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Analisis Survival

Analisis Survival. Abdul Kudus, Ph.D. E-mail : akudus69@unisba.ac.id Blog : abdulkudus.staff.unisba.ac.id. Fungsi Ketahanan (Survivor). Misalkan waktu ketahanan T mempunyai fungsi distribusi peluang dengan fungsi densitas f ( t ) Fungsi distribusi kumulatif ( cdf ) bagi T , ditulis sbg

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Analisis Survival

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  1. Analisis Survival Abdul Kudus, Ph.D. E-mail : akudus69@unisba.ac.id Blog : abdulkudus.staff.unisba.ac.id

  2. FungsiKetahanan (Survivor) • MisalkanwaktuketahananTmempunyaifungsidistribusipeluangdenganfungsidensitasf(t) • Fungsidistribusikumulatif(cdf) bagiT, ditulissbg • menyatakanpeluangwaktuketahananhidupbernilailebihkecildarit • FungsiketahanandariT, • S(t) = P(T ≥ t) = 1 − F(t) • menyatakanpeluangindividubertahanmelebihiwaktut: yakni, S(t) adalahpeluangbhwvariabelacakTmelebihit.

  3. S(t) teoritis • dlmpraktik

  4. FungsiKegagalan (Hazard) • Fungsikegagalanh(t) menyatakanlajukegagalansesaatpadawaktutdengansyaratbhwindividutsbmampubertahaansampait. • P(t ≤T<t+t|T≥t) = P(individu ‘gagal’ dlm interval [t,t+t ] | mampubertahansampait) • Fungsikegagalan ≡ lajukegagalanbersyarat • Peluang per satuanwaktu, laju: 0 sampai ∞

  5. Untuknilaittertentu, fungsikegagalanh(t) mempunyaisifatsbb: • selalutaknegatif, yaknisamaataulebihbesardari nol. • tidakpunyabatasatas.

  6. HubunganS(t) danh(t) • Ambil limit daritmenujunol

  7. FungsiKegagalanKumulatif • Perhatikanbhw • Akibatnya, S(t) = exp[-H(t)], dimana • adalahkegagalankumulatif

  8. BeberapaDistribusiParametrikutkWaktuKetahanan • Exponential() • FungsiDensitas  = 0.5  = 1.0  = 1.5

  9. 1. Weibull(,) (Pal, et al. (2006) • 2. Weibull(,) (Collett, 2003) • kegagalanmeningkatutk > 1 • kegagalanmenurunutk < 1 • HubunganantaraWeibullke-1 danke-2

  10. Statistik Deskriptif

  11. Menyusun Data utk Memahami Analisis

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