Stat

CASE 2

Comparing the Effectiveness of Treatment for Acute Otitis Media Ear Infections.

November 21st, 2017

Group 3

Aaron Lewis

Michael McDermott

Sayed Shouib

BACKGROUND

Acute Otitis media, an infection of the middle ear, is a common childhood illness. There are various ways to treat the problem. To help determine the best way, researchers conducted an experiment. The experimental design consisted of a sample of one hundred and eighty children between the ages of 10 months and two years with recurrent acute otitis media. The sample children were divided into three equal groups. Group 1 was treated by surgically removing the adenoids (adenoidectomy).  The second, Group 2, was treated with the drug Sulfafurazole.  The third, Group 3, with a placebo. Each child was tracked for 2 years during which time all symptoms and episodes of acute otitis media were recorded. (Keller, 9th Edition, p. 588)

INTRODUCTION

        In an attempt to statistically compare treatments, researchers collected data for the following variables: number of episodes of the illness, number of visits to a physician because of any illness, number of prescriptions, number of days with symptoms of respiratory infection. The treatments were compared utilizing an analysis of variance between the treatment populations. The Problem objective for researchers is to conclude that there are differences between the three groups with respect to the number of episodes, number of physician visits, number of prescriptions, and number of days with symptoms of respiratory infections.

DATA OVERVIEW

        Descriptive data was gathered on the results of the experiment. The first variable, Episodes, was observed to be unimodal across all three treatments. All three treatments appeared to display central tendency with the mean very similar to the median and mode. A box plot comparison was conducted to test for outliers. Analysis showed no significant outliers for Adenoidectomy or Sulfafurazole but did show two for the Placebo treatment. Variability for the three treatments within the Episode variable does not have significant variability.

        The second variable, Visits, was observed to be negatively skewed across all three treatments. A box plot comparison was conducted to test for outliers. Analysis showed no significant outliers. Variability for the three treatments within the Visits variable appears to vary between the treatments. This unequal variance may cause this variable to fail the Bartlett’s test.

        The third variable, prescriptions, was observed to be slightly bimodal given the Adenoidectomy and Sulfafurazole treatments but unimodal for the Placebo treatment. A box plot comparison was conducted to test for outliers. Analysis showed no significant outliers. Variability for the three treatments within the prescriptions variable does not have significant variability.

        The fourth variable, Number of days with symptoms (Days), was observed to be unimodal across all three treatments. All three treatments appeared to display central tendency with the mean very similar to the median and mode (see annex 1 for data). A box plot comparison was conducted to test for outliers. Analysis showed that Adenoidectomy contained two outliers while the placebo treatment contained four outliers. Variability for the three treatments within the Days variable does not have significant variability.

        Analysis of the descriptive data shows that the data showed be valid for further analysis, however the unequal variances in the Visits variable will need addition review and may disqualify this variable.

ANALYSIS TECHNIQUE SELECTION

        The problem objective seeks to conclude whether there is a difference in the effectiveness in treatments across the variables. As such, the problem seeks to compare the variance in means between the treatments of Group 1, Adenoidectomy, Group 2, Sulfafurazole, Group 3, a placebo. The correct analysis to test this hypothesis is a one-way Analysis of Variance or ANOVA. The problem objective seeks to compare more than two populations. The data type to be compared is interval data. The experimental design consists of independent samples. Populations are normally distributed with one factor to be considered. Considering the problem objective, type of data and experimental design the correct analysis technique is a one-way ANOVA.

ALPHA SELECTION AND JUSTIFICATION

        During the selection of Alpha the types of error must be understood. Type 1 error is the chance that a true null hypothesis is rejected.  Type 2 error is the chance that a false null hypothesis is not rejected. These two error types are applied to the analysis as follows: 

In this case the null hypothesis will always be that the population means (of each group for each variable) are equal to each other; meaning that there is no difference between the groups (surgery vs. drug vs. placebo) shown in each response variable; i.e. there is no benefit in getting the adenoidectomy or using Sulfafurazole as the outcome of the treatments in respect to the variables are statistically equal.  The alternative hypothesis will always be that one of the population means will be different than the others, presumably showing that one of the three treatments (surgery vs. drug vs. placebo) is more or less effective than the others. 

Type 1 error in this case would be concluding that there is a difference in treatments when in fact there are not.  Type 2 error would be concluding that there is no difference in the treatments when in fact there are. 

If one is to take the perspective of wanting to maximize the potential well-being of patients (by not recommending unnecessary procedures), the goal would be to minimize Type 1 error.  This is because our group views it as worse if we recommend a treatment over the others even though there is no difference between them (i.e. Type 1 error) versus concluding that there is no difference between the treatments when in fact there are (i.e. Type 2 error).  Our concern is more about not recommending unnecessary invasive procedures, our Group would rather risk not identifying the statistically better treatment.