京都大学 / 新制・課程博士 / 博士(医学) / 甲第24494号 / 医博第4936号 / 新制||医||1063(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 村川 泰裕, 教授 小杉 眞司, 教授 松田 文彦 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM

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The advancement in data acquiring technology continues to see survival data sets with many covariates. This has posed a new challenge for researchers in identifying important covariates for inference and prediction for a time-to-event response variable. In this dissertation, common Cox proportional hazards model selection techniques and a random survival forest technique were compared using five performance criteria measures. These performance measures were concordance index, integrated area under the curve, and , and R2 . To carry out this exercise, a multicentre clinical trial data set was used. A simulation study was also implemented for this comparison. To develop a Cox proportional model, a training dataset of 75% of the observations was used and the model selection techniques were implemented to select covariates. Full Cox PH models containing all covariates were also incorporated for analysis for both the clinical trial data set and simulations. The clinical trial data set showed that the full model and forward selection technique performed better with the performance metrics employed, though they do not reduce the complexity of the model as much as the Lasso technique does. The simulation studies also showed that the full model performed better than the other techniques, with the Lasso technique overpenalising the model from the simulation with the smaller data set and many covariates. AIC and BIC were less effective in computation than the rest of the variable selection techniques, but effectively reduced model complexity than their counterparts for the simulations. The integrated area under the curve was the performance metric of choice for choosing the final model for analysis on the real data set. This performance metric gave more efficient outcomes unlike the other metrics on all selection techniques. This dissertation hence showed that variable selection techniques differ according to the study design of the research as well as the performance measure used. Hence, to have a good model, it is important to not use a model selection technique in isolation. There is therefore need for further research and publish techniques that work generally well for different study designs to make the process shorter for most researchers.

In terms of pricing financial derivatives, contractual length plays a important role in pricing risk. A contract with long duration will have more associated risk in comparison with a contract with low duration, everything else equal. In this thesis work we examine whether information about the derivative contract and involved parties (the counterparty) could be used in a model to accurately predict both probability and time if the contract would terminate earlier than the predetermined contractual length. By modelling the termination time with deep neural networks and assuming the probability distribution of termination time directly, we find that it is possible to predict when early termination of derivative contracts would occur significantly more accurate than assuming that contracts will always live to their original maturity date. / För prissättningen av finansiella derivat har kontraktets längd stor roll i värderingen av risken. Ett kontrakt som sträcker sig över lång tid har mer associerad risk i jämförelse med ett kontrakt som sträcker sig över kort tid, under förutsättningen av att kontraktet i övrigt är detsamma. I detta examensarbete undersöker vi om information om derivaten och kontraktets parter (motparten) kan användas för att med kunna förutspå sannolikheten för att ett kontrakt stängs ner tidigt samt vad den verkliga tidslängden är om så är fallet. Genom att modellera tidpunkten för avslut med hjälp av neurala nätverk och genom att anta sannolikhetsfördelningen för tidpunkten för avslut, fann vi att det är möjligt att förutspå tidpunkten för tidigt avslut signifikant bättre i jämförelse mot att anta att kontraktet alltid lever till dess ursprungliga livslängd.

The goal of this research is to expand the field of conformal predictions using Random Survival Forests. The standard Conformal Random Survival Forest can predict with a fixed certainty whether something will survive up until a certain time point. This research is the first to show that there is little practical use in the standard Conformal Random Survival Forest algorithm. It turns out that the confidence guarantees of the conformal prediction framework are violated if the Standard algorithm makes predictions for a user-controlled fixed time point. To solve this challenge, this thesis proposes two algorithms that specialize in conformal predictions for a fixed point in time: a Fixed Time algorithm and a Hybrid algorithm. Both algorithms transform the survival data that is used by the split evaluation metric in the Random Survival Forest algorithm. The algorithms are evaluated and compared along six different set prediction evaluation criteria. The prediction performance of the Hybrid algorithm outperforms the prediction performance of the Fixed Time algorithm in most cases. Furthermore, the Hybrid algorithm is more stable than the Fixed Time algorithm when the predicting job extends to various time points. The hybrid Conformal Random Survival Forest should thus be considered by anyone who wants to make conformal survival predictions at usercontrolled time points. / Målet med denna avhandling är att utöka området för konformitetsprediktion med hjälp av Random Survival Forests. Standardutförandet av Conformal Random Survival Forest kan förutsäga med en viss säkerhet om någonting kommer att överleva fram till en viss tidpunkt. Denna avhandling är den första som visar att det finns liten praktisk användning i standardutförandet av Conformal Random Survival Forest-algoritmen. Det visar sig att konfidensgarantierna för konformitetsprediktionsramverket bryts om standardalgoritmen gör förutsägelser för en användarstyrd fast tidpunkt. För att lösa denna utmaning, föreslår denna avhandling två algoritmer som specialiserar sig i konformitetsprediktion för en bestämd tidpunkt: en fast-tids algoritm och en hybridalgoritm. Båda algoritmerna omvandlar den överlevnadsdata som används av den delade utvärderingsmetoden i Random Survival Forest-algoritmen. Uppskattningsförmågan för hybridalgoritmen överträffar den för fast-tids algoritmen i de flesta fall. Dessutom är hybrid algoritmen stabilare än fast-tids algoritmen när det förutsägelsejobbet sträcker sig till olika tidpunkter. Hybridalgoritmen för Conformal Random Survival Forest bör därför föredras av den som vill göra konformitetsprediktion av överlevnad vid användarstyrda tidpunkter.

