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.

Sulfation of lithocholate as a possible modifier of chenodeoxycholic acid-induced elevations of serum transaminase in patients with gallstones.

Chenodeoxycholic acid (CDC), through its metabolite, lithocholic acid (LC), is hepatotoxic in certain species. The cause of elevations of serum transaminase in 25% of humans ingesting CDC, however, is unknown, but also may be due to LC. Because efficient hepatic sulfation of LC may protect against hepatic injury, the aim of this study was to determine if sulfation of LC might modify CDC-induced elevations of transaminase. Pretreatment sulfation fraction (SF) was estimated in 63 randomly selected patients with gallstones in a double-blind randomized trial of CDC, 750 mg/d, 375 mg/d, or placebo; in 27 of these, SF was repeated at 1 or 2 yr. In four other patients, the SF was measured at 2 yr only. Serum glutamic oxaloacetic transaminase and serum glutamic pyruvic transaminase were determined monthly for 3 mo and then every 3 or 4 mo; an elevation of transaminase was defined as > 150% of the normal upper limit in asymptomatic patients. 10 muCi of (3)H-glyco-LC (sp act 84 mCi/mol) was ingested 10-12 h before fasting duodenal biliary drainage. Bile acids in bile were separated by thin-layer chromatography. The SF was estimated as a percentage of total radioactivity (scintillation counting) in sulfated glyco-LC. The standard deviation for replicate SF determinations (n = 311) was 2.1% The pretreatment SF (mean 60.7+/-1.7 SEM) correlated inversely with age (r = 0.336, P < 0.005) and directly with the obesity index (r = 0.495, P > 0.001), but was independent of sex. The SF, remeasured at 1 or 2 yr, did not change significantly with time or CDC. Among CDC-treated patients, elevations of transaminase occurred in 75% of patients with a SF < 45% vs. 11% with a SF > 45% (P < 0.001). In conclusion, a SF < 45% occurred in patients with gallstones who had a high probability of developing elevated serum transaminase when treated with CDC. Thus, sulfation of lithocholate may modify CDC-induced elevations of serum transaminase.

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.

Heart rate and blood pressure in black newborns and in white newborns.

Sixty-one full-term, appropriate-weight black newborns had higher heart rates, replicating a racial heart rate difference, but did not differ significantly in systolic blood pressure from 71 white newborns. Systolic blood pressure in the newborn is related both to the total number of feedings from birth and to the total fluid intake.

Perceptions of the coordinating center: foreword.

The relationships between the coordinating center of a clinical trial and its participants are discussed from a viewpoint of the principal investigator, the clinic coordinator, the project officer, the advisory board and the external site visitor. These perceptions of the coordinating center stress the need for cooperation, proper management of the clinical trial by the coordinating center, proper internal management of the coordinating center, and external monitoring of the coordinating center operations.

Properties of simple randomization in clinical trials.

This article presents the properties of complete randomization (e.g., coin toss) and of the random allocation rule (random permutation of n/2 of n elements). The latter is principally used in cases where the total sample size n is known exactly a priori. The likelihood of treatment imbalances is readily computed and is shown to be negligible for large trials (n greater than 200), regardless of whether a stratified randomization is used. It is shown that substantial treatment imbalances are extremely unlikely in large trials, and therefore there is likely to be no substantial effect on power. The large-sample permutational distribution of the family of linear rank tests is presented for complete randomization unconditionally and conditionally, and for the random allocation rule. Asymptotically the three are equivalent to the distribution of these tests under a sampling-based population model. Permutation tests are also presented for a stratified analysis within one or more subgroups of patients defined post hoc on the basis of a covariate. This provides a basis for analysis when some patients' responses are assumed to be missing-at-random. Using the Blackwell-Hodges model, it is shown that complete randomization eliminates the potential for selection bias, but that the random allocation rule yields a substantial potential for selection bias in an unmasked trial. Finally, the Efron model for accidental bias is used to assess the potential for bias in the estimate of treatment effect due to covariate imbalance. Asymptotically, this probability approaches zero for complete randomization and for the random allocation rule. However, for finite n, complete randomization minimizes the probability of accidental bias, whereas this probability is slightly higher with a random allocation rule. It is concluded that complete randomization has merit in large clinical trials.

Statistical properties of randomization in clinical trials.

