Effect of GLP-1 and GIP on C-peptide secretion after glucagon or mixed meal tests: Significance in assessing B-cell function in diabetes.

BACKGROUND: The aim of the study was to investigate the different B-cell responses after a glucagon stimulation test (GST) versus mixed meal tolerance test (MMTT). METHODS: We conducted GST and MMTT in 10 healthy people (aged 25-40 years) and measured C-peptide, gastric inhibitory peptide (GIP) and glucagon-like peptide-1 (GLP-1) at different time points after the administration of 1 mg i.v. glucagon for GST or a liquid mixed meal for MMTT. RESULTS: The GST stimulated C-peptide showed a mean increase of 147.1%, whereas the mean increase of MMTT stimulated C-peptide was 99.82% (Δincrease = 47.2%). Maximum C-peptide level reached with the MMTT was greater than that obtained with the GST (C-pept max MMTT = 2.35 nmol/L vs C-pep max GST = 1.9 nmol/L). A positive and linear correlation was found between the GST incremental area under the curve C-peptide and the MMTT incremental area under the curve C-peptide (r = 0.618, P = .05). After GST, there was no increment of GIP and glucagon like peptide-1 levels compared to baseline levels. A positive and linear correlation between GIP and C-peptide levels was observed only for the MMTT (r = 0.922, P = .008) indicating that in the GST, the C-peptide response is independent of the incretin axis response. CONCLUSIONS: Although the 2 stimulation tests may elicit a similar response in C-peptide secretion, B-cell response to MMTT depends on a functionally normal incretin axis. These results may have implications when investigating the B-cell response in people with diabetes and for studies in which stimulated C-peptide secretion is used as primary or secondary outcome for response to therapy.

Insulin secretion measured by stimulated C-peptide in long-established Type 1 diabetes in the Diabetes Control and Complications Trial (DCCT)/ Epidemiology of Diabetes Interventions and Complications (EDIC) cohort: a pilot study.

AIMS: To evaluate whether clinically relevant concentrations of stimulated C-peptide in response to a mixed-meal tolerance test can be detected after almost 30 years of diabetes in people included in the Diabetes Control and Complications Trial/Epidemiology of Diabetes Interventions and Complications cohort. METHODS: Mixed-meal tolerance tests were performed in a sample of 58 people. C-peptide levels were measured using a chemiluminescent immunoassay. This sample size assured a high probability of detecting C-peptide response if the true prevalence was at least 5%, a level that would justify the subsequent assessment of C-peptide in the entire cohort. RESULTS: Of the 58 participants, 17% showed a definite response, defined as one or more post-stimulus concentrations of C-peptide > 0.03 nmol/l, and measurable concentrations were found in all participants. CONCLUSIONS: These results show that a stimulated C-peptide response can be measured in some people with long-term Type 1 diabetes. Further investigation of all participants in the Diabetes Control and Complications Trial/Epidemiology of Diabetes Interventions and Complications study will help relate long-term residual C-peptide response to glycaemia over time and provide insight into the relevance of this response in terms of insulin dose, severe hypoglycaemia, retinopathy, nephropathy and macrovascular disease. Establishing the clinical relevance of long-term C-peptide responses is important in understanding the impact that therapy to preserve or improve ß-cell function may have in patients with long-term Type 1 diabetes.

A Diabetes Outcome Progression Trial (ADOPT): baseline characteristics of Type 2 diabetic patients in North America and Europe.

