Thomas A. Louis

Projecting the Number of Patients with End-Stage Renal Disease in the United States to the Year 2015

The size of the prevalent ESRD population in the United States increased dramatically during the 1990s, from 196,000 in 1991 to 382,000 in 2000. Incidence also increased considerably during the same period, from 53,000 to 93,000 per year. If previous trends in ESRD incidence and prevalence continue, then current levels of health care resources that are devoted to the care of these patients will eventually be unable to meet the demand. This study discusses a Markov model developed to predict ESRD incidence, prevalence, and mortality to the year 2015 and incorporating expected changes in age/race distributions, diabetes prevalence, ESRD incidence, and probability of death. The model predicted that by 2015 there will be 136,166 incident ESRD patients per year (lower/upper limits 110,989 to 164,550), 712,290 prevalent patients (595,046 to 842,761), and 107,760 ESRD deaths annually (96,068 to 118,220). Incidence and prevalence counts are expected to increase by 44 and 85%, respectively, from 2000 to 2015 and incidence and prevalence rates per million population by 32 and 70%, respectively. The financial and human resources that will be needed to care for these patients in 2015 will be considerably greater than in 2005.

Comparative Effectiveness of Weight-Loss Interventions in Clinical Practice

BACKGROUND Obesity and its cardiovascular complications are extremely common medical problems, but evidence on how to accomplish weight loss in clinical practice is sparse. METHODS We conducted a randomized, controlled trial to examine the effects of two behavioral weight-loss interventions in 415 obese patients with at least one cardiovascular risk factor. Participants were recruited from six primary care practices; 63.6% were women, 41.0% were black, and the mean age was 54.0 years. One intervention provided patients with weight-loss support remotely--through the telephone, a study-specific Web site, and e-mail. The other intervention provided in-person support during group and individual sessions, along with the three remote means of support. There was also a control group in which weight loss was self-directed. Outcomes were compared between each intervention group and the control group and between the two intervention groups. For both interventions, primary care providers reinforced participation at routinely scheduled visits. The trial duration was 24 months. RESULTS At baseline, the mean body-mass index (the weight in kilograms divided by the square of the height in meters) for all participants was 36.6, and the mean weight was 103.8 kg. At 24 months, the mean change in weight from baseline was -0.8 kg in the control group, -4.6 kg in the group receiving remote support only (P<0.001 for the comparison with the control group), and -5.1 kg in the group receiving in-person support (P<0.001 for the comparison with the control group). The percentage of participants who lost 5% or more of their initial weight was 18.8% in the control group, 38.2% in the group receiving remote support only, and 41.4% in the group receiving in-person support. The change in weight from baseline did not differ significantly between the two intervention groups. CONCLUSIONS In two behavioral interventions, one delivered with in-person support and the other delivered remotely, without face-to-face contact between participants and weight-loss coaches, obese patients achieved and sustained clinically significant weight loss over a period of 24 months. (Funded by the National Heart, Lung, and Blood Institute and others; ClinicalTrials.gov number, NCT00783315.).

Models for Value-Added Modeling of Teacher Effects

The use of complex value-added models that attempt to isolate the contributions of teachers or schools to student development is increasing. Several variations on these models are being applied in the research literature, and policy makers have expressed interest in using these models for evaluating teachers and schools. In this article, we present a general multivariate, longitudinal mixed-model that incorporates the complex grouping structures inherent to longitudinal student data linked to teachers. We summarize the principal existing modeling approaches, show how these approaches are special cases of the proposed model, and discuss possible extensions to model more complex data structures. We present simulation and analytical results that clarify the interplay between estimated teacher effects and repeated outcomes on students over time. We also explore the potential impact of model misspecifications, including missing student covariates and assumptions about the accumulation of teacher effects over time, on key inferences made from the models. We conclude that mixed models that account for student correlation over time are reasonably robust to such misspecifications when all the schools in the sample serve similar student populations. However, student characteristics are likely to confound estimated teacher effects when schools serve distinctly different populations.

Crossover and self-controlled designs in clinical research.

