% PAS and Streptomycin Cures for Pulmonary Tuberculosis.}~
% Data released by British Medical Research Council in 1950 (analyzed also in Armitage and Berry, 1994)
% concern efficiency of para-amino-salicylic acid (PAS), streptomycin, and their combination on treatment of
% pulmonary tuberculosis. Outcomes of sputum culture test performed on the patients after the
% treatment are categorized as 'Positive Smear', 'Negative Smear \& Positive Culture', and 'Negative Smear \& Negative Culture'.
%
% The table below summarizes findings on 273 treated patients with TB diagnosis.
%
% {\footnotesize
% \begin{center}
% \begin{tabular}{|c||c c c||c|}
% \hline
% & Smear (+) & Smear (--) \& Culture (+) & Smear (--) \& Culture (--) & Total \\ \hline
% \hline
% PAS & 56 & 30 & 13 & 99 \\
% Streptomycin & 46 & 18 & 20 & 84 \\
% PAS \& Streptomycin & 37 & 18 & 35 & 90 \\ \hline \hline
% Total & 139 & 66 & 68 & 273 \\ \hline
% \end{tabular}
% \end{center}
% }
%
% (a) There are two factors here: Cure Combination and Sputum Results. Test the hypothesis
% of their independence. Find the $p$-value and compare it to the 5\% significance level.
% Find also the rejection region for the test and confirm that your decision made by $p$-value
% is consistent with the decision based on the rejection region considerations.
%
% (b) If the factors were independent, how many patients you expect to see in
% the cell defined by PAS treatment and Positive Smear (cell in the intersection of 1st row and 1st column)?
% How many patients you expect to see in the cell defined by combination of treatments (PAS+Streptimycin)
% for which the response was Smear negative, Culture negative (cell in the intersection of 3rd row and 3rd column).
% Show your work.
%
%
% (c) Inspect the difference between observed and expected frequencies in the
% 3rd column (Smear negative, Culture negative), which represents a desirable outcome.
% Based on the signs and magnitudes of these differences, which of the three cures would you recommend?
%
%(a)
D =[ ...
56 30 13 ; %99
46 18 20 ; %84
37 18 35 ]; %90
% 139 66 68 273
[chi2,pvalue,exp] = tablerxc(D)
% chi2 = 17.6284
% pvalue = 0.0015
% exp =
% 50.4066 23.9341 24.6593
% 42.7692 20.3077 20.9231
% 45.8242 21.7582 22.4176
%(b)
e11 = 99 * 139/273 % 50.4066
e33 = 90 * 68/273 % 22.4176
%(c)
[13 20 35] - [24.6593 20.9231 22.4176]
% -11.6593 -0.9231 12.5824
% Recommend combination PAS + Streptomycin (PS). For the desirable
% outcome (column 3) the observed frequency of PS exceeds the expected.
% This means that PS is most effective cure. Analogously, the PAS alone
% is the least effective.