Estimating the distribution of heterogeneous treatment effects from treatment responses and from a predictive biomarker in a parallel-group RCT: A structural model approach

When the objective is to administer the best of two treatments to an individual, it is necessary to know his or her individual treatment effects (ITEs) and the correlation between the potential responses (PRs) and under treatments 1 and 0. Data that are generated in a parallel-group design RCT does not allow the ITE to be determined because only two samples from the marginal distributions of these PRs are observed and not the corresponding joint distribution. This is due to the “fundamental problem of causal inference.” Here, we present a counterfactual approach for estimating the joint distribution of two normally distributed responses to two treatments. This joint distribution of the PRs and can be estimated by assuming a bivariate normal distribution for the PRs and by using a normally distributed baseline biomarker functionally related to the sum . Such a functional relationship is plausible since a biomarker and the sum encode for the same information in an RCT, namely the variation between subjects. The estimation of the joint trivariate distribution is subjected to some constraints. These constraints can be framed in the context of linear regressions with regard to the proportions of variances in the responses explained and with regard to the residual variation. This presents new insights on the presence of treatment–biomarker interactions. We applied our approach to example data on exercise and heart rate and extended the approach to survival data.     

Estimating the decision curve and its precision from three study designs

The decision curve plots the net benefit of a risk model for making decisions over a range of risk thresholds, corresponding to different ratios of misclassification costs. We discuss three methods to estimate the decision curve, together with corresponding methods of inference and methods to compare two risk models at a given risk threshold. One method uses risks (R) and a binary event indicator (Y) on the entire validation cohort. This method makes no assumptions on how well-calibrated the risk model is nor on the incidence of disease in the population and is comparatively robust to model miscalibration. If one assumes that the model is well-calibrated, one can compute a much more precise estimate of based on risks R alone. However, if the risk model is miscalibrated, serious bias can result. Case–control data can also be used to estimate if the incidence (or prevalence) of the event () is known. This strategy has comparable efficiency to using the full data, and its efficiency is only modestly less than that for the full data if the incidence is estimated from the mean of Y. We estimate variances using influence functions and propose a bootstrap procedure to obtain simultaneous confidence bands around the decision curve for a range of thresholds. The influence function approach to estimate variances can also be applied to cohorts derived from complex survey samples instead of simple random samples.     

The design heatmap: A simple visualization of -optimality design problems

Optimal experimental designs are often formal and specific, and not intuitively plausible to practical experimenters. However, even in theory, there often are many different possible design points providing identical or nearly identical information compared to the design points of a strictly optimal design. In practical applications, this can be used to find designs that are a compromise between mathematical optimality and practical requirements, including preferences of experimenters. For this purpose, we propose a derivative-based two-dimensional graphical representation of the design space that, given any optimal design is already known, will show which areas of the design space are relevant for good designs and how these areas relate to each other. While existing equivalence theorems already allow such an illustration in regard to the relevance of design points only, our approach also shows whether different design points contribute the same kind of information, and thus allows tweaking of designs for practical applications, especially in regard to the splitting and combining of design points. We demonstrate the approach on a toxicological trial where a -optimal design for a dose–response experiment modeled by a four-parameter log-logistic function was requested. As these designs require a prior estimate of the relevant parameters, which is difficult to obtain in a practical situation, we also discuss an adaption of our representations to the criterion of Bayesian -optimality. While we focus on -optimality, the approach is in principle applicable to different optimality criteria as well. However, much of the computational and graphical simplicity will be lost.     

