Class of cooperative stochastic models: Exact and approximate solutions, simulations, and experiments using ionic self-assembly of nanoparticles.

We present exact and approximate results for a class of cooperative sequential adsorption models using matrix theory, mean-field theory, and computer simulations. We validate our models with two customized experiments using ionically self-assembled nanoparticles on glass slides. We also address the limitations of our models and their range of applicability. The exact results obtained using matrix theory can be applied to a variety of two-state systems with cooperative effects.

Results of the Avonex Combination Trial (ACT) in relapsing-remitting MS.

OBJECTIVE: To assess the safety, tolerability, and efficacy of interferon beta-1a (IFNbeta-1a) combined with methotrexate (MTX), i.v. methylprednisolone (IVMP), or both in patients with relapsing-remitting multiple sclerosis (RRMS) with continued disease activity on IFNbeta-1a monotherapy. METHODS: Eligibility criteria included RRMS, Expanded Disability Status Scale score 0-5.5, and > or = 1 relapse or gadolinium-enhancing MRI lesion in the prior year on IFNbeta-1a monotherapy. Participants continued weekly IFNbeta-1a 30 microg i.m. and were randomized in a 2 x 2 factorial design to adjunctive weekly placebo or MTX 20 mg p.o., with or without bimonthly IVMP 1,000 mg/day for 3 days. The primary endpoint was new or enlarged T2 lesion number at month 12 vs baseline. The study was industry-supported, collaboratively designed, and governed by an investigator Steering Committee with independent Advisory and Data Safety Monitoring committees. Study operations, MRI analyses, and aggregated data were managed by an academic coordinating center. RESULTS: The 313 participants had clinical and MRI characteristics typical of RRMS. Combinations of IFNbeta-1a with MTX or IVMP were generally safe and well tolerated. Although trends suggesting modest benefit were seen for some outcomes for IVMP, the results did not demonstrate significant benefit for either adjunctive therapy. The data suggested IVMP reduced anti-IFNbeta neutralizing antibody titers. CONCLUSIONS: This trial did not demonstrate benefit of adding low-dose oral methotrexate or every other month IV methylprednisolone to interferon beta-1a in relapsing-remitting multiple sclerosis.

Long-term outcomes in nondiabetic chronic kidney disease.

The Modification of Diet in Renal Disease (MDRD) Study examined the effects of strict blood pressure control and dietary protein restriction on the progression of kidney disease. Here, we retrospectively evaluated outcomes of nondiabetic participants with stages 2-4 chronic kidney disease (CKD) from randomized and nonrandomized cohorts of the MDRD Study. Kidney failure and survival status through December of 2000, were obtained from the US Renal Data System and the National Death Index. Event rates were calculated for kidney failure, death, and a composite outcome of death and kidney failure. In the 1666 patients, rates for kidney failure were four times higher than that for death. Kidney failure was a more likely event than death in subgroups based on baseline glomerular filtration rate, proteinuria, kidney disease etiology, gender, and race. It was only among those older than 65 that the rate for death approximated that for kidney failure. In contrast to other populations with CKD, our study of relatively young subjects with nondiabetic disease has found that the majority of the participants advanced to kidney failure with a low competing risk of death. In such patients, the primary emphasis should be on delaying progression of kidney disease.

Fetuin-A is not associated with mortality in chronic kidney disease.

Fetuin-A is a serum protein that inhibits vascular calcification such that lower levels are associated with a higher prevalence of vascular calcification and mortality risk among end-stage renal disease populations. We analyzed data of 822 persons in the Modification of Diet in Renal Disease study, a randomized, controlled trial of persons with predominantly non-diabetic stage 3-4 chronic kidney disease (CKD). Serum fetuin-A levels were measured in baseline serum. Survival status and cause of death were determined by the National Death Index. Cox proportional hazard models evaluated the association of fetuin-A levels with all-cause and cardiovascular mortality. Glomerular filtration ranged from 13 to 55 ml per min per 1.73 m(2). During a median follow-up of 9.5 years, 25% of persons died from any cause and 12% died from a cardiovascular cause. Compared to the lowest tertile, no association was found between the highest fetuin-A tertile and all-cause or cardiovascular mortality. Similarly, no association was found between fetuin-A as a continuous variable and all-cause or cardiovascular mortality. Our study shows that serum fetuin-A levels are not related to all-cause or cardiovascular mortality among persons with predominantly non-diabetic stage 3 or 4 CKD.

