# Probability Objective Probability Prior Probability Posterior Probability Conditional

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������ (Probability( -Objective Probability �������� Prior Probability ��������������� Posterior Probability

Conditional Probability ��������� B ��������� A ���� Disease -��������� x. Present D+ Absent DTrue positive False positive ray����� + Test + (a) (b) a+b (c) (d) c+d ��������� False negative a+c sensitivity a = -----a+c True negative b+d specificity d =-----b+d

} ��� �� ������ Positive Predictive value Sensitivity ������ (1 -specificity (false positive Specificity ������ /����� ( 1 -

Disease Present D+ Absent DTrue positive False positive Test + (a) (b) a+b (c) (d) c+d False negative True negative a+c b+d ������ Diagnostic Test -������ (sensitivity) -����� (specificity( -Positive predictive value (PV+) -Negative predictive value(PV(-Receiver Operating Characteristic (ROC Curve( -Likelihood ratio

����� 2 x 2 ������� Diagnostic Test Disease Present D+ True positive Test + (a) (c) False negative a+c sensitivity a = -----a+c PV+ b = -----a+b Absent DFalse positive (b) a+b (d) c+d True negative b+d specificity d =-----b+d PVd = -----c+d Prevalence a+c = a+b+c+d ------ LR+ a/(a+c) =-----b/(b+d) LRc/(a+c) =-----d/(b+d)

Disease Present True positive Test + (a) 9 (c) 1 False negative a+c 10 Absent False positive (b) 18 (d) 45 True negative b+d 63 a+b c+d 73 ������ (sensitivity( ��������� �� ���� � ) true positive) =9/10 = 90% ������� (false positive( ��������� =1/1

Disease Present True positive Test + (a) 9 (c) 1 False negative a+c 10 Absent False positive (b) 18 (d) 45 True negative b+d 63 a+b c+d 73 ����� (specificity( ���������� ) true negative) = 45/63 = 71. 43% ���� (false negative( ���������

Disease Present True positive Test + (a) 9 (c) 1 False negative a+c 10 Absent False positive (b) 18 (d) 45 True negative b+d 63 a+b 27 c+d 46 73 positive predictive value (������ ( ��������� PV+ = a/(a+b) = 9/(9+18) = 33. 33% negative predictive value (������ ( ���������� PV- = d/(c+d) = 45/(1+45) = 97. 83%

Disease Present True positive Test + (a) 9 (c) 1 False negative a+c 10 Sensitivity PV+ Prevalence LR+ LR- Absent False positive (b) 18 (d) 45 True negative b+d 63 a+b 27 c+d 46 73 = 9/10 = 90% specificity = 45/63 = 71. 43% = 9/27 = 33. 33% PV= 45/(45+1) = 97. 83% = 10/73 =13. 70% = (9/10)/(18/63) = 3. 15 = (1/10)/(45/630 = 0. 14

. diagt dp c 17 | c 17 dp | Pos. Neg. | Total -----+-----------+-----Abnormal | 9 1 | 10 Normal | 18 45 | 63 -----+-----------+-----Total | 27 46 | 73 True abnormal diagnosis defined as dp = 1 95%] ------------------------------------Sensitivity Pr( +| D) 90. 00% Specificity Pr( -|~D) 71. 43% Positive predictive value Pr( D| +) 33. 33% Negative predictive value Pr(~D| -) 97. 83% ------------------------------------Prevalence Pr(D) 13. 70% ------------------------------------- Conf. Inter[. 55. 50% 58. 65% 16. 52% 88. 47% 99. 75% 82. 11% 53. 96% 99. 94% 6. 77% 23. 75%

Positive predictive value/ Negative predictive value ������� (Prevalence rate) ��� Posterior Probability Conditional Probability PV+ (sen)(pre) ----------------(sen)(pre)+(1 -spec)(1 -pre) Prior Probability PV(sen)(pre) ----------------(sen)(pre)+(1 -spec)(1 -pre)

���� Positive predictive value/ Negative predictive ������� (Prevalence rate) ����������� 1422. =

Disease Present True positive Test + (a) 9 (c) 1 False negative a+c 10 Likelihood ratio Absent False positive (b) 18 (d) 45 True negative b+d 63 a+b c+d 73 LR+ ������������ LR+ = (9/10)/(18/63) = 3. 15 �������� TB ���������� TB �������

Disease Present True positive Test + (a) 9 (c) 1 False negative a+c 10 Absent False positive (b) 18 (d) 45 True negative b+d 63 a+b c+d 73 LR- ����������� LR- = (1/10)/(45/63) = 0. 14

Bayes’ Rule