\documentstyle[11pt]{article} % Specifies the document style. \textheight 250mm \textwidth 160mm \hoffset -15mm \begin{document} \pagestyle{empty} \vspace*{-35 mm} \begin{center} {\em Arthritis clinical trial data, reproduced from Fitzmaurice and Lipsitz (1995, p. 58).}\\ \vspace{2 mm} A, auranofin; P, placebo; 0, good; 1, poor; -, missing.\\ \vspace{5 mm} {\small \begin{tabular}{rcccccccc} \hline Patient & Gender & Age & Treatment & \multicolumn{5}{c}{Self-assessment}\\ \cline{5-9} & & & & Base-line & Week 1 & Week 5 & Week 9 & Week 13 \\ \hline 1 & M & 48 & A & 0 & 0 & 0 & 0 & 0 \\ 2 & M & 29 & A & 0 & 0 & 0 & 0 & 0 \\ 3 & M & 59 & P & 0 & 0 & 0 & 0 & 0 \\ 4 & F & 56 & P & 0 & 0 & 0 & 0 & 0 \\ 5 & M & 33 & P & 0 & 0 & 0 & 0 & 0 \\ 6 & M & 61 & P & 0 & 0 & 1 & 0 & 0 \\ 7 & M & 63 & A & 1 & 1 & 0 & - & - \\ 8 & M & 57 & P & 0 & 1 & 0 & 0 & 0 \\ 9 & M & 47 & P & 0 & 0 & 0 & 1 & 0 \\ 10 & F & 42 & A & 1 & 1 & 0 & - & 1 \\ 11 & M & 62 & A & 0 & 0 & 0 & 0 & 0 \\ 12 & M & 42 & P & 0 & 0 & 0 & 0 & 0 \\ 13 & M & 50 & A & 0 & 0 & 0 & 0 & 0 \\ 14 & F & 47 & A & 0 & 0 & - & - & - \\ 15 & M & 45 & P & 1 & 1 & 1 & 0 & 0 \\ 16 & M & 55 & A & 0 & 0 & 0 & 0 & 0 \\ 17 & M & 56 & A & 0 & 0 & 0 & 0 & 0 \\ 18 & M & 57 & P & 0 & 0 & 0 & 0 & 0 \\ 19 & F & 57 & P & 0 & 0 & 0 & 1 & - \\ 20 & M & 45 & A & 0 & 1 & 0 & 1 & 0 \\ 21 & M & 29 & A & 0 & 0 & 1 & - & - \\ 22 & F & 51 & A & 1 & 1 & 0 & 0 & 1 \\ 23 & F & 65 & P & 0 & 0 & 1 & 0 & 1 \\ 24 & F & 50 & A & 0 & 0 & 0 & 1 & 0 \\ 25 & M & 65 & A & 0 & 0 & 0 & 0 & 0 \\ 26 & F & 58 & P & 0 & 0 & 1 & 1 & 1 \\ 27 & F & 62 & A & 1 & 0 & 0 & 0 & 0 \\ 28 & F & 35 & A & 0 & 0 & 0 & 0 & 0 \\ 29 & M & 28 & A & 0 & 0 & 0 & 0 & 0 \\ 30 & M & 41 & A & 0 & 0 & 0 & - & - \\ 31 & M & 40 & P & 0 & 1 & 0 & 1 & 0 \\ 32 & M & 33 & P & 1 & 1 & 1 & 1 & 1 \\ 33 & F & 60 & P & 1 & 1 & 1 & 1 & 1 \\ 34 & M & 62 & A & 0 & 1 & 0 & 0 & 0 \\ 35 & M & 45 & P & 0 & 0 & 1 & 0 & 0 \\ 36 & M & 64 & P & 1 & 1 & 1 & 1 & 1 \\ 37 & M & 55 & P & 1 & 1 & 1 & 0 & 0 \\ 38 & M & 57 & A & 0 & 0 & 0 & 0 & - \\ 39 & M & 51 & P & 0 & 0 & 1 & 0 & 0 \\ 40 & F & 57 & A & 0 & 0 & 0 & 0 & 0 \\ 41 & M & 37 & P & 0 & 1 & 0 & - & 0 \\ 42 & M & 52 & A & 1 & 0 & 0 & 0 & - \\ 43 & M & 52 & P & 0 & 0 & - & 0 & 0 \\ 44 & M & 46 & A & 0 & 0 & 0 & 0 & 0 \\ 45 & M & 63 & A & 1 & 1 & 0 & 1 & - \\ 46 & M & 60 & P & 0 & 0 & 1 & 1 & 1 \\ 47 & M & 63 & A & 1 & 0 & - & 1 & 1 \\ 48 & F & 33 & P & 0 & 1 & 1 & 0 & - \\ 49 & M & 60 & A & 1 & 1 & 0 & 0 & 0 \\ 50 & M & 58 & A & 0 & 0 & 0 & 0 & 0 \\ 51 & M & 37 & P & 1 & 1 & 1 & 0 & 1 \\ \hline \end{tabular} } \end{center} \end{document} \newpage \begin{center} {\em Table 2. Maximum likelihood estimates, standard errors and correlations for model $\{T;{\cal M}1\}$ fitted to the auranofin data. } \vspace{3 mm} \begin{tabular}{|c|cc|cccc|} \hline Parameter & Estimate & Standard & \multicolumn{4}{c|}{Correlation} \\ & & error & $\beta_{0}$ & $\beta_{1}$ & $\lambda_{01}$ & $\lambda_{12}$ \\ \hline $\beta_{0}$ & -0.65 & 0.24 & 1.00 & & & \\ $\beta_{1}$ & -2.16 & 0.64 & -0.35 & 1.00 & & \\ $\lambda_{01}$ & 0.84 & 0.16 & -0.78 & 0.27 & 1.00 & \\ $\lambda_{12}$ & 0.45 & 0.17 & -0.42 & 0.14 & 0.33 & 1.00 \\ \hline \end{tabular} \end{center} {\footnotesize $\beta_{0}$, logit of probability of `poor' under no treatment or placebo. $\beta_{1}$, contrast to $\beta_{0}$ under auranofin. $\lambda_{01}$, log dependence ratio between `poor' at baseline and after 1 week. $\lambda_{12}$, log dependence ratio between `poor' 4 weeks apart.} \newpage \begin{center} {\em Table 3. Goodness-of-fit statistics for three combined models fitted to the obesity data.} \vspace{3 mm} {\em (a) Boys}\\ \vspace{3 mm} \begin{tabular}{|c|cccc|}\hline Model & Pearson & Deviance & Degrees & Pearson \\ & statistic & statistic & of freedom & p-value \\ \hline $\{A; {\cal L}2{\cal M}1\}$ & 27.27 & 34.48 & 25 & 0.34 \\ $\{A; {\cal L}2\}$ & 30.25 & 38.38 & 26 & 0.26 \\ $\{A; {\cal M}1\}$ & 108.7 & 78.31 & 27 & 0.000 \\ \hline \end{tabular} \vspace{5 mm} {\em (b) Girls}\\ \vspace{3 mm} \begin{tabular}{|c|cccc|}\hline Model & Pearson & Deviance & Degrees & Pearson \\ & statistic & statistic & of freedom & p-value \\ \hline $\{A; {\cal L}2{\cal M}1\}$ & 32.36 & 38.46 & 25 & 0.15 \\ $\{A; {\cal L}2\}$ & 36.01 & 45.72 & 26 & 0.091 \\ $\{A; {\cal M}1\}$ & 78.64 & 63. 09 & 27 & 0.000 \\ \hline \end{tabular} \end{center} \newpage \begin{center} {\em Table 4. Observed and fitted values of dependence ratios, from three models fitted to the obesity data.} \vspace{5 mm} {\em (a) Boys}\\ \vspace{3 mm} \begin{tabular}{|c|cccc|} \hline Source & $\tau_{12}$ & $\tau_{23}$ & $\tau_{123}$ & $\tau_{13}$ \\ \hline Observed & 3.32 & 3.15 & 11.41 & 2.89 \\ $\{A; {\cal L}2{\cal M}1\}$ & 3.19 & 3.19 & 11.19 & 2.90---2.93 \\ $\{A; {\cal L}2\}$ & 3.10 & 3.10 & 11.20 & 3.10 \\ $\{A; {\cal M}1\}$ & 3.20 & 3.20 & 10.22 & 2.18---2.34 \\ \hline \end{tabular} \vspace{5 mm} {\em (b) Girls}\\ \vspace{3 mm} \begin{tabular}{|c|cccc|} \hline Source & $\tau_{12}$ & $\tau_{23}$ & $\tau_{123}$ & $\tau_{13}$ \\ \hline Observed & 3.39 & 3.16 & 12.15 & 3.00 \\ $\{A; {\cal L}2{\cal M}1\}$ & 3.29 & 3.29 & 12.13 & 2.81---2.96 \\ $\{A; {\cal L}2\}$ & 3.17 & 3.17 & 11.90 & 3.17 \\ $\{A; {\cal M}1\}$ & 3.32 & 3.32 & 11.04 & 1.91---2.48 \\ \hline \end{tabular} \end{center} {\footnotesize For the models in which the fitted values of $\tau_{13}$ varies with cohort the range, from min to max, is reported.} \end{document}