Improving small-sample inference in group randomized trials with binary outcomes

Group Randomized Trials (GRTs) randomize groups of people to treatment or control arms instead of individually randomizing subjects. When each subject has a binary outcome, over-dispersed binomial data may result, quantified as an intra-cluster correlation (ICC). Typically, GRTs have a small number, bin , of independent clusters, each of which can be quite large. Treating the ICC as a nuisance parameter, inference for a treatment effect can be done using quasi-likelihood with a logistic link. A Wald statistic, which, under standard regularity conditions, has an asymptotic standard normal distribution, can be used to test for a marginal treatment effect. However, we have found in our setting that the Wald statistic may have a variance less than 1, resulting in a test size smaller than its nominal value. This problem is most apparent when marginal probabilities are close to 0 or 1, particularly when n is small and the ICC is not negligible. When the ICC is known, we develop a method for adjusting the estimated standard error appropriately such that the Wald statistic will approximately have a standard normal distribution. We also propose ways to handle non-nominal test sizes when the ICC is estimated. We demonstrate the utility of our methods through simulation results covering a variety of realistic settings for GRTs. Copyright © 2010 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79433/1/4101_ftp.pd

%QLS SAS Macro: A SAS Macro for Analysis of Correlated Data Using Quasi-Least Squares

Quasi-least squares (QLS) is an alternative computational approach for estimation of the correlation parameter in the framework of generalized estimating equations (GEE). QLS overcomes some limitations of GEE that were discussed in Crowder (1995). In addition, it allows for easier implementation of some correlation structures that are not available for GEE. We describe a user written SAS macro called %QLS, and demonstrate application of our macro using a clinical trial example for the comparison of two treatments for a common toenail infection. %QLS also computes the lower and upper boundaries of the correlation parameter for analysis of longitudinal binary data that were described by Prentice (1988). Furthermore, it displays a warning message if the Prentice constraints are violated. This warning is not provided in existing GEE software packages and other packages that were recently developed for application of QLS (in Stata, MATLAB, and R). %QLS allows for analysis of continuous, binary, or count data with one of the following working correlation structures: the first-order autoregressive, equicorrelated, Markov, or tri-diagonal structures.

Techniques for handling clustered binary data

Bibliography : leaves 143-153.Over the past few decades there has been increasing interest in clustered studies and hence much research has gone into the analysis of data arising from these studies. It is erroneous to treat clustered data, where observations within a cluster are correlated with each other, as one would treat independent data. It has been found that point estimates are not as greatly affected by clustering as are the standard deviations of the estimates. But as a consequence, confidence intervals and hypothesis testing are severely affected. Therefore one has to approach the analysis of clustered data with caution. Methods that specifically deal with correlated data have been developed. Analysis may be further complicated when the outcome variable of interest is binary rather than continuous. Methods for estimation of proportions, their variances, calculation of confidence intervals and a variety of techniques for testing the homogeneity of proportions have been developed over the years (Donner and Klar, 1993; Donner, 1989, and Rao and Scott, 1992). The methods developed within the context of experimental design generally involve incorporating the effect of clustering in the analysis. This cluster effect is quantified by the intracluster correlation and needs to be taken into account when estimating proportions, comparing proportions and in sample size calculations. In the context of observational studies, the effect of clustering is expressed by the design effect which is the inflation in the variance of an estimate that is due to selecting a cluster sample rather than an independent sample. Another important aspect of the analysis of complex sample data that is often neglected is sampling weights. One needs to recognise that each individual may not have the same probability of being selected. These weights adjust for this fact (Little et al, 1997). Methods for modelling correlated binary data have also been discussed quite extensively. Among the many models which have been proposed for analyzing binary clustered data are two approaches which have been studied and compared: the population-averaged and cluster-specific approach. The population-averaged model focuses on estimating the effect of a set of covariates on the marginal expectation of the response. One example of the population-averaged approach for parameter estimation is known as generalized estimating equations, proposed by Liang and Zeger (1986). It involves assuming that elements within a cluster are independent and then imposing a correlation structure on the set of responses. This is a useful application in longitudinal studies where a subject is regarded as a cluster. Then the parameters describe how the population-averaged response rather than a specific subject's response depends on the covariates of interest. On the other hand, cluster specific models introduce cluster to cluster variability in the model by including random effects terms, which are specific to the cluster, as linear predictors in the regression model (Neuhaus et al, 1991). Unlike the special case of correlated Gaussian responses, the parameters for the cluster specific model obtained for binary data describe different effects on the responses compared to that obtained from the population-averaged model. For longitudinal data, the parameters of a cluster-specific model describe how a specific individuals probability of a response depends on the covariates. The decision to use either of these modelling methods depends on the questions of interest. Cluster-specific models are useful for studying the effects of cluster-varying covariates and when an individual's response rather than an average population's response is the focus. The population-averaged model is useful when interest lies in how the average response across clusters changes with covariates. A criticism of this approach is that there may be no individual with the characteristics of the population-averaged model