AIMS: To examine baseline characteristics of patients recruited into ADOPT, a multinational trial comparing three oral glucose-lowering monotherapies. METHODS: Between April 2000 and June 2002, 4360 patients aged 30-75 years with Type 2 diabetes diagnosed for < 3 years and remaining on diet therapy alone with fasting plasma glucose levels (FPG) between 7.0 and 10.0 mmol/l were enrolled by 488 North American and European centres. Medical histories, anthropometric data and laboratory measurements were determined using common methodologies. RESULTS: The mean (SD) age of the patients was 57 (10) years, body mass index 32.2 (6.4) kg/m(2), HbA(1c) 7.4 (0.9)%; 58% were male, 88% Caucasian and 15% smoked. North American Caucasians (NAC) were younger, more obese, and more insulin resistant than European Caucasians (EUC), but had better pancreatic B-cell function. NAC had lower total, low-density lipoprotein- and high-density liporpotein-cholesterol concentrations with higher triglyceride concentrations and were more often on lipid-lowering treatment. They had lower blood pressure levels but were equally likely to be on antihypertensive treatment. Metabolic syndrome was more frequent and microalbuminuria less frequent in NAC. Within North America, NAC had lower HbA(1c) concentrations than Blacks, Hispanics and Asians despite similar or higher FPG and 30-min postchallenge glucose concentrations. CONCLUSIONS: Caucasian North American and European ADOPT patients differ with respect to adiposity, insulin resistance and metabolic syndrome prevalence. North American Blacks, Hispanics and Asians had lower HbA(1c) concentrations than NAC despite similar or higher glucose concentrations. These phenotypic differences may influence the progression of Type 2 diabetes and the response to initial oral glucose-lowering monotherapy.

Application of robust estimating equations to the analysis of quantitative longitudinal data.

A model fit by general estimating equations (GEE) has been used extensively for the analysis of longitudinal data in medical studies. To some extent, GEE tries to minimize a quadratic form of the residuals, and therefore is not robust in the sense that it, like least squares estimates, is sensitive to heavy-tailed distributions, contaminated distributions and extreme values. This paper describes the family of truncated robust estimating equations and its properties for the analysis of quantitative longitudinal data. Like GEE, the robust estimating equations aim to assess the covariate effects in the generalized linear model in the complete population of observations, but in a manner that is more robust to the influence of aberrant observations. A simulation study has been conducted to compare the finite-sample performance of GEE and the robust estimating equations under a variety of error distributions and data structures. It shows that the parameter estimates based on GEE and the robust estimating equations are approximately unbiased and the type I errors of Wald tests do not tend to be inflated. GEE is slightly more efficient with pure normal data, but the efficiency of GEE declines much more quickly than the robust estimating equations when the data become contaminated or have heavy tails, which makes the robust estimating equations advantageous with non-normal data. Both GEE and the robust estimating equations are applied to a longitudinal analysis of renal function in the Diabetes Control and Complications Trial (DCCT). For this application, GEE seems to be sensitive to the working correlation specification in that different working correlation structures may lead to different conclusions about the effect of intensive diabetes treatment. On the other hand, the robust estimating equations consistently conclude that the treatment effect is highly significant no matter which working correlation structure is used. The DCCT Research Group also demonstrated a significant effect using a mixed-effects longitudinal model.

A flexible stochastic curtailing procedure for the log-rank test.

For safety and ethical reasons, a data monitoring committee of a clinical trial may wish to assess the futility of continuing a trial if the currently available data at an interim look show no beneficial effect due to treatment, especially when accompanied by mounting evidence of treatment emergent adverse effects. Stochastic curtailing whereby conditional power is evaluated given currently observed data is one way of evaluating futility. In clinical trials that look at "time-to-event" as the primary outcome, difference between treatment groups with respect to the primary outcome is commonly evaluated using the log-rank test. Although the unconditional power function for the log-rank test has been described previously, its conditional power has not been widely investigated. We describe a method for evaluating conditional power when the log-rank test is used to assess the difference between the survival distributions of two treatment groups with respect to some failure-time outcome. The method is useful under a wide range of assumptions regarding the underlying survival distribution, patient entry distribution, losses to follow-up, and (if applicable) noncompliance, drop-ins, lag in treatment effect, and stratification. This level of applicability is attained by generalizing a flexible Markov chain approach to unconditional power computation, described previously, to compute conditional power.

Statistical considerations in the intent-to-treat principle.

