METHODS

The intermediate endpoint model for a binary outcome is described for a true binary outcome and for a dichotomization of a latent continuous outcome. Plots of true values and a simulation study are used to evaluate the different methods.

RESULTS

Distorted estimates of the intermediate endpoint effect and incorrect conclusions can result from the application of widely used methods to assess the intermediate endpoint effect. The same problem occurs for the proportion of an effect explained by an intermediate endpoint, which has been suggested as a useful measure for identifying intermediate endpoints. A solution to this problem is given based on the relationship between latent variable modeling and logistic or probit regression.

LIMITATIONS

More complicated intermediate variable models are not addressed in the study, although the methods described in the article can be extended to these more complicated models.

CONCLUSIONS

Researchers are encouraged to use an intermediate endpoint method based on the product of regression coefficients. A common method based on difference in coefficient methods can lead to distorted conclusions regarding the intermediate effect.

The Biomarker-Surrogacy Evaluation Schema: a review of the biomarker-surrogate literature and a proposal for a criterion-based, quantitative, multidimensional hierarchical levels of evidence schema for evaluating the status of biomarkers as surrogate endpoints

There are clear advantages to using biomarkers and surrogate endpoints, but concerns about clinical and statistical validity and systematic methods to evaluate these aspects hinder their efficient application. Section 2 is a systematic, historical review of the biomarker-surrogate endpoint literature with special reference to the nomenclature, the systems of classification and statistical methods developed for their evaluation. In Section 3 an explicit, criterion-based, quantitative, multidimensional hierarchical levels of evidence schema — Biomarker-Surrogacy Evaluation Schema — is proposed to evaluate and co-ordinate the multiple dimensions (biological, epidemiological, statistical, clinical trial and risk-benefit evidence) of the biomarker clinical endpoint relationships. The schema systematically evaluates and ranks the surrogacy status of biomarkers and surrogate endpoints using defined levels of evidence. The schema incorporates the three independent domains: Study Design, Target Outcome and Statistical Evaluation. Each domain has items ranked from zero to five. An additional category called Penalties incorporates additional considerations of biological plausibility, risk-benefit and generalizability. The total score (0—15) determines the level of evidence, with Level 1 the strongest and Level 5 the weakest. The term `surrogate' is restricted to markers attaining Levels 1 or 2 only. Surrogacy status of markers can then be directly compared within and across different areas of medicine to guide individual, trial-based or drug-development decisions. This schema would facilitate communication between clinical, researcher, regulatory, industry and consumer participants necessary for evaluation of the biomarker-surrogate-clinical endpoint relationship in their different settings.

Analysis of progression-free survival in oncology trials: some common statistical issues

With the advent of ever more effective second and third line cancer treatments and the growing use of 'crossover' trial designs in oncology, in which patients switch to the alternate randomized treatment upon disease progression, progression-free survival (PFS) is an increasingly important endpoint in oncologic drug development. However, several concerns exist regarding the use of PFS as a basis to compare treatments. Unlike survival, the exact time of progression is unknown, so progression times might be over-estimated and, consequently, bias may be introduced when comparing treatments. Further, it is not uncommon for randomized therapy to be stopped prior to progression being documented due to toxicity or the initiation of additional anti-cancer therapy; in such cases patients are frequently not followed further for progression and, consequently, are right-censored in the analysis. This article reviews these issues and concludes that concerns relating to the exact timing of progression are generally overstated, with analysis techniques and simple alternative endpoints available to either remove bias entirely or at least provide reassurance via supportive analyses that bias is not present. Further, it is concluded that the regularly recommended manoeuvre to censor PFS time at dropout due to toxicity or upon the initiation of additional anti-cancer therapy is likely to favour the more toxic, less efficacious treatment and so should be avoided whenever possible.

Semiparametric Inference for Surrogate Endpoints with Bivariate Censored Data

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.

