Using a balancing procedure in multicenter clinical trials. Simulation of patient allocation based on a trial of ventilation tubes for otitis media with effusion in infants

OBJECTIVE: A basic issue in randomized controlled trials (RCTs) is whether we can safely assume comparability between groups at baseline with respect to all potentially important prognostic factors. In other words, did randomization work sufficiently well? In small trials balanced allocation procedures are employed, whereas in large-scale trials simple randomization will do. The question is: When should balancing be considered? METHODS: We performed a simulation study in which we varied the number of categories in the prognostic factors and the number of patients. RESULTS: Simulation showed that, in all instances, a balancing procedure almost always led to perfect or almost perfect balance, while the imbalance with simple randomization was larger. To study the effect of balanced and random allocation on subgroup analyses in our OME trial, we compared the quotient of the width of the confidence intervals (CI). The widest CI in random allocation over the 13 hospitals was on average 13% wider than in balanced allocation. CONCLUSION: Investigators should always consider balanced allocation, especially in categories with a low number of patients and when subgroup analysis over many categories is requested.     

An evaluation of constrained randomization for the design and analysis of group‐randomized trials with binary outcomes

Group‐randomized trials are randomized studies that allocate intact groups of individuals to different comparison arms. A frequent practical limitation to adopting such research designs is that only a limited number of groups may be available, and therefore, simple randomization is unable to adequately balance multiple group‐level covariates between arms. Therefore, covariate‐based constrained randomization was proposed as an allocation technique to achieve balance. Constrained randomization involves generating a large number of possible allocation schemes, calculating a balance score that assesses covariate imbalance, limiting the randomization space to a prespecified percentage of candidate allocations, and randomly selecting one scheme to implement. When the outcome is binary, a number of statistical issues arise regarding the potential advantages of such designs in making inference. In particular, properties found for continuous outcomes may not directly apply, and additional variations on statistical tests are available. Motivated by two recent trials, we conduct a series of Monte Carlo simulations to evaluate the statistical properties of model‐based and randomization‐based tests under both simple and constrained randomization designs, with varying degrees of analysis‐based covariate adjustment. Our results indicate that constrained randomization improves the power of the linearization F‐test, the KC‐corrected GEE t‐test (Kauermann and Carroll, 2001, Journal of the American Statistical Association 96, 1387‐1396), and two permutation tests when the prognostic group‐level variables are controlled for in the analysis and the size of randomization space is reasonably small. We also demonstrate that constrained randomization reduces power loss from redundant analysis‐based adjustment for non‐prognostic covariates. Design considerations such as the choice of the balance metric and the size of randomization space are discussed.     

Restriction as a method for reducing bias in the estimation of direct effects

The direct effect of a treatment on some outcome is that part of the treatment's effect not referred through a specified covariate intermediate on the pathway between treatment and outcome. Such direct effects are often of primary interest in a data analysis. Unfortunately, standard methods of analysis (for example, stratification or modelling) do not, in general, produce consistent estimates of direct effects whether or not the covariate is ‘controlled’. Robins and co-authors have proposed two methods for estimation of direct effects applicable when reliable information is available on the covariate. We propose a third approach for reducing bias: data restriction. By restricting the analysis to strata of the data in which the effect of treatment on the covariate is small, we can (under certain assumptions) reduce bias in estimating treatment's direct effect. We discuss these points with reference to difference and ratio measures of treatment effect. The approach will sometimes be applicable even with an unmeasured or poorly measured covariate. We illustrate these points with data from an observational study of the effect of hormone replacement therapy on breast cancer. © 1998 John Wiley & Sons, Ltd.     

Validity and power considerations on hypothesis testing under minimization

Minimization, a dynamic allocation method, is gaining popularity especially in cancer clinical trials. Aiming to achieve balance on all important prognostic factors simultaneously, this procedure can lead to a substantial reduction in covariate imbalance compared with conventional randomization in small clinical trials. While minimization has generated enthusiasm, some controversy exists over the proper analysis of such a trial. Critics argue that standard testing methods that do not account for the dynamic allocation algorithm can lead to invalid statistical inference. Acknowledging this limitation, the International Conference on Harmonization E9 guideline suggests that ‘the complexity of the logistics and potential impact on analyses be carefully evaluated when considering dynamic allocation’. In this article, we investigate the proper analysis approaches to inference in a minimization design for both continuous and time‐to‐event endpoints and evaluate the validity and power of these approaches under a variety of scenarios both theoretically and empirically. Published 2016. This article is a U.S. Government work and is in the public domain in the USA     

