Real-life Applications Final Exam

%% Real-life Applications Final Exam
% Final Exam Project
% A collection of final exam questions
clc

%% This section will plot Michaelis-Menten curves
% of V-observed vs. the concentration of Remdesivir-TP for the
% velocity of the incorporation of remdesivir by viral and
% human RNA polymerase

% Virus Values
VmaxVirus = 0.75;
KmVirus = 5.7;
C = logspace(-2, 4);
VobsVirus = (VmaxVirus.*C)./(C+KmVirus);

% Human Values
VmaxHuman = 0.81;
KmHuman = 21;
VobsHuman = (VmaxHuman.*C)./(C+KmHuman);

% Graphing the functions
hold on
semilogx(VobsVirus)
semilogx(VobsHuman)
title('V Observed vs. Concentration of Remdesivir-TP for Human and Virus')
legend('Virus', 'Human', 'Location', 'best')
xlabel('Concentration of Remdesivir-TP(uM)')
ylabel('V Observed')

%% Continuing from the last section
% Determines specific values from concentrations
clc
V= [0.1 10 100];
VobsV = (VmaxVirus.*V)./(V+KmVirus)
VobsH = (VmaxHuman.*V)./(V+KmHuman)
TW = VobsV - VobsH

%% This section uses a two-tailed fishers exact test to determine whether or not
% a survival outcome is statistically significant on contingency tables
clc, clear

s1 = table([84;16], [80;20],'VariableNames',{'Experimental','Placebo'},'RowNames',{'Lived','Died'})
s2 = table([840;160], [800;200],'VariableNames',{'Experimental','Placebo'},'RowNames',{'Lived','Died'})
[h1, p1, stats1] = fishertest(s1)
[h2, p2, stats2] = fishertest(s2)

%% Continued from the last section
% Runs a simulation to help determine when a cohort size will become significant
% Will run a fishers exact test and graph the value
clc, clear

CohortSize = 20:10:2000;
CSlength = length(CohortSize);
P = [];

for i = 1:CSlength
    C = CohortSize(i);
    b = C/2 * 0.80;
    d = C/2 * 0.20;
    c = d - d * 0.20;
    a = C/2 - c;
    s = [a b
         c d];
    s = round(s);
    [h, p, stats] = fishertest(s);
    P(i) = p;
end
semilogy(P)
%plot(CohortSize, P)
xlabel('Cohort Size')
ylabel('p-values')
title('p-values vs. Cohort Size')