\documentclass[11pt]{article} \usepackage{epsfig, makeidx, amsmath} \usepackage{fancyhdr} \begin{document} \title{Evaluation of the Michigan Asthma Medicaid Surveillance System: A Component Analysis} \author{Samuel A. Student} \date{June 24, 2011} \maketitle \section{Introduction} The data use, data needs of stakeholders, distribution of data, and limitations of the Michigan Asthma Medicaid Surveillance System (MAMSS) are evaluated in this study. The MAMSS is a database that is created from the national surveillance system Community Health Automated Medicaid Processing System (CHAMPS) and is analyzed and stratified according to geographic, age, race, and type depending on requestor needs. Data from MAMSS is requested throughout the year from a variety of consumers and stakeholders. \subsection{Statement of Objectives} According to the national asthma guidelines (NHLBI, 2007), the purposes of asthma surveillance are to \begin{itemize} \item Understand the impact of asthma, including the number of people affected, its severity in the population, and its cost \item Monitor trends in treatment and management in the population \item Monitor exposure to asthma triggers \item Assist in evaluating the effect of interventions designed to reduce the burden of asthma. \end{itemize} \section{Methodology} A pilot study was conducted using members of the Asthma Network of West Michigan (ANWM). There are 55 members in ANWM. A simple random sample of 10 members was asked to fill out the data user questionnaire. All 10 were instructed to make an asthma data request of MDCH and also review the data on the MDCH website. \section{Results} The results of administering the data user questionnaire are given in Tables 1 and 2. These results will be used to assist with the quantitative portion of component analysis when it is conducted on a statewide basis. \begin{table}[tph] \caption{Results from Section 3 of the Data User Questionnaire} \centering \vspace*{1.5ex} \begin{tabular}{lcc} \hline\\[-1.5ex] Covered Expense & $\hat{\mu}$ & $\sigma $ \\[.5ex] \hline Prevalence of Asthma & 4.4 & 0.699 \\ Asthma Control & 4.5 & 0.527 \\ Asthma Management & 4.0 & 0.667 \\ Work-Related Asthma & 3.1 & 0.738 \\ Asthma Emergency Visits & 4.0 & 0.667 \\ Asthma Hospitalizations & 3.9 & 0.738 \\ Asthma Death & 3.3 & 0.949 \\ Asthma Burden Covered by Medicaid & 4.4 & 0.699 \\ Cost of Asthma & 4.4 & 0.699 \\ Healthy People 2010 & 2.9 & 0.738 \\ Methods & 3.5 & 1.509 \\ \hline \end{tabular} \end{table} \section{Conclusion} Since the study is still in progress there are no results to report or analysis to conduct at the time of this report. It will be sufficient for now to describe the plans for data management and data analysis, as well as for communicating and reporting the results and conclusions. The evaluation lead will monitor and collect all survey results from the data user questionnaire. The doctoral student volunteer will conduct, record, and transcribe the key informant interviews. Once the interviews are completed, the evaluation team will meet to review the data. SPSS will be used to generate descriptive and inferential statistics. MaxQDA will be used to analyze the transcriptions from the key informant interviews. The evaluation lead will conduct the quantitative analysis and both the evaluation lead and the student volunteer will code the transcriptions to assure rater reliability. The results of the data analysis will be provided as a report and in a presentation to the Surveillance and Epidemiology Subcommittee, a body formed by the MDCH. At that point, recommendations will be made how to improve the surveillance system and plans will be made regarding future component analyses of the system. \begin{thebibliography}{9} \item{Creswell, J. W. (2007)}, \emph{Qualitative Inquiry and Research Design: Choosing Among Five Approaches, 2nd Edition}, Thousand Oaks, CA: Sage Publications, Inc. . \item{DeVaus, David. (2006)}, \emph{Research Design in Social Research}, Thousand Oaks, CA: Sage Publications, Inc. \item{Owen, John M., (2007)}, \emph{Program Evaluation: Forms and Approaches}, The Guilford Press, New York, NY. \item{Scheaffer, R.L., Mendenhall, W., Ott, R.L. (2006)} \emph{Elementary Survey Sampling, 6th Edition}, Toronto, Ontario. Thomson Brooks/Cole. \end{thebibliography} \newpage \section{Additional latex examples} \subsection{Math equations} Consider the linear model \begin{equation} y_i = \alpha^* + x_i^\prime \beta^* + e_i, \; i=1,\ldots,n, \end{equation} where $e_1,\ldots,e_n$ are independent random variables with distribution function $F$ and density $f$, $x_i^\prime$ is the $i$th row of a known $n\times p$ matrix of centered explanatory variables $\bf{X}$, $\alpha^*$ is an intercept parameter, and $\beta^*$ is a $p\times 1$ vector of slope parameters. Consider the estimate which minimizes \begin{equation} \sum_{i=1}^n a(R(y_i-x_i^\prime \beta))(y_i-x_i^\prime \beta)\;, \end{equation} where $R(y_j-x_j^\prime \beta)$ is the rank of $y_j-x_j^\prime \beta$ among $y_1-x_1^\prime \beta, \ldots, y_n-x_n^\prime \beta$, and $a(1)\leq \cdots \leq a(n)$ is a nondecreasing set of scores. If the scores are chosen so that \[ a(j)= \varphi_F(j/(n+1))= -\frac{f^\prime(F^{-1}(j/(n+1))}{f(F^{-1} (j/(n+1))}\;, \] then the resulting estimate $\hat{\beta}_F$ is asymptotically efficient. \newpage \subsection{Graphs} What percentage of adult men are between 5'6" and 6' tall? Population surveys have shown that men's heights are approximately normally distributed with mean 5'9" and SD 3". Thus the percentage of men between 5'6" and 6' is estimated as 68\%. See Figure ~\ref{menht1} \begin{figure}[htbp] \caption{Percentage of men's heights between 66 and 72 inches} \label{menht1} \begin{center} \includegraphics[height=4in, width=3in, angle=-90]{heights1.jpg} \end{center} \end{figure} If the population of men are randomly assigned into groups of 9, and the average heights are computed for each group, what percentage of groups average between 5'6" and 6' in height? Is the answer approximately 68\%? No. In fact, more than 99\% of the groups will average between 5'6" and 6', even though only 68\% of individuals do. Why? Because {\em averages tend to include tall, short and medium heights} --- therefore averages tend to fall closer to middle than individuals. \newpage Following is a small simulation study of the behavior of the sample mean. 10 samples are drawn (each containing $n=9$ individuals) from a population with mean 69 inches and SD 3 inches. For each sample, we calculate the average. Observe that none of the samples average over 71 inches, even though many individuals do. \begin{verbatim} Heights of 10 samples of 9 men Sample (1) (2) (3) (4) (5) (6) (7) (8) (9) Ave 1: 65.5 66.8 68.9 67.8 71.9 66.8 71.0 73.1 62.6 68.27 2: 68.6 71.2 72.6 64.3 70.9 70.0 69.0 69.8 62.4 68.75 3: 67.4 67.9 67.1 68.2 70.7 68.3 67.2 68.7 67.0 68.04 4: 68.6 67.7 69.0 67.0 70.2 63.9 70.8 64.2 65.2 67.38 5: 69.8 68.4 64.9 66.1 61.0 70.2 68.4 65.2 72.8 67.42 6: 69.1 66.4 67.6 70.7 69.7 70.1 67.6 70.0 70.2 69.03 7: 68.8 67.4 70.8 71.5 68.5 65.8 67.1 72.2 64.7 68.54 8: 70.0 68.9 69.2 71.6 64.3 66.1 67.3 67.7 66.8 67.99 9: 68.4 64.1 72.7 67.2 71.2 70.8 63.1 78.1 73.2 69.86 10: 66.5 67.3 67.9 67.7 70.7 67.0 69.7 71.3 69.0 68.57 \end{verbatim} The first lesson of this chapter says: \begin{quote} \fbox{ \parbox{4in}{ \begin{verse} Averages are less variable than individuals. \end{verse} } } \end{quote} Do you see this in the simulation study? To make it easier to see, look at the SD of each column. The SD of individuals tend to be around 3.0 (the true value), but the SD of averages is much smaller. \end{document}