Surrogate Marker Evaluation from an Information Theory Perspective

The last 20 years have seen lots of work in the area of surrogate marker validation, partly devoted to frame the evaluation in a multitrial framework, leading to definitions in terms of the quality of trial- and individual-level association between a potential surrogate and a true endpoint (Buyse et al., 2000, Biostatistics 1, 49-67). A drawback is that different settings have led to different measures at the individual level. Here, we use information theory to create a unified framework, leading to a definition of surrogacy with an intuitive interpretation, offering interpretational advantages, and applicable in a wide range of situations. Our method provides a better insight into the chances of finding a good surrogate endpoint in a given situation. We further show that some of the previous proposals follow as special cases of our method. We illustrate our methodology using data from a clinical study in psychiatry.

Statistical evaluation of biomarkers as surrogate endpoints: a literature review

A valid surrogate endpoint allows correct inference to be drawn regarding the effect of an intervention on the unobserved true clinical endpoint of interest. The perceived practical and ethical advantages of substituting a surrogate endpoint for a clinical endpoint have led to a considerable number of statistical methods being proposed for the evaluation of a biomarker as a surrogate endpoint. We review the main statistical schools of thought which have developed and consider how the validation process might be arranged within the regulatory and practical constraints of the drug development process. We conclude by assessing which of the candidate statistical methods offer the best approach for surrogate endpoint evaluation.

Missing data methods for the assessment of surrogate outcomes and treatment mechanisms in clinical trial substudies

Hypotheses about the mechanisms of action by which a treatment affects a clinical outcome may prompt consideration of an alternative outcome as a potential surrogate. In many cases, due to costs or other factors, the candidate for surrogacy will only be measured for patients randomized to a substudy within the main trial. In this situation, the substudy patients provide information about links between the true and surrogate outcomes and the treatment, and these links can be exploited, using methods for handling missing covariates, to allow available information for patients not in the substudy to be incorporated into the analysis. The increased precision with which the treatment effect can be estimated using these methods, compared with using substudy data alone, in turn allows more precise estimates of measures of surrogacy. This paper reviews and compares some methods for handling missing covariate data and applies the methodology to a large heart attack trial, in order to investigate the properties of four measures for assessing the extent to which early response to thrombolytic therapy, as measured by an improvement in coronary blood flow, can be regarded as a surrogate for 30-day survival following heart attack. Design issues for substudies intended to assess treatment mechanisms are also considered. In particular, we consider how the precision of surrogate measures varies with the size of the substudy relative to the main trial. The results suggest that for reasonable surrogates, substudies substantially smaller than the main study can extract most of the available information regarding surrogacy.

Time and PSA threshold model prognosticates long-term overall and disease-specific survival in prostate cancer patients as early as 3 months after external beam radiation therapy

The specific aim of this analysis was to evaluate the capability of a time and prostate-specific antigen (PSA) threshold model to prognosticate overall survival (OS) and disease-specific survival (DSS) based on early PSA kinetics after radiotherapy for prostate cancer by retrospective review of outcomes in 918 patients. Crossing below analyzed PSA thresholds at specific defined time points reduced disease-specific death hazard ratios to relative to the cohort above threshold. The time and PSA threshold model demonstrates the ability to prognosticate OS and DSS as early as 3 months post-radiotherapy for prostate cancer.

Is Prostate-Specific Antigen a Valid Surrogate End Point for Survival in Hormonally Treated Patients With Metastatic Prostate Cancer? Joint Research of the European Organisation for Research and Treatment of Cancer, the Limburgs Universitair Centrum, and AstraZeneca Pharmaceuticals

Purpose

The long duration of phase III clinical trials of overall survival (OS) slows down the treatment-development process. It could be shortened by using surrogate end points. Prostate-specific antigen (PSA) is the most studied biomarker in prostate cancer (PCa). This study attempts to validate PSA end points as surrogates for OS in advanced PCa.

Patients and Methods

Individual data from 2,161 advanced PCa patients treated in studies comparing bicalutamide to castration were used in a meta-analytic approach to surrogate end-point validation. PSA response, PSA normalization, time to PSA progression, and longitudinal PSA measurements were considered.

