Tabel Kontingensi 2x2 3 OR dan Uji Kebebasan Khi Kuadrat1

  

Tabel Kontingensi 2x2 (3)

Rasio Odds dan Uji Kebebasan Khi-

Kuadrat

  Rasio Odds Exposure outcome

  Association measure odds that an outcome will occur given a particular exposure odds of the outcome occurring in the absence of that exposure

  

Rasio Odds

Rasio Odds

• most commonly used in case-control studies,
• can also be used in cross-sectional and cohort study designs as well (with some modifications and/or assumptions).

  Rasio ODDS Odds Sukses

   

  1

  odds  

   

  “It occurs as a parameter in the most important type of model for categorical data”

• Odds bernilai positif
• Nilai odss lebih besar dari satu, saat “sukses” lebih dipilih dibandingkan “gagal&rd
• odds = 4.0, a success is four times as likely as a failure

  Rasio Odds Pada Tabel 2x2

A1 A2

  1

   

  θ farther from 1.0 in a given direction represent stronger association.

  Rasio Odds Values of

   

  odds  

  1

  2

  2

  2

   

  odds  

  1- π

  B1 π

  1

  1

  1

   

  2

  1- π

  2

  π

  1

RASIO ODDS pada Study Cohort

  Develop Disease Do Not Develop

  Disease Exposed a b Non-Exposed c d

  The Odds that an exposed person develop disease a b

   The Odds that a non exposed person develop disease c d

   Rasio Odds : Cohort

• Odds ratio is the ratio of the odds of disease in

  the exposed to the odds of disease in the non-

  exposed

  odds that an exposed person develops the disease odds that a non exposed person develops the disease ^{a b c d}

  OR

   

   RASIO ODDS pada Study Case-Control Case Control History of Exposure a b

  No History of Exposure c d The odds that a case was exposed a c

   The odds that a control was exposed b d

  

  

Rasio Odds : Cohort

odds that a case was exposed odds that a control was exposed a c b d

  OR 

  

Odds ratio (OR) is the ratio of the odds that a case was

exposed to the odds that a control was exposed

  

Properties of OR

does not change value when the

• The odds ratio

  table orientation reverses so that the rows become the columns and the columns become the rows.

• • Thus, it is unnecessary to identify one classification

  as a response variable in order to estimate θ.
• By contrast, the relative risk requires this, and its value also depends on whether it is applied to the first or to the second outcome category.

  Both variables are response variables The odds ratio is also called the cross-product ratio, because it equals the ratio of the products π11π22 and π12π21 of cell probabilities from diagonally opposite cells.

  The sample odds ratio equals the ratio of the sample odds in the two rows,

  Ilustasi: kasus aspirin dan serangan jantung This also equals the cross-product ratio (189 × 10, 933)/(10,845 × 104). n

  189

  11 odds

     0.0174

  1 n

  Odds

  10845

  12

  0.0174

  1 OR

      1.832

   n

  Odds

  104 0.0095

  21

  2 odds

     0.0095

  2 n

  10933

  The estimated odds were

  22 83% higher for the placebo

  

Inferensia Rasio Odds

dan Log Rasio Odds

• Kecuali pada ukuran sampel sangat besar, sebaran percontohan dari OR sangat menceng (highly skewed).
• Karena kemiringan ini, statistika inferensia untuk rasio odds menggunakan alternatif dengan ukuran yang setara - logaritma natural, log (

  θ). Dengan log ( θ)=0.

• Artinya  =1 setara dengan log () dari 0.
• Log(OR) simetrik di sekitar nilai 0.
• Artinya, jika kita menukar posisi baris dan kolom akan mengubah tandanya. Misal: log(2.0) = 0.7 dan log

  kedua nilai ini mewakili kekuatan asosiasi yang sama

  (0.5) = −0.7,

• Doubling a log odds ratio corresponds to squaring an odds ra
• Sebaran dari log() tidak terlalu menceng, menyerupai bentuk lonceng
• Sebaran log () mendekati sebaran normal dengan nilai tengah log(

  ) dan galat baku

  The SE decreases as the cell

  Selang Kepercayaan untuk log( ) ˆ Z SE log 

     

  2 Ilustrasi: data aspirin

• log(1.832) = 0.605
• Galat baku =
• SK 95% untuk log ()

  0.605 ± 1.96(0.123)  (0.365, 0.846)

• SK 95% untuk 

  0.365 0.846 , e ) = (1.44, 2.33)

  [exp(0.365), exp(0.846)] = (e

• karena θ tidak mengandung 1, kemungkinan

  Kita menduga bahwa odds serangan jantung setidaknya 44% lebih tinggi pada subjek yang mengkonsumsi placebo dibandingkan dengan subjek yang mengkonsumsi aspirin ij

  =0, maka perhitungan OR adalah

  

Catatan

• Bila terdapat nilai n

  Hubungan antara OR dan RR

Jika p1 dan p2 mendekati nol, maka nilai OR akan sama dgr RR This relationship between the odds ratio and the relative risk is useful

  For some data sets direct estimation of the relative risk is not possible , yet one can estimate the odds ratio and use it to approximate the relative risk.

