Two‐phase polynomial regression models (Robison, 1964; Fuller, 1969; Gallant and Fuller, 1973; Zhan et al., 1996) are widely used in ecology, public health, and other applied fields to model nonlinear relationships. These models are characterized by the presence of threshold parameters, across which the mean functions are allowed to change. That the threshold is a parameter of the model to be estimated from the data is an essential feature of two‐phase models. It distinguishes them, and more generally, multiphase models, from the spline models and has profound implications for both computation and inference for the models. Estimation of two‐phase polynomial regression models is a nonconvex, nonsmooth optimization problem. Grid search provides high‐quality solutions to the estimation problem, but is very slow when performed by brute force. Building upon our previous work on piecewise linear two‐phase regression models estimation, we develop fast grid search algorithms for two‐phase polynomial regression models and demonstrate their performance. Furthermore, we develop bootstrap‐based pointwise and simultaneous confidence bands for mean functions. Monte Carlo studies are conducted to demonstrate the computational and statistical properties of the proposed methods. Three real datasets are used to help illustrate the application of two‐phase models, with special attention on model choice.

Fast grid search and bootstrap‐based inference for continuous two‐phase polynomial regression models

Abstract While detection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) by diagnostic reverse-transcription polymerase chain reaction (RT-PCR) is highly sensitive for viral RNA, the nucleic acid amplification of subgenomic RNAs (sgRNAs) that are the product of viral replication may more accurately identify replication. We characterized the diagnostic RNA and sgRNA detection by RT-PCR from nasal swab samples collected daily by participants in postexposure prophylaxis or treatment studies for SARS-CoV-2. Among 1932 RT-PCR–positive swab samples with sgRNA tests, 40% (767) had detectable sgRNA. Above a diagnostic RNA viral load (VL) threshold of 5.1 log10 copies/mL, 96% of samples had detectable sgRNA with VLs that followed a linear trend. The trajectories of diagnostic RNA and sgRNA VLs differed, with 80% peaking on the same day but duration of sgRNA detection being shorter (8 vs 14 days). With a large sample of daily swab samples we provide comparative sgRNA kinetics and a diagnostic RNA threshold that correlates with replicating virus independent of symptoms or duration of illness. 

/pdf/oup-accepted-manuscript-3j09s25a.pdf

OUP accepted manuscript

Nursing in the Digital Age: Harnessing telemedicine for enhanced patient care

The method of Outcalt et al., based on work developed originally by Hurst, is re‐examined to evaluate its efficacy in delineating changes in trends and identifying regime shifts in climatic‐related time series. This technique is based on the concept of the normalized rescaled running sum where temporal changes in the Hurst exponent can be used to identify climatic trends from one regime to another as each regime has a characteristic distribution that differs from the statistical characteristics of the complete time series. An examination of the temporal change in the amplitude of the normalized rescaled running sum can be used as a method to identify these regime changes, which may be either real (i.e., a true climatic shift) or induced (i.e., through a change in measurement bias, station location, or other nonclimatic influence). Examples shown here focus on examining time series of the Pacific Decadal Oscillation, Arctic thaw depth, the Northern Hemisphere snow cover extent, treeflow data from Lees Ferry (AZ), North Atlantic tropical cyclone frequency, and central England air temperatures.

Detection of climate transitions and discontinuities by Hurst rescaling

Gene copy number variation (CNV) has been increasingly associated with organismal responses to environmental stress, but we know little about the quantitative relation between CNV and phenotypic variation. In this study we quantify the relation between variation in EPSPS (5-enolpyruvylshikimate-3-phosphate synthase) copy number using digital drop PCR and variation in phenotypic glyphosate resistance in 22 populations of Amaranthus palmeri (Palmer Amaranth), a range-expanding agricultural weed. Overall, we detected a significant positive relation between population mean copy number and resistance. The majority of populations exhibited high glyphosate resistance yet maintained low-resistance individuals, resulting in bimodality in many populations. We also investigated threshold models for the relation between copy number and resistance, and found evidence for a threshold of ~15 EPSPS copies: there was a steep increase in resistance below the threshold, followed by a much shallower increase. Across 924 individuals, as copy number increased the range of variation in resistance decreased, yielding an increasing frequency of high phenotypic resistance individuals. Among populations we detected a decline in variation (s.d.) as mean phenotypic resistance increased from moderate to high, consistent with the prediction that as phenotypic resistance increases in populations, stabilizing selection decreases variation in the trait. Our study demonstrates that populations of A. palmeri can harbour wide variation in EPSPS copy number and phenotypic glyphosate resistance, reflecting the history of, and template for future, resistance evolution.

