Master thesis | Statistical Science for the Life and Behavioural Sciences (MSc)
open access
Ascertainment bias is common in genetic-epidemiological cancer studies, where sampling of high-risk families is outcome-dependent. This results in too many events in comparison to the population...Show moreAscertainment bias is common in genetic-epidemiological cancer studies, where sampling of high-risk families is outcome-dependent. This results in too many events in comparison to the population and an overrepresentation of young, affected subjects in the sample. The motivating example for this thesis is a family study where the goal is to estimate an unbiased hazard ratio (HR) for the effect of Polygenic Risk Score (PRS), a continuous score based on several Single Nucleotide Polymorphisms (SNPs), on age of breast cancer diagnosis. Weighted Cox model approaches have been proposed in this context, however their performance has never been evaluated for a continuous covariate. Two different approaches were considered, using time fixed and time dependent weights. A simulation study was conducted to assess the performance of the different approaches for scenarios where different family correlation, family size, sample size and selection criterium have been chosen. We found that under the null hypothesis, (un)weighted models behave similarly. When a covariate effect is assumed, in any scenario where the within-family correlation is low, weighting methods perform better than a naive approach; the same holds for moderate within-family correlation in combination with weak ascertainment. For strong ascertainment and/or strong within-family correlation, coverage of weighting methods is very poor and bias is high. To obtain an unbiased HR for PRS, we used high-risk breast cancer families data. Inclusion criteria were absence of high-risk mutations BRCA1 and BRCA2 and at least three affected female family members or in two members if at least one had bilateral breast cancer before age 60. A total of 101 families were selected between 1990 and 2012 by Clinical Genetic Services in four Dutch cities and one Hungarian city, with 323 (55.1%) events. The HR of PRS, adjusted by family history, was 1.29 (95% CI 1.04; 1.60), for the naive model, with a frailty variance of 0.53 which indicates rather strong within-family correlation. For none of the weighting approaches, the covariate effect of PRS adjusted for family history in a Cox model was significant (HR 1.09 and 1.09). For analysis of outcome dependently sampled survival data, weighting approaches may be used to limit ascertainment bias, for some scenarios. A note of caution is required when this approach is used in scenarios with (moderate to) strong within-family correlation. No evidence for a significant effect of PRS on age of breast cancer diagnosis was found in this studyShow less
Master thesis | Statistical Science for the Life and Behavioural Sciences (MSc)
open access
Accurate predictions of survival probabilities can be helpful to determine treatment strategies and shared decision making in medical applications, like cancer prognosis. Traditionally, the Cox...Show moreAccurate predictions of survival probabilities can be helpful to determine treatment strategies and shared decision making in medical applications, like cancer prognosis. Traditionally, the Cox proportional hazards (PH) model is used to predict survival. Yet, recently machine learning (ML) has received increased attention. ML methods learn complex relations between explanatory variables and outcomes, without the need to specify these effects beforehand. In contrast, in the Cox PH model, non-linear and interaction effects need to be specified before estimating the model. The flexibility of ML methods is believed to improve predictive accuracy, which drives the application of ML methods to survival data. One of the aims of this thesis was to compare prediction models for survival data based on machine learning methods to the traditional Cox PH model. Predictive ability was assessed by using Brier score, concordance index and calibration plots. Furthermore, software implementation and interpretability were investigated. Two ML methods, partial logistic regression models with artificial neural networks (PLANN) and random survival forest (RSF) models were considered. Predictive performance was studied in a soft tissue sarcoma cohort: a right-censored survival dataset with a small number of explanatory variables. In terms of IBS and calibration, the optimally tuned RSF models had similar predictive performance compared to the Cox model. The Cox model had better predictive performance than the RSF models in terms of C-index. One of the NN models outperformed Cox in terms of Integrated Brier Score (IBS). Also, the NN models were slightly better calibrated than the Cox PH model. It would be interesting to see whether a Cox model including non-linear effects would outperform the ML methods considered in terms of prediction. Differences between the ML methods and the Cox PH model concern the route towards finding the most optimal predictions. When estimating survival probabilities using ML methods, focus is mainly on the correct implementation of the ML algorithm: finding suitable tuning parameters, how to select the best set of tuning parameters and running the algorithm, which takes time. On the other hand, when identifying the best predicting Cox model, time is spent on specifying the model, looking at non-linear effects and evaluating goodness of fit. The initial set of tuning parameters considered for the PLANN approach resulted in non-informative NN models. This showed the importance of thorough knowledge on the characteristics of tuning parameters in the ML methods. The work in this thesis shows how survival prediction could be unreliable if the NN is not properly tuned.Show less
Master thesis | Statistical Science for the Life and Behavioural Sciences (MSc)
open access