Crossover studies (clinical trials in which each patient receives two or more treatments in sequence) and self-controlled studies (in which each patient serves as his or her own control) can produce results that are statistically and clinically valid with far fewer patients than would otherwise be required. We investigated the use of the crossover design in the 13 crossover studies that appeared in the Journal during 1978 and 1979. We considered the following important features of design and analysis as they applied to these studies: the method by which patients were assigned to initial treatment (only 7 of 13 studies used random assignment); the determination of when to switch treatments (10 of the 13 used a time-dependent rule, and 3 a less appropriate disease-state-dependent rule); blinding of the crossover point (in only 3 of the 13 studies was the crossover point concealed, but in 4 of the remaining 10 concealment was impossible); assessment of the effects of the order of treatments (included in only 1 of the 13 studies); and the use of at least minimally acceptable statistical analysis (11 of the 13 studies had such an analysis). We also report briefly on 28 additional studies of a single treatment each, in which each patient served as his or her own control before or after treatment or both. The scientific issues were much the same as in crossover studies except that self-controlled comparisons of treatments tended to be less precisely designed and conducted and to focus on clinical problems and patient groups that are especially difficult to study.

Lipid Adjustment in the Analysis of Environmental Contaminants and Human Health Risks

The literature on exposure to lipophilic agents such as polychlorinated biphenyls (PCBs) is conflicting, posing challenges for the interpretation of potential human health risks. Laboratory variation in quantifying PCBs may account for some of the conflicting study results. For example, for quantification purposes, blood is often used as a proxy for adipose tissue, which makes it necessary to model serum lipids when assessing health risks of PCBs. Using a simulation study, we evaluated four statistical models (unadjusted, standardized, adjusted, and two-stage) for the analysis of PCB exposure, serum lipids, and health outcome risk (breast cancer). We applied eight candidate true causal scenarios, depicted by directed acyclic graphs, to illustrate the ramifications of misspecification of underlying assumptions when interpreting results. Statistical models that deviated from underlying causal assumptions generated biased results. Lipid standardization, or the division of serum concentrations by serum lipids, was observed to be highly prone to bias. We conclude that investigators must consider biology, biologic medium (e.g., nonfasting blood samples), laboratory measurement, and other underlying modeling assumptions when devising a statistical plan for assessing health outcomes in relation to environmental exposures.

