$M$

$T$

$\overline{T}$

$\overline{T}$

$T$

$\overline{M}$

Résultats

Calculs intermédiaires

$VPP=P_T(M)$  

Prévalence : P(M)

$VPN=P_{\overline T}(\overline M)$

La valeur prédictive positive (VPP) du test est :

\text{La probabilité d'être malade}\ 
\text{sachant que le test est positif : }

Prévalence

Spécificité

Sensibilité

VPP=P_T(M)

Valeurs prédictives positives et négatives 
VPP et VPN en fonction de la prévalence P(M).

Expression

r(x) = (x^(2) * (3 - (2 * x)))
M = (-2.991401578936725, 2.606519781155281)
A = (-4.615393754145556, 1.4352886016244057)
f = Segment(A, M)
D = Point(f)
n = Segment(A, D)
g = OrthogonalLine(A, yAxis)
C = (-0.7784364589090961, 3.304845988115541)
h = Segment(M, C)
i = OrthogonalLine(M, yAxis)
C' = Mirror(C, i)
C'_1 = Mirror(C, g)
C'' = Mirror(C', g)
B' = Mirror(M, g)
j = Segment(A, B')
k = Segment(B', C'')
l = Segment(B', C'_1)
p1: r(n / f)
m = Segment(M, C')
text1: "P(M)=" + (LaTeX[p1]) + ""
p1': 1 - p1
text2: "" + p1' + ""
E = Point(h)
F = Point(l)
p = Segment(M, E)
p2: r(p / h)
q = Segment(B', F)
p3: r(q / h)
text4: "P_{\overline M} \left(\, \overline T \,\right )=" + (LaTeX[p3]) + ""
text3: "P_M(T)=" + (LaTeX[p2]) + ""
p2': 1 - p2
p3': 1 - p3
text5: "" + p2' + ""
text6: "" + p3' + ""
PT: (p1 * p2) + (p1' * p3')
PMT: (p1 * p2 / PT)
texte1: "P(M\cap T)=" + (LaTeX[p1]) + "\times" + (LaTeX[p2]) + ""
texte2: "P(\overline{M}\cap \overline{T})=" + (LaTeX[p1']) + " \times " + (LaTeX[p3]) + ""
texte3: "P(M\cap \overline{T})= " + (LaTeX[p1]) + " \times  " + (LaTeX[p2']) + ""
texte4: "P(\overline{M}\cap T)= " + (LaTeX[p1']) + " \times  " + (LaTeX[p3']) + ""
texte5: "\text{La probabilité que le test soit positif est :}\\
P(T)=P(M\cap T)+P(\overline{M}\cap T)\approx" + (LaTeX[PT]) + ""
a = false
b = false
vpp(x) = ((p2 * x)) / (((p2 + p3 - 1) * x) + 1 - p3)
VPP(x) = If[0 ≤ x ≤ 1, vpp]
VPPcour: (p1, PMT)
vpn(x) = ((1 - x) * p3 / (((-x) * (p2 + p3 - 1)) + p3))
VPN(x) = If[0 ≤ x ≤ 1, vpn(x)]
B: (p1, VPN(p1))
c(x) = x > 1.01
d(y) = y > 1.015
texte10: "
P_T(M)=\frac{P(M\cap T)}{P(T)}\approx " + (LaTeX[PMT]) + ""
s = OrthogonalLine(VPPcour, yAxis)
G = Intersect(s, yAxis)
t = Segment(VPPcour, G)
texte14: "" + (LaTeX[PMT]) + ""
coeff1: p2 + p3 - 1
coeff2: 1 - p3
VPPaff(x) = ((p2 * x)) / ((coeff1 * x) + coeff2)
texte15: "VPP(x)=" + (LaTeX[VPPaff]) + ""
e = false