Profile Likelihood Estimation Applied To The Semi-parametric Models With Survival Data

<p><b>In this thesis, we have investigated the efficiency of profile likelihood in the estimation of parameters from the Cox Proportional Hazards (PH) cure model and joint model of longitudinal and survival data. For the profile likelihood approach in the joint model of longitudinal and survival data, Hsieh et al. (2006) stated “No distributional or asymptotic theory is available to date, and even the standard errors (SEs), defined as the standard deviations of the parametric estimators, are difficult to obtain”. The reason behind this difficulty is the estimator of baseline hazard which involves implicit function in the profile likelihood estimation (Hirose and Liu, 2020). Hence finding the estimated SE of the parametric estimators from the Cox PH cure model and joint model using profile likelihood approach is a great challenge. Therefore, bootstrap method has been suggested to get the estimated standard errors while using the profile likelihood approach (Hsieh et al., 2006).</b></p> <p>To solve the difficulty, we have expanded the profile likelihood function directly without assuming the derivative of the profile likelihood score function and obtain the explicit form of the SE estimator using the profile likelihood score function. Our proposed alternative approach gives us not only analytical understanding of the profile likelihood estimation, but also provides closed form formula to compute the standard error of the profile likelihood maximum likelihood estimator in terms of profile likelihood score function. To show the advantage of our proposed approach in medical and clinical studies, we have analysed the simulated and real-life data, and compared our results with the output obtained from the smcure, JM(method: ’Cox-PH-GH’) and joineRML R-packages. The outputs suggest that the bootstrap method and our proposed approach have provided similar and comparable results. In addition, the average computation times of our approach are much less compared to the above mentioned R-packages.</p>

Profile Likelihood Estimation Applied To The Semi-parametric Models With Survival Data

<p><b>In this thesis, we have investigated the efficiency of profile likelihood in the estimation of parameters from the Cox Proportional Hazards (PH) cure model and joint model of longitudinal and survival data. For the profile likelihood approach in the joint model of longitudinal and survival data, Hsieh et al. (2006) stated “No distributional or asymptotic theory is available to date, and even the standard errors (SEs), defined as the standard deviations of the parametric estimators, are difficult to obtain”. The reason behind this difficulty is the estimator of baseline hazard which involves implicit function in the profile likelihood estimation (Hirose and Liu, 2020). Hence finding the estimated SE of the parametric estimators from the Cox PH cure model and joint model using profile likelihood approach is a great challenge. Therefore, bootstrap method has been suggested to get the estimated standard errors while using the profile likelihood approach (Hsieh et al., 2006).</b></p> <p>To solve the difficulty, we have expanded the profile likelihood function directly without assuming the derivative of the profile likelihood score function and obtain the explicit form of the SE estimator using the profile likelihood score function. Our proposed alternative approach gives us not only analytical understanding of the profile likelihood estimation, but also provides closed form formula to compute the standard error of the profile likelihood maximum likelihood estimator in terms of profile likelihood score function. To show the advantage of our proposed approach in medical and clinical studies, we have analysed the simulated and real-life data, and compared our results with the output obtained from the smcure, JM(method: ’Cox-PH-GH’) and joineRML R-packages. The outputs suggest that the bootstrap method and our proposed approach have provided similar and comparable results. In addition, the average computation times of our approach are much less compared to the above mentioned R-packages.</p>

Phylourny: Predicting the Knock-out-phase of Tournaments via Phylogenetic Methods by example of the UEFA EURO 2020

The prediction of knock-out tournaments represents an area of large public interest and active academic as well as industrial research. Here, we leverage the computational analogies between calculating the so-called phylogenetic likelihood score used in the area of molecular evolution and efficiently calculating, instead of approximating via simulations, the exact per-team winning probabilities, given a pairwise win probability matrix P. We implement and make available our method as open-source code and deploy it to calculate the winning probabilities for all teams participating at the knock-out phase of the UEFA EURO 2020 football tournament. We use three different P matrices to conduct predictions, two inferred via our own simple method and one computed by experts in the field. According to this expert P matrix which we trust most, we find that the most probable final is France versus England and that England has a slightly higher probability to win the title. The ability to efficiently and exactly compute winning probabilities, apart from improving and accelerating predictions, might allow for the development of novel methods to compute P.