A new approach to modelling interactions between treatment and continuous covariates in clinical trials by using fractional polynomials

We consider modelling interaction between a categoric covariate T and a continuous covariate Z in a regression model. Here T represents the two treatment arms in a parallel-group clinical trial and Z is a prognostic factor which may influence response to treatment (known as a predictive factor). Generalization to more than two treatments is straightforward. The usual approach to analysis is to categorize Z into groups according to cutpoint(s) and to analyse the interaction in a model with main effects and multiplicative terms. The cutpoint approach raises several well-known and difficult issues for the analyst. We propose an alternative approach based on fractional polynomial (FP) modelling of Z in all patients and at each level of T. Other prognostic variables can also be incorporated by first constructing a multivariable adjustment model which may contain binary covariates and FP transformations of continuous covariates other than Z. The main step involves FP modelling of Z and testing equality of regression coefficients between treatment groups in an interaction model adjusted for other covariates. Extensive experience suggests that a two-term fractional polynomial (FP2) function may describe the effect of a prognostic factor on a survival outcome quite well. In a controlled trial, this FP2 function describes the prognostic effect averaged over the treatment groups. We refit this function in each treatment group to see if there are substantial differences between groups. Allowing different parameter values for the chosen FP2 function is flexible enough to detect such differences. Within the same algorithm we can also deal with the conceptually different cases of a predefined hypothesis of interaction or searching for interactions. We demonstrate the ability of the approach to detect and display treatment/covariate interactions in two examples from controlled trials in cancer.     

Squeezing the Balloon: Propensity Scores and Unmeasured Covariate Balance

Objective

To assess the covariate balancing properties of propensity score-based algorithms in which covariates affecting treatment choice are both measured and unmeasured.

Data Sources/Study Setting

A simulation model of treatment choice and outcome.

Study Design

Simulation.

Data Collection/Extraction Methods

Eight simulation scenarios varied with the values placed on measured and unmeasured covariates and the strength of the relationships between the measured and unmeasured covariates. The balance of both measured and unmeasured covariates was compared across patients either grouped or reweighted by propensity scores methods.

Principal Findings

Propensity score algorithms require unmeasured covariate variation that is unrelated to measured covariates, and they exacerbate the imbalance in this variation between treated and untreated patients relative to the full unweighted sample.

Conclusions

The balance of measured covariates between treated and untreated patients has opposite implications for unmeasured covariates in randomized and observational studies. Measured covariate balance between treated and untreated patients in randomized studies reinforces the notion that all covariates are balanced. In contrast, forced balance of measured covariates using propensity score methods in observational studies exacerbates the imbalance in the independent portion of the variation in the unmeasured covariates, which can be likened to squeezing a balloon. If the unmeasured covariates affecting treatment choice are confounders, propensity score methods can exacerbate the bias in treatment effect estimates.     

Response‐adaptive randomization for clinical trials with adjustment for covariate imbalance

In clinical trials with a small sample size, the characteristics (covariates) of patients assigned to different treatment arms may not be well balanced. This may lead to an inflated type I error rate. This problem can be more severe in trials that use response‐adaptive randomization rather than equal randomization because the former may result in smaller sample sizes for some treatment arms. We have developed a patient allocation scheme for trials with binary outcomes to adjust the covariate imbalance during response‐adaptive randomization. We used simulation studies to evaluate the performance of the proposed design. The proposed design keeps the important advantage of a standard response‐adaptive design, that is to assign more patients to the better treatment arms, and thus it is ethically appealing. On the other hand, the proposed design improves over the standard response‐adaptive design by controlling covariate imbalance between treatment arms, maintaining the nominal type I error rate, and offering greater power. Copyright © 2010 John Wiley & Sons, Ltd.     

