SAS Code Research Articles

Testing Agreement for Multi-Item Scales With the IndicesrWG(J) and AD M(J)

The most popular index of agreement has been rWG(J); more recently, the ADM(J) index also has been used. This study addresses two problems: first, how to test the statistical significance of rWG(J) and ADM(J) and, second, how to infer from the indices that were evaluated for each group about the agreement of the ensemble of groups. The authors extend the inference based on either rWG(J) or ADM(J) by focusing on multiple-item scales and on the whole ensemble of groups. Their method is based on simulations, as was done by Dunlap, Burke, and Smith-Crowe (2003) and by Cohen, Doveh, and Eick (2001). The tests are illustrated on the data of Bliese, Halverson, and Schriesheim (2002) pertaining to a sample of 2,042 U.S Army soldiers in 49 U.S. Army companies. Software for our procedures is available both as a SAS code and in the Multilevel Modeling in R package (Bliese, 2006).

A note on the estimation of the multinomial logistic model with correlated responses in SAS

We show how multinomial logistic models with correlated responses can be estimated within SAS software. To achieve this, random effects and marginal models are introduced and the respective SAS code is given. An example data set on physicians’ recommendations and preferences in traumatic brain injury rehabilitation is used for illustration. The main motivation for this work are two recent papers that recommend estimating multinomial logistic models with correlated responses by using a Poisson likelihood which is statistically correct but computationally inefficient.

JMASM 26: Hettmansperger and Mckean Linear Model Aligned Rank Test for the Single Covariate and One-Way ANCOVA Case (SAS)

A SAS program (SAS 9.1.3 release, SAS Institute, Cary, N.C.) is presented to implement the Hettmansperger and McKean (1983) linear model aligned rank test (nonparametric ANCOVA) for the single covariate and one-way ANCOVA case. As part of this program, SAS code is also provided to derive the residuals from the regression of Y on X (which is step 1 in the Hettmansperger and McKean procedure) using either ordinary least squares regression (proc reg in SAS) or robust regression with MM estimation (proc robustreg in SAS).

Group sequential t-test for clinical trials with small sample sizes across stages

Interim analyses are often applied in clinical trials for various reasons. To assess the effect of a clinical treatment, the group sequential t-test with a fixed number of interim analyses is frequently used in clinical trials. The existing critical values used in group sequential t-tests are obtained from normal approximations of t-statistics. In practice, however, normal approximation is not accurate when some sample sizes of treatment arms in some stages are small. In this paper, instead of using normal approximation, we directly obtain the critical values via a Monte Carlo method. We list some critical values for certain sample sizes and number of interim analyses, and provide some SAS code for general situations. We also consider the sample size calculation and run some simulations to check the accuracy of our critical values. The simulation results show that our critical values yield type I error probabilities that are very close to the nominal significance level, whereas the existing critical values based on normal approximation are not accurate when some sample sizes are small across stages.

Experimental Design for Two-Color Microarrays Applied in a Pre-Existing Split-Plot Experiment

Microarray applications for the study of gene expression are becoming accessible for researchers in more and more systems. Applications from field or laboratory experiments are often complicated by the need to superimpose sample pairing for two-color arrays on experimental designs that may already be complex. For example, split-plot designs are commonly used in biological systems where experiments involve two types of treatments that are not readily applied at the same scale. We demonstrate how effects that are confounded with arrays can still be estimated when there is sufficient replication. To illustrate, we evaluate three methods of sample pairing superimposed on a split-plot design with two treatments, deriving the variance associated with parameter estimates for each. Design A has levels of the whole plot treatment paired on the same microarray within a level of the subplot treatment. Design B has crossed levels paired on the same microarray. Design C has levels of the treatment applied to subplots paired on the same microarray within a whole plot. Designs A and B have lower variance than design C for comparing the levels of the whole plot treatment. Designs B and C have lower variance for comparing the levels of the subplot treatment and design C has lower variance for comparing the levels of the subplot treatment within each level of the whole plot treatment. We provide SAS code for the analyses of variance discussed.

SASweave: Literate Programming UsingSAS

SASweave is a collection of scripts that allow one to embed SAS code into a LATEX document, and automatically incorporate the results as well. SASweave is patterned after Sweave, which does the same thing for code written in R. In fact, a document may contain both SAS and R code. Besides the convenience of being able to easily incorporate SAS examples in a document, SASweave facilitates the concept of literate programming: having code, documentation, and results packaged together. Among other things, this helps to ensure that the SAS output in the document is in concordance with the code.