Frequent Hemodialysis Network (FHN) randomized trials: study design.

Observational studies suggest improvements with frequent hemodialysis (HD), but its true efficacy and safety remain uncertain. The Frequent Hemodialysis Network Trials Group is conducting two multicenter randomized trials of 250 subjects each, comparing conventional three times weekly HD with (1) in-center daily HD and (2) home nocturnal HD. Daily HD will be delivered for 1.5-2.75 h, 6 days/week, with target eK(t)/V(n) > or = 0.9/session, whereas nocturnal HD will be delivered for > or = 6 h, 6 nights/week, with target stdK(t)/V of > or = 4.0/week. Subjects will be followed for 1 year. The composite of mortality with the 12-month change in (i) left ventricular mass index (LVMI) by magnetic resonance imaging, and (ii) SF-36 RAND Physical Health Composite (PHC) are specified as co-primary outcomes. The seven main secondary outcomes are between group comparisons of: change in LVMI, change in PHC, change in Beck Depression Inventory score, change in Trail Making Test B score, change in pre-HD serum albumin, change in pre-HD serum phosphorus, and rates of non-access hospitalization or death. Changes in blood pressure and erythropoiesis will also be assessed. Safety outcomes will focus on vascular access complications and burden of treatment. Data will be obtained on the cost of delivering frequent HD compared to conventional HD. Efforts will be made to reduce bias, including blinding assessment of subjective outcomes. Because no large-scale randomized trials of frequent HD have been previously conducted, the first year has been designated a Vanguard Phase, during which feasibility of randomization, ability to deliver the interventions, and adherence will be evaluated.

Factors associated with serum leptin in patients with chronic kidney disease.

BACKGROUND AND AIMS: Serum leptin levels are elevated in patients with kidney failure. Data on the associations of serum leptin and on the relationship of leptin with both kidney function and inflammation, are limited in patients with reduced glomerular filtration rate (GFR). We evaluated the independent associations of serum leptin in patients with reduced GFR. MATERIAL AND METHODS: Serum leptin and C-reactive protein (CRP) were measured in samples from 798 participants of the Modification of Diet in Renal Disease Study. Multivariable analysis was used to evaluate the independent effects of kidney function and CRP on leptin levels. RESULTS: Median (interquartile range) of serum leptin was 9.1 ng/ml (14.0). Female gender, higher percent body fat, higher insulin levels, older age, lower GFR and higher CRP were associated with higher serum leptin levels and explained 51% of the variability in the logarithm of serum leptin levels. After adjusting for the other variables, a 10 ml/min/1.73 m2 lower GFR was associated with 6% higher mean serum leptin levels. Percent body fat and gender, explained 45% of the variability in serum leptin levels. CONCLUSIONS: Level of kidney function and CRP are associated with serum leptin in patients with reduced GFR. However, there is a stronger association between serum leptin and indices of body fat and gender in patients in the earlier stages of chronic kidney disease. 50% of the variability remains unexplained in patients with reduced GFR.

Cardiovascular disease risk factors in chronic renal insufficiency.

