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19-Sep-2000

�� , 16(4), ��-�� 1999, 394-402

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�� , �� , ��

�� : �� , �� , �� , ��

1. ��

� �� , � �� , �� . � �� (�� ) �� , �� , �� .

� �� , �� , � �� , �� , �� .^1,2

�� (odds)* �� (logit),** �� .

* ��: ��. odds, ��. odds, pari, cotes.
** ��: ��. logit, ��. logit. �� logistic transformation.

2. �� 

� �� . �� 0,20, �� 0,20 �� , ��, �� 1 �� 5 �� 4 �� 5 �� . � �� , �� , �� , �� , �� 1 �� 4 � 1:4 � 0,25.***

*** �� (p) �� 1, �� p, �� p/1-p, �� .

�� p �� (1�p), �� (p/1�p).

�� 4 �� (��. 1), �� n₁ �� n₂, �� , � ��

��

�� (�� ) ��, �� . �� 2 �� p �� p.

��

�� (��) ��

� ��

��, �� =�� (p)xL=�xL

H ��

�� , �� , �� (�) ��, ��

�� P (N⁺�^�)=�� (p)x�=�x�

�� , ��, �� (��) (��) ��

2.1. ��

�. �� S�. �� 50 �� .⁴ � �� p=0,59

�� ST, �� (��) �� 3.

�. �� CAGE. �� 0,50, �� CAGE �� 4.

�� , �� . �� 0,40�0,60, �� , ��, �.�. �� , � �� GT �� , �� . �� , �� .

�. �� . � �� . �� , �� (�) � �� , (�) �� (�) � �� . �� . �� L₁, L₂ �� L₃, �� , �� , ��

�� =�� (p)xL₁xL₂xL₃

�� 5 �� .

�� ,

�� (��)=�xL₁xL₂xL₃=0,7x1,5x1,7x2,0=3,57

��, � ��

� �� , �� , �� .�. � ��.

2.2. ��

�. �� . Ӓ �� , �� , �� . �� 6 �� (��) �� (��).

�� 0,33 (��=0,50) �� , �� , ��

�xL₁xL₂xL₃xL₄=0,50x2,11x2,55x11,7x2,87=90,34

��

�� , ��

�xL₁xL₂x�₃x�₄=0,50x2,11x2,55x0,19x0,67=0,34

��

�� , �� 0,02.

� ��, �� , �� . ��, �� , �� . �� , �� a priori �� .

�. �� . �� 0,50. �� (�) �� , �� 0,20, (�) �� , �� L=4,5 �� =0,125. �� 0,50, ��

��, ��, � �� , �� , �� 0,50 �� 0,50, �� , �� , �� (�) �� . �� 7 �� .

� �� (��) �� 0,71, �� 0,53. �� , � �� 0,34. � �� (=0,20) �� . ��, � �� 0,34 �� . ��, � �� 0,50. ��, ��, �� .

� �� 0,20 �� 0,0138, �� . � ��, ��, �� , �� , �� 0,50.

��, � �� , �� .

�. �� . �� 100% �� 20% �� , �� 1%. � �� , �� .⁴ �� ;

�� 0,01/0,99=0,01 ��

�� , �� 0,01x5x5=0,25 �� =0,20.

��, �� , �� , � �� (L) �� 1 �� 0,01x5x1=0,05 �� =0,04.

� �� 0,04 �� 0,20. �� , �� .

3. �� 

�� (logit) �� (��) �� (odds) �� p.

� �� , �� Bayes �� . �� Bayes �� B� �� , �� .

�� lnL₁... lnLn �� , �� (�, �� , �� ),* � �� Bayes ��

ln �� =logit (p)+lnL₁+...lnLn

* �� ��  �� weight of evidence. O �� valeur informative (�� ) � poids informatif (�� ). �� .

�� (lnL) �� (score) �� 100, ��

��=100 �� (��)=100 �� (p)+100 lnL₁+...+100 lnLn

��

� �� p �� (��, �� ) �� , �� .7,8

�� , � �� p �� (p). �� (p₁�p₂) �� , �.�. �� , ��

� �� , �� .�. � �� (��. 1). � �� .