Results

The known association between PSA and OS at the individual patient level was confirmed. The association between the effect of intervention on any PSA end point and on OS was generally low (determination coefficient, < 0.69).

Conclusion

It is a common misconception that high correlation between biomarkers and true end point justify the use of the former as surrogates. To statistically validate surrogate end points, a high correlation between the treatment effects on the surrogate and true end point needs to be established across groups of patients treated with two alternative interventions. The levels of association observed in this study indicate that the effect of hormonal treatment on OS cannot be predicted with a high degree of precision from observed treatment effects on PSA end points, and thus statistical validity is unproven. In practice, non-null treatment effects on OS can be predicted only from precisely estimated large effects on time to PSA progression (TTPP; hazard ratio, < 0.50).

Objective Response to Chemotherapy As a Potential Surrogate End Point of Survival in Metastatic Breast Cancer Patients

Purpose

To assess the validity of objective response to chemotherapy as a surrogate end point for survival in metastatic breast cancer.

Patients and Methods

We carried out a meta-analysis on individual data from 2,126 metastatic breast cancer patients who were enrolled onto 10 randomized trials comparing standard versus intensified epirubicin-containing chemotherapy.

Results

The intensified chemotherapy was associated with a significantly higher tumor response rate compared with standard chemotherapy (pooled odds ratio for nonresponse, 0.60; 95% CI, 0.51 to 0.72). The intensified regimens also led to better (although not significant) survival (pooled odds ratio, 0.94; 95% CI, 0.86 to 1.04; P = .22). Tumor response was a highly significant predictor of survival (P < .0001). When tumor response was introduced in the Cox model, the hazard ratio in favor of experimental treatment changed from 0.94 to 1.005 (95% CI, 0.91 to 1.11; P = .92), indicating that no residual effect of the experimental treatment on survival was present once tumor response was adjusted for. This suggests that the overall survival benefit of intensified epirubicin was a result of the increase in response rate. The median survival time of patients with complete response and partial response was 28.8 months (95% CI, 25.4 to 45.3 months) and 21.3 months (95% CI, 19.2 to 22.4 months), respectively; whereas, the median survival time of patients with no response was 14.6 months (95% CI, 13.9 to 15.4 months).

Conclusion

These results support the hypothesis that the achievement of an objective response to chemotherapy in metastatic breast cancer is associated with a true survival benefit. The potential role of objective response as a surrogate end point for survival in chemotherapy trials of metastatic breast cancer warrants further investigation.

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.

Alternative endpoints for mortality in studies of patients with atrial fibrillation: The AFFIRM study experience

OBJECTIVES

The purpose of this study was to examine possible alternatives for death, particularly hospitalization for cardiovascular reasons (CV hospitalization), as an endpoint in studies of atrial fibrillation (AF) using the Atrial Fibrillation Follow-up Investigation of Rhythm Management (AFFIRM) database.

BACKGROUND

AF is associated with increased mortality, but large numbers of patients are needed to demonstrate even a moderate effect of a therapy on mortality.

METHODS

AFFIRM studied 4,060 patients with AF, randomized to either rate-control or rhythm-control strategy with death as the primary endpoint.

RESULTS

Only CV hospitalization occurred more frequently than death. Like death, CV hospitalization was more frequent in the rhythm-control arm (46% vs 36%, P < .001) overall but not in a cohort that attempted to exclude those CV hospitalizations possibly related to treatment strategy (e.g., cardioversion, 24% vs 27%). In either model there was no interaction of CV hospitalization (analyzed as a time-dependent covariate) with treatment arm (P = .18 and P = .21, respectively). CV hospitalization was highly predictive of death in both treatment arms (P < .001) in either model, but after this event, there was no difference in time to death. A composite endpoint of CV hospitalization combined with death might increase power and reduce the size of trials of therapy for AF in such patients.