Reclassifying DIS-III-R Alcohol Use Disorders to DSM-IV Criteria in a Sample of Convicted Impaired Drivers

This study used data gathered from the Diagnostic Interview Schedule, Version Three, Revised (DIS-III-R), which calculated diagnoses based on the Diagnostic and Statistical Manual of Mental Disorders, Third Edition, Revised (DSM-III-R), criteria and rescored the data to be compatible with the criteria of the Fourth Edition of the DSM (DSM-IV) for lifetime alcohol abuse and dependence. A psychologist reassigned questions from the DIS-III-R according to DSM-IV criteria. Another clinician evaluated the rescoring criteria and discrepancies were discussed and resolved. Using these criteria, SAS code was written to automate the rescoring of responses to DIS-III-R questions to DSM-IV diagnoses from a population of DWI offenders. There was a fair-to-good level of agreement between the DSM-III-R and rescored DSM-IV diagnoses (kappa = .65). Three hundred forty-eight subjects classified as alcohol dependent using DSMIII- R were reclassified as alcohol abuse in the DSM-IV rescore. Among subjects who were alcohol dependent based on DIS-III-R criteria, the distribution of DSM-IV diagnoses was similar across gender, age, and ethnic groups. There was no difference in agreement between DSMIII- R and the rescored DSM-IV diagnoses by age category. However, women and Hispanics had significantly higher weighted kappa statistics than men and non-Hispanic whites. Our rescoring results were consistent with earlier studies that compared DSM-III-R and DSM-IV diagnoses. Here, we offer an approach that may be useful to investigators who used the DIS-III-R in earlier studies. The DIS-III-R questions corresponding to DSM-IV criteria for alcohol abuse and alcohol dependence are on our Web site at www.bhrcs.org, along with the scoring algorithm.

GIS-BASED NICHE MODELING FOR MAPPING SPECIES' HABITAT

Ecological "niche modeling" using presence-only locality data and large-scale environmental variables provides a powerful tool for identifying and mapping suitable habitat for species over large spatial extents. We describe a niche modeling approach that identifies a minimum (rather than an optimum) set of basic habitat requirements for a species, based on the assumption that constant environmental relationships in a species' distribution (i.e., variables that maintain a consistent value where the species occurs) are most likely to be associated with limiting factors. Environmental variables that take on a wide range of values where a species occurs are less informative because they do not limit a species' distribution, at least over the range of variation sampled. This approach is operationalized by partitioning Mahalanobis D2 (standardized difference between values of a set of environmental variables for any point and mean values for those same variables calculated from all points at which a species was detected) into independent components. The smallest of these components represents the linear combination of variables with minimum variance; increasingly larger components represent larger variances and are increasingly less limiting. We illustrate this approach using the California Gnatcatcher (Polioptila californica Brewster) and provide SAS code to implement it.

Estimation of nutrient requirements using broken-line regression analysis1

We evaluated and compared various broken-line regression models and SAS (SAS Inst. Inc., Cary, NC) procedures for estimating nutrient requirements from nutrient dose response data. We used the SAS (Version 9) procedures NLIN and NLMixed and the response data of Parr et al. (2003), who evaluated the isoleucine requirement of growing swine. The SAS NLIN was used to fit 2 different broken-line regression models: a simple 2 straight-line, one-breakpoint model and a quadratic broken-line model in which the response below the single breakpoint was quadratic; there was a plateau above the breakpoint. The latter was fit using 2 different approaches in NLIN. We also used SAS NLMixed to fit 3 different broken-line models: the 2 straight-line, one-breakpoint model that included a random component for the plateau; the quadratic broken-line model that included a random component for the plateau; and the quadratic broken-line model that included random components for both the plateau and the slope of the curve below the requirement. The best fit (greater adjusted R2; least log likelihood) was achieved using SAS NLMixed and the quadratic model with a random component for asymptote included in the model. Model descriptions, SAS code, and output are presented and discussed. Additionally, we provide other examples of possible models and discuss approaches to handling difficult-to-fit data.

Using the score method to construct asymmetric confidence intervals: An SAS program for content validation in scale development

Expert review sessions are often conducted to determine the content validity of scale items. The accurate quantification of content validity is usually limited by a relatively small number of experts as well as by a small number of rating categories. These factors, combined with the bounded and discrete nature of rating scale categories, hinder use of traditional methods for computing standard errors and confidence intervals. Using an application of the score method, researchers can construct an asymmetric interval that is better suited for these situations. SAS code is provided to automate the computations, and a discussion of two methods for using the obtained results for content validation decision-making follows.