Effects of Antihypertensive Therapy on Serum Lipids

Several comprehensive reviews have recently been published on investigations of the effects of different antihypertensive agents on serum lipid levels [1-18]. However, the large number of studies has made it difficult to precisely compare and contrast the relative effects of different agents, each of which were investigated in a different clinical setting. We therefore did a meta-analysis of 474 studies, using multiple linear regression weighted by inverse variance and study quality. This regression analysis allowed us to compare the relative effects of different antihypertensive agents on serum lipid levels in different patient populations. We investigated not only the effects of agents but also the interactive effects of dose, treatment duration, age, race, sex, and body mass index. Methods Study Selection We used MEDLINE searches, bibliographies found in comprehensive reviews, and bibliographies supplied by major pharmaceutical companies to locate clinical trials that examined the effects of antihypertensive agents on blood pressure and levels of fasting total cholesterol, low-density lipoprotein (LDL) cholesterol, high-density lipoprotein (HDL) cholesterol, triglycerides, or very-low-density lipoprotein (VLDL) cholesterol. For the two MEDLINE searches, we used the keywords hypertension therapy, human, and cholesterol or hypertension, therapy, human, and lipids. The search period extended from 1966 through 1993. We also examined the bibliographies of all review articles located through the MEDLINE searches and wrote to major pharmaceutical companies to obtain bibliographies with information on the effects of antihypertensive medications on lipids. The reports of the studies were in English, French, Spanish, Italian, or German. We did not include abstracts and proceedings from scientific meetings. We included only studies that reported the means of lipid values before and after treatment, the absolute change in lipid values before and after treatment, or the mean lipid values at baseline and the mean percentage change that would allow us to estimate the absolute change as the product of the baseline and the percentage change. Multiple Linear Regression We used multiple linear regression to determine the relative magnitude and independent effects of different agents, classes of agents, treatment durations, patient characteristics, and study design features on lipids in controlled and uncontrolled studies [19]. We included each group of patients treated with one or more antihypertensive agents as a separate case in the analysis. The regression was weighted by the product of the estimated inverse variance of the change in end point and a study quality index: Wi = Qi/(Vi+ 2), where Wi is the regression weight for the i-th study group, Vi is the estimated within-study variance, and 2 is an estimate of the between-study variability of the effects of different agents [20]. The value was calculated as a fraction (1/2 to 1/5) of the median estimated Vi value across all studies. Qi is the study quality index. We estimated Vi for end points using the variance of the values before and after treatment for each experimental group: Vi(X Y) = Vi(X) + Vi(Y) 2 XY x radical(Vi[X]) x radical(Vi[Y]), where X and Y are the means of the treatment and baseline measurements, respectively, and XY is the correlation coefficient between X and Y, estimated from the experimental group means across all studies. Qi is the sum of points for the following: inclusion (+0.5) and exclusion (+0.5) criteria, masked investigators (+1.0) and study participants (+1.0), random allocation (+3.0), a placebo control group (+2.0), randomized, controlled design (+2.0), multiagent comparison (+1.0), crossover design (+1.0), simple before-and-after treatment with one experimental group (3.0),sequential treatment with multiple agents (2.0), a run-in period (+2.0) with placebo (+1.0), lipoprotein measurements using analytical (+2.0) or routine (+1.0) techniques, use of frozen samples (1.0), lipid values reported to only two places (3.0), values reported without an estimate of variability (2.0), lipid (2.0)or blood pressure (1.0) values estimated from a figure, age (1.0) or sex (1.0) missing, final sample size less than 50% of initial size (1.0), publication as a supplement or letter (1.0), and support from public funding (+1.0). No uniformly applied indices for quality are available in published meta-analyses. Therefore, the index that we selected for study quality was necessarily arbitrary but included features frequently used in assessing study quality in meta-analysis [21-23]. The relative weights given to individual components of the quality index were also arbitrary and were based loosely on literature suggesting the relative importance of different study design features for validity. For example, it has been reported that nonrandom studies overestimated effect size by about one third compared with randomized studies [24, 25]. We therefore chose a weighting factor of 3.0 to reflect the relative importance of this study design feature. The quality index was normally distributed over a range that gives threefold more weight to a study of the 95th percentile than to a study of the 5th percentile. The regression weight (Wi) was normally distributed. A sensitivity analysis was done on some of the final regression models to determine the effect at the regression weighting on the results. There were few differences in the models whether regression was weighted by Wi, Q (i), or sample size or was unweighted (data not shown). When the regression analysis was limited to studies with regression weight values greater as opposed to less than the median, the results for agents represented by an adequate number of studies in both groups were also similar (data not shown). Thus, with respect to regression weighting, the results appeared to be robust. We identified the independent predictor variables, agent and patient characteristics, using a P value less than 0.05 to enter a stepwise, multiple linear regression model. We classified agents as diuretics, thiazide-like diuretics, loop diuretics, potassium-sparing diuretics, -blockers, cardioselective -blockers, -blockers with intrinsic sympathomimetic activity, -blockers, central sympatholytic agents, angiotensin-converting enzyme inhibitors, calcium antagonists, dihydropyridine calcium antagonists, or vasodilators. Some agents shared more than one characteristic, and some groups were treated with combinations, such as combined and -blocker therapy. We also investigated the potential interactive effects of specific drug combinations and analyzed the effects of diuretic dose. We defined high dose as follows: for hydrochlorothiazide and chlorthalidone, greater than 50 mg/d; for chlorthiazide, greater than 500 mg/d; for bendroflumethiazide and indapamide, greater than 5 mg/d; and for cyclothiazide, greater than 2 mg/d [26]. Treatment with a low-sodium diet under rigidly controlled conditions in a hospital or metabolic unit was included as a covariate. The magnitude of sodium restriction varied. Treatment with a low-fat diet, when the diet was accompanied by antihypertensive therapy, was also used as a covariate if patients were obviously given diet instruction and follow-up as part of the study. Untreated or placebo groups were included as pooled controls. We analyzed the proportion of patients in each experimental group who were male, diabetic, or black. Age, body mass index, and baseline end point values for lipids and blood pressure were each standardized to a mean of 0 and a standard deviation of 1. Because the effects of study duration and patient characteristics on lipids were unlikely to be the same for different agents, these effects were investigated as interactions with each agent class. Finally, we examined whether individual agents, if included in more than two studies, differed from others in their class. Because the number of individual agents was large relative to the number of studies that examined each agent, we used a P value of less than 0.025 as a minimum model entry criteria. Data on age were available for 93% of the 945 groups, and patient sex was reported in 88%. We estimated missing body mass indexes using the regression relation among mean body weight, sex, and body mass index generated from cases with complete data. Data on actual body mass index, or body mass index estimated from body weight and sex, were available for 57% of the groups. The proportion of black patients was reported in only 22% of studies. Most studies that did not mention race were from areas of the world where the number of blacks would be expected to be low, and we estimated that the proportion of black persons was zero in studies that did not indicate otherwise. Missing value substitutions for age were randomly selected from cases in which age was known. For other variables, we used regression relations to estimate the missing value by randomly selecting a value from a normal distribution with a mean determined by the regression relation and the standard deviation for cases in which data were not missing. We examined errors introduced by including missing value substitutes. Specifically, the multiple imputation method of Rubin and Schenker [27] was used with five sets of complete data generated by supplying randomly selected substitutes for each missing value. We examined normalized and studentized residuals using histogram and probability plots. In each case, the residuals appeared to be normally distributed, and normal probability plots of observed compared with expected values were nearly linear. For each model, we identified 10 outliers and examined the effect of removing these cases. Coefficients are the mean of the means of the regression coefficients from five models, in which each model was generated with a different set of randomly imputed missing values. We generated confidence intervals using a combined variance of

