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ex03.tex
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\documentclass[a4paper,11pt]{article}
\usepackage{CJK}
\usepackage{graphicx}
\usepackage{amsmath,amssymb,amsopn}
\usepackage[english]{babel}
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\usepackage{url}
\usepackage{enumerate}
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\geometry{paperwidth=18.4cm,paperheight=26cm}
\setlength{\parindent}{0em}
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\title{\small{BI476: Biostatistics - Case Studies}\\
\Large{Exercise 03 - Designing Clinical Trials}
}
\author{Spring, 2018}
\date{}
\begin{document}
\begin{CJK*}{UTF8}{gbsn}
\maketitle
\section{Answer the following questions}
\begin{enumerate}[(1)]
\item Can we draw a conclusion of equivalence based on the insignificance result
of superiority trial? If not, then outline the statistical testing on how
to prove that a treatment $T$ is equivalent to $B$ in a parallel trial?
\item Which test requires a larger sample size for the same $\delta_0$, $\alpha$,
power, equivalence trial or non-inferiority trial?
\item How to deal with the non-compliance of the participants in a clinical trial?
\item When aren't the double-blind feasible in a clinical trial?
\item As we have talked about selection bias in the observational study, it is a
more severe issue in a randomized controlled trial. Can you use some
example to illustrate the types of selection biases in an RCT.
\item Illustrate how block randomization could be used to randomly allocate
treatments to 30 patients with an allocation ratio of 1:2 using a block
size of 6.
\end{enumerate}
\section{Data analysis of continuous outcome}
An RCT was conducted to compare two therapies for pain relief after the wisdom tooth
extraction surgery. A dual-therapy (Acetaminophen+lbuprofen) was compared againt a
mono-therapy (lbuprofen only). The primary outcome is the post-surgery pain measure
at an interval of 15 minutes within a follow-up of 120 minutes. The pain was measured
in a scal of 0 (no pain) to 100 (worst pain).
\begin{table}[t]
\caption{The follow-up pain data after wisdom-tooth extraction surgery}
\begin{tabular}{rccccccc}
\hline
& \multicolumn{3}{c}{lbuprofen} & &\multicolumn{3}{c}{Acetaminophen+lbuprofen}\\
\cline{2-4} \cline{6-8}
Time (min) & Mean (mm) & S.D. (mm) & N & & Mean (mm) & S.D. (mm) & N\\
\hline
15 & 27.9 & 14.8 & 24 & & 18.2 & 13.1 & 24\\
30 & 32.6 & 24.4 & 25 & & 25.3 & 20.9 & 25\\
45 & 35.5 & 23.2 & 22 & & 28.7 & 23.3 & 20\\
60 & 31.3 & 18.9 & 19 & & 25.1 & 22.8 & 23\\
75 & 29.9 & 18.8 & 24 & & 14.9 & 13.8 & 24\\
90 & 23.8 & 17.9 & 22 & & 15 & 14.2 & 24\\
105 & 22.7 & 16.4 & 21 & & 13.7 & 12.8 & 19\\
120 & 20.9 & 17.2 & 24 & & 15.2 & 14.4 & 23\\
\hline
\end{tabular}
\end{table}
\begin{enumerate}[(1)]
\item Conduct a $t$-test to compare the treatment effects of the two therapies
at each time point. Give also the 95\% confidence interval.
\item What kind of assumptions should we make when we conduct a $t$-test? So,
is it plausible to use $t$-test here? Should we use a nonparametic
approach, instead?
\item We can also calcualte the weighted average of the pain scores across
the time points for every patient:
\begin{table}[h]
\begin{tabular}{rccccccc}
\hline
& \multicolumn{3}{c}{lbuprofen} & &\multicolumn{3}{c}{Acetaminophen+lbuprofen}\\
\cline{2-4} \cline{6-8}
& Mean (mm) & S.D. (mm) & N & & Mean (mm) & S.D. (mm) & N\\
\hline
summary & 27.9 & 13.6 & 25 & & 19.5 & 12.3 & 26\\
\hline
\end{tabular}
\end{table}
Can you conduct the $t$-test only on the weighted mean to compare the treatment effect.
\item You can count the number of the tests for all the time points with $p$-value
less than 0.05, and then arrive at the final conclusion.
\item The other approach is to only use the weighted average to reach the conclusion.
Which one do you prefer? Why?
\item If the pain reduction $\delta=-8$ is clinically significant, can the sample
size in this trial achieve a power of 0.90 to detect such reduction? (Hint:
$\alpha=0.05$)
\item Can you find some flaws for the above study design? Comment.
\item Try to figure out a method to give the best estimate of the effect of
Acetaminophen in pain relief following the wisdom-tooth extraction?
\end{enumerate}
\section{Clinical trial design}
An RCT was comparing the psychological treatment (\textbf{CBT}) with the exercise program
(\textbf{EX}) for patient suffering from moderate to severe anxiety. Patients are randomized
to treatment using \textbf{deterministic minimization} controlling for gender and severity. After
65 patients have entered the trial. The number of patients with each characteristic is summarized
in the following table:
\begin{table}
\caption{Number of patients for each characteristic}
\center{
\begin{tabular}{llcc}
& & \multicolumn{2}{c}{Treatment}\\
\cline{3-4}
\multicolumn{2}{l}{Characteristics} & CBT & EX\\
\hline
\multirow{2}{*}{Gender} & Male & 18 & 15\\
& Female & 15 & 17\\
\hline
\multirow{2}{*}{Severity} & Moderate & 22 & 21\\
& Severe & 11 & 11\\
\hline
\end{tabular}}
\end{table}
\begin{enumerate}[(1)]
\item How many patients have been allocated to each treatment?
\item If the 66$^{\textrm{th}}$ is a male and moderately severe patient,
which treatment would he be allocated?
\item The 67$^{\textrm{th}}$ is a female and moderately severe patient,
which treatment would she be allocated?
\end{enumerate}
\section{Case study}
Read this article, and answer the following questions.\\
\begin{quote}
Petter Quist-Paulsen. Randomised controlledtrial of smoking cessation
intervention after admission for coronary heart disease. BMJ 2003;327:1254.
\end{quote}
\begin{enumerate}[(1)]
\item Using a $z$-test of proportions, check the analysis for Table 2 of
the paper to compare the smoking cessation rates in intervention
group and control group at 12 months. Report also the $95\%$
confidence interval of the treatment effect.
\item Summarize the results of the above analysis in your own words.
\item How does the author deal with the missing data? Since we have talked about
intention-to-treat analysis, how does it deal with the missing data?
Compare the results with the article.
\item Comparing the lost-to-follow-up rates between the intervention and
control group, what conclusion can you draw from this analysis?
\end{enumerate}
\section{Case study}
A randomized controlled equivalence trial is conducted to test whether a new \textbf{generic
drug} is of equal efficacy to the current \textbf{standard drug}. Here is the partial result:
\begin{verbatim}
| Obs Mean Std. Err. Std. Dev. [90% Conf. Interval]
---------+-------------------------------------------------------
Standard | 42 35.2 2.79289 18.1 30.49991 39.90009
Generic | 41 34.1 2.79551 17.9 29.39278 38.80722
---------+-------------------------------------------------------
\end{verbatim}
The investigators suggest that a difference of 5 is clinically significant. Using the above
data, tell whether the new generic drug is equivalent to the current standard drug under the
significance level of $\alpha=0.05$.
\end{CJK*}
\end{document}