Incorporating prognostic factors into causal estimators: A comparison of methods for randomised controlled trials with a time‐to‐event outcome

In randomised controlled trials, the effect of treatment on those who comply with allocation to active treatment can be estimated by comparing their outcome to those in the comparison group who would have complied with active treatment had they been allocated to it. We compare three estimators of the causal effect of treatment on compliers when this is a parameter in a proportional hazards model and quantify the bias due to omitting baseline prognostic factors. Causal estimates are found directly by maximising a novel partial likelihood; based on a structural proportional hazards model; and based on a ‘corrected dataset’ derived after fitting a rank‐preserving structural failure time model. Where necessary, we extend these methods to incorporate baseline covariates. Comparisons use simulated data and a real data example. Analysing the simulated data, we found that all three methods are accurate when an important covariate was included in the proportional hazards model (maximum bias 5.4%). However, failure to adjust for this prognostic factor meant that causal treatment effects were underestimated (maximum bias 11.4%), because estimators were based on a misspecified marginal proportional hazards model. Analysing the real data example, we found that adjusting causal estimators is important to correct for residual imbalances in prognostic factors present between trial arms after randomisation. Our results show that methods of estimating causal treatment effects for time‐to‐event outcomes should be extended to incorporate covariates, thus providing an informative compliment to the corresponding intention‐to‐treat analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Quality of life as a prognostic factor of overall survival in patients with advanced hepatocellular carcinoma: results from two French clinical trials

AIM: The aims of our study were to assess quality of life (QoL) as a prognostic factor of overall survival (OS) and to determine whether QoL data improved three prognostic classifications among French patients with advanced hepatocellular carcinoma (HCC). METHODS: We pooled two randomized clinical trials conducted by the Fédération Francophone de Cancérologie Digestive in a palliative setting. In each trial QoL was assessed at baseline using the Spitzer QoL Index (0-10). Three prognostic classifications were calculated: Okuda, Cancer of the Liver Italian Program (CLIP), and Barcelona Clinic Liver Cancer group (BCLC) scores. To explore whether the scores could be improved by including QoL, univariate Cox analyses of all potential baseline predictors were performed. A final multivariate Cox model was constructed including only significant multivariate baseline variables likely to result in improvement of each scoring system. In order to retain the best prognostic variable to add for each score, we compared Akaike information criterion, likelihood ratio, and Harrell's C-index. Cox analyses were stratified for each trial. RESULTS: Among 538 included patients, QoL at baseline was available for 489 patients (90%). Longer median OS was significantly associated with higher Spitzer scores at baseline, ranging from 2.17 months (Spitzer=3) to 8.93 months (Spitzer=10). Variables retained in the multivariate Cox model were: jaundice, hepatomegaly, hepatalgia, portal thrombosis, alphafetoprotein, bilirubin, albumin, small HCC, and Spitzer QoL Index (hazard ratio=0.84 95% CI [0.79-0.90]). According to Harrell's C-index, QoL was the best prognostic variable to add. CLIP plus the Spitzer QoL Index had the most discriminating value (C=0.71). CONCLUSIONS: Our results suggest that QoL is an independent prognostic factor for survival in HCC patients with mainly alcoholic cirrhosis. The prognostic value of CLIP score could be improved by adding Spitzer QOL Index scores.     

Patient-reported outcomes helped predict survival in multiple myeloma using partial least squares analysis

OBJECTIVE: The prognostic value of Patient-Reported Outcomes (PRO) in predicting mortality during treatment of multiple myeloma (MM) patients was assessed using partial least square (PLS) regression, a statistical method that is well-adapted for highly correlated data. STUDY DESIGN AND SETTING: Four PRO measures, The European Organisation for Research and Treatment of Cancer (EORTC) QLQ-C30, the EORTC QLQ-MY24, the FACIT-Fatigue scale, and the FACT/GOG-Ntx scale, were administered during a trial designed to evaluate the efficacy and safety of bortezomib (VELCADE 1.3mg/m(2)) in MM patients (N=202). Clinical and PRO data were analyzed for predictive value by univariate and multivariate logistic regression methods and then by PLS regression. RESULTS: Fifteen baseline PRO parameters were significant in predicting mortality during treatment when univariate logistic regression was used. In contrast, only two variables were retained in the multivariate analysis, as correlated variables were excluded from the model. Using PLS regression, 14 of the 21 PRO predictors were significant in predicting mortality. Clinical and PRO data used together increased the predictive power of all models compared to clinical data alone. CONCLUSION: The prognostic value of PRO was established and was more informative using PLS regression. PLS regression may therefore be a valuable method for analyzing PRO data.     