Findings From the Reanalysis of the NINDS Tissue Plasminogen Activator for Acute Ischemic Stroke Treatment Trial

Background and Purpose— Following publication of concerns about the results of the National Institute of Neurological Disorders and Stroke (NINDS) intravenous tissue plasminogen activator (t-PA) in acute stroke treatment trial, NINDS commissioned an independent committee “to address whether there is concern that eligible stroke patients may not benefit from t-PA given according to the protocol used in the trials and, whether the subgroup imbalance (in baseline stroke severity) invalidates the entire trial.” Methods— The original NINDS trial data were reanalyzed to assess the t-PA treatment effect, the effect of the baseline imbalance in stroke severity between the treatment groups on the t-PA treatment effect, and whether subgroups of patients did not benefit from receiving t-PA. Results— A clinically important and statistically significant benefit of t-PA therapy was identified despite subgroup imbalances in baseline stroke severity and an increased incidence of symptomatic intracerebral hemorrhage in t-PA treated patients. The adjusted t-PA to placebo odds ratio (OR) of a favorable outcome was 2.1 (95% CI, 1.5 to 2.9). Although these exploratory analyses found no statistical evidence that the t-PA treatment effect differed among patient subgroups, the study was not powered to detect subgroup treatment differences. Conclusions— These findings support the use of t-PA to treat patients with acute ischemic stroke within 3 hours of onset under the NINDS t-PA trial protocol. Health professionals should work collaboratively to develop guidelines to ensure appropriate use of t-PA in acute ischemic stroke patients.

Estimating a Population of Parameter Values Using Bayes and Empirical Bayes Methods

Abstract In standard Bayes and empirical Bayes component decision problems, estimating inidividual parameters is the primary goal. In multiple comparison problems and in comparisons of histograms of estimates, however, the primary goal is to produce parameter estimates that can be considered as an ensemble. For example, the histogram of estimates should be a good estimate of the histogram of parameters. Standard methods of estimating by the posterior expectation do minimize symmetric, componentwise losses such as squared error, but they produce ensembles of estimates with a sample variance smaller than the posterior expected sample variance for parameters. In this article we propose new Bayes and empirical Bayes estimates that minimize a distance function between the empirical cdf of the estimates and the true parameters. These estimators are weighted averages of the prior mean and the data, with weight on the data being approximately the square root of that for the posterior expectation. We give theoreti...

Empirical Bayes Confidence Intervals Based on Bootstrap Samples

Abstract Consider the model with data generated by the following two-stage process. First, a parameter θ is sampled from a prior distribution G, and then an observation is sampled from the conditional distribution f(y | θ). If the prior distribution is known, then the Bayes estimate under squared error loss is the posterior expectation of θ conditional on the data y. For example, if G is Gaussian with mean μ and variance τ2 and f(y | θ) is Gaussian with mean θ and variance σ2, then the posterior distribution is Gaussian with mean B μ + (1 – B)y and variance σ2(1 – B), where B = σ2/(σ2 + τ2). Inferences about θ are based on this distribution. We study the application of the bootstrap to situations where the prior must be estimated from the data (empirical Bayes methods). For this model, we observe data Y T = [Y 1, …, Y K]T, each independent Y K following the compound model described previously. As first shown by James and Stein (1961), setting each θk equal to its estimated posterior mean, where , and , pr...

Designs for experiments--parallel comparisons of treatment.

Clinical trials of medical treatments often compare two treated groups or a treated group with a separate but concurrent control group. We have examined a consecutive series of 47 such parallel studies reported in the Journal in 1978-1979, including 35 with random assignment to the treated or control group, to discover how this approach is actually used. A major strength of these studies as a group was the frequent use of randomized treatment assignment. Common problems included lack of sufficient detail about methods of randomization, failure to provide enough detail about patient sources, and insufficient use of multivariate statistical techniques and of statistical modeling. We emphasize the importance of avoiding bias by balancing prognostic factors when assigning patients to treatments, reducing bias by modeling the influence of prognostic factors on response, and increasing precision by modeling. We also advocate the careful consideration of the relevance of a treatment comparison within the study to the external world of clinical practice.