Defence by duplication: The relation between phenotypic glyphosate resistance and EPSPS gene copy number variation in Amaranthus palmeri.

We introduce a new type of threshold regression models called upper hinge models. Under this type of threshold models, there only exists an association between the predictor of interest and the outcome when the predictor is less than some threshold value. Just like hinge models, upper hinge models can be seen as a special case of the more general segmented or two-phase regression models. The importance of studying upper hinge models is that even though they only have one fewer degree of freedom than segmented models, they can be estimated with much greater efficiency. We develop a new fast grid search algorithm to estimate upper hinge linear regression models. The new algorithm reduces the computational complexity of the search algorithm dramatically and renders the existing fast grid search algorithm inadmissible. The fast grid search algorithm makes it feasible to construct bootstrap confidence intervals for upper hinge linear regression models; for upper hinge generalized linear models of non-Gaussian family, we derive asymptotic normality to facilitate construction of model-robust confidence intervals. We perform numerical experiments and illustrate the proposed methods with two real data examples from the ecology literature.

Estimation and inference for upper hinge regression models

Due to widespread healthcare workforce shortages, many patients living in remote and rural North America currently have reduced access to various medical specialists. These shortages, coupled with the aging North American population, highlight the need to transform contemporary healthcare delivery systems. The exchange of medical information via telecommunication technology, known as telemedicine, offers promising solutions to address the medical needs of an aging population and the increased demand for specialty medical services. This progressive movement has also improved access to quality health care by mitigating the current shortage of trained subspecialists. Minimizing the effects of these shortages is particularly urgent in the care of cancer patients, many of whom require regular follow-up and close monitoring. Cancer patients living in remote areas of North America have reduced access to specialized care and, thus, have unacceptably high mortality and morbidity rates. Teleoncology, or the use of telemedicine to provide oncology services remotely, has the ability to improve access to high-quality care and assist in alleviating the burden of some of the severe adverse events associated with cancer. In this review, the authors describe how recent advances in teleoncology can reduce healthcare disparities and improve future cancer care in North America.

Teleoncology: Novel Approaches for Improving Cancer Care in North America

While dermal piercings have become increasingly popular, there is limited dermatologic literature detailing a standard removal technique. Dermal piercings are often removed in the emergency department using non-serrated hemostats and a rocking motion until the anchor can be pulled through the skin. Removal by these means may lead to unnecessary damage to the skin, infections, and scarring. This article describes a straightforward technique for extracting dermal piercings that does not require the patient to know the size or type of dermal anchor. A detailed description, with corresponding images, is provided as a step-by-step guide on implementing a punch removal technique for dermal piercings. Dermatologists can implement this technique to remove piercings without knowing the underlying anchor type. This punch removal technique offers a solution for removing a variety of dermal piercings and subsequent scar tissue while minimizing scar formation and leaving patients with more cosmetically appealing skin.

pdf/step-by-step-guide-to-the-punch-removal-technique-for-dermal-4x8k79hior.pdf

Step-by-Step Guide to the Punch Removal Technique for Dermal Piercing: A Surgical Pearl

As a common step in refining their scientific inquiry, investigators are often interested in performing some screening of a collection of given statistical hypotheses. For example, they may wish to determine whether any one of several patient characteristics are associated with a health outcome of interest. Existing generic methods for testing a multivariate hypothesis — such as multiplicity corrections applied to individual hypothesis tests — can easily be applied across a variety of problems but can suffer from low power in some settings. Tailor-made procedures can attain higher power by building around problem-specific information but typically cannot be easily adapted to novel settings. In this work, we propose a general framework for testing a multivariate point null hypothesis in which the test statistic is adaptively selected to provide increased power. We present theoretical large-sample guarantees for our test under both fixed and local alternatives. In simulation studies, we show that tests created using our framework can perform as well as tailor-made methods when the latter are available, and we illustrate how our procedure can be used to create tests in two settings in which tailor-made methods are not currently available.

A general adaptive framework for multivariate point null testing

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Papers

Estimation and inference for upper hinge regression models

Teleoncology: Novel Approaches for Improving Cancer Care in North America

Step-by-Step Guide to the Punch Removal Technique for Dermal Piercing: A Surgical Pearl

A general adaptive framework for multivariate point null testing