2.3.1: Exercises (Case Study - Malaria Vaccine)

\exercisesheader{} % 25 \eoce{\qt{Side effects of Avandia\label{randomization_avandia}} Rosiglitazone is the active ingredient in the controversial type~2 diabetes medicine Avandia and has been linked to an increased risk of serious cardiovascular problems such as stroke, heart failure, and death. A common alternative treatment is pioglitazone, the active ingredient in a diabetes medicine called Actos. In a nationwide retrospective observational study of 227,571 Medicare beneficiaries aged 65 years or older, it was found that 2,593 of the 67,593 patients using rosiglitazone and 5,386 of the 159,978 using pioglitazone had serious cardiovascular problems. These data are summarized in the contingency table below. \footfullcite{Graham:2010} \begin{center} \begin{tabular}{ll cc c} & & \multicolumn{2}{c}{\textit{Cardiovascular problems}} \\ \cline{3-4} & & Yes & No & Total \\ \cline{2-5} \multirow{2}{*}{\textit{Treatment}} & Rosiglitazone & 2,593 & 65,000 & 67,593 \\ & Pioglitazone & 5,386 & 154,592 & 159,978 \\ \cline{2-5} & Total & 7,979 & 219,592 & 227,571 \end{tabular} \end{center} \begin{parts} \item Determine if each of the following statements is true or false. If false, explain why. \textit{Be careful:} The reasoning may be wrong even if the statement's conclusion is correct. In such cases, the statement should be considered false. \begin{subparts} \item Since more patients on pioglitazone had cardiovascular problems (5,386 vs. 2,593), we can conclude that the rate of cardiovascular problems for those on a pioglitazone treatment is higher. \item The data suggest that diabetic patients who are taking rosiglitazone are more likely to have cardiovascular problems since the rate of incidence was (2,593 / 67,593 = 0.038) 3.8\% for patients on this treatment, while it was only (5,386 / 159,978 = 0.034) 3.4\% for patients on pioglitazone. \item The fact that the rate of incidence is higher for the rosiglitazone group proves that rosiglitazone causes serious cardiovascular problems. \item Based on the information provided so far, we cannot tell if the difference between the rates of incidences is due to a relationship between the two variables or due to chance. \end{subparts} \item What proportion of all patients had cardiovascular problems? \item If the type of treatment and having cardiovascular problems were independent, about how many patients in the rosiglitazone group would we expect to have had cardiovascular problems? \item We can investigate the relationship between outcome and treatment in this study using a randomization technique. While in reality we would carry out the simulations required for randomization using statistical software, suppose we actually simulate using index cards. In order to simulate from the independence model, which states that the outcomes were independent of the treatment, we write whether or not each patient had a cardiovascular problem on cards, shuffled all the cards together, then deal them into two groups of size 67,593 and 159,978. We repeat this simulation 1,000 times and each time record the number of people in the rosiglitazone group who had cardiovascular problems. Use the relative frequency histogram of these counts to answer (i)-(iii). \end{parts} \begin{minipage}[c]{0.5\textwidth} \begin{subparts} \item What are the claims being tested? \item Compared to the number calculated in part~(c), which would provide more support for the alternative hypothesis, \textit{more} or \textit{fewer} patients with cardiovascular problems in the rosiglitazone group? \item What do the simulation results suggest about the relationship between taking rosiglitazone and having cardiovascular problems in diabetic patients? \end{subparts} \end{minipage} \begin{minipage}[c]{0.5\textwidth} \Figures[A histogram is shown for "Simulated rosiglitazone cardiovascular events", where values range between 2250 to 2450. The histogram, starting from the left, starts with bins that have low values until about 2280, at which point the bins rises gradually until rising steeply starting at 2320 to a peak at about 2360. The bins decline sharply at about 2380 to about half of the height of the peak, and then gradually decline out to 2460 before being zero after that point.]