This is the first of five articles on the properties of different randomization procedures used in clinical trials. This paper presents definitions and discussions of the statistical properties of randomization procedures as they relate to both the design of a clinical trial and the statistical analysis of trial results. The subsequent papers consider, respectively, the properties of simple (complete), permuted-block (i.e., blocked), and urn (adaptive biased-coin) randomization. The properties described herein are the probabilities of treatment imbalances and the potential effects on the power of statistical tests; the permutational basis for statistical tests; and the potential for experimental biases in the assessment of treatment effects due either to the predictability of the random allocations (selection bias) or the susceptibility of the randomization procedure to covariate imbalances (accidental bias). For most randomization procedures, the probabilities of overall treatment imbalances are readily computed, even when a stratified randomization is used. This is important because treatment imbalance may affect statistical power. It is shown, however, that treatment imbalance must be substantial before power is more than trivially affected. The differences between a population versus a permutation model as a basis for a statistical test are reviewed. It is argued that a population model can only be invoked in clinical trials as an untestable assumption, rather than being formally based on sampling at random from a population. On the other hand, a permutational analysis based on the randomization actually employed requires no assumptions regarding the origin of the samples of patients studied. The large sample permutational distribution of the family of linear rank tests is described as a basis for easily conducting a variety of permutation tests. Subgroup (stratified) analyses, analyses when some data are missing, and regression model analyses are also discussed. The Blackwell-Hodges model for selection bias in the composition of the study groups is described. The expected selection bias associated with a randomization procedure is a function of the predictability of the treatment allocations and is readily evaluated for any sequence of treatment assignments. In an unmasked study, the potential for selection bias may be substantial with highly predictable sequences. Finally, the Efron model for accidental bias in the estimate of treatment effect in a linear model is described. This is important because the potential for accidental bias is equivalent to the potential for a covariate imbalance.(ABSTRACT TRUNCATED AT 400 WORDS)

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.

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.

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.

Introduction to sample size determination and power analysis for clinical trials.

The importance of sample size evaluation in clinical trials is reviewed and a general method is presented from which specific equations are derived for sample size determination or the analysis of power for a wide variety os statistical procedures. The method is discussed and illustrated in relation to the t test, tests for proportions, tests of survival time, and tests for correlations as they commonly occur in clinical trials. Most of the specific equations reduce to a simple general form for which tables are presented.

Sequential clinical trials for normal variates using interval composite hypotheses.

Sequential methods have become increasingly important for the monitoring of patient safety during clinical trials. However, the typical Wald sequential probability ratio test (SPRT), which compares two simple hypotheses, often presents anomalies which can be attributed to an inadequate representation of the parameter space. The use of composite null and alternative hypothesis in sequential clinical trials is explored and the resulting sequential rules are examined. It is shown that the SPRT and the Bayes formulations using Bayes odds ratios are equivalent in terms of the weighted likelihood ratio (WLR). The WLR is obtained for normal variates when the null hypothesis restricts the mean to (i) an interval and (ii) a point, in each case with complementary alternatives, as well as the one-sided formulation with a half-open interval. Applications to clinical trials include large-samples procedures, the comparative binomial trial and the comparison of survival distributions. Illustrative sequential boundaries are presented and the features of these different formulations are compared and discussed. Mixed sequential rules are considered within the framework for ethical stopping rules proposed by Meier (1979, Clinical Pharmacology and Therapeutics 25, 633--640).

Estimators and tests in the analysis of multiple nonindependent 2 x 2 tables with partially missing observations.

We present methods for the analysis of a K-variate binary measure for two independent groups where some observations may be incomplete, as in the case of K repeated measures in a comparative trial. For the K 2 X 2 tables, let theta = (theta 1,..., theta K) be a vector of association parameters where theta k is a measure of association that is a continuous function of the probabilities pi ik in each group (i = 1, 2; k = 1,..., K), such as the log odds ratio or log relative risk. The asymptotic distribution of the estimates theta = (theta 1,..., theta K) is derived. Under the assumption that theta k = theta for all k, we describe the maximally efficient linear estimator theta of the common parameter theta. Tests of contrasts on the theta are presented which provide a test of homogeneity Ha: theta k = theta l for all k not equal to l. We then present maximally efficient tests of aggregate association Hb: theta = theta 0, where theta 0 is a given value. It is shown that the test of aggregate association Hb is asymptotically independent of the preliminary test of homogeneity Ha. These methods generalize the efficient estimators of Gart (1962, Biometrics 18, 601-610), and the Cochran (1954, Biometrics 10, 417-451), Mantel-Haenszel (1959, Journal of the National Cancer Institute 22, 719-748), and Radhakrishna (1965, Biometrics 21, 86-98) tests to nonindependent tables. The methods are illustrated with an analysis of repeated morphologic evaluations of liver biopsies obtained in the National Cooperative Gallstone Study.