Evaluating Risks from Antibacterial Medication Therapy

ABSTRACT EVALUATING RISKS FROM ANTIBACTERIAL MEDICATION THERAPY USING AN OBSERVATIONAL PRIMARY CARE DATABASE Sharon B. Meropol Joshua P. Metlay Virtually everyone in the U.S. is exposed to antibacterial drugs at some point in their lives. It is important to understand the benefits and risks related to these medications with nearly universal public exposure. Most information on antibacterial drug-associated adverse events comes from spontaneous reports. Without an unexposed control group, it is impossible to know the real risks for treated vs. untreated patients. We used an electronic medical record database to select a cohort of office visits for non-bacterial acute respiratory tract infections (excluding patients with pneumonia, sinusitis, or acute exacerbations of chronic bronchitis), and compared outcomes of antibacterial drug-exposed vs. -unexposed patients. By limiting our assessment to visits with acute nonspecific respiratory infections, we promoted comparability between exposed and unexposed patients. To further control for confounding by indication and practice, we explored methods to promote further comparability between exposure groups. Our rare outcome presented an additional analytic challenge. Antibacterial drug prescribing for acute nonspecific respiratory infections decreased over the study period, but, in contrast to the U.S., broad spectrum antibacterial prescribing remained low. Conditional fixed effects linear regression provided stable estimates of exposure effects on rare outcomes; results were similar to those using more traditional methods for binary outcomes. Patients with acute nonspecific respiratory infections treated with antibacterial drugs were not at increased risk of severe adverse events compared to untreated patients. Patients with acute nonspecific respiratory infections exposed to antibacterials had a small decreased risk of pneumonia hospitalizations vs. unexposed patients. This very small measurable benefit of antibacterial drug therapy for acute nonspecific respiratory infections at the patient level must be weighed against the public health risk of emerging antibacterial resistance. Our data provide valuable point estimates of risks and benefits that can be used to inform future decision analysis and guideline recommendations for patients with acute nonspecific respiratory infections. Ultimately, improved point-of-care diagnostic testing may help direct antibacterial drugs to the subset of patients most likely to derive benefit

A randomized controlled trial of pharmacist-led therapeutic carbohydrate and energy restriction in type 2 diabetes

Type 2 diabetes can be treated, and sometimes reversed, with dietary interventions; however, strategies to implement these interventions while addressing medication changes are lacking. We conducted a 12-week pragmatic, community-based parallel-group randomized controlled trial (ClinicalTrials.gov: NCT03181165) evaluating the effect of a low-carbohydrate (<50 g), energy-restricted diet (~850-1100 kcal/day; Pharm-TCR; n = 98) compared to treatment-as-usual (TAU; n = 90), delivered by community pharmacists, on glucose-lowering medication use, cardiometabolic health, and health-related quality of life. The Pharm-TCR intervention was effective in reducing the need for glucose-lowering medications through complete discontinuation of medications (35.7%; n = 35 vs. 0%; n = 0 in TAU; p < 0.0001) and reduced medication effect score compared to TAU. These reductions occurred concurrently with clinically meaningful improvements in hemoglobin A1C, anthropometrics, blood pressure, and triglycerides (all p < 0.0001). These data indicate community pharmacists are a viable and innovative option for implementing short-term nutritional interventions for people with type 2 diabetes, particularly when medication management is a safety concern

Addressing Geographic Confounding through Spatial Propensity Score Analysis for Hierarchical Data

