A New Mixture Model With Cure Rate Applied to Breast Cancer Data.

We introduce a new modelling for long-term survival models, assuming that the number of competing causes follows a mixture of Poisson and the Birnbaum-Saunders distribution. In this context, we present some statistical properties of our model and demonstrate that the promotion time model emerges as a limiting case. We delve into detailed discussions of specific models within this class. Notably, we examine the expected number of competing causes, which depends on covariates. This allows for direct modeling of the cure rate as a function of covariates. We present an Expectation-Maximization (EM) algorithm for parameter estimation, to discuss the estimation via maximum likelihood (ML) and provide insights into parameter inference for this model. Additionally, we outline sufficient conditions for ensuring the consistency and asymptotic normal distribution of ML estimators. To evaluate the performance of our estimation method, we conduct a Monte Carlo simulation to provide asymptotic properties and a power study of LR test by contrasting our methodology against the promotion time model. To demonstrate the practical applicability of our model, we apply it to a real medical dataset from a population-based study of incidence of breast cancer in São Paulo, Brazil. Our results illustrate that the proposed model can outperform traditional approaches in terms of model fitting, highlighting its potential utility in real-world scenarios.

Reliable estimation of tree branch lengths using deep neural networks.

A phylogenetic tree represents hypothesized evolutionary history for a set of taxa. Besides the branching patterns (i.e., tree topology), phylogenies contain information about the evolutionary distances (i.e. branch lengths) between all taxa in the tree, which include extant taxa (external nodes) and their last common ancestors (internal nodes). During phylogenetic tree inference, the branch lengths are typically co-estimated along with other phylogenetic parameters during tree topology space exploration. There are well-known regions of the branch length parameter space where accurate estimation of phylogenetic trees is especially difficult. Several novel studies have recently demonstrated that machine learning approaches have the potential to help solve phylogenetic problems with greater accuracy and computational efficiency. In this study, as a proof of concept, we sought to explore the possibility of machine learning models to predict branch lengths. To that end, we designed several deep learning frameworks to estimate branch lengths on fixed tree topologies from multiple sequence alignments or its representations. Our results show that deep learning methods can exhibit superior performance in some difficult regions of branch length parameter space. For example, in contrast to maximum likelihood inference, which is typically used for estimating branch lengths, deep learning methods are more efficient and accurate. In general, we find that our neural networks achieve similar accuracy to a Bayesian approach and are the best-performing methods when inferring long branches that are associated with distantly related taxa. Together, our findings represent a next step toward accurate, fast, and reliable phylogenetic inference with machine learning approaches.

Health Care Provider Clustering Using Fusion Penalty in Quasi-Likelihood.

There has been growing research interest in developing methodology to evaluate the health care providers' performance with respect to a patient outcome. Random and fixed effects models are traditionally used for such a purpose. We propose a new method, using a fusion penalty to cluster health care providers based on quasi-likelihood. Without any priori knowledge of grouping information, our method provides a desirable data-driven approach for automatically clustering health care providers into different groups based on their performance. Further, the quasi-likelihood is more flexible and robust than the regular likelihood in that no distributional assumption is needed. An efficient alternating direction method of multipliers algorithm is developed to implement the proposed method. We show that the proposed method enjoys the oracle properties; namely, it performs as well as if the true group structure were known in advance. The consistency and asymptotic normality of the estimators are established. Simulation studies and analysis of the national kidney transplant registry data demonstrate the utility and validity of our method.

A new power G-family of distributions: Properties, estimation, and applications.

This article suggests a new method to expand a family of life distributions by adding a parameter to the family, increasing its flexibility. It is called the extended Modi-G family of distributions. We derived the general statistical properties of the proposed family. Different methods of estimation were presented to estimate the parameters for the proposed family, such as maximum likelihood, ordinary least square, weighted least square, Anderson Darling, right-tailed Anderson-Darling, Cramér-von Mises, and maximum product of spacing methods. A special sub-model with three parameters called extended Modi exponential distribution was derived along with different shapes of its density and hazard functions. Randomly generated data sets and different estimation methods were used to illustrate the behavior of parameters of the proposal sub-model. To illustrate the importance of the proposed family over the other well-known methods, applications to medicine and geology data sets were analyzed.