Evidence for Depressed Reproduction of Golden Eagles in Washington

Beginning in 1977 the Washington Department of Fish and Wildlife conducted annual surveys to determine statewide golden eagle (Aquila chrysaetos) occupancy and productivity. Current interest in the regional and national status of the species prompted our investigation to determine utility of historical data in assessing trends in reproduction, and to test efficacy of a sampling protocol that surveyed randomly selected territories and also accounted for detection probability. We found evidence indicating poor reproduction from 38 annual surveys conducted at 301 known territories statewide between 1977 and 2014. At 256 territories in eastern Washington, USA, apparent occupancy was low ( = 50.9%) and nesting success declined by 22%. All reproductive parameters were higher than at 45 territories in western Washington. We tested efficacy of a sampling protocol in 2013 and 2014 by surveying 108 randomly selected eastern territories. Probability of detecting eagles for these years from ground (= 89%) was greater than from air (= 66%). Our estimate of territory occupancy, corrected by probability of detection, was lower in 2013 (= 56.7%, 95% CI = 46.3–66.7%) than in 2014 (= 73.7%, 95% CI = 64.8–81.7%), as was the estimated number of breeding pairs (2013: = 158, 95% CI = 151–164; 2014: = 187, 95% CI = 182–192). Higher productivity (young/occupied territory) in 2013 (= 0.59, 95% CI = 0.40–0.82) than in 2014 (= 0.41, 95% CI = 0.27–0.59) and lower proportions of ≥1 immature eagle among nesting pairs in 2013 (16%) than in 2014 (31%), suggested higher immature pairing among sampled pairs contributed to inter-year differences in these reproductive parameters. Current and historical evidence for depressed golden eagle nesting in Washington is consistent with documented effects from habitat conversion, prey declines, lead contamination, and wind power development. We recommend future surveys in eastern Washington adhere to the random sampling protocol and conduct surveys at regular intervals to allow for trend analysis of reproductive parameters to better monitor golden eagle status. Surveys in western Washington, conducted exclusively from ground at all nests, will improve detection and cost efficiency. © 2020 The Wildlife Society.     

Intuitive and broadly applicable definitions of niche and fitness differences

Explaining nature’s biodiversity is a key challenge for science. To persist, populations must be able to grow faster when rare, a feature called negative frequency dependence and quantified as ‘niche differences’ () in modern coexistence theory. Here, we first show that available definitions of differ in how link to species interactions, are difficult to interpret and often apply to specific community types only. We then present a new definition of that is intuitive and applicable to a broader set of (modelled and empirical) communities than is currently the case, filling a main gap in the literature. Given , we also redefine fitness differences () and illustrate how and determine coexistence. Finally, we demonstrate how to apply our definitions to theoretical models and experimental data, and provide ideas on how they can facilitate comparison and synthesis in community ecology.     

On construction of single‐arm two‐stage designs with consideration of both response and toxicity

When establishing a treatment in clinical trials, it is important to evaluate both effectiveness and toxicity. In phase II clinical trials, multinomial data are collected in m‐stage designs, especially in two‐stage () design. Exact tests on two proportions, for the response rate and for the nontoxicity rate, should be employed due to limited sample sizes. However, existing tests use certain parameter configurations at the boundary of null hypothesis space to determine rejection regions without showing that the maximum Type I error rate is achieved at the boundary of null hypothesis. In this paper, we show that the power function for each test in a large family of tests is nondecreasing in both and ; identify the parameter configurations at which the maximum Type I error rate and the minimum power are achieved and derive level‐α tests; provide optimal two‐stage designs with the least expected total sample size and the optimization algorithm; and extend the results to the case of . Some R‐codes are given in the Supporting Information.     

A nonparametric method of estimation of the population size in capture–recapture experiments

A recent method for estimating a lower bound of the population size in capture–recapture samples is studied. Specifically, some asymptotic properties, such as strong consistency and asymptotic normality, are provided. The introduced estimator is based on the empirical probability generating function (pgf) of the observed data, and it is consistent for count distributions having a log-convex pgf (-class). This is a large family that includes mixed and compound Poisson distributions, and their independent sums and finite mixtures as well. The finite-sample performance of the lower bound estimator is assessed via simulation showing a better behavior than some close competitors. Several examples of application are also analyzed and discussed.     

Anthropogenic Disturbance and Population Viability of Woodland Caribou in Ontario