{}{eoce/randomization_avandia}{randomization_avandia} \\ \end{minipage} }{} \D{\newpage} % 26 \eoce{\qt{Heart transplants\label{randomization_heart_transplants}} The Stanford University Heart Transplant Study was conducted to determine whether an experimental heart transplant program increased lifespan. Each patient entering the program was designated an official heart transplant candidate, meaning that he was gravely ill and would most likely benefit from a new heart. Some patients got a transplant and some did not. The variable \texttt{transplant} indicates which group the patients were in; patients in the treatment group got a transplant and those in the control group did not. Of the 34 patients in the control group, 30 died. Of the 69 people in the treatment group, 45 died. Another variable called \texttt{survived} was used to indicate whether or not the patient was alive at the end of the study. \footfullcite{Turnbull+Brown+Hu:1974} \begin{center} \Figures[A mosaic plot for variables "experiment group" (primary split) and "survived". The first tall rectangle for the "control" experiment group is about half the width of the second tall rectangle for "treatment". When looking at the secondary split for the control group, the "alive" outcome represents about 10\% of the height and "dead" represents about 90\% of the height. When looking at the secondary split for the treatment group, the "alive" outcome represents about 35\% of the height and "dead" represents about 65\% of the height.]{0.48}{eoce/randomization_heart_transplants}{randomization_heart_transplants_mosaic} \Figures[A side-by-side box plot is shown for the variable "Survival Time (days)" for two box plots labeled "control" and "survived". The axis for survival time spans 0 to about 1800. The box for the control group spans about 0 to 50 with the median line at about 20, and the whiskers extend down to 0 and up to about 125. There are five observations shown beyond the upper whisker at locations of about 150, 250, 300, 400, and 1400. The box for the treatment spans about 100 to 650 with the median line about 250, and the whiskers extend down to 0 and up to about 1400. There are a few points beyond the upper whiskers at about 1550, 1575, and 1800.]{0.48}{eoce/randomization_heart_transplants}{randomization_heart_transplants_box} \end{center} \begin{parts} \item Based on the mosaic plot, is survival independent of whether or not the patient got a transplant? Explain your reasoning. \item What do the box plots below suggest about the efficacy (effectiveness) of the heart transplant treatment. \item What proportion of patients in the treatment group and what proportion of patients in the control group died? \item One approach for investigating whether or not the treatment is effective is to use a randomization technique. \begin{subparts} \item What are the claims being tested? \item The paragraph below describes the set up for such approach, if we were to do it without using statistical software. Fill in the blanks with a number or phrase, whichever is appropriate. \begin{adjustwidth}{2em}{2em} We write \textit{alive} on \rule{2cm}{0.5pt} cards representing patients who were alive at the end of the study, and \textit{dead} on \rule{2cm}{0.5pt} cards representing patients who were not. Then, we shuffle these cards and split them into two groups: one group of size \rule{2cm}{0.5pt} representing treatment, and another group of size \rule{2cm}{0.5pt} representing control. We calculate the difference between the proportion of \textit{dead} cards in the treatment and control groups (treatment - control) and record this value. We repeat this 100 times to build a distribution centered at \rule{2cm}{0.5pt}. Lastly, we calculate the fraction of simulations where the simulated differences in proportions are \rule{2cm}{0.5pt}. If this fraction is low, we conclude that it is unlikely to have observed such an outcome by chance and that the null hypothesis should be rejected in favor of the alternative. \end{adjustwidth} \item What do the simulation results shown below suggest about the effectiveness of the transplant program? \end{subparts} \end{parts} \begin{center} \Figures[A stacked dot plot is shown for what appears to be about 100 points on the variable "Simulated Differences in Proportions", which spans values of -0.25 to 0.25. There are 11 stacks of points, which are located at the following locations and in the following approximate quantities: 2 points at -0.23, 1 point at -0.19, 8 at -0.14, 15 points at -0.10, 18 points at -0.05, 20 points at -0.01, 12 points at 0.04, 10 points at 0.08, 6 points at 0.12, 4 points at 0.17, and 3 points at 0.21.]{0.6}{eoce/randomization_heart_transplants}{randomization_heart_transplants_rando} \end{center} }{}