Bayesovo prostorsko glajenje – lastnosti in uporaba na podatkih Registra raka RS

Korat, Sara (author), Zadnik, Vesna (mentor), Pohar Perme, Maja (comentor)

Pri raziskovanju pojavnosti, razširjenosti, tveganja in umrljivosti bolezni se podatki velikokrat prikazujejo na zemljevidih, razdeljenih glede na določeno geografsko enoto (npr. naselje, občina, upravna enota, statistična regija, mreža kvadratov premera 1km). Glede na vrednost kazalnika se lahko enote med sabo primerjajo in s tem nakazujejo na morebitna “žarišča” pojava bolezni. Določitev npr. tveganj določene bolezni je še posebej na majhnih geografskih enotah lahko problematična, saj je potrebno upoštevati prostorsko avtokorelacijo (opažanja na lokacijah, ki so blizu druga drugi, so si bolj podobna) in vzorčno variabilnost (do razlik med območji lahko pride zaradi majhne populacije ali heterogenosti posameznikov znotraj območij). Modelov t.i. prostorskega glajenja, ki zmanjšujejo predvsem ekstremne odklone in upoštevajo prostorsko avtokorelacijo in vzorčno variabilnost, je veliko. V magistrski nalogi smo uporabili model BYM s CAR porazdelitvijo za prostorsko komponento. Prvi način, s katerim lahko izračunamo glajene vrednosti relativnih tveganj so uveljavljene MCMC metode z uporabo Gibbsovega vzorčevalnika, drugi pristop pa je z aproksimativno metodo INLA. Gibbs za izračune porabi veliko časa, ker pa je INLA aproksimativna metoda, so izračuni glajenih vrednosti veliko hitrejši. Prostorsko glajenje smo najprej izvedli na realnih podatkih Registra raka Republike Slovenije za število novih primerov raka v obdobju od leta 2006 do 2015 po občinah, kjer smo opazovali pojav raka na dojkah pri ženskah do vključno 49. leta starosti. V nekaterih primerih smo poleg podatkov o sosednjih občinah, v model vključili tudi kovariato slovenske različice kazalnika primanjkljaja. Slovenske občine imajo zelo različno število prebivalcev in posledično se število rakov neenakomerno razporeja po njih. V občinah z majhno populacijo je variabilnost kazalnika velika izključno zaradi majhnega števila primerov, zato je v praksi takšne podatke potrebno prostorsko gladiti. V drugem delu naloge smo primerjavo obeh pristopov naredili tudi na generiranih podatkih, s čimer smo poskušali splošneje odgovoriti na vprašanja, kako se metodi obnašata v različnih situacijah. Na podatkih in simulacijah smo sicer kje lahko opazili minimalne razlike med metodama, vendar za splošen nasvet, kdaj uporabiti katero metodo, bi raziskovanje bilo potrebno nadaljevati.

• Language: Slovenian
• Keywords: Integrirana gnezdena Laplace-ova aproksimacija, Gibbsov vzorčevalnik, metode Monte Carlo Markovske verige, pogojna avtoregresivna porazdelitev, Besag-York-Mollié model, prostorsko glajenje, simulacije, kazalnik primanjkljaja
• Work type: Master's thesis/paper
• Organization: FE - Faculty of Electrical Engineering
• Year: 2020
• PID: 20.500.12556/RUL-119210
• Publication date in RUL: 04.09.2020

Secondary language

• Language: English
• Title: Bayesian spatial smoothing - properties and application to the Slovenian Cancer Registry data

Abstract

When researching the incidence, prevalence, risk and mortality of diseases, we often present the data on maps, divided by a specific geographical unit (e.g. settlement, municipality, administrative unit, statistical region, a grid of squares with a diameter of 1 km). The geographical units can be compared between themselves based on the value of an indicator and thus indicate possible "hotspots" of the disease. Determining, for example, the risk of a particular disease can be problematic, especially on small geographical units, as spatial autocorrelation (observations on geographically closer regions are more alike) and sample variability (the difference can come from the small population or the heterogeneity of the individuals) have to be accounted for. There is an abundance of the so-called spatial smoothing models, which mainly reduce extreme deviations, and take into account spatial autocorrelation and sample variability. In the Master's thesis, we have used the BYM model with the CAR distribution for the spatial component. One approach to calculating the smoothed values of relative risk is with the established MCMC methods, using the Gibbs sampler, whereas the other is to use the approximative method INLA. When using the Gibbs sampler to calculate smoothed values, the calculations take a long time, unlike when using INLA, as INLA is an approximative method. Spatial smoothing was first performed on the real number of new cancer cases in the period from 2006 to 2015 by municipalities, obtained from the Cancer Registry of Republic of Slovenia, where we observed the occurrence of breast cancer among women up to including 49 years old. In some cases, we have, additionally to the neighbourhood data, also included the Slovenian version of the deprivation index as a covariate. Slovenian municipalities highly vary in the number of inhabitants, therefore the number of cancer cases is unevenly distributed among them. In municipalities with a small population, the variability of the indicator is high solely due to the small number of cases, therefore in practice, such data needs to be spatially smoothed. In the second part of the thesis, we have made a comparison of both methods on generated data, trying to generally answer the question of how the methods behave in different situations. When using the methods on real and generated data, we were able to observe minimal differences between them. However, for some general advice on when to use which, additional research is required.

• Keywords: Integrated nested Laplace approximation, Gibbs sampling, Markov Chain Monte Carlo methods, conditional autoregressive distribution, Besag-York-Mollié model, spatial smoothing, simulations, deprivation index