20.500.12556/RUL-185203 Ovrednotenje predpostavke proporcionalnih obetov v ordinalni regresiji Evaluation of the Proportional Odds Assumption in Ordinal Regression Ordinalne odzivne spremenljivke so vse bolj pogoste v klinični praksi, saj ponujajo več informacij kot dihotomni izidi. Odzivna spremenljivka pripada naravno urejenim kategorijam, kot so na primer stopnja bolečine ali stadij bolezni, pri čemer odzivov ni mogoče meriti na številski lestvici. Pri njihovem modeliranju se raziskovalci pogosto soočajo z izbiro med parsimončnimi in fleksibilnimi modeli. Parsimonični modeli temeljijo na manjšem številu parametrov, močnejših strukturnih predpostavkah in upoštevajo ordinalno strukturo podatkov. Fleksibilni modeli urejenost kategorij zanemarijo in tako omogočajo manj omejujoče modeliranje, vendar na račun večje kompleksnosti modela. Pomembna metodološka dilema pri ordinalni regresiji je predpostavka sorazmernih obetov (angl. proportional odds, PO), na kateri temelji kumulativni ordinalni regresijski model. V praksi je ta predpostavka pogosto vsaj delno kršena, kar postavlja vprašanje, ali je ordinalni model še vedno ustrezna izbira ali pa je bolj smiselna uporaba fleksibilnejšega modela, kot je multinomialni logistični model, ki ordinalnosti ne predpostavlja. Namen magistrske naloge je bil oceniti vpliv kršitev predpostavke PO na napovedno uspešnost modelov in opredeliti okoliščine, v katerih je uporaba kumulativnega ordinalnega modela še vedno smiselna. V magistrski nalogi smo primerjali kumulativni ordinalni regresijski model s predpostavko sorazmernih obetov in multinomialni logistični regresijski model kot njegovo alternativo. Modela smo primerjali na krajši simulacij in na realnih kliničnih podatkih kardiotokogramov. V simulaciji smo modela ovrednotili na različnih velikostih vzorcev (n = 200, 1000, 10000) za tri stopnje kršitve predpostavke PO (brez kršitve, šibka in močna kršitev). Napovedno uspešnost smo ocenili z uporabo srednje kvadratne napake napovedanih verjetnosti (RMSE), natančnostjo in kalibracijo napovedi. V študiji primera smo modela uporabili za napovedovanje ordinalne spremenljivke stanja ploda (normalno, sumljivo in patološko stanje). Modeliranje smo naredili na podlagi spremenljivk kardiotokografskih meritev. Za oba modela smo izvedli interno validacijo in analizo stabilnosti ocen. Z rezultati simulacije smo ugotovili, da kumulativni PO model v večini scenarijev dosega primerljivo ali boljšo napovedno uspešnost in natančnost kot multinomialni model, predvsem pri manjših vzorcih. Ob močni kršitvi predpostavke PO in velikih vzorcih multinomialni model doseže boljše rezultate. Rezultati so pokazali, da kršenje PO nima vpliva na kalibracijsko presečišče, ima pa vpliv na naklon, s katerim ugotovimo večjo stopnjo preprileganja pri multinomialnem modelu. V študiji primera večina spremenljivk ni izpolnjevala predpostavke PO. V kumulativni model so bile po metodi postopnega izključevanja glede na kriterij BIC najpogosteje izbrane spremenljivke, ki so predpostavko vsaj delno izpolnjevale, podobno pa je veljalo tudi za multinomialni model. Izbrane spremenljivke sovpadajo z dejavniki, ki se uporabljajo pri kliničnem razvrščanju stanja ploda. V študiji primera je multinomialni model dosegel boljšo napovedno uspešnost in natančnost, medtem ko je kumulativni PO model imel boljši kalibracijski naklon, zlasti pri napovedovanju patološkega izida. Z nalogo smo ugotovili, da je kumulativni PO model pogosto primerna izbira tudi ob zmernih kršitvah predpostavke PO za manjše in zmerno velike vzorce, saj ohranja dobro napovedno uspešnost ob večji interpretabilnosti in manjši kompleksnosti modela. Če pa imamo na voljo dovolj velike vzorce, potem ni omejitev za uporabo bolj fleksibilnega modela, pri čemer ostaja odprto vprašanje, kako veliki morajo biti za njihovo zanesljivo uporabo. Ordinal response variables are common in clinical practice, as they provide more information than binary outcomes. The response variable belongs to naturally ordered categories, such as pain severity or disease stage, where the responses cannot be measured on a numerical scale. When modeling these