Gilbert W. Fellingham

Adequacy of approximations to distributions of test statistics in complex mixed linear models

A recent study of lady beetle antennae was a small sample repeated measures design involving a complex covariance structure. Distributions of test statistics based on mixed models fitted to such data are unknown, but two recently developed methods for approximating the distributions of test statistics in mixed linear models have been included as options in the latest release of the MIXED procedure of SAS®. One method (FC, from Fai and Cornelius) computes degrees of freedom of an approximating F distribution for the test statistic using spectral decomposition of the hypothesis matrix together with repeated application of a method for single-degree-of-freedom tests. The other method (KR, from Kenward and Roger) adjusts the estimated covariance matrix of the parameter estimates, computes a scale adjustment to the test statistic, and computes the degrees of freedom of an approximating F distribution. Using the two methods, p values for a hypothesis of interest in the lady beetle study were quite different. Simulation studies on the Proc MIXED implementation of these methods showed that Type I error rates of both methods are affected by covariance structure complexity, sample size, and imbalance. Nonetheless, the KR method performs well in situations with fairly complicated covariance structures when sample sizes are moderate to small and the design is reasonably balanced. The KR method should be used in preference to the FC method, although it had inflated Type I error rates for complex covariance structures combined with small sample sizes.

Relative and Absolute Reliability of the KT-2000 Arthrometer for Uninjured Knees Testing at 67, 89, 134, and 178 N and Manual Maximum Forces

We assessed the reliability of the KT-2000 knee ar thrometer at 67, 89, 134, and 178 N and at manual maximum forces on 30 college students who were free from present or previous knee injuries. Two examiners tested all subjects on two occasions. Anterior laxity (P < 0.0001) and side-to-side difference (P < 0.05) sig nificantly increased as force increased. There was a significant difference (P < 0.0001) between testers for anterior laxity but not for side-to-side difference. We used intraclass correlation coefficients to estimate rel ative reliability. Anterior laxity intraclass correlation co efficients (2,1) between testers ranged from 0.81 to 0.86 and within tester correlations ranged from 0.92 to 0.95. Intraclass correlation coefficients for between testers for side-to-side differences ranged from 0.38 to 0.58 and within tester correlations ranged from 0.53 to 0.64. Subject-to-subject variability needs to be taken into account when interpreting intraclass correlation coefficient values. Our absolute reliability estimates (95% confidence intervals) were small, indicating little variability. Our data demonstrate the KT-2000 arthrom eter to be reliable. Researchers should present both relative and absolute reliability estimates, although we believe absolute estimates are of greater clinical value. Side-to-side differences are better discriminators than individual absolute values. We recommend that a <3 mm side-to-side difference be used to indicate stable knees.

Limitations of Ordinary Least Squares Models in Analyzing Repeated Measures Data

PURPOSE To a) introduce and present the advantages of linear mixed models using generalized least squares (GLS) when analyzing repeated measures data; and b) show how model misspecification and an inappropriate analysis using repeated measures ANOVA with ordinary least squares (OLS) methodology can negatively impact the probability of occurrence of Type I error. METHODS The effects of three strength-training groups were simulated. Strength gains had two slope conditions: null (no gain), and moderate (moderate gain). Ten subjects were hypothetically measured at five time points, and the correlation between measurements within a subject was modeled as compound symmetric (CS), autoregressive lag 1 (AR(1)), and random coefficients (RC). A thousand data sets were generated for each correlation structure. Then, each was analyzed four times--once using OLS, and three times using GLS, assuming the following variance/covariance structures: CS, AR(1), and RC. RESULTS OLS produced substantially inflated probabilities of Type I errors when the variance/covariance structure of the data set was not CS. The RC model was less affected by the actual variance/covariance structure of the data set, and gave good estimates across all conditions. CONCLUSIONS Using OLS to analyze repeated measures data is inappropriate when the covariance structure is not known to be CS. Random coefficients growth curve models may be useful when the variance/covariance structure of the data set is unknown.

VO2max estimation from a submaximal 1-mile track jog for fit college-age individuals.