This paper describes some of the statistical considerations in the intent-to-treat design and analysis of clinical trials. The pivotal property of a clinical trial is the assignment of treatments to patients at random. Randomization alone, however, is not sufficient to provide an unbiased comparison of therapies. An additional requirement is that the set of patients contributing to an analysis provides an unbiased assessment of treatment effects, or that any missing data are ignorable. A sufficient condition to provide an unbiased comparison is to obtain complete data on all randomized subjects. This can be achieved by an intent-to-treat design wherein all patients are followed until death or the end of the trial, or until the outcome event is reached in a time-to-event trial, irrespective of whether the patient is still receiving or complying with the assigned treatment. The properties of this strategy are contrasted with those of an efficacy subset analysis in which patients and observable patient data are excluded from the analysis on the basis of information obtained postrandomization. I describe the potential bias that can be introduced by such postrandomization exclusions and the pursuant effects on type I error probabilities. Especially in a large study, the inflation in type I error probability can be severe, 0.50 or higher, even when the null hypothesis is true. Standard statistical methods for the analysis of censored or incomplete observations all require the assumption of missing at random to some degree, and none of these methods adjust for the potential bias introduced by post hoc subset selection. Nor is such adjustment possible unless one posits a model that relates the missing observations to other observed information for each subject-models that are inherently untestable. Further, the subset selection bias is confounded with the subset-specific treatment effect, and the two components are not identifiable without additional untestable assumptions. Methods for sensitivity analysis to assess the impact of bias in the efficacy subset analysis are described. It is generally believed that the efficacy subset analysis has greater power than the intent-to-treat analysis. However, even when the efficacy subset analysis is assumed to be unbiased, or have a true type I error probability equal to the desired level alpha, situations are described where the intent-to-treat analysis in fact has greater power than the efficacy subset analysis. The intent-to-treat design, wherein all possible patients continue to be followed, is especially powerful when an effective treatment arrests progression of disease during its administration. Thus, a patient benefits long after the patient becomes noncompliant or the treatment is terminated. In such cases, a landmark analysis using the observations from the last patient evaluation is likely to prove more powerful than life-table or longitudinal analyses. Examples are described.

Worst-rank score analysis with informatively missing observations in clinical trials.

Many randomized clinical trials schedule subjects to undergo some assessment at a fixed time (or times) after the initiation of treatment. Often, these follow-up measurements may be missing for some subjects because a disease-related event occurred prior to the time of the follow-up observation. For example, a study of congestive heart failure may schedule patients to undergo exercise testing at 12 weeks, but this measurement may be missing for those who died of heart disease during the study. In such cases, the measurements are informatively missing because mortality from heart disease and a decline in exercise both indicate progression of the underlying disease. It is inappropriate, therefore, to treat these missing observations as missing-at-random and ignore them in the analysis. In one approach to this problem, investigators have included such patients in the analysis of the follow-up data by assigning a rank that represents a "worst-rank score" relative to those actually observed. Some, however, have criticized this procedure as having the potential to produce biased results. In this paper, we explore the statistical properties of such an analysis. We show under a specific model that the imputation of a worst-rank score for informatively missing observations provides an unbiased test against a restricted alternative. We also describe generalizations that employ the actual times of the informative event. We present an example from a study of congestive heart failure. Last, we discuss the implications of this approach and of other methods.

Skin collagen glycation, glycoxidation, and crosslinking are lower in subjects with long-term intensive versus conventional therapy of type 1 diabetes: relevance of glycated collagen products versus HbA1c as markers of diabetic complications. DCCT Skin Collagen Ancillary Study Group. Diabetes Control and Complications Trial.

The relationships between long-term intensive control of glycemia and indicators of skin collagen glycation (furosine), glycoxidation (pentosidine and N(epsilon)-[carboxymethyl]-lysine [CML]), and crosslinking (acid and pepsin solubility) were examined in 216 patients with type 1 diabetes from the primary prevention and secondary intervention cohorts of the Diabetes Control and Complications Trial. By comparison with conventional treatment, 5 years of intensive treatment was associated with 30-32% lower furosine, 9% lower pentosidine, 9-13% lower CML, 24% higher acid-soluble collagen, and 50% higher pepsin-soluble collagen. All of these differences were statistically significant in the subjects of the primary prevention cohort (P < 0.006-0.001) and also of the secondary intervention cohort (P < 0.015-0.001) with the exception of CML and acid-soluble collagen. Age- and duration-adjusted collagen variables were significantly associated with the HbA1c value nearest the biopsy and with cumulative prior HbA1c values. Multiple logistic regression analyses with six nonredundant collagen parameters as independent variables and various expressions of retinopathy, nephropathy, and neuropathy outcomes as dependent variables showed that the complications were significantly associated with the full set of collagen variables. Surprisingly, the percentage of total variance (R2) in complications explained by the collagen variables ranged from 19 to 36% with the intensive treatment and from 14 to 51% with conventional treatment. These associations generally remained significant even after adjustment for HbA1c, and, most unexpectedly, in conventionally treated subjects, glycated collagen was the parameter most consistently associated with diabetic complications. Continued monitoring of these subjects may determine whether glycation products in the skin, and especially the early Amadori product (furosine), have the potential to be predictors of the future risk of developing complications, and perhaps be even better predictors than glycated hemoglobin (HbA1c).