Reliable forecasting of infectious disease epidemics is critical for decision-making regarding the allocation of public health resources. Until now, efforts have mostly been devoted to...Show moreReliable forecasting of infectious disease epidemics is critical for decision-making regarding the allocation of public health resources. Until now, efforts have mostly been devoted to understanding disease transmission rather than forecasting. The present thesis took a Bayesian approach to forecasting epidemics, focusing on modelling the time between successive observed infection events using a Gamma generalised linear model (GLM). Specifically, a tailored sampler was introduced to solve common convergence problems associated with the use of the inverse link function. The posterior distribution obtained from the Bayesian Gamma GLM was then used to forecast stochastically. This approach was extended to diseases with different transmission dynamics, as described by traditional compartmental epidemiological models: susceptible-infectious (SI), susceptible-infectioussusceptible (SIS) and susceptible-infectious-recovered (SIR). The calibration of the forecasting technique was evaluated using probability integral transform (PIT) histograms in a large simulation study. Results showed that forecasts of SI and SIS-type epidemics in an early growth phase underestimated true future values. Across epidemic types, there was evidence of overdispersion in the forecasts. Furthermore, the method was applied to data from the Meningococcal disease, serogroup W outbreak in the Netherlands between 2012 and 2018. Forecasts suggested the outbreak has reached an equilibrium of approximately 50-55 new observed cases per 6 months. Avenues for future research are provided, with a focus on how we could improve the Bayesian approach and adapt the method to account for covariates of interest.Show less
Master thesis | Statistical Science for the Life and Behavioural Sciences (MSc)
open access
The Inverse Probability of Treatment Weighted (IPTW) estimators can be used to correctly estimate the parameters of marginal structural models (MSMs) for causal effects using observational data and...Show moreThe Inverse Probability of Treatment Weighted (IPTW) estimators can be used to correctly estimate the parameters of marginal structural models (MSMs) for causal effects using observational data and a number of assumptions. In this thesis we focus on the positivity assumption which holds when there is a positive probability of receiving every level of an exposure variable for every combination of values defined by the observed confounders in the analysis. When the positivity assumption is violated, the resulting IPTW estimators may become very unstable and exhibit high variability. However, the severity with which this impacts the IPTW estimators under different conditions is not widely known or understood. In particular, to our knowledge, no existing study has investigated violations of the positivity assumption for survival analysis, or in a time dependent context more generally. This is surprising because MSMs are often applied in practice precisely because they adjust for time-dependent confounding. A novelty of this thesis is to investigate the effect of positivity violations on the performance of the IPTW-estimator in a survival context in which time dependent confounding is present. We approach the problem in a simulation setting. One reason why the effects of positivity violations in a survival context have not been systematically studied is that existing algorithms for generating suitable data are intensive and challenging to implement. An added value of this thesis is to cast some light on this process in the hope that it will encourage other researchers to broach the subject in the future. We implement an existing algorithm in R and then extend that algorithm to incorporate violations of the positivity assumption that are propagated through time. A simulation study was carried out using the extended algorithm. We investigate how the IPTW estimators respond as strict violations of the positivity assumption become increasingly severe. As part of this study we examine the finite sample properties of the estimator and how it behaves for varied lengths of follow-up time. We also consider the case where the positivity assumption is not strictly violated but some exposure levels are rare within certain levels of the confounder. Our results indicate that even relatively benign violations of the positivity assumption can be a problem in the time-dependent context. We also find that, contrary to expectations, positivity violations are worse for studies of shorter duration. More optimistically, near violations of the positivity assumption do not appear to be serious under realistic circumstances.Show less
Master thesis | Statistical Science for the Life and Behavioural Sciences (MSc)
open access
Liver transplantation -i.e. the replacement of a diseased liver with healthy liver of another person, is the most effective therapeutic strategy for patients with end-stage liver disease....Show moreLiver transplantation -i.e. the replacement of a diseased liver with healthy liver of another person, is the most effective therapeutic strategy for patients with end-stage liver disease. Predicting survival of patients after liver transplantation is regarded as one of the most challenging areas in medicine. Hence, selecting the best prediction model is of paramount importance. Machine learning - field of computer science where specific algorithms are used to learn and make predictions on data - has lately received increased attention in the medical field due to contribution in medical imaging, ability to diagnose diseases and its great potential for personalized treatment. In survival analysis, machine learning implementation is difficult due to censored data. In this thesis, survival random forests and partial logistic artificial neural networks have been applied. Cox model has been exclusively used due to its easy implementation and straightforward interpretation. The model is however restricted to the proportionality of hazards assumption whereas the machine learning techniques do not make any assumptions. Nowadays, there is a strong discussion in the medical field about machine learning and if it has greater potential than Cox models when it comes to complex data. Criticism to machine learning is related to unsuitable performance measures and lack of interpretability which is important for the medical personnel. The potential of machine learning is investigated for large data of 62294 patients in USA for 106 prognostic factors selected from over 600; 52 donor’s characteristics and 54 patient’s characteristics. A meticulous