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\footnotesize
\noindent Statistica Sinica {\bf 13}(2003), 179-187
\vspace{3pc} \normalsize

\centerline{\large\bf INTERVAL ESTIMATION OF TREATMENT EFFECTS}
\vspace{2pt}
\centerline{\large\bf IN DOUBLE CONSENT RANDOMIZED DESIGN}
\vspace{.25cm}
\centerline{Kung-Jong Lui and Chii-Dean Lin}
\vspace{.4cm}
\centerline{\it San Diego State University}
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\begin{quotation}
\noindent {\it Abstract:}
The double consent randomized design, in which the physician and
the patient know exactly what treatment the patient receives, has been
proposed to alleviate the concern in carrying out a conventional randomized
trial.  In the latter, the assignment of patients to treatments after
obtaining patients' informed consents depends completely on a chance
mechanism. We develop four interval estimators, two using the delta method
or the principle of Fieller's Theorem calculated over the pooled samples of
eligible patients, and two  %using the same method or principle
calculated over the samples excluding patients who have treatment preference.
Using Monte Carlo simulation, we evaluate and compare the performance of these
estimators in a variety of situations.  We note that the estimators using the
principle of Fieller's Theorem outperform those derived from the delta
method with respect to both coverage probability and average length in almost
all situations considered here.  We further note that when the expected number
of patients who have no treatment preference is moderate or large (say $\geq
25$) per treatment, the interval estimator using Fieller's Theorem calculated
over the restricted samples is generally more efficient than those calculated
over the entire pooled samples without much loss of accuracy as measured by
coverage probability.  On the other hand, when the expected number of
patients who have no treatment preference is small, the coverage probability
for the estimators calculated over the restricted samples tends to be less
than the desired confidence level, while the coverage probability of the
estimator using Fieller's Theorem on the  pooled samples may still agree
with the desired confidence level.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Delta method, Fieller's theorem, interval estimation,
 randomized consent design.\par
\end{quotation}
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