Group sequential monitoring of distribution-free analyses of repeated measures.

In many clinical trials the principal analysis consists of a 1 degree of freedom test based on an aggregate summary statistic for a set of repeated measures. Various methods have been proposed for the marginal analysis of such repeated measures that entail estimates of a measure of treatment group difference (the treatment effect) at each of K repeated measures and a consistent estimate of the covariance matrix, where asymptotically these estimates are normally distributed. One can then obtain an overall large sample 1-d.f. test of group differences, such as by taking the average of these K estimates. These methods include the Wei-Lachin family of multivariate rank tests and a corresponding multivariate analysis using the Mann-Whitney difference estimator as a measure of treatment group differences. Other methods, such as O'Brien's non-parametric test, are based on a single summary score for each patient, such as the within-patient mean value. These, and other such methods, allow for some observations to be missing at random. Herein I employ sequential data augmentation to conduct group sequential analyses using a 1 degree of freedom test from a multivariate Mann-Whitney analysis and for the O'Brien rank test. Su and Lachin used this method to perform group sequential analyses of a vector of Hodges-Lehmann estimators. By augmentating the data from the sequential looks in a single analysis, one obtains an estimate of the covariance of the estimates at each look, from which one obtains an estimate of the correlations among the sequential 1-d.f. test statistics. I describe a simple secant algorithm to determine the group sequential boundaries based on recursive integration of the standard multivariate normal distribution with the estimated correlation matrix. Although the boundary obtains readily using the method of Slud and Wei, the more flexible method of Lan and DeMets may be preferred. The true information fraction at each look, needed to apply the spending function method of Lan and DeMets, however, is unknown. Thus, I also describe the use of a surrogate measure of information.

The efficacy of tolrestat in the treatment of diabetic peripheral neuropathy. A meta-analysis of individual patient data.

OBJECTIVE: The aim of this meta-analysis was to review the existent evidence on the effectiveness of tolrestat in the treatment of diabetic peripheral neuropathy. RESEARCH DESIGN AND METHODS: Individual patient data on 738 subjects from the three randomized clinical trials published on this topic were analyzed using changes in motor nerve conduction velocities (NCVs) as endpoints. Nerves investigated included median, ulnar, tibial, and peroneal. RESULTS: The pooled analysis of NCV taken as a continuous measurement showed a significant treatment effect, the magnitude of this benefit being approximately equal to 1 m/s for all the nerves investigated. When looking at the proportion of patients experiencing a loss of NCV of at least 1 or 2 m/s in at least two out of the four nerves investigated, it emerged that treatment reduced by > 40% the risk of such outcomes after adjusting for patients' characteristics. The odds ratios relative to the placebo group were 1.82 (1.30-2.52) and 1.70 (1.15-2.48) for a decrease of 1 and 2 m/s, that is, placebo-treated patients have an 82 and 70% increased risk for a loss of nerve function of 1 and 2 m/s, respectively. No statistically significant difference in treatment effect emerged after stratification according to baseline motor NCV and glycated hemoglobin levels. CONCLUSIONS: After a treatment duration ranging between 24-52 weeks, patients treated with tolrestat had a reduced risk for developing nerve function loss compared with placebo-treated patients. Future long-term trials are needed to evaluate the impact of the treatment on more clinically meaningful endpoints such as the development of foot complications.

Nonparametric test of stochastic ordering for multiple longitudinal measures.

We present a nonparametric approach that tests whether multiple longitudinal measures tend in the same direction over time. It is not required that each measure have the same number of serial observations, or that the observations be evenly spaced. The test and related estimators of group differences are based on the multivariate rank test of Wei and Lachin (1) and multivariate Mann-Whitney shift estimators of Thall and Lachin (2) and Lachin (3). An example is given using a subset of exercise data from a clinical trial of vesnarinone in congestive heart failure.

Sequential monitoring of survival data with the Wilcoxon statistic.