Properties of permuted-block randomization in clinical trials.

This article describes some of the important statistical properties of the commonly used permuted-block design, also known simply as blocked-randomization. Under a permutation model for statistical tests, proper analyses should employ tests that incorporate the blocking used in the randomization. These include the block-stratified Mantel-Haenszel chi-square test for binary data, the blocked analysis of variance F test, and the blocked nonparametric linear rank test. It is common, however, to ignore the blocking in the analysis. For these tests, it is shown that the size of a test obtained from an analysis incorporating the blocking (say T), versus an analysis ignoring the blocking (say TI), is related to the intrablock correlation coefficient (R) as TI = T(1-R). For blocks of common length 2m, the range of R is from -1/(2m-1) to 1. Thus, if there is a positive intrablock correlation, which is more likely than not for m greater than 1, an analysis ignoring blocking will be unduly conservative. Permutation tests are also presented for the case of stratified analyses within one or more subgroups of patients defined post hoc on the basis of a covariate. This provides a basis for the analysis when responses from some patients are assumed to be missing-at-random. An alternative strategy that requires no assumptions is to perform the analysis using only the subset of complete blocks in which no observations are missing. The Blackwell-Hodges model is used to assess the potential for selection bias induced by investigator attempts to guess which treatment is more likely to be assigned to each incoming patient. In an unmasked trial, the permuted-block design provides substantial potential for selection bias in the comparison of treatments due to the predictability of the assignments that is induced by the requirement of balance within blocks. Further, this bias is not eliminated by the use of random block sizes. We also modify the Blackwell-Hodges model to allow for selection bias only when the investigator is able to discern the next assignment with certainty. This type of bias is reduced by the use of random block sizes and is eliminated only if the possible block sizes are unknown to the investigators. Finally, the Efron model for accidental bias is used to assess the potential for bias in the estimation of treatment effects due to covariate imbalances. For the permuted-block design, the variance of this bias approaches that of complete randomization as the half-block length m----infinity.(ABSTRACT TRUNCATED AT 400 WORDS)

Properties of the urn randomization in clinical trials.

In this article we review the important statistical properties of the urn randomization (design) for assigning patients to treatment groups in a clinical trial. The urn design is the most widely studied member of the family of adaptive biased-coin designs. Such designs are a compromise between designs that yield perfect balance in treatment assignments and complete randomization which eliminates experimental bias. The urn design forces a small-sized trial to be balanced but approaches complete randomization as the size of the trial (n) increases. Thus, the urn design is not as vulnerable to experimental bias as are other restricted randomization procedures. In a clinical trial it may be difficult to postulate that the study subjects constitute a random sample from a well-defined homogeneous population. In this case, a randomization model provides a preferred basis for statistical inference. We describe the large-sample permutational null distributions of linear rank statistics for testing the equality of treatment groups based on the urn design. In general, these permutation tests may be different from those based on the population model, which is equivalent to assuming complete randomization. Poststratified subgroup analyses can also be performed on the basis of the urn design permutational distribution. This provides a basis for analyzing the subset of patients with observed responses when some patients' responses can be assumed to be missing-at-random. For multiple mutually exclusive strata, these tests are correlated. For this case, a combined covariate-adjusted test of treatment effect is described. Finally, we show how to generalize the urn design to a prospectively stratified trial with a fairly large number of strata.

Evaluation of sample size and power for analyses of survival with allowance for nonuniform patient entry, losses to follow-up, noncompliance, and stratification.

When designing a clinical trial to test the equality of survival distributions for two treatment groups, the usual assumptions are exponential survival, uniform patient entry, full compliance, and censoring only administratively at the end of the trial. Various authors have presented methods for estimation of sample size or power under these assumptions, some of which allow for an R-year accrual period with T total years of study, T greater than R. The method of Lachin (1981, Controlled Clinical Trials 2, 93-113) is extended to allow for cases where patients enter the trial in a nonuniform manner over time, patients may exit from the trial due to loss to follow-up (other than administrative), other patients may continue follow-up although failing to comply with the treatment regimen, and a stratified analysis may be planned according to one or more prognostic covariates.