One of the most challenging tasks in wildlife conservation and management is to clarify how spatial variation in land cover due to anthropogenic disturbance influences wildlife demography and long-term viability. To evaluate this, we compared rates of survival and population growth by woodland caribou (Rangifer tarandus caribou) from 2 study sites in northern Ontario, Canada that differed in the degree of anthropogenic disturbance because of commercial logging and road development, resulting in differences in predation risk due to gray wolves (Canis lupus). We used an individual-based model for population viability analysis (PVA) that incorporated adaptive patterns of caribou movement in relation to predation risk and food availability to predict stochastic variation in rates of caribou survival. Field estimates of annual survival rates for adult female caribou in the unlogged ( 0.90) and logged ( 0.76) study sites recorded during 2010–2014 did not differ significantly (P > 0.05) from values predicted by the individual-based PVA model (unlogged: = 0.87; logged: 0.79). Outcomes from the individual-based PVA model and a simpler stage-structured matrix model suggest that substantial differences in adult survival largely due to wolf predation are likely to lead to long-term decline of woodland caribou in the commercially logged landscape, whereas the unlogged landscape should be considerably more capable of sustaining caribou. Estimates of population growth rates (λ) for the 2010–2014 period differed little between the matrix model and the individual-based PVA model for the unlogged (matrix model = 1.01; individual-based model = 0.98) and logged landscape (matrix model = 0.88; individual-based model = 0.89). We applied the spatially explicit PVA model to assess the viability of woodland caribou across 14 woodland caribou ranges in Ontario. Outcomes of these simulations suggest that woodland caribou ranges that have experienced significant levels of commercial forestry activities in the past had annual growth rates <0.89, whereas caribou ranges that had not experienced commercial forestry operations had population growth rates >0.96. These differences were strongly related to regional variation in wolf densities. Our results suggest that increased wolf predation risk due to anthropogenic disturbance is of sufficient magnitude to cause appreciable risk of population decline in woodland caribou in Ontario. © 2020 The Authors. The Journal of Wildlife Management published by Wiley Periodicals, Inc. on behalf of The Wildlife Society.     

Optimal Strategies for Managing Wildlife Harvest Under System Change

Wildlife populations are experiencing shifting dynamics due to climate and landscape change. Management policies that fail to account for non-stationary dynamics may fail to achieve management objectives. We establish a framework for understanding optimal strategies for managing a theoretical harvested population under non-stationarity. Building from harvest theory, we develop scenarios representing changes in population growth rate () or carrying capacity () and derive time-dependent optimal harvest policies using stochastic dynamic programming. We then evaluate the cost of falsely assuming stationarity by comparing the outcomes of forward projections in which either the optimal policy or a stationary policy is applied. When declines over time, the stationary policy leads to an underharvest of the population, resulting in less harvest over the short term but leaving the population in a higher-value state. When declines over time, the stationary policy leads to overharvest, resulting in greater harvest returns in the short term but leaving the population in a lower and potentially more vulnerable state. This work demonstrates the basic properties of time-dependent harvest management and provides a framework for evaluating the many outstanding questions about optimal management strategies under climate change. Published 2021. This article is a U.S. Government work and is in the public domain in the USA.     

Another chemolithotrophic metabolism missing in nature: sulfur comproportionation

Chemotrophic microorganisms gain energy for cellular functions by catalyzing oxidation–reduction (redox) reactions that are out of equilibrium. Calculations of the Gibbs energy ( ΔG _r ) can identify whether a reaction is thermodynamically favourable and quantify the accompanying energy yield at the temperature, pressure and chemical composition in the system of interest. Based on carefully calculated values of ΔG _r , we predict a novel microbial metabolism – sulfur comproportionation (3H₂S + + 2H⁺ ⇌ 4S⁰ + 4H₂O). We show that at elevated concentrations of sulfide and sulfate in acidic environments over a broad temperature range, this putative metabolism can be exergonic ( ΔG _r <0), yielding ~30–50 kJ mol⁻¹. We suggest that this may be sufficient energy to support a chemolithotrophic metabolism currently missing from the literature. Other versions of this metabolism, comproportionation to thiosulfate (H₂S + ⇌ + H₂O) and to sulfite (H₂S + 3 ⇌ 4 + 2H⁺), are only moderately exergonic or endergonic even at ideal geochemical conditions. Natural and impacted environments, including sulfidic karst systems, shallow-sea hydrothermal vents, sites of acid mine drainage, and acid–sulfate crater lakes, may be ideal hunting grounds for finding microbial sulfur comproportionators.     

Mean growth rate when rare is not a reliable metric for persistence of species

The coexistence of many species within ecological communities poses a long‐standing theoretical puzzle. Modern coexistence theory (MCT) and related techniques explore this phenomenon by examining the chance of a species population growing from rarity in the presence of all other species. The mean growth rate when rare, , is used in MCT as a metric that measures persistence properties (like invasibility or time to extinction) of a population. Here we critique this reliance on and show that it fails to capture the effect of temporal random abundance variations on persistence properties. The problem becomes particularly severe when an increase in the amplitude of stochastic temporal environmental variations leads to an increase in , since at the same time it enhances random abundance fluctuations and the two effects are inherently intertwined. In this case, the chance of invasion and the mean extinction time of a population may even go down as increases.     