Fibrosis-Net: A Tailored Deep Convolutional Neural Network Design For Prediction of Pulmonary Fibrosis Progression From Chest CT Images

Background: Pulmonary fibrosis is a devastating chronic lung disease that causes irreparable lung tissue scarring and damage, resulting in progressive loss in lung capacity and has no known cure. A critical step in the treatment and management of pulmonary fibrosis is the assessment of lung function decline, with computed tomography (CT) imaging being a particularly effective method for determining the extent of lung damage caused by pulmonary fibrosis. Motivated by this, we introduce Fibrosis-Net, a deep convolutional neural network design tailored for the prediction of pulmonary fibrosis progression from chest CT images. More specifically, machine-driven design exploration was leveraged to determine a strong architectural design for CT lung analysis, upon which we build a customized network design tailored for predicting forced vital capacity (FVC) based on a patient's CT scan, initial spirometry measurement, and clinical metadata. Finally, we leverage an explainability-driven performance validation strategy to study the decision-making behaviour of Fibrosis-Net as to verify that predictions are based on relevant visual indicators in CT images.Results: Experiments using a patient cohort from the OSIC Pulmonary Fibrosis Progression Challenge showed that the proposed Fibrosis-Net is able to achieve a significantly higher modified Laplace Log Likelihood score than the winning solutions on the challenge. Furthermore, explainability-driven performance validation demonstrated that the proposed Fibrosis-Net exhibits correct decision-making behaviour by leveraging clinically-relevant visual indicators in CT images when making predictions on pulmonary fibrosis progress. Conclusion: Fibrosis-Net is able to achieve a significantly higher modified Laplace Log Likelihood score than the winning solutions on the OSIC Pulmonary Fibrosis Progression Challenge, and has been shown to exhibit correct decision-making behaviour when making predictions. Fibrosis-Net is available to the general public in an open-source and open access manner as part of the OpenMedAI initiative. While Fibrosis-Net is not yet a production-ready clinical assessment solution, we hope that its release will encourage researchers, clinicians, and citizen data scientists alike to leverage and build upon it.

Dissecting incongruence between concatenation- and quartet-based approaches in phylogenomic data

Topological conflict or incongruence is widespread in phylogenomic data. Concatenation- and coalescent-based approaches often result in incongruent topologies, but the causes of this conflict can be difficult to characterize. We examined incongruence stemming from conflict between likelihood-based signal (quantified by the difference in gene-wise log likelihood score or ΔGLS) and quartet-based topological signal (quantified by the difference in gene-wise quartet score or ΔGQS) for every gene in three phylogenomic studies in animals, fungi, and plants, which were chosen because their concatenation-based IQ-TREE (T1) and quartet-based ASTRAL (T2) phylogenies are known to produce eight conflicting internal branches (bipartitions). By comparing the types of phylogenetic signal for all genes in these three data matrices, we found that 30% - 36% of genes in each data matrix are inconsistent, that is, each of these genes has higher log likelihood score for T1 versus T2 (i.e., ΔGLS &gt;0) whereas its T1 topology has lower quartet score than its T2 topology (i.e., ΔGQS &lt;0) or vice versa. Comparison of inconsistent and consistent genes using a variety of metrics (e.g., evolutionary rate, gene tree topology, distribution of branch lengths, hidden paralogy, and gene tree discordance) showed that inconsistent genes are more likely to recover neither T1 nor T2 and have higher levels of gene tree discordance than consistent genes. Simulation analyses demonstrate that removal of inconsistent genes from datasets with low levels of incomplete lineage sorting (ILS) and low and medium levels of gene tree estimation error (GTEE) reduced incongruence and increased accuracy. In contrast, removal of inconsistent genes from datasets with medium and high ILS levels and high GTEE levels eliminated or extensively reduced incongruence, but the resulting congruent species phylogenies were not always topologically identical to the true species trees.

A Discriminative Multi-Output Gaussian Processes Scheme for Brain Electrical Activity Analysis

The study of brain electrical activity (BEA) from different cognitive conditions has attracted a lot of interest in the last decade due to the high number of possible applications that could be generated from it. In this work, a discriminative framework for BEA via electroencephalography (EEG) is proposed based on multi-output Gaussian Processes (MOGPs) with a specialized spectral kernel. First, a signal segmentation stage is executed, and the channels from the EEG are used as the model outputs. Then, a novel covariance function within the MOGP known as the multispectral mixture kernel (MOSM) allows us to find and quantify the relationships between different channels. Several MOGPs are trained from different conditions grouped in bi-class problems, and the discrimination is performed based on the likelihood score of the test signals against all the models. Finally, the mean likelihood is computed to predict the correspondence of new inputs with each class’s existing models. Results show that this framework allows us to model the EEG signals adequately using generative models and allows analyzing the relationships between channels of the EEG for a particular condition. At the same time, the set of trained MOGPs is well suited to discriminate new input data.

An improved mode of running PASTA

PASTA is a method for estimating alignments and trees that has been able to provide excellent accuracy on large sequence datasets. By design, PASTA operates using iteration, in which the tree from the previous iteration is used to inform a divide-and-conquer strategy during which a new alignment is computed on the sequence dataset, and then a new maximum likelihood tree is estimated on the new alignment. In its default setting, PASTA runs for three iterations and returns that alignment/tree pair from the last iteration. Here we use both biological and simulated nucleotide datasets to show that returning the alignment/tree pair that has the best maximum likelihood score improves on the default usage.