Ocenjevanje in primerjava krivulj čistega preživetja

Pavlič, Klemen (author), Pohar Perme, Maja (mentor)

Namen dela Analiza relativnega preživetja je podpodročje analize preživetja, ki se ukvarja s sotveganji, ko razlog smrti ni znan ali ni zanesljiv. Najpogosteje se uporablja pri analizi preživetja bolnikov z rakom. Obstaja več mer, ki jih lahko poročamo. Pri ocenjevanju teh mer manjkajočo informacijo o razlogu smrti nadomestimo z informacijo o tveganju za smrt iz drugih vzrokov, ki jo dobimo iz populacijskih tabel umrljivosti. Znotraj področja analize relativnega preživetja se pogosto poroča mera imenovana čisto preživetje. Ta po definiciji ni odvisna od tveganja za smrt iz drugih vzrokov, vendar pa njena definicija temelji na predpostavkah, ki jih ne moremo testirati na podatkih. Uporaba te mere je zato vprašljiva. To delo ima tri glavne cilje. Prvi je definirati novo mero, ki ne bo temeljila na nepreverljivih predpostavkah, ki so potrebne za definicijo čistega preživetja, in raziskati povezavo med novo mero in čistim preživetjem. Drugi cilj je predlagati cenilki za novo mero in njeno varianco ter raziskati njune lastnosti. Zadnji cilj je raziskati in primerjati metode za primerjavo krivulj čistega preživetja. Hipoteze Nova mera, ki je definirana v tem delu, temelji na manj predpostavkah kot čisto preživetje. Kot taka nudi alternativo čistemu preživetju z nesporno interpretacijo. Predlagana cenilka je enostavno razumljiva, saj izhaja neposredno iz definicije mere, prav tako pa omogoča enostavno implementacijo mere v različne programske pakete. Nudi tudi razširitev na podatke z diskretno merjenim časom in ima željene lastnosti. Test oblike log-rank je primerljiv s testom koeficienta iz aditivnega regresijskega modela. Odzivata se na iste alternativne hipoteze. Metode Lastnosti nove mere, njene cenilke in metode za primerjavo krivulj čistega preživetja bomo raziskali teoretično in s simulacijami ter jih ilustrirali na pravih podatkih. Vlekli bomo vzporednice z znanimi rezultati iz analize preživetja. Za konstrukcijo nove cenilke bomo uporabili psevdo vrednosti, za konstrukcije cenilke njene variance pa si bomo pomagali z martingali in procesi štetja. Pri zadnjem delu bomo izhajali iz znane zveze med testom log-rank in testom koeficienta iz Coxovega modela. Rezultati Predlagana cenilka nove mere daje praktično identične rezultate kot cenilka PP za čisto preživetje. To kaže, da imata nova mera in čisto preživetje enake ocenjene vrednosti, razlika je le v interpretaciji. Pri tem ta pri novi meri temelji na manj predpostavkah. Predlagali smo dve cenilki za ocenjevanje variance nove cenilke. Prva je natančna in daje tudi pokritja, ki se ujemajo z nominalno vrednostjo, druga pa je aproksimativna in rahlo podceni varianco, a so razlike v primerih, ki jih lahko pričakujemo v praksi, minimalne. Novo cenilko smo razširili tudi na podatke z diskretno merjenim časom, kjer ima manjšo pristranskost kot cenilka PP, prav tako pa daje tudi pokritja, ki so bližje nominalni vrednosti. Test oblike log-rank in test koeficienta iz aditivnega regresijskega modela nista identična, vendar se obnašata podobno. Odzivata se na iste alternativne hipoteze in sta podobno neobčutljiva za nesorazmerna tveganja. Test oblike log-rank smo dodali v R paket relsurv.

• Language: Slovenian
• Keywords: relativno preživetje, čisto preživetje, psevdo vrednost, log-rank test, regresijski model
• Work type: Doctoral dissertation
• Organization: MF - Faculty of Medicine
• Year: 2018
• PID: 20.500.12556/RUL-100767
• COBISS.SI-ID: 33726681
• Publication date in RUL: 13.04.2018

Secondary language

• Language: English
• Title: Estimation and comparison of net survival curves

Abstract

Objectives Relative survival analyses is a subfield of survival analysis that deals with competing risks data where the cause of death information is unavailable or unreliable. It is typically used to investigate survival of cancer patients and several measures are estimated to achieve this. For all of them the population mortality tables are used as an external source of information that substitutes the missing cause of death information. Net survival measure is particularly popular, it does not depend on the hazard of dying from other causes by definition. However, the definition itself relies on assumptions that cannot be tested from the data and this makes the use of this measure questionable. The goal of this work is threefold. First, to propose a new measure that does not rely on these questionable assumptions and to investigate its association with net survival. Secondly, to provide a new approach to estimation of this measure and explore its properties. Thirdly, to investigate the methods for comparison of net survival between different groups and to compare them. Hypotheses The new measure presented in this work relies on fewer assumptions and has an interpretation that does not depend on them. It provides an alternative to the net survival measure. The estimation approach proposed in this work is simple to understand and easy to implement in different statistical packages. It allows extensions to discretely measured time and has desirable properties. The log-rank type test and the test of a coefficient from the additive regression model are comparable. They respond to the same alternatives. Methods The properties of the new measure, the new estimator and the comparison of methods for comparison of net survival curves between groups are analysed theoretically, by simulations and illustrated on real data. We try to draw parallels to classical survival whenever possible. We use pseudo observations to construct the estimator of the new measure. We use counting processes and martingales for the derivation of variance of the new estimation approach. In the last part, we build on the known association between the Cox model and log-rank test. Results Pseudo observations are used as estimators of individual quantities in the construction of the new estimator which is their first usage outside regression modelling. The proposed estimator of the new measure gives practically identical results as the PP estimator of net survival, the only difference being the interpretation where the new measure requires fewer assumptions. The estimators of the variance of the new estimator work well. The precise formula gives coverages close to the nominal level whereas the approximate formula slightly underestimates the variance. The new estimation approach works well with discretely measured time. It has smaller bias than the PP estimator and coverages closer to the nominal level. As such, it outperforms the PP estimator when used with wider intervals. The log-rank type test and the test of coefficient from the additive regression model are not identical but they behave in the same way. They both respond to the same alternatives and perform equally poorly against crossing hazard alternatives. We implemented the log-rank type test in the R package relsurv.

• Keywords: relative survival, net survival, pseudo observation, log-rank test, regression model