New algorithm for treatment allocation reduced selection bias and loss of power in small trials

OBJECTIVE: In clinical trials, patients become available for treatment sequentially. Especially in trials with a small number of patients, loss of power may become an important issue, if treatments are not allocated equally or if prognostic factors differ between the treatment groups. We present a new algorithm for sequential allocation of two treatments in small clinical trials, which is concerned with the reduction of both selection bias and imbalance. STUDY DESIGN AND SETTING: With the algorithm, an element of chance is added to the treatment as allocated by minimization. The amount of chance depends on the actual amount of imbalance of treatment allocations of the patients already enrolled. The sensitivity to imbalance may be tuned. We performed trial simulations with different numbers of patients and prognostic factors, in which we quantified loss of power and selection bias. RESULTS: With our method, selection bias is smaller than with minimization, and loss of power is lower than with pure randomization or treatment allocation according to a biased coin principle. CONCLUSION: Our method combines the conflicting aims of reduction of bias by predictability and reduction of loss of power, as a result of imbalance. The method may be of use in small trials.     

Recommendations for choosing an analysis method that controls Type I error for unbalanced cluster sample designs with Gaussian outcomes

We used theoretical and simulation‐based approaches to study Type I error rates for one‐stage and two‐stage analytic methods for cluster‐randomized designs. The one‐stage approach uses the observed data as outcomes and accounts for within‐cluster correlation using a general linear mixed model. The two‐stage model uses the cluster specific means as the outcomes in a general linear univariate model. We demonstrate analytically that both one‐stage and two‐stage models achieve exact Type I error rates when cluster sizes are equal. With unbalanced data, an exact size α test does not exist, and Type I error inflation may occur. Via simulation, we compare the Type I error rates for four one‐stage and six two‐stage hypothesis testing approaches for unbalanced data. With unbalanced data, the two‐stage model, weighted by the inverse of the estimated theoretical variance of the cluster means, and with variance constrained to be positive, provided the best Type I error control for studies having at least six clusters per arm. The one‐stage model with Kenward–Roger degrees of freedom and unconstrained variance performed well for studies having at least 14 clusters per arm. The popular analytic method of using a one‐stage model with denominator degrees of freedom appropriate for balanced data performed poorly for small sample sizes and low intracluster correlation. Because small sample sizes and low intracluster correlation are common features of cluster‐randomized trials, the Kenward–Roger method is the preferred one‐stage approach. Copyright © 2015 John Wiley & Sons, Ltd.     

A random walk model for evaluating clinical trials involving serial observations

For clinical trials where the variable of interest is ordered and categorical (for example, disease severity, symptom scale), and where measurements are taken at intervals, it might be possible to achieve a greater discrimination between the efficacy of treatments by modelling each patient's progress as a stochastic process. The random walk is a simple, easily interpreted model that can be fitted by maximum likelihood using a maximization routine with inference based on standard likelihood theory. In general the model can allow for randomly censored data, incorporates measured prognostic factors, and inference is conditional on the (possibly non-random) allocation of patients. Tests of fit and of model assumptions are proposed, and application to two therapeutic trials of gastroenterological disorders are presented. The model gave measures of the rate of, and variability in, improvement for patients under different treatments. A small simulation study suggested that the model is more powerful than considering the difference between initial and final scores, even when applied to data generated by a mechanism other than the random walk model assumed in the analysis. It thus provides a useful additional statistical method for evaluating clinical trials.     

Analysis of time-dependent covariates in a regressive relative survival model

Relative survival is a method for assessing prognostic factors for disease-specific mortality. However, most relative survival models assume that the effect of covariate on disease-specific mortality is fixed-in-time, which may not hold in some studies and requires adapted modelling. We propose an extension of the Esteve et al. regressive relative survival model that uses the counting process approach to accommodate time-dependent effect of a predictor's on disease-specific mortality. This approach had shown its robustness, and the properties of the counting process give a simple and attractive computational solution to model time-dependent covariates. Our approach is illustrated with the data from the Stanford Heart Transplant Study and with data from a hospital-based study on invasive breast cancer. Advantages of modelling time-dependent covariates in relative survival analysis are discussed.     

