One-step targeted maximum likelihood estimation for time-to-event outcomes

Researchers in observational survival analysis are interested in not only estimating survival curve nonparametrically but also having statistical inference for the parameter. We consider right-censored failure time data where we observe n independent and identically distributed observations of a vector random variable consisting of baseline covariates, a binary treatment at baseline, a survival time subject to right censoring, and the censoring indicator. We assume the baseline covariates are allowed to affect the treatment and censoring so that an estimator that ignores covariate information would be inconsistent. The goal is to use these data to estimate the counterfactual average survival curve of the population if all subjects are assigned the same treatment at baseline. Existing observational survival analysis methods do not result in monotone survival curve estimators, which is undesirable and may lose efficiency by not constraining the shape of the estimator using the prior knowledge of the estimand. In this paper, we present a one-step Targeted Maximum Likelihood Estimator (TMLE) for estimating the counterfactual average survival curve. We show that this new TMLE can be executed via recursion in small local updates. We demonstrate the finite sample performance of this one-step TMLE in simulations and an application to a monoclonal gammopathy data.     

Large scale maximum average power multiple inference on time-course count data with application to RNA-seq analysis

Experiments that longitudinally collect RNA sequencing (RNA-seq) data can provide transformative insights in biology research by revealing the dynamic patterns of genes. Such experiments create a great demand for new analytic approaches to identify differentially expressed (DE) genes based on large-scale time-course count data. Existing methods, however, are suboptimal with respect to power and may lack theoretical justification. Furthermore, most existing tests are designed to distinguish among conditions based on overall differential patterns across time, though in practice, a variety of composite hypotheses are of more scientific interest. Finally, some current methods may fail to control the false discovery rate. In this paper, we propose a new model and testing procedure to address the above issues simultaneously. Specifically, conditional on a latent Gaussian mixture with evolving means, we model the data by negative binomial distributions. Motivated by Storey (2007) and Hwang and Liu (2010), we introduce a general testing framework based on the proposed model and show that the proposed test enjoys the optimality property of maximum average power. The test allows not only identification of traditional DE genes but also testing of a variety of composite hypotheses of biological interest. We establish the identifiability of the proposed model, implement the proposed method via efficient algorithms, and demonstrate its good performance via simulation studies. The procedure reveals interesting biological insights, when applied to data from an experiment that examines the effect of varying light environments on the fundamental physiology of the marine diatom Phaeodactylum tricornutum.     

Partial least squares for functional joint models with applications to the Alzheimer's disease neuroimaging initiative study

Many biomedical studies have identified important imaging biomarkers that are associated with both repeated clinical measures and a survival outcome. The functional joint model (FJM) framework, proposed by Li and Luo in 2017, investigates the association between repeated clinical measures and survival data, while adjusting for both high-dimensional images and low-dimensional covariates based on the functional principal component analysis (FPCA). In this paper, we propose a novel algorithm for the estimation of FJM based on the functional partial least squares (FPLS). Our numerical studies demonstrate that, compared to FPCA, the proposed FPLS algorithm can yield more accurate and robust estimation and prediction performance in many important scenarios. We apply the proposed FPLS algorithm to a neuroimaging study. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.     

A Bayesian multi-risks survival (MRS) model in the presence of double censorings

Semi-competing risks data include the time to a nonterminating event and the time to a terminating event, while competing risks data include the time to more than one terminating event. Our work is motivated by a prostate cancer study, which has one nonterminating event and two terminating events with both semi-competing risks and competing risks present as well as two censoring times. In this paper, we propose a new multi-risks survival (MRS) model for this type of data. In addition, the proposed MRS model can accommodate noninformative right-censoring times for nonterminating and terminating events. Properties of the proposed MRS model are examined in detail. Theoretical and empirical results show that the estimates of the cumulative incidence function for a nonterminating event may be biased if the information on a terminating event is ignored. A Markov chain Monte Carlo sampling algorithm is also developed. Our methodology is further assessed using simulations and also an analysis of the real data from a prostate cancer study. As a result, a prostate-specific antigen velocity greater than 2.0 ng/mL per year and higher biopsy Gleason scores are positively associated with a shorter time to death due to prostate cancer.     

