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.

The effects of chenodiol on biliary lipids and their association with gallstone dissolution in the National Cooperative Gallstone Study (NCGS).

The National Cooperative Gallstone Study was a double-masked trial conducted to determine the efficacy and safety of chenodeoxycholic acid (chenodiol) for dissolution of cholesterol gallstones. Patients with radiolucent gallstones were randomly allocated to either a high dose (750 mg/d, n = 305) or low dose (375 mg/d, n = 306) of chenodiol or placebo (n = 305) administered for 2 yr. Specimens of gallbladder bile were obtained for biliary lipid analysis on 50% of all white obtained for biliary lipid analysis on 50% of all white patients at base line and after 3-mo therapy, on 45% at 12 mo, and on 36% at 24 mo. Among these specimens, 20% were inadequate for analysis. For analysis of data, available values during therapy were averaged up to time of dissolution, study exit, or study termination. In the high-dose group, percent chenodiol (molar percent of all bile acids) increased markedly and remained high during the 2 yr of follow-up. Also, molar percent cholesterol decreased significantly and remained low during the 2 yr of follow-up. In the low-dose group, percent chenodiol increased and remained significantly increased. Percent cholesterol saturation decreased at 3 mo, but at 24 mo it was not different from that in the placebo group, suggesting a physiological adaptation to the low dose by 2 yr. 79% of patients on high dose had greater than 70% chenodiol. Among these, half showed unsaturated bile (less than 100% cholesterol saturation) while the remainder were supersaturated; in the former group with unsaturated bile, 23% had complete dissolution and 51% had partial (greater than 50% reduction in stone size) or complete dissolution. In contrast, those with over 70% chenodiol and supersaturated bile had only 5% complete dissolution. Thus, development of unsaturated bile was a major factor associated with gallstone dissolution. The data also indicate that values for percent cholesterol saturation were a better predictor of gallstone dissolution than molar percent chenodiol, although a high percent chenodiol usually was required to obtain unsaturation.

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.

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).

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.

Validation of a computer-assisted method for estimating the number and volume of gallstones visualized by cholecystography.

It is likely that in the near future there will be widespread use of medicinal therapy to dissolve gallstones. The efficacy of medicinal therapy can best be determined by attempting to relate the total surface area of a collection of gallstones to the composition of bile in patients undergoing therapy. Surface area, in turn, can be directly related to gallstone size and number. In this study, involving 48 cholecystectomized patients, we have shown that standard cholecystography, together with a computer-assisted method of metrology, can effectively monitor the above parameters. Determinations of the standard deviation of 1) replicate readings (35.8%) and 2) averaged metrology estimates compared with actual stone volumes (42.9%), as well as correlation of actual stone volumes with averaged metrology estimates (r = 0.961), indicated the magnitude of assessed change in stone volume that would be necessary to accept a roentgenographic decrease or increase in stone size with 95% confidence. Even with the increased precision found in the computer-assisted method as described, to attain a 98% certainty of some volume change it was necessary to have metrology volume change of 50% or more. Actual stone counts were without significant error in 87.5% of the determinations.

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.

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.

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.

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.

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).

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)

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.

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.