Clinical risk modelling with machine learning: adverse outcomes of pregnancy

As a complex biological process, there are various health issues that are related to pregnancy. Prenatal care, a type of preventative healthcare at different points in gestation is comprised of management, treatment, and mitigation of such issues. This also includes risk prediction for adverse pregnancy outcomes, where probabilistic modelling is used to calculate individual’s risk at the early stages of pregnancy. This type of modelling can have a definite clinical scope such as in prenatal screening, and an educational aim where awareness of a healthy lifestyle is promoted, such as in health education. Currently, the most used models are based on traditional statistical approaches, as they provide sufficient predictive power and are easily interpreted by clinicians. Machine learning, a subfield of data science, contains methods for building probabilistic models with multidimensional data. Compared to existing prediction models related to prenatal care, machine learning models can provide better results by fitting more intricate nonlinear decision boundary areas, improve data-driven model fitting by generating synthetic data, and by providing more automation for routine model adjustment processes. This thesis presents the evaluation of machine learning methods to prenatal screening and health education prediction problems, along with novel methods for generating synthetic rare disorder data to be used for modelling, and an adaptive system for continuously adjusting a prediction model to the changing patient population. This way the thesis addresses all the four main entities related to predicting adverse outcomes of pregnancy: the mother or patient, the clinician, the screening laboratory and the developer or manufacturer of screening materials and systems.Kliinisen riskin mallinnus koneoppimismenetelmin: raskaudelle haitalliset lopputulemat Raskaus on kompleksinen biologinen prosessi, jonka etenemiseen liittyy useita terveysongelmia. Äitiyshoito voidaan kuvata ennalta ehkäiseväksi terveydenhuolloksi, jossa pyritään käsittelemään, hoitamaan ja lievittämään kyseisiä ongelmia. Tähän hoitoon sisältyy myös raskauden haitallisten lopputulemien riskilaskenta, missä probabilistista mallinnusta hyödynnetään määrittämään yksilön riski raskauden varhaisissa vaiheissa. Tällä mallinnuksella voi olla selkeä kliininen tarkoitus kuten prenataaliseulonta, tai terveyssivistyksellinen tarkoitus missä odottavalle äidille esitellään raskauden kannalta terveellisiä elämäntapoja. Tällä hetkellä eniten käytössä olevat ennustemallit perustuvat perinteiseen tilastolliseen mallinnukseen, sille ne tarjoavat riittävän ennustetehokkuuden ja ovat helposti tulkittavissa. Koneoppiminen on datatieteen osa-alue, joka pitää sisällään menetelmiä millä voidaan mallintaa moniulotteista dataa ennustekäyttöön. Verrattuna olemassa oleviin äitiyshoidon ennustemalleihin, koneoppiminen mahdollistaa parempien ennustetulosten tuottamisen sovittamalla hienojakoisempia epälineaarisia päätösalueita, tehostamalla datakeskeisten mallien sovitusta luomalla synteettisiä havaintoja ja tarjoamalla enemmän automaatiota rutiininomaiseen mallien hienosäätöön. Tämä väitös esittelee koneoppimismenetelmien evaluaation prenataaliseulonta-ja terveyssivistysongelmiin, ja uusia menetelmiä harvinaisten sairauksien datan luomiseen mallinnustarkoituksiin ja jatkuvan ennustemallin hienosäätämisen järjestelmän muuttuvia potilaspopulaatiota varten. Näin väitös käy läpi kaikki neljä asianomaista jotka liittyvät haitallisten lopputulemien ennustamiseen: odottava äiti eli potilas, kliinikko, seulontalaboratorio ja seulonnassa käytettävien materiaalien ja järjestelmien kehittäjä tai valmistaja

A Tool for Producing Verified, Explainable Proofs

Mathematicians are reluctant to use interactive theorem provers. In this thesis I argue that this is because proof assistants don't emphasise explanations of proofs; and that in order to produce good explanations, the system must create proofs in a manner that mimics how humans would create proofs. My research goals are to determine what constitutes a human-like proof and to represent human-like reasoning within an interactive theorem prover to create formalised, understandable proofs. Another goal is to produce a framework to visualise the goal states of this system. To demonstrate this, I present HumanProof: a piece of software built for the Lean 3 theorem prover. It is used for interactively creating proofs that resemble how human mathematicians reason. The system provides a visual, hierarchical representation of the goal and a system for suggesting available inference rules. The system produces output in the form of both natural language and formal proof terms which are checked by Lean's kernel. This is made possible with the use of a structured goal state system which interfaces with Lean's tactic system which is detailed in Chapter 3. In Chapter 4, I present the subtasks automation planning subsystem, which is used to produce equality proofs in a human-like fashion. The basic strategy of the subtasks system is break a given equality problem in to a hierarchy of tasks and then maintain a stack of these tasks in order to determine the order in which to apply equational rewriting moves. This process produces equality chains for simple problems without having to resort to brute force or specialised procedures such as normalisation. This makes proofs more human-like by breaking the problem into a hierarchical set of tasks in the same way that a human would. To produce the interface for this software, I also created the ProofWidgets system for Lean 3. This system is detailed in Chapter 5. The ProofWidgets system uses Lean's metaprogramming framework to allow users to write their own interactive, web-based user interfaces to display within the VSCode editor and in an online web-editor. The entire tactic state is available to the rendering engine, and hence expression structure and types of subexpressions can be explored interactively. The ProofWidgets system also allows the user interface to interactively edit the proof document, enabling a truly interactive modality for creating proofs; human-like or not. In Chapter 6, the system is evaluated by asking real mathematicians about the output of the system, and what it means for a proof to be understandable to them. The user group study asks participants to rank and comment on proofs created by HumanProof alongside natural language and pure Lean proofs. The study finds that participants generally prefer the HumanProof format over the Lean format. The verbal responses collected during the study indicate that providing intuition and signposting are the most important properties of a proof that aid understanding.EPSR