When a spending function is used in sequential data monitoring of a clinical trial, it is important to know the information fraction at the times of interim analysis. In a maximum duration designed study, the information fraction is unknown when data are monitored, and it has to be estimated. The modified Wilcoxon statistic developed by Peto and Peto and modified by Prentice is often used to compare two survival curves in a clinical trial. We give guidelines for estimating the information fraction in a maximum duration trial when this statistic is employed. When there is a relatively low event rate or the survival time is approximately exponential, the information fraction for the Peto-Peto-Prentice Wilcoxon statistic is very close to that of the popular logrank statistic. In other cases, it would be helpful to estimate the information fraction as a function of elapsed calendar time. We discuss both group sequential and continuous monitoring.

Martingales without tears.

This pedagogical paper presents a casual introduction to martingales, or fair gambling processes. Our objective is to describe the concept of a martingale and its application to common statistical tests used in the analysis of survival data, but without the mathematical rigor required for formal proofs. We use heuristic arguments to demonstrate that the logrank statistic evaluated over followup time is a fair gambling process, and introduce some mathematical notation and terminology along the way. We then employ the counting process approach to show that the logrank statistic computed over followup time can be expressed as the difference of two martingale transforms, and thus is a martingale. These ideas are first time introduced in the context of a discrete time process, and are then generalized to a continuous time process. With slight modifications, the same idea extends from the logrank to other weighted Mantel-Haenszel statistics computed over time.

The use of response-adaptive designs in clinical trials.

Response-adaptive designs in clinical trials are schemes for patient assignment to treatment, the goal of which is to place more patients on the better treatment based on patient responses already accrued in the trial. While ethically attractive at first glance, these designs have had very little use in practice; yet the statistical literature is rich on this subject. We discuss procedures and properties of these designs. Particular focus is given to the randomized play-the-winner rule of Wei and Durham, which was used in the ECMO trial. We also discuss reasons for the lack of use of these models, and areas of current and future research to address the weaknesses of these methods. We conclude that these designs may be applicable in some situations and describe conditions under which such a trial may be feasible.

Use of spending functions for occasional or continuous monitoring of data in clinical trials.

In many clinical trials, data are monitored periodically by an external data monitoring committee (DMC). Usually the frequency of these interim 'looks' at the data is prespecified. However, the progress of a clinical trial is unpredictable; often the schedule of looks must be modified. The Lan-DeMets procedure provides a spending function approach which does not require prespecification of the frequency or timing of interim looks. The procedure was developed based on the principle of a continuous Brownian motion process. In this paper we employ more elementary concepts to describe a procedure which is based upon the continuous monitoring of emerging data. The approach is flexible in that it applies to both continuous data monitoring and occasional interim monitoring. Examples are given from real clinical trials.

The effect of intensive treatment of diabetes on the development and progression of long-term complications in insulin-dependent diabetes mellitus.

BACKGROUND: Long-term microvascular and neurologic complications cause major morbidity and mortality in patients with insulin-dependent diabetes mellitus (IDDM). We examined whether intensive treatment with the goal of maintaining blood glucose concentrations close to the normal range could decrease the frequency and severity of these complications. METHODS: A total of 1441 patients with IDDM--726 with no retinopathy at base line (the primary-prevention cohort) and 715 with mild retinopathy (the secondary-intervention cohort) were randomly assigned to intensive therapy administered either with an external insulin pump or by three or more daily insulin injections and guided by frequent blood glucose monitoring or to conventional therapy with one or two daily insulin injections. The patients were followed for a mean of 6.5 years, and the appearance and progression of retinopathy and other complications were assessed regularly. RESULTS: In the primary-prevention cohort, intensive therapy reduced the adjusted mean risk for the development of retinopathy by 76 percent (95 percent confidence interval, 62 to 85 percent), as compared with conventional therapy. In the secondary-intervention cohort, intensive therapy slowed the progression of retinopathy by 54 percent (95 percent confidence interval, 39 to 66 percent) and reduced the development of proliferative or severe nonproliferative retinopathy by 47 percent (95 percent confidence interval, 14 to 67 percent). In the two cohorts combined, intensive therapy reduced the occurrence of microalbuminuria (urinary albumin excretion of > or = 40 mg per 24 hours) by 39 percent (95 percent confidence interval, 21 to 52 percent), that of albuminuria (urinary albumin excretion of > or = 300 mg per 24 hours) by 54 percent (95 percent confidence interval 19 to 74 percent), and that of clinical neuropathy by 60 percent (95 percent confidence interval, 38 to 74 percent). The chief adverse event associated with intensive therapy was a two-to-threefold increase in severe hypoglycemia. CONCLUSIONS: Intensive therapy effectively delays the onset and slows the progression of diabetic retinopathy, nephropathy, and neuropathy in patients with IDDM.