variables, researchers often face a choice between parsimonious and flexible models. Parsimonious models are based on a smaller number of parameters, stronger structural assumptions, and account for the ordinal structure of the data. Flexible models ignore the order of categories, allowing less restrictive modeling at the cost of increased model complexity. An important methodological dilemma in ordinal regression is the proportional odds (PO) assumption on which the cumulative ordinal regression model is based. In practice, this assumption is often at least partially violated, raising the question of whether an ordinal model remains appropriate or whether a more flexible alternative, such as the multinomial logistic model, should be preferred. The purpose of this master’s thesis was to assess the impact of PO assumption violations on model predictive performance and to determine under which conditions the cumulative ordinal model remains a suitable choice. The cumulative PO ordinal regression model was compared with the multinomial logistic regression model as a more flexible alternative. Model performance was evaluated through simulation studies as well as an application to real clinical cardiotocography data. In the simulation study, model performance was assessed across different sample sizes (n = 200, 1000, 10000) and three levels of PO assumption violation (none, mild, and severe). Predictive performance was evaluated using the root mean squared error (RMSE) of predicted probabilities, accuracy, and calibration of predictions. In the case study, both models were used to predict an ordinal fetal state (normal, suspect, and pathologic). Modeling was based on cardiotocographic measurement variables. For both models, internal validation and stability analyses were performed. Simulation results showed that the cumulative PO model achieved comparable or better predictive performance and accuracy in most scenarios, particularly for smaller sample sizes. Under strong violations of the PO assumption and large sample sizes, the multinomial model performed better. Calibration results indicated that PO violations did not affect the calibration intercept but influenced the calibration slope, with the multinomial model showing a higher tendency toward overfitting. In the case study, most predictors did not fully satisfy the PO assumption. Backward elimination based on the BIC criterion in the cumulative model primarily retained variables that at least partially satisfied the assumption, and a similar pattern was also observed for the multinomial model. The selected predictors aligned with factors commonly used in clinical fetal state classification. In the case study, the multinomial model achieved better predictive performance and accuracy, while the cumulative PO model showed a better calibration slope, particularly when predicting pathological outcomes. Overall, the results demonstrate that the cumulative PO model remains a valid and often preferable choice even under moderate violations of the PO assumption, as it preserves good predictive performance while offering improved interpretability and lower model complexity. If sufficiently large samples are available, there are no restrictions on using a more flexible model. However, the question of how large the samples need to be for reliable use remains open. ordinalna regresija kumulativni regresijski model multinomialni model sorazmerni obeti kardiotokografski podatki ordinal regression cumulative regression model multinomial model proportional odds cardiotocography data true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2026-07-28 12:05:21 2026-07-28 12:05:43 2026-07-29 04:03:38 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 63264 286234883 Gosnjak_Tanja_-_Ovrednotenje_predpostavke_proporcionalnih_obetov_v_ordinalni_regresiji.pdf Gosnjak_Tanja_-_Ovrednotenje_predpostavke_proporcionalnih_obetov_v_ordinalni_regresiji.pdf 1 6A0A54436B7877AE76E239B6E738B089 776cce63224d4d38b006e9052064197e97e8f4b30a60b0986994dfb0ccbbd281 a7c324b3-8a6b-11f1-9b0d-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=243509 Fakulteta za elektrotehniko 0 0 0