A robust cis-Mendelian randomization method with application to drug target discovery.

Mendelian randomization (MR) uses genetic variants as instrumental variables (IVs) to investigate causal relationships between traits. Unlike conventional MR, cis-MR focuses on a single genomic region using only cis-SNPs. For example, using cis-pQTLs for a protein as exposure for a disease opens a cost-effective path for drug target discovery. However, few methods effectively handle pleiotropy and linkage disequilibrium (LD) of cis-SNPs. Here, we propose cisMR-cML, a method based on constrained maximum likelihood, robust to IV assumption violations with strong theoretical support. We further clarify the severe but largely neglected consequences of the current practice of modeling marginal, instead of conditional genetic effects, and only using exposure-associated SNPs in cis-MR analysis. Numerical studies demonstrated our method's superiority over other existing methods. In a drug-target analysis for coronary artery disease (CAD), including a proteome-wide application, we identified three potential drug targets, PCSK9, COLEC11 and FGFR1 for CAD.

Maximum Likelihood Estimation for Unrooted 3-Leaf Trees: An Analytic Solution for the CFN Model.

Maximum likelihood estimation is among the most widely-used methods for inferring phylogenetic trees from sequence data. This paper solves the problem of computing solutions to the maximum likelihood problem for 3-leaf trees under the 2-state symmetric mutation model (CFN model). Our main result is a closed-form solution to the maximum likelihood problem for unrooted 3-leaf trees, given generic data; this result characterizes all of the ways that a maximum likelihood estimate can fail to exist for generic data and provides theoretical validation for predictions made in Parks and Goldman (Syst Biol 63(5):798-811, 2014). Our proof makes use of both classical tools for studying group-based phylogenetic models such as Hadamard conjugation and reparameterization in terms of Fourier coordinates, as well as more recent results concerning the semi-algebraic constraints of the CFN model. To be able to put these into practice, we also give a complete characterization to test genericity.

Pairwise kinship inference and pedigree reconstruction using 91 microhaplotypes.

Kinship inference has been a major issue in forensic genetics, and it remains to be solved when there is no prior hypothesis and the relationships between multiple individuals are unknown. In this study, we genotyped 91 microhaplotypes from 46 pedigree samples using massive parallel sequencing and inferred their relatedness by calculating the likelihood ratio (LR). Based on simulated and real data, different treatments were applied in the presence and absence of relatedness assumptions. The pedigree of multiple individuals was reconstructed by calculating pedigree likelihoods based on real pedigree samples. The results showed that the 91 MHs could discriminate pairs of second-degree relatives from unrelated individuals. And more highly polymorphic loci were needed to discriminate the pairs of second-degree or more distant relative from other degrees of relationship, but correct classification could be obtained by expanding the suspected relationship searched to other relationships with lower LR values. Multiple individuals with unknown relationships can be successfully reconstructed if they are closely related. Our study provides a solution for kinship inference when there are no prior assumptions, and explores the possibility of pedigree reconstruction when the relationships of multiple individuals are unknown.

Comparison of WAIC and posterior predictive approaches for N-mixture models.

Hierarchical models are common for ecological analysis, but determining appropriate model selection methods remains an ongoing challenge. To confront this challenge, a suitable method is needed to evaluate and compare available candidate models. We compared performance of conditional WAIC, a joint-likelihood approach to WAIC (WAICj), and posterior-predictive loss for selecting between candidate N-mixture models. We tested these model selection criteria on simulated single-season N-mixture models, simulated multi-season N-mixture models with temporal auto-correlation, and three case studies of single-season N-mixture models based on eBird data. WAICj proved more accurate than the standard conditional formulation or posterior-predictive loss, even when models were temporally correlated, suggesting WAICj is a robust alternative to model selection for N-mixture models.

Bayesian Analysis of Multi-Factorial Experimental Designs Using SEM.