The primary purpose of this study was to develop a submaximal field test for the estimation of maximal oxygen uptake (VO2max) using a 1-mile track jog. A second purpose was to determine the accuracy of the 1.5-mile run in estimating VO2max for both male and female subjects. VO2max was measured in 149 relatively fit college students (males = 88, females = 61) 18-29 yr using a treadmill protocol (mean +/- SD; VO2max = 47.7 +/- 6.3 ml.kg-1 x min-1). Multiple regression analysis (N = 54) to estimate VO2max from the submaximal, steady-state 1-mile track jog yielded the following validation (V) model (r(adi) = 0.87, SEE = 3.0 ml.kg-1 x min-1): VO2max = 100.5 + 8.344* GENDER (0 = female; 1 = male) - 0.1636* BODY MASS (kg) - 1.438* JOG TIME (min.mile-1) - 0.1928* HEART RATE (bpm). To help ensure that a submaximal level of exertion was realized for the 1-mile track jog, elapsed jog time was restricted to > or = 8.0 min for males and > or = 9.0 min for females and exercise HR to < or = 180 bpm. Cross-validation (CV) of the 1-mile track jog comparing observed and estimated VO2max (N = 52) resulted in radj = 0.84, SEE = 3.1 ml.kg-1 x min-1. Multiple regression analysis (N = 50) to estimate VO2max from the 1.5-mile run (V:N = 49, radj = 0.90, SEE = 2.8 ml.kg-1 x min-1; CV: N = 47, radj = 0.82, SEE = 3.9 ml.kg-1 x min-1), used elapsed run time, body mass, and gender as independent variables.(ABSTRACT TRUNCATED AT 250 WORDS)

Performance of the Kenward–Roger Method when the Covariance Structure is Selected Using AIC and BIC

ABSTRACT This study investigated Type I error rates for tests of fixed effects in mixed linear models using Wald F-statistics with the Kenward–Roger adjustment. Data were generated using 15 covariance structures. Correct covariance structures as well as those selected using the Akaikes Information Criterion (AIC) and Schwarzs Bayesian Information Criterion (BIC) criteria were examined. Performance of the AIC and BIC criteria in selecting the true covariance structure was also studied. Type I error rates for the correct models were often adequate depending on the sample size and complexity of covariance structure. Type I error rates for the best AIC and BIC models were always higher than target values, but those obtained using BIC were closer to the target value than those obtained using AIC. For unbalanced data, Type I error rates for the between-subjects effect were closer to target values for positive pairing while those for the within-subject effect were closer for negative pairing. Success of AIC and BIC in selecting the correct covariance structure was low.

Cardiovascular risk reductions associated with aggressive lifestyle modification and cardiac rehabilitation

BACKGROUND Patients who have been treated for coronary heart disease can enroll in traditional cardiac rehabilitation, the Ornish Program, or no rehabilitation at all. No study has compared the impact of each on cardiovascular disease risk (CVD) factors. METHODS The current study compared CVD risk changes in post coronary artery bypass graft or percutaneous coronary intervention procedure patients who participated in the Ornish Heart Disease Reversing Program, a traditional cardiac rehabilitation, and a control group that received no formal cardiac risk-reduction program. This was a longitudinal, observational study of 84 patients receiving CVD standard of care who elected to participate in 1 of the 3 study groups. Assessments of CVD risk factors and anginal severity were obtained at baseline, 3 months, and 6 months. RESULTS Ornish program participants had significantly greater reductions in anginal frequency, body weight, body mass index, systolic blood pressure, total cholesterol, low-density lipoprotein cholesterol, glucose, dietary fat, and increases in complex carbohydrates than were documented in the rehabilitation or control groups. The control group experienced the greatest reduction in anginal pain severity, but also had significantly higher systolic blood pressure, total cholesterol, and low-density lipoprotein cholesterol. CONCLUSIONS These findings suggest that CVD patients who choose to participate in the Ornish program can experience greater improvements in CVD risks than patients who choose to participate in traditional cardiac rehabilitation or no formal program.

Fibrinolytic response during exercise and epinephrine infusion in the same subjects

To determine whether exercise-induced increases in tissue plasminogen activator (t-PA) were related to plasma epinephrine concentration during exercise, 14 healthy men (aged 24 to 62 years) were studied during epinephrine infusions (10, 25 and 50 ng/kg per min) and graded supine bicycle exercise, beginning at 33 W and increasing in 33-W increments until exhaustion. Plasma epinephrine, active and total t-PA, active plasminogen activator inhibitor type 1 (PAI-1) and t-PA/PAI-1 complex concentrations were measured at each exercise and infusion level. During epinephrine infusion, active and total t-PA levels increased linearly with the plasma epinephrine concentration (respective slopes [+/- SEM] of 0.062 +/- 0.003 and 0.076 +/- 0.003 pmol/ng epinephrine). During exercise, t-PA levels did not increase until plasma epinephrine levels increased, after which both active and total t-PA levels again increased linearly with the plasma epinephrine concentration, but at twice the rate observed with epinephrine infusion (0.131 +/- 0.005 and 0.147 +/- 0.005 pmol/ng, respectively). The t-PA level in blood was directly proportional to the plasma epinephrine concentration during both exercise and epinephrine infusion, suggesting that epinephrine release during exercise stimulates t-PA secretion. In these healthy subjects, active plasminogen activator inhibitor type 1 and t-PA/PAI-1 complex levels were low (41 +/- 11 and 21 +/- 5 pmol/liter, respectively) and did not change significantly during exercise or epinephrine infusion. It is concluded that approximately 50% of the increase in t-PA during exercise is due to stimulated release of t-PA by epinephrine.(ABSTRACT TRUNCATED AT 250 WORDS)

Prediction of Maximum Oxygen Consumption from Walking, Jogging, or Running.

