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Metode N on- parametrik utk Data Survival

Metode N on- parametrik utk Data Survival. Taksiran Tabel Masa Hidup ( Life Table ) utk Fungsi Ketahanan. Untuk melihat ketahanan hidup dari sekumpulan individu yg merupakan sampel acak dr populasi . Perluasan dari frekuensi relatif utk data tersensor .

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Metode N on- parametrik utk Data Survival

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  1. Metode Non-parametrikutk Data Survival TaksiranTabelMasaHidup (Life Table) utkFungsiKetahanan • Untukmelihatketahananhidupdarisekumpulanindividuygmerupakansampelacakdrpopulasi. • Perluasandarifrekuensirelatifutk data tersensor. • Misal data waktuketahanankitabuatmenjadi k buah interval yakniI1, ..., Ik. I1 I2 Ij Ik ( ( ( ( ] ] ] ] 0 1 2 j-1 j k-1 k

  2. ni = #bertahanhidupmelewatiawal interval Ii di = #matipada interval Ii wi = #tersensorpada interval Ii pi = P(bertahanmelewati Ii | hiduppadaawal Ii) qi = 1  pi S(k) = P(T > k) I1 I2 Ii Ik ( ( ( ( ] ] ] ] 0 1 2 i-1 i k-1 k

  3. Taksiran Kaplan-Meier utkFungsiKetahanan • Misaladanindividudgnwaktuketahananhidupnyat1, t2, tndanadarindividu yang mati, dimanar ≤ n. Waktumeninggalnyadiurutkan • Misalnj = #individuygmasihhidupsesaatsebelumt(j)termasukygmeninggal pd t(j), j = 1,2,…,r • dj = #individuygmeninggal pd t(j) • P(mati pd [t(j)-, t(j)]) = dj/nj, dimanalebarselangwaktuygkecil • P(bertahanmelewati [t(j)-, t(j)]) = (nj -dj)/nj

  4. Utkt(k) ≤ t < t(k+1), dimanak = 1,2,…, r, taksiran Kaplan-Meier fungsiketahanan • dgnutkt < t(1)dant(r+1) = ∞ • Contoh: Data ttgwaktusampaiberhentinyapemakaian IUD dari 18 wanita (dlmminggu).

  5. Taksiran Kaplan-Meier drfungsiKetahanan

  6. SelangKepercayaanbagiNilaidariFungsiKetahanan • Selangkepercayaanadalahsuatuselang yang sedemikiansehinggaadapeluangtertentubhwnilaifungsiketahananygsebenarnyaterkandungdalamselangini. • Dgnasumsibahwaberdistribusi N(S(t),var{ }), dimana • Selangkepercayaan 100(1-)% bagiS(t), utkttertentuadalah

  7. MenaksirFungsiKetahanandengan SAS • data IUD; • input disctime status @@; • CARDS; • 10 1 13 0 18 0 19 1 23 0 30 1 36 1 38 0 54 0 • 56 0 59 1 75 1 93 1 97 1 104 0 107 1 107 0 107 0 • ; • PROCLIFETEST plots=(s); • time disctime*status(0); • RUN;

  8. Standard Number Number disctime Survival Failure Error Failed Left   0.000 1.0000 0 0 0 18 10.000 0.9444 0.0556 0.0540 1 17 13.000* . . . 1 16 18.000* . . . 1 15 19.000 0.8815 0.1185 0.0790 2 14 23.000* . . . 2 13 30.000 0.8137 0.1863 0.0978 3 12 36.000 0.7459 0.2541 0.1107 4 11 38.000* . . . 4 10 54.000* . . . 4 9 56.000* . . . 4 8 59.000 0.6526 0.3474 0.1303 5 7 75.000 0.5594 0.4406 0.1412 6 6 93.000 0.4662 0.5338 0.1452 7 5 97.000 0.3729 0.6271 0.1430 8 4 104.000* . . . 8 3 107.000 0.2486 0.7514 0.1392 9 2 107.000* . . . 9 1 107.000* . . . 9 0

  9. MenaksirFungsiKetahanandenganSplus/R • disctime <- c(10,13,18,19,23,30,36,38,54,56,59,75,93, • 97,104,107,107,107) • status <- c(1,0,0,1,0,1,1,0,0,0,1,1,1,1,0,1,0,0) • library(survival) • estS <- survfit(Surv(iud,status)~1,conf.type="plain") • plot(estS,conf.int=T,xlab="Discontinuation time (in weeks)", ylab="Estimated survivor function")

  10. time n.riskn.event survival std.err lower 95% CI upper 95% CI 10 18 1 0.944 0.0540 0.8386 1.000 19 15 1 0.881 0.0790 0.7267 1.000 30 13 1 0.814 0.0978 0.6220 1.000 36 12 1 0.746 0.1107 0.5290 0.963 59 8 1 0.653 0.1303 0.3972 0.908 75 7 1 0.559 0.1412 0.2827 0.836 93 6 1 0.466 0.1452 0.1816 0.751 97 5 1 0.373 0.1430 0.0927 0.653 107 3 1 0.249 0.1392 0.0000 0.522

  11. Taksiran Kaplan-Meier bagifungsiKetahanan

  12. Taksiran Kaplan-Meier bagiFungsiKegagalan • Cara pertamautkmenaksirfungsikegagalanpadawaktut(j) : • Taksirankegagalan pd selangt(j) ≤ t < t(j+1) : • adalahtaksiranlajukegagalan per satuanwaktudlmselang [t(j),t(j+1)).

  13. MenaksirFungsiKegagalanKumulatif • DenganH(t) = - log S(t), danjikaadalahtaksiran KM drfungsikegagalan, makaadalahtaksirankegagalankumulatifsampaiwaktut. • Karena , makataksirannya • yaknijumlahkumulatifdaritaksiranpeluangmatidariselangpertamasampaiselangke-k, k = 1,2,…,r.

  14. MenaksirFungsiKegagalandanFungsiKegagalanKumulatifMenggunakanSplus/R • esth <- hazard.km(estS) • esth • par(mfrow=c(2,1)) • plot(esth$time,esth$hitilde,type=“s”) • plot(esth$time,esth$hihat,type=“s”) • plot(esth$time,esth$Hhat,type="s”) • plot(esth$time,esth$Htilde,type="s”) • Function SPlus/R hazard.kmdapatdiperolehdari: • http://www.mth.pdx.edu/~mara/TK.R.functions.R.txt

  15. time nidihihathitildeHhatse.HhatHtildese.Htilde 10 18 1 0.0062 0.0556 0.0572 0.0572 0.0556 0.0556 19 15 1 0.0061 0.0667 0.1262 0.0896 0.1222 0.0868 30 13 1 0.0128 0.0769 0.2062 0.1202 0.1991 0.1160 36 12 1 0.0036 0.0833 0.2932 0.1484 0.2825 0.1428 59 8 1 0.0078 0.1250 0.4267 0.1997 0.4075 0.1898 75 7 1 0.0079 0.1429 0.5809 0.2524 0.5503 0.2375 93 6 1 0.0417 0.1667 0.7632 0.3115 0.7170 0.2902 97 5 1 0.0200 0.2000 0.9864 0.3834 0.9170 0.3524 107 3 1 NA 0.3333 1.3918 0.5601 1.2503 0.4851

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