  

Rasio Odds pada studi case-control

• Table 2.4 refers to a study that investigated the relationship between smoking and myocardial infarction.
• The first column refers.
• Each case was matched with two

  to 262 young and middle-aged women (age < 69) admitted to 30

  control patients admitted to the same

  coronary care units in northern Italy with acute MI during a 5-year period

  hospitals with other acute disorders.

• The controls fall in the second column of the table.

• All subjects were classified according to whether they had ever been smokers.
• The “yes” group consists of women who were current smokers or ex-smokers, whereas the “no” group consists of women who never were smokers.We refer to this variableas smoking status.
• The study, which uses a retrospective design to look into the past, is called a case –control study.
• Such studies are common in health-related applications, for instance to ensure a sufficiently large sample ofsubjects having the disease studied.

  Tidak bisa menghitung proporsi penderita MI pada kelompok smoker (atau non-smoker)

  Karena untuk setiap penderita MI kita pasangkan dengan 2 orang kontrol

  Untuk wanita penderita MI, proporsi yang merupakan perokok sebesalr172/262 = 0.656, Sedangkan untuk wanita bukan penderita MI, proporsi perokok sebesar 173/519 = 0.333

Peubah respon

  P eu bah pe nje las

  When the sampling design is retrospective

  , we can construct conditional distributions for the explanatory variable

  , within levels of the fixed response.

• In Table 2.4, the sample odds ratio is [0.656/(1 −

  

0.656)]/[0.333/(1 − 0.333)] = (172 × 346)/(173 ×

90) = 3.8.

• The estimated odds of ever being a smoker were

  about 2 for the MI cases (i.e., 0.656/0.344) and

  about 1/2 for the controls (i.e.,0.333/0.667), yielding an odds ratio of about 2/(1/2) = 4.

• • For Table 2.4, we cannot estimate the relative risk

  of MI or the difference of proportions suffering

  MI.
• Binomial sample  column, dependent because

  1MI paired with 2 control

  Bagaimana mengukur keeratan hubungan 2 peubah??

Korelasi

  Hubungan linear pearson spearman

  Data Nominal ? Tahun 1900 Pearson chi- squared statistic

  Karl Pearson

   A contingency table is a two-way table showing the contingency between two variables where the variables have been classified into mutually exclusive categories and the cell entries are frequencies.

  

Uji Kebebasan Khi - Kuadrat

• Mengukur asosiasi antara dua peubah.

• Korelasi Pearson and Spearman tidak dapat diterapkan pada data degan skala pengukuran nominal

• • Khi-kuadrat digunakan untuk data nominal dalam

  tabel kontingensi

  

Statistik Uji (pearson chi-squared &

likelihood chi squared)

• Pearson statistic X2 is a score statistic. (This means that X2 is based on a covariance

  matrix for the counts that is estimated under H0.)

• The Pearson X2 and likelihood-ratio G2 provide separate test statistics, but they share many properties and usually provide the same conclusions.

• The convergence is quicker for X2 than G2.
• The chi-squared approximation is often poor for G2 when some expected frequencies are less than about 5.

  Menghitung Nilai Harapan Party Identification

  Independent

  Dem Republic Total

ocrat an

762 327 468

  Females 1577

  703,7 484 293 477 Males

  1200

Total 1246 566 945 2757

703,7

  2. 1940022/2757 =

  Ilustrasi: Data smoker-lung cancer

Lung Cancer Total

  Yes No Smoker 120 30 150 Non

  40

  50

  90 Smoker Total 160 80 240 Hipotesis

H : Tidak ada asosiasi antara kebiasaan merokok

dan penyakit kanker paru-paru H : Ada asosiasi antara kebiasaan merokok dan

  1

  penyakit kanker paru-paru

x

  

(120 50)

 

  5 

  Nilai Rasio Odds

x

  

(40 30)

  

Syntax SAS

Data aspirin;

  input smoking $ cancer $ frec ; cards; smoker yes 120 smoker no 30 non_smoker yes 40 non_smoker no 50 ;

  proc freq data=aspirin order=data;

  tables smoking*cancer/nopercent nocol norow expected; exact or chisq; weight frec;

  run;

  Output

  Mengubah posisi tabel kontingensi

Warning !!

  Lebih dari 20% cell dengan nilai Dua Solusi: harapan > 5, kita tidak bisa

  1. Menggabungkan kategori menggunakan Chi Square test

  2. Gunakan Exact Fisher test

  

Menggabungkan Kategori

  Daya Listik

  Total >300.000-

Penghasilan

  750.000 > 1.000.000-

  2.000.000 450 & 900 watt

  37

  11

  48 1300 & 3500 watt

  2

  10

  12 Total

  39

  21

  50 Uji Pasti Fisher ? Pertemuan Selanjutnya