Tabel Kontingensi 2x2 (3)

Transkripsi

1 Tabel Kontingensi 2x2 (3) Rasio Odds dan Uji Kebebasan Khi- Kuadrat Rasio ODDS It occurs as a parameter in the most important type of model for categorical data Odds Sukses odds = π ( 1 π ) Odds bernilai positif Nilai odss lebih besar dari satu, saat sukses lebih dipilih dibandingkan gagal odds = 4.0, a success is four times as likely as a failure 2 1

2 Rasio Odds Pada Tabel 2x2 A1 A2 B1 π 1 1-π π 1 1 odds1 = ( 1 π1) B2 π 2 1-π π 2 2 odds2 = ( 1 π ) 2 Rasio Odds Values of θ farther from 1.0 in a given direction represent stronger association. 3 Properties of OR The odds ratio does not change value when the 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. 4 2

3 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, 5 Ilustasi: kasus aspirin dan serangan jantung odds odds n = = = n n = = = n OR Odds This also equals the cross-product ratio (189 10, 933)/(10, ) = θ = = = Odds The estimated odds were 83% higher for the placebo group. 6 3

4 Inferensia Rasio Odds dan Log Rasio Odds Kecuali pada ukuran sampel sangat besar, sebaran percontohan dari OR sangat menceng (highly hl skewed). Karena kemiringan ini, statistika inferensia untuk rasio odds menggunakan alternatif dengan ukuran yang setara - logaritma natural, log (θ). Dengan log (θ)=0. Artinya θ =1 setara dengan log (θ) dari 0. 7 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(0.5) = 0.7, kedua nilai i ini i mewakili kekuatan k asosiasi i yang sama Doubling a log odds ratio corresponds to squaring an odds ratio. Sebaran dari log(θ) tidak terlalu menceng, menyerupai bentuk lonceng Sebaran log (θ) mendekati sebaran normal dengan nilai tengah log(θ) dan galat baku The SE decreases as the cell counts increase. 8 4

5 Selang Kepercayaan untuk log(θ) log ˆ θ ± Z SE Ilustrasi: data aspirin log(1.832) = α 2 ( ) Galat baku = SK 95% untuk log (θ) ± 1.96(0.123) (0.365, 0.846) SK 95% untuk θ [exp(0.365), exp(0.846)] = (e 0.365, e ) = (1.44, 2.33) karena θ tidak mengandung 1, kemungkinan serangan jantung berbeda untuk kedua kelompok. 9 Kita menduga bahwa odds serangan jantung setidaknya 44% lebih tinggi pada subjek yang mengkonsumsi placebo dibandingkan dengan subjek yang mengkonsumsi aspirin 10 5

6 Catatan Bila terdapat nilai n ij =0, maka perhitungan OR d l adalah 11 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. 12 6

7 Rasio Odds pada studi case-control Table 2.4 refers to a study that investigated the relationship between smoking and myocardial infarction. to 262 young and middle-aged women (age < 69) admitted to 30 coronary care units in northern Italy with acute MI during a 5-year period The first column refers. Each case was matched with two control patients admitted to the same hospitals with other acute disorders. The controls fall in the second 13 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. 14 7

8 penjelas Peubah respon Tidak bisa menghitung proporsi penderita MI pada kelompok smoker (atau non-smoker) Peubah When the sampling design is Karena untuk setiap retrospective, we can construct penderita MI kita pasangkan dengan 2 orang kontrol conditional distributions for the explanatory variable, within levels of the fixed response. Untuk wanita penderita MI, proporsi yang merupakan perokok sebesalr172/262 = 0.656, Sedangkan untuk wanita bukan penderita MI, proporsi perokok sebesar 173/519 = In Table 2.4, the sample odds ratio is [0.656/( )]/[0.333/( )] = ( )/(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 16 8

9 Types of Observational study Tugas!! Cari tahu macam2 tipe studi observasi beserta penjelasan dan contohnya!! 17 Bagaimana mengukur keeratan hubungan 2 peubah?? Korelasi Hubungan linear Data Nominal? pearson spearman 18 9

10 Tahun 1900 Karl Pearson Pearson chisquared statistic 19 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 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. 10

11 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. When H0 is true and the expected frequencies are large, the two statistics have the same 22 chi-squared distribution, and their numerical values are similar. 11

12 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 Menghitung Nilai Harapan Dem ocrat Party Identification Independent Republic an Total Females ,7 Males Total *1577= /2757 = 703,7 12

13 25 Ilustrasi: Data smoker-lung cancer Lung Cancer Total Yes No Smoker Non Smoker Total

14 Hipotesis H 0 : Tidak ada asosiasi antara kebiasaan merokok dan penyakit kanker paru-paru H 1 : Ada asosiasi antara kebiasaan merokok dan penyakit kanker paru-paru Nilai Rasio Odds (120x50) θ = = 5 (40x30) 27 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; 28 14

15 Output

16 31 Mengubah posisi tabel kontingensi 32 16

17 33 Warning!! Lebih dari 20% cell dengan nilai harapan > 5, kita tidak bisa menggunakan Chi Square test Dua Solusi: 1. Menggabungkan kategori 2. Gunakan Exact Fisher test 17

18 Menggabungkan Kategori Daya Listik Penghasilan Total > > & 900 watt & 3500 watt Total Uji Pasti Fisher? Pertemuan Selanjutnya 36 18