Latent repeated measures ANOVA (L-RM-ANOVA) has recently been proposed as an alternative to traditional repeated measures ANOVA. L-RM-ANOVA builds upon structural equation modeling and enables researchers to investigate interindividual differences in main/interaction effects, examine custom contrasts, incorporate a measurement model, and account for missing data. However, L-RM-ANOVA uses maximum likelihood and thus cannot incorporate prior information and can have poor statistical properties in small samples. We show how L-RM-ANOVA can be used with Bayesian estimation to resolve the aforementioned issues. We demonstrate how to place informative priors on model parameters that constitute main and interaction effects. We further show how to place weakly informative priors on standardized parameters which can be used when no prior information is available. We conclude that Bayesian estimation can lower Type 1 error and bias, and increase power and efficiency when priors are chosen adequately. We demonstrate the approach using a real empirical example and guide the readers through specification of the model. We argue that ANOVA tables and incomplete descriptive statistics are not sufficient information to specify informative priors, and we identify which parameter estimates should be reported in future research; thereby promoting cumulative research.

Multivariate disturbance filtering in auditory fNIRS signals using maximum likelihood gradient estimation method: Feasibility study using sound quality indices.

Functional near-infrared spectroscopy (fNIRS) technology has been widely used to analyze biomechanics and diagnose brain activity. Despite being a promising tool for assessing the brain cortex status, this system is susceptible to disturbances and noise from electrical instrumentation and basal metabolism. In this study, an alternative filtering method, maximum likelihood generalized extended stochastic gradient (ML-GESG) estimation, is proposed to overcome the limitations of these disturbance factors. The proposed algorithm was designed to reduce multiple disturbances originating from heartbeats, breathing, shivering, and instrumental noises as multivariate parameters. To evaluate the effectiveness of the algorithm in filtering involuntary signals, a comparative analysis was conducted with a conventional filtering method, using hemodynamic responses to auditory stimuli and psycho-acoustic factors as quality indices. Using auditory sound stimuli consisting of 12 voice sources (six males and six females), the fNIRS test was configured with 18 channels and conducted on 10 volunteers. The psycho-acoustic factors of loudness and sharpness were used to evaluate physiological responses to the stimuli. Applying the proposed filtering method, the oxygenated hemoglobin concentration correlated better with the psychoacoustic analysis of each auditory stimulus than that of the conventional filtering method.

Fast and Accurate Estimation of Selection Coefficients and Allele Histories from Ancient and Modern DNA.

We here present CLUES2, a full-likelihood method to infer natural selection from sequence data that is an extension of the method CLUES. We make several substantial improvements to the CLUES method that greatly increases both its applicability and its speed. We add the ability to use ancestral recombination graphs on ancient data as emissions to the underlying hidden Markov model, which enables CLUES2 to use both temporal and linkage information to make estimates of selection coefficients. We also fully implement the ability to estimate distinct selection coefficients in different epochs, which allows for the analysis of changes in selective pressures through time, as well as selection with dominance. In addition, we greatly increase the computational efficiency of CLUES2 over CLUES using several approximations to the forward-backward algorithms and develop a new way to reconstruct historic allele frequencies by integrating over the uncertainty in the estimation of the selection coefficients. We illustrate the accuracy of CLUES2 through extensive simulations and validate the importance sampling framework for integrating over the uncertainty in the inference of gene trees. We also show that CLUES2 is well-calibrated by showing that under the null hypothesis, the distribution of log-likelihood ratios follows a χ2 distribution with the appropriate degrees of freedom. We run CLUES2 on a set of recently published ancient human data from Western Eurasia and test for evidence of changing selection coefficients through time. We find significant evidence of changing selective pressures in several genes correlated with the introduction of agriculture to Europe and the ensuing dietary and demographic shifts of that time. In particular, our analysis supports previous hypotheses of strong selection on lactase persistence during periods of ancient famines and attenuated selection in more modern periods.

Phylogenetic insights into the Salicaceae: The evolution of willows and beyond.