Abstract The purpose of this study was to develop a submaximal, 1.5-mile endurance test for college-aged students using walking, jogging, or running exercise. College students (N = 101: 52 men, 47 women), ages 18–26 years, successfully completed the 1.5-mile test twice, and a maximal graded exercise test. Participants were instructed to achieve a “somewhat hard” exercise intensity (rating of perceived exertion = 13) and maintain a steady pace throughout each 1.5-mile test. Multiple linear regression generated the following prediction equation: VO2max = 65.404 + 7.707 × gender (1 = male; 0 = female) − 0.159 × body mass (kg) − 0.843 × elapsed exercise time (min; walking, jogging, or running). This equation shows acceptable validity (R = .86, SEE = 3.37 ml•kg1 •min−1) similar to the accuracy of comparable field tests, and reliability (ICC = .93) is also comparable to similar models. The statistical shrinkage is minimal (Rpress = 0.85, SEEpress = 3.51 ml•kg1 •min−1); hence, it should provide comparable results when applied to other similar samples. A regression model (R = .90, and SEE = 2.87 ml•kg1 •min−1) including exercise heart rate was also developed: VO2max = 100.162 + 7.301 × gender (1 = male; 0 = female) − 0.164 × body mass (kg) − 1.273 × elapsed exercise time − 0.156 × exercise heart rate, for those who have access to electronic heart rate monitors. This submaximal 1.5-mile test accurately predicts maximal oxygen uptake (VO2max) without measuring heart rate and is similar to the 1.5-mile run in that it allows for mass testing and requires only a flat, measured distance and a stopwatch. Further, it can accommodate a wide range of fitness levels (from walkers to runners).

Effect of water running and cycling on maximum oxygen consumption and 2-mile run performance

This study compared water running, cycling, and run ning for maintaining VO2max and 2-mile run perform ance over a 6-week training period. Thirty-two trained subjects between the ages of 18 and 26 were evaluated for maximum oxygen uptake (VO2max) and 2-mile run performance. Subjects were stratified by a 2-mile run pretest into high, medium, and low performance levels and then randomly assigned to water running, cycling, or running training. The three groups trained with similar frequency, duration, and intensity over a 6-week period. After 6 weeks of training, all of the groups made a small but statistically significant decrease in fitness (VO2max), but no change in 2-mile run time. However, there were no differences with respect to either training modality or pretraining performance level. It was concluded that over a 6-week period, runners who cannot run because of soft tissue injury can maintain VO2max and 2-mile run performance similar to running training with either cycling or water running.

Effects of a 4-Week Exercise Program on Balance Using Elastic Tubing as a Perturbation Force for Individuals With a History of Ankle Sprains

STUDY DESIGN Randomized controlled trial with pretraining, posttraining, and follow-up repeated measures. OBJECTIVE To determine the effectiveness of a 4-week elastic resistance exercise program on balance in subjects with and without a history of sprained ankles. BACKGROUND Several researchers have suggested that improving balance may help alleviate the symptoms of functional ankle instability and reduce the rate of recurrent ankle sprains. METHODS AND MEASURES Forty subjects (20 males, 20 females; 20 subjects with chronic ankle instability [CAI], 20 healthy) participated in the study. Ten subjects (5 males, 5 females) from each CAI and healthy group were randomly assigned to either the exercise or control group, resulting in a total of 4 groups. Total travel distance of the center of pressure, monitored using a force platform, was measured before training, after 4 weeks of training, and at a 4-week follow-up. RESULTS There were no interactions between gender, ankle sprain history, or training groups. Balance significantly improved in subjects with and without a history of ankle sprains following 4 weeks of elastic resistance exercises. Mean improvement in balance for the exercise group following training, reflected through a decrease in total travel distance, was -11.1 cm (95% confidence interval: -14.0 to -8.2 cm). These improvements in balance were retained 4 weeks after training. CONCLUSIONS Balance was improved after 4 weeks of elastic resistance exercise in subjects with and without a history of lateral ankle sprains. Balance improvements persisted 4 weeks following the treatment cessation.