Relative efficiency of using summary versus individual data in random-effects meta-analysis

Meta-analysis is a statistical methodology for combining information from diverse sources so that a more reliable and efficient conclusion can be reached. It can be conducted by either synthesizing study-level summary statistics or drawing inference from an overarching model for individual participant data (IPD) if available. The latter is often viewed as the “gold standard.” For random-effects models, however, it remains not fully understood whether the use of IPD indeed gains efficiency over summary statistics. In this paper, we examine the relative efficiency of the two methods under a general likelihood inference setting. We show theoretically and numerically that summary-statistics-based analysis is at most as efficient as IPD analysis, provided that the random effects follow the Gaussian distribution, and maximum likelihood estimation is used to obtain summary statistics. More specifically, (i) the two methods are equivalent in an asymptotic sense; and (ii) summary-statistics-based inference can incur an appreciable loss of efficiency if the sample sizes are not sufficiently large. Our results are established under the assumption that the between-study heterogeneity parameter remains constant regardless of the sample sizes, which is different from a previous study. Our findings are confirmed by the analyses of simulated data sets and a real-world study of alcohol interventions.     

A resurrection study reveals limited evolution of thermal performance in response to recent climate change across the geographic range of the scarlet monkeyflower

Evolutionary rescue can prevent populations from declining under climate change, and should be more likely at high-latitude, “leading” edges of species’ ranges due to greater temperature anomalies and gene flow from warm-adapted populations. Using a resurrection study with seeds collected before and after a 7-year period of record warming, we tested for thermal adaptation in the scarlet monkeyflower Mimulus cardinalis. We grew ancestors and descendants from northern-edge, central, and southern-edge populations across eight temperatures. Despite recent climate anomalies, populations showed limited evolution of thermal performance curves. However, one southern population evolved a narrower thermal performance breadth by 1.31°C, which matches the direction and magnitude of the average decrease in seasonality experienced. Consistent with the climate variability hypothesis, thermal performance breadth increased with temperature seasonality across the species’ geographic range. Inconsistent with performance trade-offs between low and high temperatures across populations, we did not detect a positive relationship between thermal optimum and mean temperature. These findings fail to support the hypothesis that evolutionary response to climate change is greatest at the leading edge, and suggest that the evolution of thermal performance is unlikely to rescue most populations from the detrimental effects of rapidly changing climate.     

When sinks become sources: Adaptive colonization in asexuals*

The establishment of a population into a new empty habitat outside of its initial niche is a phenomenon akin to evolutionary rescue in the presence of immigration. It underlies a wide range of processes, such as biological invasions by alien organisms, host shifts in pathogens, or the emergence of resistance to pesticides or antibiotics from untreated areas. We derive an analytically tractable framework to describe the evolutionary and demographic dynamics of asexual populations in a source-sink system. We analyze the influence of several factors on the establishment success in the sink, and on the time until establishment. To this aim, we use a classic phenotype-fitness landscape (Fisher's geometrical model in n dimensions) where the source and sink habitats have different phenotypic optima. In case of successful establishment, the mean fitness in the sink follows a typical four-phases trajectory. The waiting time to establishment is independent of the immigration rate and has a “U-shaped” dependence on the mutation rate, until some threshold where lethal mutagenesis impedes establishment and the sink population remains so. We use these results to get some insight into possible effects of several management strategies.     

Non-linear molecular pattern classification using molecular beacons with multiple targets

In vitro pattern classification has been highlighted as an important future application of DNA computing. Previous work has demonstrated the feasibility of linear classifiers using DNA-based molecular computing. However, complex tasks require non-linear classification capability. Here we design a molecular beacon that can interact with multiple targets and experimentally shows that its fluorescent signals form a complex radial-basis function, enabling it to be used as a building block for non-linear molecular classification in vitro. The proposed method was successfully applied to solving artificial and real-world classification problems: XOR and microRNA expression patterns.