The Salicaceae includes approximately 54 genera and over 1,400 species with a cosmopolitan distribution. Members of the family are well-known for their diverse secondary plant metabolites, and they play crucial roles in tropical and temperate forest ecosystems. Phylogenetic reconstruction of the Salicaceae has been historically challenging due to the limitations of molecular markers and the extensive history of hybridization and polyploidy within the family. Our study employs whole-genome sequencing of 74 species to generate an extensive phylogeny of the Salicaceae. We generated two RAD-Seq enriched whole-genome sequence datasets and extracted two additional gene sets corresponding to the universal Angiosperms353 and Salicaceae-specific targeted-capture arrays. We reconstructed maximum likelihood-based molecular phylogenies using supermatrix and coalescent-based supertree approaches. Our fossil-calibrated phylogeny estimates that the Salicaceae originated around 128 million years ago and unravels the complex taxonomic relationships within the family. Our findings confirm the non-monophyly of the subgenus Salix s.l. and further support the merging of subgenera Chamaetia and Vetrix, both of which exhibit intricate patterns within and among different sections. Overall, our study not only enhances our understanding of the evolution of the Salicaceae, but also provides valuable insights into the complex relationships within the family.

Exploring the phylogeny and depth evolution of cusk eels and their relatives (Ophidiiformes: Ophidioidei).

With 289 known species in 51 genera, the ophidiiform family Ophidiidae together with their relatives from the Carapidae (36 species in eight genera) of the same suborder Ophidioidei dominate the deep sea, but some occur also in shallow water habitats. Despite their high species diversity in the deep sea and wide bathymetric distributions, their phylogenetic relationships and evolution remain unexplored due in part to sampling difficulties. Thanks to the biodiversity exploratory program entitled "Tropical Deep-Sea Benthos" and joint efforts between Taiwan and French teams for sampling from different localities across the Indo-West Pacific over the last two decades, we are able to compile comprehensive datasets for investigations. In this study, 59 samples representing 36 of 59 known ophidioid genera are selected and used to construct a multi-gene dataset to infer the phylogenetic relationships of ophidioid fishes and their relatives. Our results reveal that the Ophidiidae forms a paraphyletic group with respect to the Carapidae. The four main clades of Ophidioidei resolved are the (1) clade comprising species from the subfamily Brotulinae; (2) clade that includes species in the genera Acanthonus and Xyelacyba; (3) clade grouping Hypopleuron caninum with species from the family Carapidae; and (4) clade containing the species in the subfamily Brotulotaenilinae, Neobythitinae (in part), and Ophidiinae. Accordingly, we suggest the following new revisions based on our results and proposed morphological diagnoses. The subfamily Brotulinae should be elevated to the family level. The genera Xyelacyba and probably Tauredophidium (unsampled in this study) should be included in the newly established family Acanthonidae with Acanthonus. The families Carapidae and Ophidiidae are re-defined. Our time-calibrated phylogenetic and ancestral depth reconstructions enable us to clarify the evolutionary history of ophidiiform fishes and infer past patterns of species distributions at different depths. While Ophidiiformes is inferred to have originated in shallow waters around 96.25 million years ago (Mya), the common ancestor to the Ophidioidei is inferred to have invaded the deep sea around 90.22 Mya, the dates coinciding with the global anoxic event of the OAE2. The observed bathymetric distribution patterns in Ophidioidei most likely point to the mesopelagic zone as the center of origin and diversification. This was followed by multiple events of depth transitions or range expansions towards either shallower waters or greater depth zones, which were likely triggered by past climate changes during the Paleogene-Neogene.

Propensity weighting plus adjustment in proportional hazards model is not doubly robust.

Recently, it has become common for applied works to combine commonly used survival analysis modeling methods, such as the multivariable Cox model and propensity score weighting, with the intention of forming a doubly robust estimator of an exposure effect hazard ratio that is unbiased in large samples when either the Cox model or the propensity score model is correctly specified. This combination does not, in general, produce a doubly robust estimator, even after regression standardization, when there is truly a causal effect. We demonstrate via simulation this lack of double robustness for the semiparametric Cox model, the Weibull proportional hazards model, and a simple proportional hazards flexible parametric model, with both the latter models fit via maximum likelihood. We provide a novel proof that the combination of propensity score weighting and a proportional hazards survival model, fit either via full or partial likelihood, is consistent under the null of no causal effect of the exposure on the outcome under particular censoring mechanisms if either the propensity score or the outcome model is correctly specified and contains all confounders. Given our results suggesting that double robustness only exists under the null, we outline 2 simple alternative estimators that are doubly robust for the survival difference at a given time point (in the above sense), provided the censoring mechanism can be correctly modeled, and one doubly robust method of estimation for the full survival curve. We provide R code to use these estimators for estimation and inference in the supporting information.