comparison is performed between 3 proportional hazards models and machine learning techniques. For the artificial neural network novel extensions are provided to its original specification using state-of-the-art R software. A variety of measures is employed not only from survival field but also from simple classification setting. In this project, it is of particular interest the identification of potential risk factors post-operatively. Two survival outcomes are reported: overall survival (time to death since operation) and failure-free survival (minimum time between graft-failure and death since operation). In this thesis, it is shown that machine learning techniques can be a useful tool for both prediction and interpretation. Random survival forest shows in general better predictive performance than Cox models. Neural networks can reach comparable performance with the Cox models and even perform better in some classification metrics. However, high instability is present due to the lack of a global performance evaluation measure in survival setting.Show less
Master thesis | Statistical Science for the Life and Behavioural Sciences (MSc)
open access
Over the past years there has been an increased interest in applying machine learning (ML) techniques to medical research. With the growing availability of mixed data - clinical and genomic for...Show moreOver the past years there has been an increased interest in applying machine learning (ML) techniques to medical research. With the growing availability of mixed data - clinical and genomic for instance - ML methods, which have great potential for modelling complex data, have been increasingly applied. Few publications however have seen clinical applications, and the trend towards ML has been criticised for a lack of attention towards proper validation and towards the use of appropriate performance measures to quantify the model performance. Initially, in the context of medical research, machine learning methods were mainly used for diagnosis and detections, but the last years have seen a vast increase in ML modelling for the purpose of cancer prediction and prognosis. The latter trend has given rise to various adaptations of traditional ML approaches to censored survival data. Two such approaches - Biganzoli's survival neural network and Ishwaran's random survival forest - are evaluated in this thesis. They are compared to a statistical model - the well-used Cox proportional hazards model - in an application to a clinical dataset with 7 variables, measured on 2025 osteosarcoma patients- the EURAMOS-1 clinical trial. The purpose of this thesis is two-fold; 1) performing an in-depth comparison of the two ML methods and gaining insight into the potential of ML for clinical data with a limited number of predictors; 2) adding to existing osteosarcoma literature, in which ML methods have a very limited presence. The analyses performed on the EURAMOS data are reinforced by a simulation study, which is novel in the approach it takes to ensure that the simulated data closely mimics the original. This thesis shows that for the EURAMOS-1 osteosarcoma data the Cox proportional hazard model is suitable, and that both ML approaches have limited added benefit. Appropriate performance measures are identified for assessing neural network and random survival forest performance. For the survival neural network a modification to an existing measure is proposed to aid in identifying network instability - a known neural network pitfall. For the random survival forest it is shown that while suitable for distinguishing high and low risk patients, it results in unreliable individual survival predictions. An additional, unrelated chapter has been included in this thesis, detailing the application of a dynamic prediction model to the EURAMOS-1 osteosarcoma data.Show less
Master thesis | Statistical Science for the Life and Behavioural Sciences (MSc)
open access
The area under the receiver operating characteristic (ROC) curve (AUC) is a commonly used measurement for the discriminative ability of a model. For the time to event variable in survival analysis...Show moreThe area under the receiver operating characteristic (ROC) curve (AUC) is a commonly used measurement for the discriminative ability of a model. For the time to event variable in survival analysis the case and control sets will vary over time, thus a dynamic definition of AUC is required. We choose the dynamic AUC defined by incident true positive rate and dynamic false positive rate (I/D AUC) proposed by Heagerty and Zheng [6]. However, the difficulty to empirically obtain the incident true positive rate is hampering the estimation of dynamic AUC. Thus, several semi-parametric and non-parametric estimators are proposed. Heagerty and Zheng [6] proposed the semi-parametric estimation method based on Cox model. The non-parametric estimates using intermediate concordance measure with LOWESS smoothing is raised by van Houwelingen and Putter [14]. Based on the same intermediate concordance measure, SahaChaudhuri and Heagerty suggested to use locally weighted mean rank smoothing [10]. Recently, Shen et al proposed a semi-parametric method by adopting fractional polynomial to fit the dynamic AUC [12]. In this thesis, we compare the performance of these methods with different configuration in a series of simulations. The plain Cox methods is not recommended when the proportional hazards assumption is not satisfied. The Cox model with time-varying coefficients are relatively stable when the marker has a mediocre effect. For the non-parametric methods, a too wide span/bandwidth may lead to large bias, and a too narrow span/bandwidth may lead to unstable estimates, thus, the trade-off between the bias and the standard deviation has to be made. For fractional polynomial, adding extra fractional polynomial terms does not benefit the performance. In addition, many researchers observed a decreasing trend of I/D AUC over time in their empirical studies [10][12][6], yet Pepe et al. held the opinion that the I/D AUC may be an increasing function over time [7]. We investigate the trend of I/D AUC under a Cox model and binary marker setting. However, we observe that under certain Cox models, the I/D AUC curve first increases then decreases, thus I/D AUC is not necessarily a decreasing function of time.Show less