�� , �� , �� (��. 1�). � �� (��. 1�), �� .

4. �� 

�� (N �� ͖) �� (�+ �� T�).

��

�� , �� , ��

� ��

�� (��),* ��

* �� (�� ): �� , �� .

� �� , �� , �� (odds ratio) ��

� �� (�� ) ��

** �� �� �� �� �� .

�� , � ��

� �� ad� �� bc� (cross-product ratio). � �� b � c �� . �� (a, b, c, d) �� , ��

�� (�) �� (�) �� (n₁+n₂).

�� , �� (�) �� a/c �� (͖) �� b/d ��, ��, � ��

�� -��, � �� , �� (�� ) � �� , �� .

�� 1 �� L=�=1 �� . �� , ��, �� . H �� , �� . � �� , �� .

�� (L, �), � �� , ��

�� L�� =�� .

�� -�� , � �� a/a+b �� a/b �� c/c+d �� c/d. �� , � ��

�� . � �� (��) �� .⁸

5. �� 

�� (��) �� ^4,8 (�)

�� 95% ��

� �� : ln(�)�1,96x�� (ln�)

� �� : ln(�)+1,96x�� (ln�).

�� , �� (O) ��

��

�� (��) �� (��) �� 8.⁴

� �� (�� ) �� (=51,2), �� (=28,7). � �� : (�) �� * �� (�) �� (�), �� . �� , � �� .

* To �� (��) �� .

� �� . � �� L (lnL) �� (ln�). � �� , ��, �� ln (L)�ln(�)=3,36=ln(�) �, �� 100, �� 336 �� , �� 394 �� .

�� 9 ��, �� , � �� 100 �� .

� ��, �� , ��

� �� (ϒ) �� (�� 28,7), �� (�� 32).

� �� (ϴ)=ln26=3,26

�� (��) �� (ϴ) ��

�� 95% ��

exp (ln26�1,96x0,79)=exp (3,26�1,55)

��, �� 5,5 �� 122. �� , �� . �� , �� .

6. �� 

�� , �� , 10.000 �� , �.�., �� . �� . �� 10.

�� (100 �� 9900 �� ) � ��-�� (��) �� 10/10.000=0,001. � �� 9/100=0,09 �� 1/9900, � ��

� �� . � �� , �� , �� 9/10=0,9, �� 91/9990=0,009 ��

��

�� p=0,001, � ��

��

��, � ��

�� (�), � �� p �� :

� �� p �� , �� p �� . � �� , �� . �� , � �� .⁴

7. �� -��

�� , � �� . �� -�� 11.

� �� x²

� �� * �� (ϴ), ��

� �� -��.^2,8,9

* �� , �� , �� . � �� .

��

�� . ��. �� , ��, 1970
GREENLAND S. Probability logic and probabilistic induction. Epidemiology 1988, 9:322�332
MACARTNEY FJ. Diagnostic logic. In: Phillips C (ed) Logic in medicine. Publ by BMJ, London, 1988
GRENIER S. Evaluation de la decision medicale. Introduction a l� analyse medico-�conomique. Masson, Paris, 1996
CUMMINGS SR, LILLINGSTON GA, RICHARD RJ. Estimating the probability of malignancy in solitary pulmonary nodules. A Bayesian approach. Am Rev Respir Dis 1986, 134:449�452
STANILAND JR, DITCHBURN J, DE DOMBAL FT. Clinical presentation of acute abdomen: study of 600 patients. Br Med J 1972, 3:393�398
SACKETT DL, HAYNES RB, GUYATT GH, TUGWELL P. Clinical Epidemiology. 2nd ed. Little Brown and Co, London, 1991
ROTHMAN KJ, GREENLAND S. Modern Epidemiology. 2nd ed. Lippincott, Philadelphia, 1997
�� . � �� . ��  1997, 14:373�374

� 2000, �� c��