The effects of hurricanes on the stochastic population growth of the endemic epiphytic orchid Broughtonia cubensis living in Cuba

We carried out a posthurricane evaluation of Broughtonia cubensis (Lindl.) Cogn., an endemic Cuban epiphytic orchid, after Hurricane Ivan (2004). We studied the transient responses in the stochastic dynamics of the species at three different sites over 13 successive years (2006–2019), monitored plot inventories (464 individuals in 10 transects) and built stochastic population models. The deterministic stochastic growth rate values () did not significantly differ (F = 2.76; p > 0.076) among the three sites over the 2006–2019 period. The long-term stochastic growth rate was 0.973 [0.932, 1.034]. The matrix elements that had the largest effect on were the transition to and stasis within the largest size class. Transient responses explained an average of 86% of the variation in the observed population growth rates , compared to 4% of the variation in the vital rates . Because transient dynamics are dependent on the population size composition, we ran extinction risk analyses under two scenarios: a population composed mainly of juveniles and another composed mainly of adults. There was little risk of falling below the quasi-extinction threshold before 25 year for both juveniles and adults. However, the risk of quasi-extinction was almost certain for both size classes by 80 year. We also simulated the effect of increasing the hurricane occurrence probability over 80 year on the population. There was little risk of extinction before 20 year in the baseline model, but there was a significant risk of extinction within 5 year when 90% of the individuals were affected by a new hurricane event.     

Optimal rotation of insecticides to prevent the evolution of resistance in a structured environment

Several strategies have been used in insecticide resistance management to prevent the evolution of resistance, but the spatial aspects of insecticide application are crucially important among these strategies. Here, we consider a structured environment that consists of on-farm and off-farm fields where crops are planted periodically in on-farm fields during cultivation periods. We define the basic reproduction rate () of resistance as the expected number of offspring of a resistant individual divided by that of a susceptible individual under the condition that the proportion of resistance is extremely small; it is measured as the quantity per cycle of the cultivation period. We calculate using realistic dose-survival curves under a given fitness cost of resistance genes. The evolution of resistance occurs if and only if the value is larger than 0. Then, we propose a procedure for calculating the optimal design of rotational spraying that prevents the evolution of resistance, that is, the evolutionary stable strategy (ESS) for farmers, satisfying the mortality required for managing the abundance of insects. We consider the following controllable factors in calculating the optimal design: the dose of insecticide, the number of sprays, the number of different types of insecticides and potentially, the size of on-farm fields.     

Comparison of normal distribution–based and nonparametric decision limits on the GH‐2000 score for detecting growth hormone misuse (doping) in sport

This paper is motivated by the GH‐2000 biomarker test, though the discussion is applicable to other diagnostic tests. The GH‐2000 biomarker test has been developed as a powerful technique to detect growth hormone misuse by athletes, based on the GH‐2000 score. Decision limits on the GH‐2000 score have been developed and incorporated into the guidelines of the World Anti‐Doping Agency (WADA). These decision limits are constructed, however, under the assumption that the GH‐2000 score follows a normal distribution. As it is difficult to affirm the normality of a distribution based on a finite sample, nonparametric decision limits, readily available in the statistical literature, are viable alternatives. In this paper, we compare the normal distribution–based and nonparametric decision limits. We show that the decision limit based on the normal distribution may deviate significantly from the nominal confidence level or nominal FPR when the distribution of the GH‐2000 score departs only slightly from the normal distribution. While a nonparametric decision limit does not assume any specific distribution of the GH‐2000 score and always guarantees the nominal confidence level and FPR, it requires a much larger sample size than the normal distribution–based decision limit. Due to the stringent FPR of the GH‐2000 biomarker test used by WADA, the sample sizes currently available are much too small, and it will take many years of testing to have the minimum sample size required, in order to use the nonparametric decision limits. Large sample theory about the normal distribution–based and nonparametric decision limits is also developed in this paper to help understanding their behaviours when the sample size is large.     