Design and analysis of computer experiments is an area focusing on efficient data collection (e.g., space-filling designs), surrogate modeling (e.g., Gaussian process models), and uncertainty quantification. Survival analysis focuses on modeling the period of time until a certain event happens. Data collection, prediction, and uncertainty quantification are also fundamental in survival models. In this dissertation, the proposed methods are motivated by a wide range of real world applications, including high-performance computing (HPC) variability data, jet engine reliability data, Titan GPU lifetime data, and pine tree survival data. This dissertation is to explore interfaces on computer experiments and survival analysis with the above applications. Chapter 1 provides a general introduction to computer experiments and survival analysis. Chapter 2 focuses on the HPC variability management application. We investigate the applicability of space-filling designs and statistical surrogates in the HPC variability management setting, in terms of design efficiency, prediction accuracy, and scalability. A comprehensive comparison of the design strategies and predictive methods is conducted to study the combinations' performance in prediction accuracy. Chapter 3 focuses on the reliability prediction application. With the availability of multi-channel sensor data, a single degradation index is needed to be compatible with most existing models. We propose a flexible framework with multi-sensory data to model the nonlinear relationship between sensors and the degradation process. We also involve the automatic variable selection to exclude sensors that have no effect on the underlying degradation process. Chapter 4 investigates inference approaches for spatial survival analysis under the Bayesian framework. The Markov chain Monte Carlo (MCMC) approaches and variational inferences performance are studied for two survival models, the cumulative exposure model and the proportional hazard (PH) model. The Titan GPU data and pine tree survival data are used to illustrate the capability of variational inference on spatial survival models. Chapter 5 provides some general conclusions. / Doctor of Philosophy / This dissertation focus on three projects related to computer experiments and survival analysis. Design and analysis of the computer experiment is an area focusing on efficient data collection, building predictive models, and uncertainty quantification. Survival analysis focuses on modeling the period of time until a certain event happens. Data collection, prediction, and uncertainty quantification are also fundamental in survival models. Thus, this dissertation aims to explore interfaces between computer experiments and survival analysis with real world applications. High performance computing systems aggregate a large number of computers to achieve high computing speed. The first project investigates the applicability of space-filling designs and statistical predictive models in the HPC variability management setting, in terms of design efficiency, prediction accuracy, and scalability. A comprehensive comparison of the design strategies and predictive methods is conducted to study the combinations' performance in prediction accuracy. The second project focuses on building a degradation index that describes the product's underlying degradation process. With the availability of multi-channel sensor data, a single degradation index is needed to be compatible with most existing models. We propose a flexible framework with multi-sensory data to model the nonlinear relationship between sensors and the degradation process. We also involve the automatic variable selection to exclude sensors that have no effect on the underlying degradation process. The spatial survival data are often observed when the survival data are collected over a spatial region. The third project studies inference approaches for spatial survival analysis under the Bayesian framework. The commonly used inference method, Markov chain Monte Carlo (MCMC) approach and the approximate inference approach, variational inference's performance are studied for two survival models. The Titan GPU data and pine tree survival data are used to illustrate the capability of variational inference on spatial survival models.

Survival analysis is an essential statistics and machine learning field in various critical applications like medical research and predictive maintenance. In these domains understanding models' predictions is paramount. While machine learning techniques are increasingly applied to enhance the predictive performance of survival models, they simultaneously sacrifice transparency and explainability.  Survival models, in contrast to regular machine learning models, predict functions rather than point estimates like regression and classification models. This creates a challenge regarding explaining such models using the known off-the-shelf machine learning explanation techniques, like Shapley Values, Counterfactual examples, and others.    Censoring is also a major issue in survival analysis where the target time variable is not fully observed for all subjects. Moreover, in predictive maintenance settings, recorded events do not always map to actual failures, where some components could be replaced because it is considered faulty or about to fail in the future based on an expert's opinion. Censoring and noisy labels create problems in terms of modeling and evaluation that require to be addressed during the development and evaluation of the survival models. Considering the challenges in survival modeling and the differences from regular machine learning models, this thesis aims to bridge this gap by facilitating the use of machine learning explanation methods to produce plausible and actionable explanations for survival models. It also aims to enhance survival modeling and evaluation revealing a better insight into the differences among the compared survival models. In this thesis, we propose two methods for explaining survival models which rely on discovering survival patterns in the model's predictions that group the studied subjects into significantly different survival groups. Each pattern reflects a specific survival behavior common to all the subjects in their respective group. We utilize these patterns to explain the predictions of the studied model in two ways. In the first, we employ a classification proxy model that can capture the relationship between the descriptive features of subjects and the learned survival patterns. Explaining such a proxy model using Shapley Values provides insights into the feature attribution of belonging to a specific survival pattern. In the second method, we addressed the "what if?" question by generating plausible and actionable counterfactual examples that would change the predicted pattern of the studied subject. Such counterfactual examples provide insights into actionable changes required to enhance the survivability of subjects. We also propose a variational-inference-based generative model for estimating the time-to-event distribution. The model relies on a regression-based loss function with the ability to handle censored cases. It also relies on sampling for estimating the conditional probability of event times. Moreover, we propose a decomposition of the C-index into a weighted harmonic average of two quantities, the concordance among the observed events and the concordance between observed and censored cases. These two quantities, weighted by a factor representing the balance between the two, can reveal differences between survival models previously unseen using only the total Concordance index. This can give insight into the performances of different models and their relation to the characteristics of the studied data. Finally, as part of enhancing survival modeling, we propose an algorithm that can correct erroneous event labels in predictive maintenance time-to-event data. we adopt an expectation-maximization-like approach utilizing a genetic algorithm to find better labels that would maximize the survival model's performance. Over iteration, the algorithm builds confidence about events' assignments which improves the search in the following iterations until convergence. We performed experiments on real and synthetic data showing that our proposed methods enhance the performance in survival modeling and can reveal the underlying factors contributing to the explainability of survival models' behavior and performance.

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