Kuongorora Kupona muZviverengero
Kuongorora kupona ibazi rehuwandu hwehuwandu hunotarisa pakutevedzera nekuongorora nguva kusvika chiitiko chaitika. Chiitiko ichi chingave kufa kwemurwere, kudzoka kwechirwere, kutadza kwezvikamu zvemuchina, kudzingwa kwevatengi, kana nguva kusvika munhu ari kutsvaga basa awana basa. Chinhu chikuru chinobatsira pakuongorora kupona kupfuura mamwe matekiniki ehuwandu hwe ...
Mukutsvaga kwezvokurapa, ongororo yekupona inowanzo shandiswa kuenzanisa kushanda kwemishonga zvichibva panguva yekupona; muinjiniya, kufungidzira hupenyu hwezvikamu; uye mubhizinesi, kufanotaura kuchengetedza kwevatengi. Nekubatanidza pfungwa dzezvingangoitika, kufungidzira kusingaenzaniswi, uye mamodheru ekudzoka, ongororo yekupona inova chishandiso chakakosha mukuita sarudzo dzinotungamirirwa nedata.
Pfungwa huru: nguva yechiitiko uye kuvharwa kwemhosva
Pakati pekuongorora kupona pane shanduko isina kurongeka \(T\) inomiririra nguva kusvika chiitiko chaitika. Semuenzaniso, \(T\) inogona kunge iri nhamba yemazuva mushure mekurapwa kusvika murwere adzokera kuchirwere. Zvisinei, vaongorori havawanzo cherechedza \(T\) yese. Kune nzira dzakasiyana siyana dzekudzora chirwere:
1. Kuongororwa kwakarurama: Izvi zvinowanzoitika, semuenzaniso, kana murwere asina kusangana nechiitiko pakupera kwechidzidzo, kana murwere paanosiya chidzidzo. Tinongoziva chete kuti \(T\) yakakura kupfuura nguva yekupedzisira yakaonekwa.
2. Kuongororwa kweruboshwe (kuongorora kweruboshwe): Chiitiko ichi chakaitika kusati kwatanga kuonekwa, asi nguva chaiyo haizivikanwe.
3. Nguva yekuongorora: Chiitiko ichi chinozivikanwa kuti chakaitika pakati penguva mbiri dzekutarisa (semuenzaniso, murwere anoongororwa mwedzi wega wega uye chiitiko ichi chinozivikanwa kuti chakaitika pakati pemwedzi wechipiri newechitatu).
Nzira zhinji dzakakurumbira (dzakadai seKaplan-Meier neCox models) dzinonyanya kutarisa nyaya yekudzivirira kodzero.
Mabasa ekurarama uye njodzi
Kuongorora kupona kunoshandisa mabasa maviri makuru:
1) Basa rekupona
Basa rekurarama rinotsanangurwa se:
\[
S(t) = P(T > t)
\]
Kureva kuti, \(S(t)\) mukana wekuti munhu/chinhu chirarame nguva yadarika \(t\). Semuenzaniso, \(S(12)=0{,}80\) zvinogona kududzirwa zvichireva kuti 80% yevanhu vanotarisirwa kunge vasina kusangana nechiitiko ichi panosvika mwedzi gumi nemiviri.