BACKGROUND: Coronary heart disease (CHD) is an important cause of morbidity and mortality in end-stage renal disease (ESRD). Prevention of CHD in ESRD requires identification and treatment of coronary risk factors in chronic renal insufficiency (CRI). METHODS: We evaluated the prevalence of "traditional coronary risk factors" in CRI in 1,795 patients enrolled in the baseline period of Modification of Diet in Renal Disease (MDRD) Study. Using a cross-sectional design, we determined the relationship of these risk factors to the level of glomerular filtration rate (GFR) and proteinuria. We also predicted the CHD risk in the MDRD Study baseline cohort using the coronary point score. RESULTS: 64.0% had blood pressure > or = 130/85 mmHg despite antihypertensive therapy. 64.2% had LDL cholesterol > or = 130 mg/dl, while 38.3% had HDL cholesterol < 35 mg/dl. After adjustment for age, gender and the presence of diabetes, GFR was inversely associated with systolic blood pressure and positively associated with HDL cholesterol, but not associated with total or LDL cholesterol. After adjustment for age. gender and the presence of diabetes, proteinuria was positively associated with systolic and diastolic blood pressure, total serum cholesterol and LDL cholesterol, and inversely associated with HDL cholesterol. Nonetheless, the predicted CHD risk, even at a very low GFR, was similar to the risk in the general population and lower than the observed rate of de novo CHD in incident dialysis patients. CONCLUSIONS: "Traditional coronary risk factors" are highly prevalent in CRI and vary with the level of renal function. However, the coronary point score does not appear to explain the extent of increased CHD risk in ESRD. Non-traditional risk factors may also contribute to CHD in ESRD.

Analysis of change in the presence of informative censoring: application to a longitudinal clinical trial of progressive renal disease.

The rate of change in a continuous variable, measured serially over time, is often used as an outcome in longitudinal studies or clinical trials. When patients terminate the study before the scheduled end of the study, there is a potential for bias in estimation of rate of change using standard methods which ignore the missing data mechanism. These methods include the use of unweighted generalized estimating equations methods and likelihood-based methods assuming an ignorable missing data mechanism. We present a model for analysis of informatively censored data, based on an extension of the two-stage linear random effects model, where each subject's random intercept and slope are allowed to be associated with an underlying time to event. The joint distribution of the continuous responses and the time-to-event variable are then estimated via maximum likelihood using the EM algorithm, and using the bootstrap to calculate standard errors. We illustrate this methodology and compare it to simpler approaches and usual maximum likelihood using data from a multi-centre study of the effects of diet and blood pressure control on progression of renal disease, the Modification of Diet in Renal Disease (MDRD) Study. Sensitivity analyses and simulations are used to evaluate the performance of this methodology in the context of the MDRD data, under various scenarios where the drop-out mechanism is ignorable as well as non-ignorable.

Design and statistical issues of the hemodialysis (HEMO) study.

The Hemodialysis Study is a multicenter clinical trial of hemodialysis prescriptions for patients with end stage renal disease. Participants from over 65 dialysis facilities associated with 15 clinical centers in the United States are randomized in a 2 x 2 factorial design to dialysis prescriptions targeted to a standard dose or a high dose, and to either low or high flux membranes. The primary outcome variable is mortality; major secondary outcomes are defined based on hospitalizations due to cardiovascular or infectious complications, and on the decline of serum albumin. The Outcome Committee, consisting of study investigators, uses a blinded review system to classify causes of death and hospitalizations related to the major secondary outcomes. The dialysis dose intervention is directed by the Data Coordinating Center using urea kinetic modeling programs that analyze results from dialysis treatments to monitor adherence to the study targets, adjust suggested dialysis prescriptions, and assist in trouble-shooting problems with the delivery of dialysis. The study design has adequate power to detect reductions in mortality rate equal to 25% of the projected baseline mortality rate for both of the interventions.

Adenoma size and number are predictive of adenoma recurrence: implications for surveillance colonoscopy.

BACKGROUND: Three-year colonoscopic surveillance after initial polypectomy may not be required for all patients. Those with multiple baseline polyps and large adenomas, implicated as predictors of colon cancer, merit close observation. Conversely, patients with single small adenomas may be subjected to early endoscopic surveillance unnecessarily. METHODS: From our Adenoma Registry we evaluated patient and adenoma characteristics in 697 patients. All had an adenoma recurrence within 3 years of a positive baseline colonoscopy. Potential risk factors studied were age, gender, number of adenomas, size of largest adenoma and histology. We defined a significant outcome as size of 1 cm or greater, tubulovillous or villous histology, high-grade dysplasia, carcinoma in situ, invasive cancer, or 4 or more adenomas. RESULTS: Having 3 or more adenomas on initial colonoscopy with at least 1 measuring 1 cm or larger greatly increased the chance of a significant finding on the first surveillance colonoscopy. Conversely, patients with 1 or 2 adenomas all measuring less than 1 cm were at extremely low risk of an important outcome within 3 years. CONCLUSIONS: Patients with 1 or 2 adenomas all measuring less than 1 cm are an identified low risk group and their first surveillance examination may be delayed beyond the standard 3 years.

