201 Final

% Again Part of my 201 Class
% removed identifying features
% Similar to Final Exam Applications paste

%% Question 1b
clc, clear, clf

% Virus Values
VmaxVirus = 0.75;   % Vmax for Virus
KmVirus = 5.7;      % Km for Virus
C = logspace(-2, 4);        % Creating equally spaced log vector from 10^-2 to 10^4
VobsVirus = (VmaxVirus.*C)./(C+KmVirus);    % Vobs function for Virus in terms of Vmax, Km, and variable

% Human Values
VmaxHuman = 0.81;       % Vmax for Human
KmHuman = 21;           % Km for Human
VobsHuman = (VmaxHuman.*C)./(C+KmHuman);        % Creating Vobs for Human in terms of Vmax, KM, and variable

% Graphing the functions
hold on         % Hold on so I can plot two functions on one figure
semilogx(VobsVirus)         % Plotting Virus function on log x-axis
semilogx(VobsHuman)         % Plotting Human function on log x-axis
title('V Observed vs. Concentration of Remdesivir-TP for Human and Virus')      % Title for figure
legend('Virus', 'Human', 'Location', 'best')    % Creating legend to differentiate between functions in the best location
xlabel('Concentration of Remdesivir-TP(uM)')    % Horizontal label
ylabel('V Observed')            % Vertical label
hold off        % Removes hold on graph
%% Question 1c

V = [0.01 0.1 1 10]        % [uM] Creating a concentration vector
VobsV = (VmaxVirus.*V)./(V+KmVirus)        % Creating Vobs function for Virus with set concentrations
VobsH = (VmaxHuman.*V)./(V+KmHuman)        % Creating Vobs function for Human with set concentrations
TW = VobsV - VobsH         % Therapeutic window
%% Question 2a
clc, clear, clf

s1 = table([84;16],[80;20],'VariableNames',{'Experimental','Placebo'},'RowNames',{'Lived', 'Died'})         % Creating table for scenario 1
s2 = table([840;160],[800;200],'VariableNames',{'Experimental','Placebo'},'RowNames',{'Lived', 'Died'})     % Creating table for scenario 2
[h1, p1, stats1] = fishertest(s1)       % Performing fisher's exact test on scenario 1 and getting values from results
[h2, p2, stats2] = fishertest(s2)       % Performing fisher's exact test on scenario 2 and getting values from results
%% Question 2b
clc, clear, clf

CohortSize =[20 200 2000 20000];       % Creating cohort sizes vector

for i = 1:length(CohortSize)      % Beginning of the for loop that runs for length of the cohort vector
    C = CohortSize(i);          % Reallocating the cohort size into a vector with a smaller name
    b = C/2 * 0.80;      % Taking half of the cohort size and then saying 80% of this new group will live with placebo arm
    d = C/2 * 0.20;     % Taking half of the cohort size and then saying 20% of this new group will die with placebo arm
    c = d*.80;        % The number of patient who died with the experimental arm happens to be 80% in value of patients who died with the placebo arm
    a = C/2 - c;       % Taking half of cohort size and subtracting the amount of the patients who died with experimental arm leaves the survivors with experimental arm
    s = [a b
         c d];          % Creating vector for the contingency table
    s = round(s);       % round all the numbers within the vector
    [~, P(i), ~] = fishertest(s);      % Perform the fisher's exact test and saving the p-values

end         % end for loop


semilogy(CohortSize, P)         % Plot p-values vs. cohort size with log y-axis
xlabel('Cohort Size')           % horizontal label
ylabel('p-values')      % vertical label
title('p-values vs. Cohort Size')       % Title for figure