2) Basa renjodzi
Basa renjodzi (risk rate) rinotsanangura njodzi yechiitiko "ikozvino" chero bedzi munhu wacho akapona kusvika panguva iyoyo:
\[
h(t) = \lim_{\Delta t \to 0} \frac{P(t \le T < t+\Delta t \mid T \ge t)}{\Delta t} \] Njodzi haisi mukana, asi chiyero. Munyaya yekurapa, njodzi yakakura inoreva njodzi yakakura yekusangana nechiitiko panguva iyoyo kune vanhu vari kurarama. Pfungwa idzi mbiri dzakabatana ne: \[ S(t)=\exp\left(-\int_0^th(u)\,du\right) \] Hukama uhwu hwakakosha nekuti mamwe mamodheru anotarisa panjodzi uye obva aderedza kupona, kana zvinopesana. Kufungidzira kusiri kweparametric: Kaplan–Meier Imwe yenzira dzinozivikanwa zvikuru mukuongorora kupona iKaplan–Meier estimator, inova kufungidzira kusiri kweparametric kwebasa rekurarama pasina kufunga nezvekugoverwa kwakatarwa. Iyi estimator inogadzira curve yekupona sechibereko chemukana wekupona panguva yega yega yechiitiko. Mukufunga, Kaplan–Meier anoverenga: - panguva yega yega yechiitiko \(t_i\), - \(d_i\) = nhamba yezviitiko pa \(t_i\), - \(n_i\) = nhamba yevanhu "vari panjodzi" nguva pfupi yapfuura \(t_i\), wobva: \[ \hat{S}(t) = \prod_{t_i \le t}\left(1 - \frac{d_i}{n_i}\right) \] Zvakanakira zveKaplan–Meier ndeizvi: - zviri nyore kududzira kuburikidza nema-survival curves, - anogona kubata right censoring, - anobatsira pakutsvaga data uye kuenzanisa mapoka. Zvisinei, Kaplan–Meier inonyanya kutsanangura. Kuti uedze kana ma-survival curves maviri akasiyana zvakanyanya, log-rank test ndiyo inowanzo shandiswa. Kuenzanisa kweboka: bvunzo yelog-rank Bvunzo yelog-rank inoshandiswa kuyedza fungidziro yekuti pane musiyano here mukupona pakati pemapoka maviri (kana anopfuura), semuenzaniso boka rekurapa A vs boka rekurapa B. Bvunzo iyi inoenzanisa huwandu hwezviitiko "zvakaonekwa" nenhamba "inotarisirwa" panguva yega yega yechiitiko, tichifunga nezvehuwandu hwevanhu vachiri panjodzi.
Log-rank inoshanda kana musiyano wengozi unofungidzirwa pakati pemapoka ukaramba uripo nekufamba kwenguva. Kana njodzi dzikayambuka, dudziro yacho inova yakaoma uye mimwe miedzo inogona kufungwa nezvayo. Regression model: Cox Proportional Hazards Kana vaongorori vachida kusanganisira covariates dzakawanda (zera, bonde, biomarker, rudzi rwekurapa, nezvimwewo), nzira inowanzo shandiswa ndiyo Cox Proportional Hazards Model. Cox model inoratidza njodzi yega yega ne covariate \(X\) se: \[ h(t \mid X) = h_0(t)\exp(\beta^\top X) \] apo: - \(h_0(t)\) ndiyo baseline hazard (hapana chikonzero chekutsanangura chimiro chayo), - \(\beta\) ndiyo parameter inofanirwa kufungidzirwa. Dudziro huru yeCox ndeye kuburikidza nechiyero chengozi (HR): \[ HR = \exp(\beta) \] Kana \(HR = 1{,}5\), boka rine covariate yakati rine njodzi ka1,5 (50% yakakwira) kupfuura boka rekutarisa, tichifunga kuti mamwe ma covariate anogara aripo. Zvakanakira zveCox model: - inochinjika nekuti haidi fomu rekugovera rakakosha re \(h_0(t))\), - inogona kusanganisira ma covariates akawanda, - kududzira kuburikidza nechiyero chengozi kuri nyore. Dambudziko guru reCox model nderekufungidzira kwengozi dzinoenderana, kureva kuti, chiyero chenjodzi pakati pemapoka chinofungidzirwa kuti chinogara kwenguva refu. Kufungidzira uku kunogona kuongororwa kuburikidza ne: - magirafu e log(-log(S(t))) pakati pemapoka, - Schoenfeld residuals, - nzira ye covariates inoshanduka nguva kana fungidziro ikasazadzikiswa. Mamodheru eParametric: Exponential, Weibull, nedzimwe Kusiyana neCox yesemiparametric, mamodheru eparametric anofunga fomu rakati rekugovera kwenguva yekupona, semuenzaniso: - Exponential: njodzi inogara iripo nekufamba kwenguva, - Weibull: njodzi inogona kuwedzera kana kuderera, - Log-normal uye Log-logistic: inobatsira kune mapatani enjodzi asiri emonotonic. Mamodheru eParametric anobudirira mu: - kufanotaura kwenguva refu, - kufungidzira huwandu hwakadai sehupenyu hwepakati (kana hwatsanangurwa), - kushanda zvakanaka kana fungidziro dzekugovera dzakarurama. Zvisinei, kana fungidziro dzekugovera dzisiri dzechokwadi, mhedzisiro inogona kunge yakarerekera. Nokudaro, sarudzo yemodheru inofanirwa kufunga nezvekuongorora, AIC/BIC, uye kukodzera kwecurve.