Dietary protein restriction and the progression of chronic renal disease: what have all of the results of the MDRD study shown? Modification of Diet in Renal Disease Study group.

The Modification of Diet in Renal Disease (MDRD) Study was the largest randomized clinical trial to test the hypothesis that protein restriction slows the progression of chronic renal disease. However, the primary results published in 1994 were not conclusive with regard to the efficacy of this intervention. Many physicians interpreted the failure of the MDRD Study to demonstrate a beneficial effect of protein restriction over a 2- to 3-yr period as proving that this therapy does not slow disease progression. The authors believe that this viewpoint is incorrect, and is the result of misinterpretation of inconclusive evidence as evidence in favor of the null hypothesis. Since then, numerous secondary analyses of the MDRD Study have been undertaken to clarify the effect of protein restriction on the rate of decline in GFR, urine protein excretion, and onset of end-stage renal disease. This review describes some of the principles of secondary analyses of randomized clinical trials, presents the results of these analyses from the MDRD Study, and compares them with results from other randomized clinical trials. Although these secondary results cannot be regarded as definitive, the authors conclude that the balance of evidence is more consistent with the hypothesis of a beneficial effect of protein restriction than with the contrary hypothesis of no beneficial effect. Until additional data become available, physicians must continue to make recommendations in the absence of conclusive results. The authors suggest that physicians incorporate the results of these secondary analyses into their interpretation of the findings of the MDRD Study.

Changing glomerular filtration with progression from impaired glucose tolerance to Type II diabetes mellitus.

Glomerular filtration rate (iothalamate clearance) was measured serially for 48 months in 26 Pima Indians with impaired glucose tolerance and 27 with normal glucose tolerance. At baseline, the mean glomerular filtration rate (SEM) was 133+/-8 ml/min in subjects with impaired glucose tolerance and 123+/-5 ml/min in those with normal glucose tolerance (p = 0.12). In the 12 subjects with impaired glucose tolerance who progressed to Type II (non-insulin-dependent) diabetes during follow-up, mean glomerular filtration rate increased by 30% (p = 0.011). Among the remaining 14 subjects with impaired glucose tolerance, 12 reverted to normoglycaemia. The glomerular filtration rate both at baseline and after 48 months in this subgroup exceeded the values of subjects with normal glucose tolerance by 20 % (p = 0.008) and 14% (p=0.013), respectively. A pronounced rise in the glomerular filtration rate occurs at the onset of Type II diabetes but a trend to hyperfiltration is also present in those with impaired glucose tolerance.

The natural history of untreated duodenal and ampullary adenomas in patients with familial adenomatous polyposis followed in an endoscopic surveillance program.

BACKGROUND: Endoscopic surveillance is recommended for patients with familial adenomatous polyposis (FAP) because of the high prevalence of duodenal adenomas and the risk of periampullary cancer. The aim of this study was to assess the natural history of untreated duodenal and ampullary adenomas in FAP patients during surveillance. METHODS: One hundred fourteen FAP patients who had 2 or more surveillance examinations were followed for a mean of 51 months (range, 10 to 151 months). RESULTS: Duodenal polyps progressed in size in 26% (25 of 95), number in 32% (34 of 106), and histology in 11% (5 of 45) of patients. Morphology and histology of the main duodenal papilla progressed in 14% (15 of 110) and 11% (12 of 105) of patients, respectively. The histologic progression was mild except for one patient who developed a periampullary cancer. CONCLUSIONS: A minority of FAP patients had progression of endoscopic features and histology of duodenal polyps or the main duodenal papilla when followed over 4 years. An endoscopic surveillance interval of at least 3 years may be appropriate for the majority of untreated patients with FAP. Factors that stratify patients as being at the highest risk of periampullary cancer and thus requiring more intensive surveillance are yet to be determined.