The impact of covariate adjustment at randomization and analysis for binary outcomes: understanding differences between superiority and noninferiority trials

The question of when to adjust for important prognostic covariates often arises in the design of clinical trials, and there remain various opinions on whether to adjust during both randomization and analysis, at randomization alone, or at analysis alone. Furthermore, little is known about the impact of covariate adjustment in the context of noninferiority (NI) designs. The current simulation‐based research explores this issue in the NI setting, as compared with the typical superiority setting, by assessing the differential impact on power, type I error, and bias in the treatment estimate as well as its standard error, in the context of logistic regression under both simple and covariate adjusted permuted block randomization algorithms. In both the superiority and NI settings, failure to adjust for covariates that influence outcome in the analysis phase, regardless of prior adjustment at randomization, results in treatment estimates that are biased toward zero, with standard errors that are deflated. However, as no treatment difference is approached under the null hypothesis in superiority and under the alternative in NI, this results in decreased power and nominal or conservative (deflated) type I error in the context of superiority but inflated power and type I error under NI. Results from the simulation study suggest that, regardless of the use of the covariate in randomization, it is appropriate to adjust for important prognostic covariates in analysis, as this yields nearly unbiased estimates of treatment as well as nominal type I error. Copyright © 2015 John Wiley & Sons, Ltd.     

Randomized controlled trials with time-to-event outcomes: how much does prespecified covariate adjustment increase power?

PURPOSE: We evaluated the effects of various strategies of covariate adjustment on type I error, power, and potential reduction in sample size in randomized controlled trials (RCTs) with time-to-event outcomes. METHODS: We used Cox models in simulated data sets with different treatment effects (hazard ratios [HRs] = 1, 1.4, and 1.7), covariate effects (HRs = 1, 2, and 5), covariate prevalences (10% and 50%), and censoring levels (no, low, and high). Treatment and a single covariate were dichotomous. We examined the sample size that gives the same power as an unadjusted analysis for three strategies: prespecified, significant predictive, and significant imbalance. RESULTS: Type I error generally was at the nominal level. The power to detect a true treatment effect was greater with adjusted than unadjusted analyses, especially with prespecified and significant-predictive strategies. Potential reductions in sample size with a covariate HR between 2 and 5 were between 15% and 44% (covariate prevalence 50%) and between 4% and 12% (covariate prevalence 10%). The significant-imbalance strategy yielded small reductions. The reduction was greater with stronger covariate effects, but was independent of treatment effect, sample size, and censoring level. CONCLUSIONS: Adjustment for one predictive baseline characteristic yields greater power to detect a true treatment effect than unadjusted analysis, without inflation of type I error and with potentially moderate reductions in sample size. Analysis of RCTs with time-to-event outcomes should adjust for predictive covariates.     

Evaluation of subset matching methods and forms of covariate balance

This paper conducts a Monte Carlo simulation study to evaluate the performance of multivariate matching methods that select a subset of treatment and control observations. The matching methods studied are the widely used nearest neighbor matching with propensity score calipers and the more recently proposed methods, optimal matching of an optimally chosen subset and optimal cardinality matching. The main findings are: (i) covariate balance, as measured by differences in means, variance ratios, Kolmogorov–Smirnov distances, and cross‐match test statistics, is better with cardinality matching because by construction it satisfies balance requirements; (ii) for given levels of covariate balance, the matched samples are larger with cardinality matching than with the other methods; (iii) in terms of covariate distances, optimal subset matching performs best; (iv) treatment effect estimates from cardinality matching have lower root‐mean‐square errors, provided strong requirements for balance, specifically, fine balance, or strength‐k balance, plus close mean balance. In standard practice, a matched sample is considered to be balanced if the absolute differences in means of the covariates across treatment groups are smaller than 0.1 standard deviations. However, the simulation results suggest that stronger forms of balance should be pursued in order to remove systematic biases due to observed covariates when a difference in means treatment effect estimator is used. In particular, if the true outcome model is additive, then marginal distributions should be balanced, and if the true outcome model is additive with interactions, then low‐dimensional joints should be balanced. Copyright © 2016 John Wiley & Sons, Ltd.     