Robust analysis of stepped wedge trials using composite likelihood models.

Stepped wedge trials (SWTs) are a type of cluster randomized trial that involve repeated measures on clusters and design-induced confounding between time and treatment. Although mixed models are commonly used to analyze SWTs, they are susceptible to misspecification particularly for cluster-longitudinal designs such as SWTs. Mixed model estimation leverages both "horizontal" or within-cluster information and "vertical" or between-cluster information. To use horizontal information in a mixed model, both the mean model and correlation structure must be correctly specified or accounted for, since time is confounded with treatment and measurements are likely correlated within clusters. Alternative non-parametric methods have been proposed that use only vertical information; these are more robust because between-cluster comparisons in a SWT preserve randomization, but these non-parametric methods are not very efficient. We propose a composite likelihood method that focuses on vertical information, but has the flexibility to recover efficiency by using additional horizontal information. We compare the properties and performance of various methods, using simulations based on COVID-19 data and a demonstration of application to the LIRE trial. We found that a vertical composite likelihood model that leverages baseline data is more robust than traditional methods, and more efficient than methods that use only vertical information. We hope that these results demonstrate the potential value of model-based vertical methods for SWTs with a large number of clusters, and that these new tools are useful to researchers who are concerned about misspecification of traditional models.

Treatments for undefined log ratios in matching analyses.

A challenge in carrying out matching analyses is to deal with undefined log ratios. If any reinforcer or response rate equals zero, the logarithm of the ratio is undefined: data are unsuitable for analyses. There have been some tentative solutions, but they had not been thoroughly investigated. The purpose of this article is to assess the adequacy of five treatments: omit undefined ratios, use full information maximum likelihood, replace undefined ratios by the mean divided by 100, replace them by a constant 1/10, and add the constant .50 to ratios. Based on simulations, the treatments are compared on their estimations of variance accounted for, sensitivity, and bias. The results show that full information maximum likelihood and omiting undefined ratios had the best overall performance, with negligibly biased and more accurate estimates than mean divided by 100, constant 1/10, and constant .50. The study suggests that mean divided by 100, constant 1/10, and constant .50 should be avoided and recommends full information maximum likelihood to deal with undefined log ratios in matching analyses.

Measures of fragmentation of rest activity patterns: mathematical properties and interpretability based on accelerometer real life data.

Accelerometers, devices that measure body movements, have become valuable tools for studying the fragmentation of rest-activity patterns, a core circadian rhythm dimension, using metrics such as inter-daily stability (IS), intradaily variability (IV), transition probability (TP), and self-similarity parameter (named α ). However, their use remains mainly empirical. Therefore, we investigated the mathematical properties and interpretability of rest-activity fragmentation metrics by providing mathematical proofs for the ranges of IS and IV, proposing maximum likelihood and Bayesian estimators for TP, introducing the activity balance index (ABI) metric, a transformation of α , and describing distributions of these metrics in real-life setting. Analysis of accelerometer data from 2,859 individuals (age=60-83 years, 21.1% women) from the Whitehall II cohort (UK) shows modest correlations between the metrics, except for ABI and α . Sociodemographic (age, sex, education, employment status) and clinical (body mass index (BMI), and number of morbidities) factors were associated with these metrics, with differences observed according to metrics. For example, a difference of 5 units in BMI was associated with all metrics (differences ranging between -0.261 (95% CI -0.302, -0.220) to 0.228 (0.18, 0.268) for standardised TP rest to activity during the awake period and TP activity to rest during the awake period, respectively). These results reinforce the value of these rest-activity fragmentation metrics in epidemiological and clinical studies to examine their role for health. This paper expands on a set of methods that have previously demonstrated empirical value, improves the theoretical foundation for these methods, and evaluates their empirical use in a large dataset.