Calcium supplements for the prevention of colorectal adenomas. Calcium Polyp Prevention Study Group.

BACKGROUND AND METHODS: Laboratory, clinical, and epidemiologic evidence suggests that calcium may help prevent colorectal adenomas. We conducted a randomized, double-blind trial of the effect of supplementation with calcium carbonate on the recurrence of colorectal adenomas. We randomly assigned 930 subjects (mean age, 61 years; 72 percent men) with a recent history of colorectal adenomas to receive either calcium carbonate (3 g [1200 mg of elemental calcium] daily) or placebo, with follow-up colonoscopies one and four years after the qualifying examination. The primary end point was the proportion of subjects in whom at least one adenoma was detected after the first follow-up endoscopy but up to (and including) the second follow-up examination. Risk ratios for the recurrence of adenomas were adjusted for age, sex, lifetime number of adenomas before the study, clinical center, and length of the surveillance period. RESULTS: The subjects in the calcium group had a lower risk of recurrent adenomas. Among the 913 subjects who underwent at least one study colonoscopy, the adjusted risk ratio for any recurrence of adenoma with calcium as compared with placebo was 0.85 (95 percent confidence interval, 0.74 to 0.98; P=0.03). The main analysis was based on the 832 subjects (409 in the calcium group and 423 in the placebo group) who completed both follow-up examinations. At least one adenoma was diagnosed between the first and second follow-up endoscopies in 127 subjects in the calcium group (31 percent) and 159 subjects in the placebo group (38 percent); the adjusted risk ratio was 0.81 (95 percent confidence interval, 0.67 to 0.99; P=0.04). The adjusted ratio of the average number of adenomas in the calcium group to that in the placebo group was 0.76 (95 percent confidence interval, 0.60 to 0.96; P=0.02). The effect of calcium was independent of initial dietary fat and calcium intake. CONCLUSIONS: Calcium supplementation is associated with a significant - though moderate - reduction in the risk of recurrent colorectal adenomas.

Calcium supplements and colorectal adenomas. Polyp Prevention Study Group.

Experimental and observational findings suggest that calcium intake may protect against colorectal neoplasia. To investigate this hypothesis, we conducted a randomized, double-blind trial of colorectal adenoma recurrence. Nine hundred thirty patients with a recent history of colorectal adenomas were randomly given calcium carbonate (3 gm daily; 1200 mg elemental calcium) or placebo, with follow-up colonoscopies one and four years after the qualifying examination. The main analysis focused on new adenomas found after the first follow-up endoscopy, up to (and including) the second follow-up examination. Risk ratios of at least one recurrent adenoma and ratios of the average numbers of adenomas were calculated as measures of calcium effect. There was a lower risk of recurrent adenomas in subjects assigned calcium. Eight hundred thirty-two patients had two follow-up examinations and were included in the main analysis; the adjusted risk ratio of one or more adenomas was 0.81 (95% CI 0.67 to 0.99); the adjusted ratio of the average numbers of adenomas was 0.76 (95% CI 0.60 to 0.96). Among subjects who had at least one follow-up colonoscopy, the adjusted risk ratio of one or more recurrent adenomas was 0.85 (95% CI 0.74 to 0.98). The effect of calcium seemed independent of initial dietary fat and calcium intake. No toxicity was associated with supplementation. These findings indicate that calcium supplementation has a modest protective effect against colorectal adenomas, precursors of most colorectal cancers.

Effect of a ketoacid-aminoacid-supplemented very low protein diet on the progression of advanced renal disease: a reanalysis of the MDRD feasibility study.