Motivated by recent work exploring cluster-level confounding in multilevel observational data, we develop methods specifically addressing geographic confounding, which occurs when measured or potentially unmeasured confounding factors vary by geographic location. Accounting for this source of confounding achieves spatially-balanced global estimates of the treatment effect of interest, allowing researchers to compare individuals as if they were residentially similar and leading to policy decisions that benefit patients and areas most in need. This dissertation consists of three aims: 1. To develop a hierarchical spatial doubly robust estimator in propensity score analysis framework; 2. To develop spatial propensity score matching methods for hierarchical data; 3. To apply spatial propensity score matching to more complex analyses of spatially varying, zero-inflated outcomes. Each of these aims strives to explore the issue of geographic confounding and contribute to its resolution. Aim 1 seeks to build upon multilevel propensity score methods through augmentation of modeling with spatial random effects to create a spatially balanced estimator that is demonstrated in simulation to exhibit favorable performance under various sample sizes and levels of spatial heterogeneity. Aim 2 seeks to develop methods in a propensity score matching framework, allowing for a more complete understanding of geographic confounding remediation techniques and extensions to additional applications. Finally, as modeling non-binary, spatially varying outcomes can prove challenging, Aim 3 seeks to incorporate spatial matching to alleviate geographic imbalance to allow for a minimally confounded analysis. We apply the spatial matching approach to the analysis of zero-inflated count outcomes

Improving Small-Sample Inference in Group Randomized Trials and Other Sources of Correlated Binary Outcomes.

Group Randomized Trials (GRTs), along with many other types of studies, commonly can be composed of a small to moderate number of independent clusters of correlated data. In this dissertation, we focus on statistical inference in these settings. Particularly, we concentrate on test size and estimation variability when a marginal model is employed. Our first focus is in a general GRT setting in which a logistic regression only implements an indicator of treatment assignment. A Wald test, using a model-based standard error, for a marginal treatment effect can tend to have a realized test size smaller than its nominal value. We therefore propose a pseudo-Wald statistic that consistently produces test sizes at their nominal value, therefore increasing or maintaining power. Our second focus is on the estimation performance of QIF as compared to GEE when the number of clusters is not large, with a focus on GRT settings. GEE is commonly used for the analysis of correlated data, while QIF is a newer method with the theoretical advantage of being equally or more efficient. Therefore, it would be reasonable to believe that QIF should maintain or increase power in GRTs, which typically have low power. We show, however, that QIF may not have this advantage in GRT settings, and estimates from QIF can have greater variability than estimates from GEE due to the empirical impact of imbalance in cluster sizes and covariates, therefore concluding GEE is a more appropriate method in these settings. We finally focus on improving the small-sample estimation performance of QIF. Specifically, we propose multiple alternative weighting matrices to use in QIF that combat its small-sample deficiencies. These weighting matrices are expected to perform better in small-sample settings, such as for GRTs, but maintain QIF's large-sample advantages. We compare the performances of the proposed QIF modifications via simulations, which show they can improve small-sample estimation. We also demonstrate that two of the proposed QIF versions work best.Ph.D.BiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89710/1/pwestgat_1.pd

Exact Approaches for Bias Detection and Avoidance with Small, Sparse, or Correlated Categorical Data

Every day, traditional statistical methodology are used world wide to study a variety of topics and provides insight regarding countless subjects. Each technique is based on a distinct set of assumptions to ensure valid results. Additionally, many statistical approaches rely on large sample behavior and may collapse or degenerate in the presence of small, spare, or correlated data. This dissertation details several advancements to detect these conditions, avoid their consequences, and analyze data in a different way to yield trustworthy results. One of the most commonly used modeling techniques for outcomes with only two possible categorical values (eg. live/die, pass/fail, better/worse, ect.) is logistic regression. While some potential complications with this approach are widely known, many investigators are unaware that their particular data does not meet the foundational assumptions, since they are not easy to verify. We have developed a routine for determining if a researcher should be concerned about potential bias in logistic regression results, so they can take steps to mitigate the bias or use a different procedure altogether to model the data. Correlated data may arise from common situations such as multi-site medical studies, research on family units, or investigations on student achievement within classrooms. In these circumstance the associations between cluster members must be included in any statistical analysis testing the hypothesis of a connection be-tween two variables in order for results to be valid. Previously investigators had to choose between using a method intended for small or sparse data while assuming independence between observations or a method that allowed for correlation between observations, while requiring large samples to be reliable. We present a new method that allows for small, clustered samples to be assessed for a relationship between a two-level predictor (eg. treatment/control) and a categorical outcome (eg. low/medium/high)