The identification of functional motifs in temporal gene expression analysis

The identification of transcription factor binding sites is essential to the understanding of the regulation of gene expression and the reconstruction of genetic regulatory networks. The in silico identification of cis-regulatory motifs is challenging due to sequence variability and lack of sufficient data to generate consensus motifs that are of quantitative or even qualitative predictive value. To determine functional motifs in gene expression, we propose a strategy to adopt false discovery rate (FDR) and estimate motif effects to evaluate combinatorial analysis of motif candidates and temporal gene expression data. The method decreases the number of predicted motifs, which can then be confirmed by genetic analysis. To assess the method we used simulated motif/expression data to evaluate parameters. We applied this approach to experimental data for a group of iron responsive genes in Salmonella typhimurium 14028S. The method identified known and potentially new ferric-uptake regulator (Fur) binding sites. In addition, we identified uncharacterized functional motif candidates that correlated with specific patterns of expression. A SAS code for the simulation and analysis gene expression data is available from the first author upon request.

Forecasting Default with the KMV-Merton Model

We examine the accuracy and contribution of the default forecasting model based on Merton's (1974) bond pricing model and developed by the KMV corporation. Comparing the KMV-Merton model to a similar but much simpler alternative, we find that it performs slightly worse as a predictor in hazard models and in out of sample forecasts. Moreover, several other forecasting variables are also important predictors, and fitted hazard model values outperform KMV-Merton default probabilities out of sample. Implied default probabilities from credit default swaps and corporate bond yield spreads are only weakly correlated with KMV-Merton default probabilities after adjusting for agency ratings, bond characteristics, and our alternative predictor. We conclude that the KMV-Merton model does not produce a sufficient statistic for the probability of default, and it appears to be possible to construct such a sufficient statistic without solving the simultaneous nonlinear equations required by the KMV-Merton model. We include the SAS code we use to calculate KMV-Merton default probabilities in an appendix.

AUTOMATIC MODEL SELECTION IN THE MIXED MODELS FRAMEWORK

Stepwise model selection is a commonly used technique in regression when there are many candidate independent variables and limited time to develop a model. This approach was adapted to the mixed models framework and gives good results, established by simulation with a known model and by application to real world data. Model selection is done using an information criterion (selected by the user). The application is primarily written in Perl. The Perl code tracks which variables are in or out of the model, calculates the information criterion, and writes and submits SAS code. Proc Mixed in SAS is used to compute the log-likelihood for a model, which is used to calculate the information criterion, which then is used to judge whether the model has improved by adding or dropping a variable, or by changing the covariance structure of the residuals. The software is currently restricted to the case where the random part of the model is assumed to be known, but how to augment the software to also select the structure for the random part of the model is discussed.

Handling drop-out in longitudinal studies.

Drop-out is a prevalent complication in the analysis of data from longitudinal studies, and remains an active area of research for statisticians and other quantitative methodologists. This tutorial is designed to synthesize and illustrate the broad array of techniques that are used to address outcome-related drop-out, with emphasis on regression-based methods. We begin with a review of important assumptions underlying likelihood-based and semi-parametric models, followed by an overview of models and methods used to draw inferences from incomplete longitudinal data. The majority of the tutorial is devoted to detailed analysis of two studies with substantial rates of drop-out, designed to illustrate the use of effective methods that are relatively easy to apply: in the first example, we use both semi-parametric and fully parametric models to analyse repeated binary responses from a clinical trial of smoking cessation interventions; in the second, pattern mixture models are used to analyse longitudinal CD4 counts from an observational cohort study of HIV-infected women. In each example, we describe exploratory analyses, model formulation, estimation methodology and interpretation of results. Analyses of incomplete data requires making unverifiable assumptions, and these are discussed in detail within the context of each application. Relevant SAS code is provided.

Assessing the Probability of Bankruptcy

We assess whether two popular accounting-based measures, Altman’s (1968) Z-Score and Ohlson’s (1980) O-Score, effectively summarize publicly-available information about the probability of bankruptcy. We compare the relative information content of these Scores to a market-based measure of the probability of bankruptcy that we develop based on the Black–Scholes–Merton option-pricing model, BSM-Prob. Our tests show that BSM-Prob provides significantly more information than either of the two accounting-based measures. This finding is robust to various modifications of Z-Score and O-Score, including updating the coefficients, making industry adjustments, and decomposing them into their lagged levels and changes. We recommend that researchers use BSM-Prob instead of Z-Score and O-Score in their studies and provide the SAS code to calculate BSM-Prob.