BACKGROUND: We reanalyzed the data of the Modification of Diet in Renal Disease (MDRD) feasibility study to ascertain the effects of ketoacid- and aminoacid-supplemented very low protein diets. METHODS: Sixty-six patients with advanced renal disease (Study B, baseline glomerular filtration rate (GFR) 7.5-24 ml/min/1.73 m2) were randomly assigned to a low protein diet (L, 0.575 g/kg/d), or a very low protein diet (0.28 g/kg/d) supplemented either with a ketoacid-aminoacid mixture (diet K) or with a mixture of essential aminoacids (diet J). Thirty patients with moderate renal disease (Study A, baseline GFR 25-80 ml/min/1.73 m2) were randomly assigned to a usual protein diet (M, 1.2 g/kg/d), diet L, or diet K. Mean follow-up was 14 months. RESULTS: In Study B, GFR decline differed among the three diets (p = 0.028). Pairwise comparisons showed that the mean +/- SE GFR decline in ml/min/mo in diet K [-0.250+/-0.072] was slower than in diet J [-0.533+/-0.074] (p = 0.008) despite similar achieved protein intakes. The mean GFR decline in diet L [-0.394+/-0.068] was intermediate between, and did not differ significantly from the rates of decline in the other two groups. In Study A, consistent with a hemodynamic effect, the mean GFR decline varied directly with the reduction in protein intake in diets M, L and K (p = 0.028) during the first four months of follow-up, but thereafter did not differ among the diet groups (p = 0.76). CONCLUSION: The study suggests that supplementation of a very low protein diet with the ketoacid-aminoacid mixture used in this feasibility study slowed the progression of advanced renal disease more than supplementation with an amino acid mixture.

Adenoma characteristics at first colonoscopy as predictors of adenoma recurrence and characteristics at follow-up. The Polyp Prevention Study Group.

BACKGROUND & AIMS: All patients with colorectal adenomas may not require identical follow-up. We aimed to determine if adenoma characteristics at initial colonoscopy could predict adenoma recurrence or characteristics at follow-up. METHODS: The number of adenomas and the size, type, and degree of atypia in 479 patients in a polyp prevention trial were evaluated as predictors of the same characteristics at follow-up using odds ratios (ORs) with 95% confidence intervals (CIs). Multiple logistic regression analysis was performed to determine if several baseline characteristics were simultaneously associated with outcome. RESULTS: Although several characteristics were significant predictors of recurrence univariately, by multivariate analysis, multiple adenomas at follow-up were more likely when patients had > or = 3 baseline adenomas (OR, 2.25; 95% CI, 1.20-4.21) or at least 1 tubulovillous adenoma (OR, 2.12; 95% CI, 1.12-4.02). No specific characteristic was associated with recurrence of high-risk polyps (> or = 1 cm, villous, severe atypia). Seventy percent of patients with 1 or 2 baseline adenomas had no recurrence, and only 3.3% had any adenomas of clinical concern. CONCLUSIONS: Number and type of baseline adenomas predict recurrent adenomas, but the recurrence is rarely of clinical concern. Patients with 1 or 2 tubular adenomas constitute a low-risk group for whom follow-up might be extended beyond 3 years.

ICU admission score for predicting morbidity and mortality risk after coronary artery bypass grafting.

BACKGROUND: This study was performed to develop an intensive care unit (ICU) admission risk score based on preoperative condition and intraoperative events. This score provides a tool with which to judge the effects of ICU quality of care on outcome. METHODS: Data were collected prospectively on 4,918 patients (study group n = 2,793 and a validation data set n = 2,125) undergoing coronary artery bypass grafting alone or combined with a valve or carotid procedure between January 1, 1993, and March 31, 1995. Data were analyzed by univariate and multiple logistic regression with the end points of hospital mortality and serious ICU morbidity (stroke, low cardiac output, myocardial infarction, prolonged ventilation, serious infection, renal failure, or death). RESULTS: Eight risk factors predicted hospital mortality at ICU admission, and these factors and five others predicted morbidity. A clinical score, weighted equally for morbidity and mortality, was developed. All models fit according to the Hosmer-Lemeshow goodness-of-fit test. This score applies equally well to patients undergoing isolated coronary artery bypass grafting. CONCLUSIONS: This model is complementary to our previously reported preoperative model, allowing the process of ICU care to be measured independent of the operative care. Sequential scoring also allows updated prognoses at different points in the continuum of care.