Interpretable prediction of mortality in liver transplant recipients based on machine learning.

BACKGROUND: Accurate prediction of the mortality of post-liver transplantation is an important but challenging task. It relates to optimizing organ allocation and estimating the risk of possible dysfunction. Existing risk scoring models, such as the Balance of Risk (BAR) score and the Survival Outcomes Following Liver Transplantation (SOFT) score, do not predict the mortality of post-liver transplantation with sufficient accuracy. In this study, we evaluate the performance of machine learning models and establish an explainable machine learning model for predicting mortality in liver transplant recipients. METHOD: The optimal feature set for the prediction of the mortality was selected by a wrapper method based on binary particle swarm optimization (BPSO). With the selected optimal feature set, seven machine learning models were applied to predict mortality over different time windows. The best-performing model was used to predict mortality through a comprehensive comparison and evaluation. An interpretable approach based on machine learning and SHapley Additive exPlanations (SHAP) is used to explicitly explain the model's decision and make new discoveries. RESULTS: With regard to predictive power, our results demonstrated that the feature set selected by BPSO outperformed both the feature set in the existing risk score model (BAR score, SOFT score) and the feature set processed by principal component analysis (PCA). The best-performing model, extreme gradient boosting (XGBoost), was found to improve the Area Under a Curve (AUC) values for mortality prediction by 6.7%, 11.6%, and 17.4% at 3 months, 3 years, and 10 years, respectively, compared to the SOFT score. The main predictors of mortality and their impact were discussed for different age groups and different follow-up periods. CONCLUSIONS: Our analysis demonstrates that XGBoost can be an ideal method to assess the mortality risk in liver transplantation. In combination with the SHAP approach, the proposed framework provides a more intuitive and comprehensive interpretation of the predictive model, thereby allowing the clinician to better understand the decision-making process of the model and the impact of factors associated with mortality risk in liver transplantation.

Zipf's laws of meaning in Catalan.

In his pioneering research, G. K. Zipf formulated a couple of statistical laws on the relationship between the frequency of a word with its number of meanings: the law of meaning distribution, relating the frequency of a word and its frequency rank, and the meaning-frequency law, relating the frequency of a word with its number of meanings. Although these laws were formulated more than half a century ago, they have been only investigated in a few languages. Here we present the first study of these laws in Catalan. We verify these laws in Catalan via the relationship among their exponents and that of the rank-frequency law. We present a new protocol for the analysis of these Zipfian laws that can be extended to other languages. We report the first evidence of two marked regimes for these laws in written language and speech, paralleling the two regimes in Zipf's rank-frequency law in large multi-author corpora discovered in early 2000s. Finally, the implications of these two regimes will be discussed.

When is Menzerath-Altmann law mathematically trivial? A new approach.

Menzerath's law, the tendency of Z (the mean size of the parts) to decrease as X (the number of parts) increases, is found in language, music and genomes. Recently, it has been argued that the presence of the law in genomes is an inevitable consequence of the fact that Z=Y/X, which would imply that Z scales with X as Z ∼ 1/X. That scaling is a very particular case of Menzerath-Altmann law that has been rejected by means of a correlation test between X and Y in genomes, being X the number of chromosomes of a species, Y its genome size in bases and Z the mean chromosome size. Here we review the statistical foundations of that test and consider three non-parametric tests based upon different correlation metrics and one parametric test to evaluate if Z ∼ 1/X in genomes. The most powerful test is a new non-parametric one based upon the correlation ratio, which is able to reject Z ∼ 1/X in nine out of 11 taxonomic groups and detect a borderline group. Rather than a fact, Z ∼ 1/X is a baseline that real genomes do not meet. The view of Menzerath-Altmann law as inevitable is seriously flawed.

The evolution of the exponent of Zipf's law in language ontogeny.

It is well-known that word frequencies arrange themselves according to Zipf's law. However, little is known about the dependency of the parameters of the law and the complexity of a communication system. Many models of the evolution of language assume that the exponent of the law remains constant as the complexity of a communication systems increases. Using longitudinal studies of child language, we analysed the word rank distribution for the speech of children and adults participating in conversations. The adults typically included family members (e.g., parents) or the investigators conducting the research. Our analysis of the evolution of Zipf's law yields two main unexpected results. First, in children the exponent of the law tends to decrease over time while this tendency is weaker in adults, thus suggesting this is not a mere mirror effect of adult speech. Second, although the exponent of the law is more stable in adults, their exponents fall below 1 which is the typical value of the exponent assumed in both children and adults. Our analysis also shows a tendency of the mean length of utterances (MLU), a simple estimate of syntactic complexity, to increase as the exponent decreases. The parallel evolution of the exponent and a simple indicator of syntactic complexity (MLU) supports the hypothesis that the exponent of Zipf's law and linguistic complexity are inter-related. The assumption that Zipf's law for word ranks is a power-law with a constant exponent of one in both adults and children needs to be revised.

Random models of Menzerath-Altmann law in genomes.

Recently, a random breakage model has been proposed to explain the negative correlation between mean chromosome length and chromosome number that is found in many groups of species and is consistent with Menzerath-Altmann law, a statistical law that defines the dependency between the mean size of the whole and the number of parts in quantitative linguistics. Here, the central assumption of the model, namely that genome size is independent from chromosome number is reviewed. This assumption is shown to be unrealistic from the perspective of chromosome structure and the statistical analysis of real genomes. A general class of random models, including that random breakage model, is analyzed. For any model within this class, a power law with an exponent of -1 is predicted for the expectation of the mean chromosome size as a function of chromosome length, a functional dependency that is not supported by real genomes. The random breakage and variants keeping genome size and chromosome number independent raise no serious objection to the relevance of correlations consistent with Menzerath-Altmann law across taxonomic groups and the possibility of a connection between human language and genomes through that law.