Mashandisirwo anoshanda muminda yakasiyana-siyana 1. Hutano nezvirwere: nguva yekufa, kudzoka kwegomarara, nguva yekupora kana kudzokera shure, kuongororwa kwekurapwa. 2. Unyanzvi nekuvimbika: nguva yekutadza kwezvikamu, kuongorora waranti, kuronga kuchengetedza. 3. Bhizinesi nekushambadzira: nguva yekuchinja kwevatengi, nguva yekutengazve, kuchengetedza vashandisi veapplication. 4. Zvemagariro nehupfumi: nguva yekushaya basa, nguva yekuroorana, nguva yekudzidza kusvika wapedza kudzidza. Neruzivo rwakakodzera, kuongorora kupona kunobatsira masangano kunzwisisa mashandiro esimba resisisitimu uye zvinhu zvinokurumidzisa kana kunonoka kuitika kwezviitiko. Pfungwa dzakakosha mukuita kwekuongorora kupona Zvinhu zvakawanda zvinofanirwa kutariswa kuti zviongororwe zvakajeka uye zvakavimbika: - Tsanangura chiitiko zvakajeka: semuenzaniso, "kukundikana" kunofanira kunge kwakafanana (kunosanganisira kukuvara kudiki here?). - Sarudza nguva yakabva: semuenzaniso, kubva pakuongororwa, kubva pakutanga kwekurapwa, kana kubva pakuiswa kwezvikamu. - Kuongorora hakufanirwe kunge kusingape ruzivo: zvakanaka, mukana wekuongororwa hausi wengozi yechiitiko mushure mekudzora macovariates. Kana kuongorora kuchipa ruzivo, nzira yakakosha inodiwa. - Hunhu hwedata uye kutevera: kurasikirwa kwedata rekutevera kunogona kukanganisa mhedziso. - Kuongorora mhando: tarisa fungidziro yengozi dzinoenderana neCox kana kuti kugoverwa kwakakodzera kwemamodeli eparametric. Mhedziso Kuongorora kupona inzira ine simba yekuverenga nguva yechiitiko, kunyanya kana data riine kuvharwa. Uchishandisa maturusi akadai sebvunzo yeKaplan-Meier, bvunzo yelog-rank, muenzaniso wengozi dzinoenderana neCox, uye mamodeli eparametric, vaongorori vanogona kufungidzira mikana yekupona, kuenzanisa mapoka, uye kuongorora pesvedzero yecovariates panjodzi yechiitiko. Kunzwisisa pfungwa dzekupona nenjodzi, pamwe nekufungisisa zvakanyatsonaka kwefungidziro dzemuenzaniso uye mhando yedata, ndizvo zvakakosha pakuona mhedzisiro yekuongorora kupona yakavimbika inobatsira pakuita sarudzo muminda yakasiyana-siyana. Kana uchida, ndinogona kupa vhezheni yedzidzo yechinyorwa chino (nemareferensi), kana kusanganisira mienzaniso yekuverenga nemifananidzo yeKaplan-Meier curves uye kududzirwa kwehuwandu hwengozi.