CONCLUSIONS

In patients with AF such as those in the AFFIRM study, CV hospitalization has many attributes of a surrogate for mortality. More research on CV hospitalization, alone or as part of a composite endpoint, is warranted.

A perspective on surrogate endpoints in controlled clinical trials

The last couple of decades have seen a large amount of activity in the area of surrogate marker and surrogate endpoint validation, both from a clinical and a statistical perspective. Prentice made a pivotal contribution in the context of a single trial. Subsequently, the framework he proposed has been discussed, criticized, and extended. An important class of extensions considers several rather than a single trial. Recently, a lot of work has been done in this so-called hierarchical or meta-analytic framework. In this paper, we review both the single trial and the hierarchical framework. A number of applications, scattered throughout the literature, are brought together. We outline the statistical issues involved in trying to validate surrogate endpoints. Clearly statistical evidence should only be seen as a component in a decision making process that also involves a number of clinical and biological considerations.

Exploring the relationship between surrogates and clinical outcomes: analysis of individual patient data vs. meta-regression on group-level summary statistics

There has been an increasing interest in exploring the relationship between a surrogate and a clinical outcome. Two different statistical approaches have been taken by researchers to quantify the treatment effect on the clinical outcome explained by the surrogate endpoint: 1) analysis based on individual patient data (IPD), and 2) meta-regression based on summary statistics from published literature. An analysis based on IPD models the associations between the surrogate and clinical outcome for patients directly and is able to adjust for patient-level covariates. A meta-regression models the trial-level associations using group-level summary statistics and trial-level covariates. The results from these two approaches can be quite disparate and researchers may reach different conclusions on scientific questions that they wish to answer. We demonstrate that the typical summary statistics, such as group means and event counts, do not provide a set of sufficient statistics for estimating the underlying relationship between the surrogate and clinical outcome for patients. Consequently, the associations derived from meta-regression do not necessarily reflect the causal relationship for patients and should be interpreted with caution. A meta-analysis of antiresorptive agents for osteoporosis serves to illustrate the magnitude of differences between the two approaches.

Development of biomarkers in multiple sclerosis

Multiple sclerosis is a complex disease, as several pathophysiological processes (including inflammation, demyelination, axonal damage and repair mechanisms) participate in the disease process. Furthermore, as new pathological evidence reveals, these processes are not uniformly represented across patient populations but can selectively predominate in individual patients, thus contributing to the heterogeneity in phenotypic expression of the disease, its prognosis and response to therapies. While the armamentarium of available therapies for multiple sclerosis broadens, little is known about factors that predict treatment response in individual patients to a specific drug. More importantly, we are beginning to understand that, analogous to cancer therapy, the successful therapeutic strategy in multiple sclerosis might ultimately involve the combination of different therapeutics targeting several dominant pathophysiological processes. The development of these process-specific therapies will be impossible without the use of biomarkers that reflect the targeted process, can select patient population in which the targeted process is prevailing and can aid during the more rapid screening of therapeutic agents in the early phase of their development. This review summarizes the general concepts of biomarkers and their potential use as surrogate endpoints and tailors these concepts to specific applications in multiple sclerosis research.

Statistics in clinical trials

Statistical developments over the past several years are described in this review. Efforts in phase I studies have focused on efficient estimation of maximum tolerated dose. Issues investigated for phase II trials include incorporation of multiple endpoints and randomization. For phase III trials, methods to reduce time or use the sample size more efficiently have been investigated. However, design innovations come with costs, including possible increased risk of incorrect conclusions. Other recent challenging statistical developments in clinical trials relate to use of complementary outcomes such as quality of life and to associated biologic questions, including the emergence of the field of genomics.

A perfect correlate does not a surrogate make

BACKGROUND

There is common belief among some medical researchers that if a potential surrogate endpoint is highly correlated with a true endpoint, then a positive (or negative) difference in potential surrogate endpoints between randomization groups would imply a positive (or negative) difference in unobserved true endpoints between randomization groups. We investigate this belief when the potential surrogate and unobserved true endpoints are perfectly correlated within each randomization group.