Group sequential distribution-free methods for the analysis of multivariate observations.

Many studies involve the collection of multivariate observations, such as repeated measures, on two groups of subjects who are recruited over time, i.e., with staggered entry of subjects. Various marginal distribution-free multivariate methods have been proposed for the analyses of such multivariate observations where some measures may be missing at random. Using the multivariate U statistic of Wei and Johnson (1985, Biometrika 72, 359-364), we describe the group sequential analysis of such a study where the multivariate observations are observed sequentially--both within and among subjects. We describe a multivariate generalization of the Hodges and Lehmann (1963, Annals of Mathematical Statistics 34, 598-611) estimator of a location shift that can be obtained via the multivariate U statistic with the Mann-Whitney-Wilcoxon kernel. We then describe large-sample group sequential interval estimators and tests based on an aggregate estimate of the location shift combined over all of the repeated measures. We also describe how the same steps could be employed to perform a group sequential analysis based on any one of the variety of marginal multivariate methods that have been proposed. These methods are applied to a real-life example.

Some large-sample distribution-free estimators and tests for multivariate partially incomplete data from two populations.

The most common instance of multivariate observations is the case of repeated measures over time. The two most widely used methods for the analysis of K repeated measures for two groups are the K degrees of freedom (d.f.) T2 MANOVA F-test and the within-subjects 1 degree of freedom ANOVA F-test. Both require complete samples from normally distributed populations. In this paper, I describe alternative K and 1 d.f. distribution-free procedures which allow for randomly missing observations. These include a large-sample analysis of means, the Wei and Lachin multivariate Wilcoxon test with estimates of the Mann-Whitney parameter, and a multivariate Hodges-Lehmann location shift estimator based on the multivariate U-statistic of Wei and Johnson. Each of these methods provides a distribution-free K-variate estimate of the magnitude of group differences which can be used as the basis for an overall test of group differences. These tests include the K d.f. omnibus T2-like test, 1 d.f. tests of restricted hypotheses, such as the Wei-Lachin multivariate one-sided test of stochastic ordering, and the test of general association based on a minimum variance generalized least squares (GLS) estimate of the average group difference. I then describe covariate stratified-adjusted GLS estimates and tests of group differences. This approach also provides tests of homogeneity (interaction) for within-subjects and between-subjects effects. I illustrate these analyses with an analysis of repeated cholesterol measurements in two groups of patients, stratified by sex. Such analyses provide an overall distribution-free summary estimate and test of the treatment effect obtained by combining the group differences over both time (repeated measures) and strata.

Power and sample size evaluation for the McNemar test with application to matched case-control studies.

Various expressions have appeared for sample size calculation based on the power function of McNemar's test for paired or matched proportions, especially with reference to a matched case-control study. These differ principally with respect to the expression for the variance of the statistic under the alternative hypothesis. In addition to the conditional power function, I identify and compare four distinct unconditional expressions. I show that the unconditional calculation of Schlesselman for the matched case-control study can be expressed as a first-order unconditional calculation as described by Miettinen. Corrections to Schlesselman's unconditional expression presented by Fleiss and Levin and by Dupont, which use different models to describe exposure association among matched cases and controls, are also equivalent to a first-order unconditional calculation. I present a simplification of these corrections that directly provides the underlying table of cell probabilities, from which one can perform any of the alternative sample size calculations. Also, I compare the four unconditional sample size expressions relative to the exact power function. The conclusion is that Miettinen's first-order expression tends to underestimate sample size, while his second-order expression is usually fairly accurate, though possibly slightly anti-conservative. A multinomial-based expression presented by Connor, among others, is also fairly accurate and is usually slightly conservative. Finally, a local unconditional expression of Mitra, among others, tends to be excessively conservative.