Improved individual identification in DNA mixtures of unrelated or related contributors through massively parallel sequencing.

DNA mixtures are a common sample type in forensic genetics, and we typically assume that contributors to the mixture are unrelated when calculating the likelihood ratio (LR). However, scenarios involving mixtures with related contributors, such as in family murder or incest cases, can also be encountered. Compared to the mixtures with unrelated contributors, the kinship within the mixture would bring additional challenges for the inference of the number of contributors (NOC) and the construction of probabilistic genotyping models. To evaluate the influence of potential kinship on the individual identification of the person of interest (POI), we conducted simulations of two-person (2 P) and three-person (3 P) DNA mixtures containing unrelated or related contributors (parent-child, full-sibling, and uncle-nephew) at different mixing ratios (for 2 P: 1:1, 4:1, 9:1, and 19:1; for 3 P: 1:1:1, 2:1:1, 5:4:1, and 10:5:1), and performed massively parallel sequencing (MPS) using MGIEasy Signature Identification Library Prep Kit on MGI platform. In addition, in silico simulations of mixtures with unrelated and related contributors were also performed. In this study, we evaluated 1): the MPS performance; 2) the influence of multiple genetic markers on determining the presence of related contributors and inferring the NOC within the mixture; 3) the probability distribution of MAC (maximum allele count) and TAC (total allele count) based on in silico mixture profiles; 4) trends in LR values with and without considering kinship in mixtures with related and unrelated contributors; 5) trends in LR values with length- and sequence-based STR genotypes. Results indicated that multiple numbers and types of genetic markers positively influenced kinship and NOC inference in a mixture. The LR values of POI were strongly dependent on the mixing ratio. Non- and correct-kinship hypotheses essentially did not affect the individual identification of the major POI; the correct kinship hypothesis yielded more conservative LR values; the incorrect kinship hypothesis did not necessarily lead to the failure of POI individual identification. However, it is noteworthy that these considerations could lead to uncertain outcomes in the identification of minor contributors. Compared to length-based STR genotyping, using sequence-based STR genotype increases the individual identification power of the POI, concurrently improving the accuracy of mixing ratio inference using EuroForMix. In conclusion, the MGIEasy Signature Identification Library Prep kit demonstrated robust individual identification power, which is a viable MPS panel for forensic DNA mixture interpretations, whether involving unrelated or related contributors.

A collaborative study on the precision of the Markov chain Monte Carlo algorithms used for DNA profile interpretation.

Several fully continuous probabilistic genotyping software (PGS) use Markov chain Monte Carlo algorithms (MCMC) to assign weights to different proposed genotype combinations at a locus. Replicate interpretations of the same profile in these software are expected not to produce identical weights and likelihood ratio (LR) values due to the Monte Carlo aspect. This paper reports a detailed precision study under reproducibility conditions conducted as a collaborative exercise across the National Institute of Standards and Technology (NIST), Federal Bureau of Investigation (FBI), and Institute of Environmental Science and Research (ESR). Replicate interpretations generated across the three laboratories used the same input files, software version, and settings but different random number seed and different computers. This work demonstrates that using different computers to analyze replicate interpretations does not contribute to any variations in LR values. The study quantifies the magnitude of differences in the assigned LRs that is only due to run-to-run MCMC variability and addresses the potential explanations for the observed differences.

Prevalence of male DNA on female worn undergarments. How small datasets may support robust opinions in activity level evaluative reporting.

In cases of sexual assault, the interpretation of biological traces on clothing, and particularly undergarments, may be complex. This is especially so when the complainant and defendant interact socially, for instance as (ex-)partners or by co-habitation. Here we present the results from a study where latent male DNA on female worn undergarments is recovered in four groups with different levels of male-female social interaction. The results conform to prior expectation, in that less interaction tend to result in less male DNA on undergarments. We explore the use of these experimental data for evaluative reporting given activity level propositions in a mock case scenario. We show how the selection of different populations to represent the social interaction between complainant and defendant may affect the strength of the evidence. We further show how datasets of limited size can be used for robust activity level evaluative reporting.