METHODS

We use a graphical approach. The vertical axis is the unobserved true endpoint and the horizontal axis is the potential surrogate endpoint. Perfect correlation within each randomization group implies that, for each randomization group, potential surrogate and true endpoints are related by a straight line. In this scenario the investigator does not know the slopes or intercepts. We consider a plausible example where the slope of the line is higher for the experimental group than for the control group.

RESULTS

In our example with unknown lines, a decrease in mean potential surrogate endpoints from control to experimental groups corresponds to an increase in mean true endpoint from control to experimental groups. Thus the potential surrogate endpoints give the wrong inference. Similar results hold for binary potential surrogate and true outcomes (although the notion of correlation does not apply). The potential surrogate endpoint would give the correct inference if either (i) the unknown lines for the two group coincided, which means that the distribution of true endpoint conditional on potential surrogate endpoint does not depend on treatment group, which is called the Prentice Criterion or (ii) if one could accurately predict the lines based on data from prior studies.

CONCLUSION

Perfect correlation between potential surrogate and unobserved true outcomes within randomized groups does not guarantee correct inference based on a potential surrogate endpoint. Even in early phase trials, investigators should not base conclusions on potential surrogate endpoints in which the only validation is high correlation with the true endpoint within a group.

Proportion of treatment effect (PTE) explained by a surrogate marker

In time-varying covariate analysis of clinical survival data, it is often of interest to estimate the proportion of treatment effect (PTE), along with its confidence intervals, explained by a surrogate marker. The conventional procedure for such an analysis fits data into two working models separately to estimate the treatment effects before and after adjustment of the covariate. The construction of confidence intervals for the PTE under the conventional procedure lacks support by standard statistical software such as SAS, and could be very computationally demanding even after the support is available in the future. To overcome this problem, we propose a new procedure to simplify the computation. Under the new procedure, the treatment effects before and after adjustment of the covariate are simultaneously estimated from a single model. More important than saving computational effort, the new procedure can also be effectively applied to multiple-covariate models for the decomposition of overall treatment effect and for the comparison of PTE among several surrogate markers. The new procedure is applied to the motivating data example from the LIFE study, and demonstrates flexibility that the conventional procedure currently lacks.

Relation between tumour response to first-line chemotherapy and survival in advanced colorectal cancer: a meta-analysis. Meta-Analysis Group in Cancer

BACKGROUND

Treatment of advanced colorectal cancer has progressed substantially. However, improvements in response rates have not always translated into significant survival benefits. Doubts have therefore been raised about the usefulness of tumour response as a clinical endpoint.

METHODS

This meta-analysis was done on individual data from 3791 patients enrolled in 25 randomised trials of first-line treatment with standard bolus intravenous fluoropyrimidines versus experimental treatments (fluorouracil plus leucovorin, fluorouracil plus methotrexate, fluorouracil continuous infusion, or hepatic-arterial infusion of floxuridine). Analyses were by intention to treat.

FINDINGS

Compared with bolus fluoropyrimidines, experimental fluoropyrimidines led to significantly higher tumour response rates (454 responses among 2031 patients vs 209 among 1760; odds ratio 0.48 [95% CI 0.40-0.57], p<0.0001) and better survival (1808 deaths among 2031 vs 1580 among 1760; hazard ratio 0.90 [0.84-0.97], p=0.003). The survival benefits could be explained by the higher tumour response rates. However, a treatment that lowered the odds of failure to respond by 50% would be expected to decrease the odds of death by only 6%. In addition, less than half of the variability of the survival benefits in the 25 trials could be explained by the variability of the response benefits in these trials.

INTERPRETATION

These analyses confirm that an increase in tumour response rate translates into an increase in overall survival for patients with advanced colorectal cancer. However, in the context of individual trials, knowledge that a treatment has benefits on tumour response does not allow accurate prediction of the ultimate benefit on survival.