Bootstrapping Exercise Results 1 Header : Bootstrapping Exercise Results Bootstrapping Results of Exercise Therapy and Education for Patients with Congestive Heart Failure

When studies are conducted over a period of time, the sample size typically decreases. In a study of the effects of exercise therapy and education with recovering congestive heart failure (CHF) patients (Brubaker, Witta, & Angelopoulus, 2003), the sample size decreased from over 40 to 9 participants after an 18-month time span. Although the quality of life (QOL) scales and measures of physical ability showed improvement, these results were limited to 9 participants. Thus, there was some question concerning the generalizability of this study to other patients with congestive heart failure. The purpose of this study was two-fold: (1) to use the bootstrapping procedure to provide the confidence intervals and estimate generalization error of both physical and quality of life results for that study, and (2) to estimate the probability of sample results as extreme as the observed sample using permutation methods. Most of the findings from this study support the findings from the original study and provide further evidence of the importance of the exercise and education treatment used in the original study. Further, this is not the only study in which improvement in physical measures and QOL constructs have shown improvement. Although the majority of studies on patients with CHF are less than six-months in duration, evidence has been provided that exercise tolerance and QOL can increase significantly following a supervised exercise program (Holst, Kaye, Richardson, Krum, Prior, Aggarwal, Wolfe, & Bergin, 2001; Quittan, Sturm,Wiesinger, Pacher, & Fialka-Moser, 1999; Tokmakova, Dobreva, & Kostianev, 1999). Bootstrapping Exercise Results 3 Approximately 4.7 million Americans suffer from congestive heart failure (CHF). About seven percent of the total cost of heart disease each year is due to this condition (Heart and Stroke Facts, 2002). In addition, median survival rates following onset of CHF are just 1.7 and 3.2 years for men and women, respectively (Ho, Anderson, Kannel, Grossman, & Levy, 1993). Frequent hospital admissions, poor physical condition, and emotional distress produce a decreased quality of life (QOL) among heart failure patients (Cafagna, Ponte, & Burri , 1997; Steptoe, Mohabir, Mahon, & McKenna, 2000). Yet, when studies are conducted over a period of time, the sample size typically decreases. In a study of the effects of exercise therapy and education with recovering congestive heart failure patients (Brubaker, Witta, & Angelopoulos, 2003), the sample size decreased from over 40 to 9 participants after an 18 month time span. Although the quality of life scales and measures of physical ability showed improvement in this study, these results were limited to 9 participants. Thus there was some question concerning the generalizability of this study to other congestive heart failure patients. The purpose of this study was two-fold: (1) to use the bootstrapping procedure to provide the confidence intervals and estimate generalization error of both physical and quality of life results for that study, and (2) to estimate the probability of sample results as extreme as the observed sample using permutation methods. Related Literature One goal of statistical significance testing is to generalize to the population from sample statistics (Mooney & Duval, 1993). “In most cases theory is forced to use asymptotic algebra, producing results that apply only when the sample size is very large” (Kennedy, 1998). If asymptotic results are relied upon when using a small sample, the level of accuracy may not be assured and assumptions pre-requisite to the statistic used may be violated. Thus results produced may be questionable. The most commonly used method of estimating generalization error is to divide the sample in half, using one half of the data as the “test” set and the other half to estimate the model. One problem with this method is reduction in sample size (see Weiss & Kulikowski, 1991) which, of course, affects statistical significance testing. More recently, some of the statistical software packages (SPSS 11.5) will remove one participant and estimate the model, iteratively until the model has been estimated with each participant removed in a procedure similar to the jackknife method. Although this procedure preserves sample size and is excellent to test the influence of each individual participant, because only one participant is removed each time, it is a poor method of providing generalization error. Monte Carlo methods have also been used to test generalization error. However, when these methods are used, the error estimate is typically drawn from a normal distribution. Consequently the value of these studies in testing generalizability is questionable. Bootstrapping Exercise Results 4 Problems in using current methods have lead to increased use of resampling methods. The bootstrap and permutation (randomization) tests are part of these resampling methods. Resampling methods require fewer assumptions than traditional methods and, in most instances are more accurate than classical methods. These methods permit accurate calculation of confidence intervals, and do not require normal distributions or large sample sizes (Howell, 2003). Further, resampling methods are intuitive for each procedure and do not require special new formulas.