A multivariate meta-analysis approach for reducing the impact of outcome reporting bias in systematic reviews

Multivariate meta‐analysis allows the joint synthesis of multiple correlated outcomes from randomised trials, and is an alternative to a separate univariate meta‐analysis of each outcome independently. Usually not all trials report all outcomes; furthermore, outcome reporting bias (ORB) within trials, where an outcome is measured and analysed but not reported on the basis of the results, may cause a biased set of the evidence to be available for some outcomes, potentially affecting the significance and direction of meta‐analysis results. The multivariate approach, however, allows one to ‘borrow strength’ across correlated outcomes, to potentially reduce the impact of ORB. Assuming ORB missing data mechanisms, we aim to investigate the magnitude of bias in the pooled treatment effect estimates for multiple outcomes using univariate meta‐analysis, and to determine whether the ‘borrowing of strength’ from multivariate meta‐analysis can reduce the impact of ORB. A simulation study was conducted for a bivariate fixed effect meta‐analysis of two correlated outcomes. The approach is illustrated by application to a Cochrane systematic review. Results show that the ‘borrowing of strength’ from a multivariate meta‐analysis can reduce the impact of ORB on the pooled treatment effect estimates. We also examine the use of the Pearson correlation as a novel approach for dealing with missing within‐study correlations, and provide an extension to bivariate random‐effects models that reduce ORB in the presence of heterogeneity. Copyright © 2012 John Wiley & Sons, Ltd.     

A balanced hazard ratio for risk group evaluation from survival data

Common clinical studies assess the quality of prognostic factors, such as gene expression signatures, clinical variables or environmental factors, and cluster patients into various risk groups. Typical examples include cancer clinical trials where patients are clustered into high or low risk groups. Whenever applied to survival data analysis, such groups are intended to represent patients with similar survival odds and to select the most appropriate therapy accordingly. The relevance of such risk groups, and of the related prognostic factors, is typically assessed through the computation of a hazard ratio. We first stress three limitations of assessing risk groups through the hazard ratio: (1) it may promote the definition of arbitrarily unbalanced risk groups; (2) an apparently optimal group hazard ratio can be largely inconsistent with the p‐value commonly associated to it; and (3) some marginal changes between risk group proportions may lead to highly different hazard ratio values. Those issues could lead to inappropriate comparisons between various prognostic factors. Next, we propose the balanced hazard ratio to solve those issues. This new performance metric keeps an intuitive interpretation and is as simple to compute. We also show how the balanced hazard ratio leads to a natural cut‐off choice to define risk groups from continuous risk scores. The proposed methodology is validated through controlled experiments for which a prescribed cut‐off value is defined by design. Further results are also reported on several cancer prognosis studies, and the proposed methodology could be applied more generally to assess the quality of any prognostic markers. Copyright © 2015 John Wiley & Sons, Ltd.     

Self-reported health-related quality of life predicts survival for patients with advanced gastric cancer treated with first-line chemotherapy

Purpose To determine whether patients’ self-reported quality-of-life (QOL) parameters could predict survival for patients with advanced gastric cancer (AGC) treated with first-line chemotherapy, we performed this analysis based on the data obtained from 254 patients enrolled in three consecutive prospective randomized trials at a single institution. Methods Consenting patients with AGC received first-line chemotherapy as specified in the protocols. QOL was assessed at baseline using the European Organisation for Research and Treatment of Cancer (EORTC) QLQ-C30 questionnaires. Baseline univariate and multivariate analyses were performed on the QOL data and the recognized clinical predictors for survival. Results Of 254 patients, 164 completed the QOL questionnaire at baseline. All patients received fluorouracil-containing first-line chemotherapy for AGC. With 88% observed deaths and a reported median survival of 9.5 months [95% confidence interval (CI) 8.8–10.2 months], there were no significant differences in survival between patients with or without QOL data. The final Cox multivariate model revealed four prognostic factors: age [hazard ratio (HR) 2.08, 95% CI 1.32–3.33, P = 0.002], bone metastasis (HR 2.70, 95% CI 1.30–5.56, P = 0.008), hemoglobin (HR 0.58, 95% CI 0.37–0.92, P = 0.020), and social functioning (HR 0.40, 95% CI 0.23–0.64, P = 0.001). When adjusting for clinical parameters, social functioning was an independently significant prognostic factor for longer survival. Conclusion Baseline social functioning, along with age, presence of bone metastasis, and baseline hemoglobin level, independently predicts survival of AGC patients treated with first-line chemotherapy. QOL assessment should be routinely included to provide useful prognostic information concerning AGC patients.