Number of days, number of subjects, and sources of variation in longitudinal intervention or crossover feeding trials with multiple days of measurement

Dietary studies are often conducted as longitudinal intervention or crossover trials using multiple days of measurement on each subject during each of several measurement periods, and determining the required numbers of days and subjects is important in designing these studies. Linear mixed statistical models were used to derive equations for precision, statistical power and sample size (number of days and number of subjects) and to obtain estimates of between-subject, period-to-period, and day-to-day variation needed to apply the equations. Two cohorts of an on-going exercise intervention study, and a crossover study of Olestra, each with 14 d of measurement/subject per period, were used to obtain estimates of variability for energy and macronutrient intake. Numerical examples illustrate how the equations for calculating the number of days or number of subjects are applied in typical situations, and sample SAS code is given. It was found that between-subject, period-to-period, and day-to-day variation all contributed significantly to the variation in energy and macronutrient intake. The ratio of period-to-period and day-to-day standard deviations controls the trade-off between the number of days and the number of subjects, and this remained relatively stable across studies and energy and macronutrient intake variables. The greatest gains in precision were seen over the first few measurement days. Greater precision and fewer required days were noted in the study (Olestra) that exerted greater control over the subjects and diets during the feeding protocol.

JMASM8: Using SAS To Perform Two-Way Analysis Of Variance Under Variance Heterogeneity

We present SAS code to implement the method proposed by Brunner et al. (1997) for performing two-way analysis of variance under variance heterogeneity.

Semi-automated sensitivity analysis to assess systematic errors in observational data.

Published epidemiologic research usually provides a quantitative assessment of random error for effect estimates, but no quantitative assessment of systematic error. Sensitivity analysis can provide such an assessment. We describe a method to reconstruct epidemiologic data, accounting for biases, and to display the results of repeated reconstructions as an assessment of error. We illustrate with a study of the effect of less-than-definitive therapy on breast cancer mortality. We developed SAS code to reconstruct the data that would have been observed had a set of systematic errors been absent, and to convey the results. After 4,000 reconstructions of the example data, we obtained a median estimate of relative hazard equal to 1.5 with a 95% simulation interval of 0.8-2.8. The relative hazard obtained by conventional analysis equaled 2.0, with a 95% confidence interval of 1.2-3.4. Our method of sensitivity analysis can be used to quantify the systematic error for an estimate of effect and to describe that error in figures, tables, or text. In the example, the sources of error biased the conventional relative hazard away from the null, and that error was not accurately communicated by the conventional confidence interval.

Analysis of Variance (ANOVA) Models in Lower Extremity Wounds

Consider a study in which 2 new treatments are being compared with a control group. One way to compare outcomes would simply be to compare the 2 treatments with the control and the 2 treatments against each using 3 Student t tests (t test). If we were to compare 4 treatment groups, then we would need to use 6 t tests. The difficulty with using multiple t tests is that as the number of groups increases, so will the likelihood of finding a difference between any pair of groups simply by change when no real difference exists by definition a Type I error. If we were to perform 3 separate t tests each at alpha = .05, the experimental error rate increases to .14. As the number of multiple t tests increases, the experiment-wise error rate increases rather rapidly. The solution to the experimental error rate problem is to use analysis of variance (ANOVA) methods. Three basic ANOVA designs are reviewed that give hypothetical examples drawn from the literature to illustrate single-factor ANOVA, repeated measures ANOVA, and randomized block ANOVA. "No frills" SPSS or SAS code for each of these designs and examples used are available from the author on request.

Performance of Confidence Intervals in Regression Models with Unbalanced One-Fold Nested Error Structures

In this article we consider the problem of constructing confidence intervals for a linear regression model with unbalanced nested error structure. A popular approach is the likelihood-based method employed by PROC MIXED of SAS. In this article, we examine the ability of MIXED to produce confidence intervals that maintain the stated confidence coefficient. Our results suggest that intervals for the regression coefficients work well, but intervals for the variance component associated with the primary level cannot be recommended. Accordingly, we propose alternative methods for constructing confidence intervals on the primary level variance component. Computer simulation is used to compare the proposed methods. A numerical example and SAS code are provided to demonstrate the methods.