Isotopically anomalous organic carbon in the aftermath of the Marinoan snowball Earth

Throughout most of the sedimentary record, the marine carbon cycle is interpreted as being in isotopic steady state. This is most commonly inferred via isotopic reconstructions, where two export fluxes (organic carbon and carbonate) are offset by a constant isotopic fractionation of ~25 (termed ). Sedimentary deposits immediately overlying the Marinoan snowball Earth diamictites, however, stray from this prediction. In stratigraphic sections from the Ol Formation (Mongolia) and Sheepbed Formation (Canada), we observe a temporary excursion where the organic matter has anomalously heavy C and is grossly decoupled from the carbonate C. This signal may reflect the unique biogeochemical conditions that persisted in the aftermath of snowball Earth. For example, physical oceanographic modeling suggests that a strong density gradient caused the ocean to remain stratified for about 50,000 years after termination of the Marinoan snowball event, during which time the surface ocean and continental weathering consumed the large atmospheric CO₂ reservoir. Further, we now better understand how C records of carbonate can be post‐depostionally altered and thus be misleading. In an attempt to explain the observed carbon isotope record, we developed a model that tracks the fluxes and isotopic values of carbon between the surface ocean, deep ocean, and atmosphere. By comparing the model output to the sedimentary data, stratification alone cannot generate the anomalous observed isotopic signal. Reproducing the heavy C in organic matter requires the progressively diminishing contribution of an additional anomalous source of organic matter. The exact source of this organic matter is unclear.     

Theoretical study of the Raman optical activity spectra of with M = Co,Rh

Vibrational Raman optical activity (ROA) spectra were calculated under off-resonance, near-resonance, and at-resonance conditions for ( A ) and under off-resonance conditions for ( B ) using a new driver software for calculating the ROA intensities from complex (damped) time-dependent linear response Kohn-Sham theory. The off-resonance spectra of A and B show many similarities. At an incident laser wavelength of 532 nm, used in commercial ROA spectrometers, the spectrum of A is enhanced by near-resonance with the ligand-field transitions of the complex. The near-resonance spectrum exhibits many qualitative differences compared with the off-resonance case, but it remains bi-signate. Even under full resonance with the ligand-field electronic transitions, the ROA spectrum of A remains bi-signate when the electronic transitions are broadened such as to yield absorption line widths that are comparable with those in the experimental UV-vis absorption and electronic circular dichroism spectra.     

An estimator of the Opportunity for Selection that is independent of mean fitness

Variation among individuals in number of offspring (fitness, k) sets an upper limit to the evolutionary response to selection. This constraint is quantified by Crow's Opportunity for Selection (I), which is the variance in relative fitness (I = σ²_k/(u_k)²). Crow's I has been widely used but remains controversial because it depends on mean offspring number in a sample (). Here, I used a generalized Wright-Fisher model that allows for unequal probabilities of producing offspring to evaluate behavior of Crow's I and related indices under a wide range of sampling scenarios. Analytical and numerical results are congruent and show that rescaling the sample variance (s²_k) to its expected value at a fixed removes dependence of I on mean offspring number, but the result still depends on choice of . A new index is introduced, Δ_I = Π– E(Î_drift) = Π– 1/, which makes Î independent of sample without the need for variance rescaling. Δ_I has a straightforward interpretation as the component of variance in relative fitness that exceeds that expected under a null model of random reproductive success. Δ_I can be used to directly compare estimates of the Opportunity for Selection for samples from different studies, different sexes, and different life stages.     

The genetic architecture of maternal effects across ontogeny in the red deer

Maternal effects, either environmental or genetic in origin, are an underappreciated source of phenotypic variance in natural populations. Maternal genetic effects have the potential to constrain or enhance the evolution of offspring traits depending on their magnitude and their genetic correlation with direct genetic effects. We estimated the maternal effect variance and its genetic component for 12 traits expressed over the life history in a pedigreed population of wild red deer (morphology, survival/longevity, breeding success). We only found support for maternal genetic effect variance in the two neonatal morphological traits: birth weight ( = 0.31) and birth leg length ( = 0.17). For these two traits, the genetic correlation between maternal and direct additive effects was not significantly different from zero, indicating no constraint to evolution from genetic architecture. In contrast, variance in maternal genetic effects enhanced the additive genetic variance available to respond to natural selection. Maternal effect variance was negligible for late-life traits. We found no evidence for sex differences in either the direct or maternal genetic architecture of offspring traits. Our results suggest that maternal genetic effect variance declines over the lifetime, but also that this additional heritable genetic variation may facilitate evolutionary responses of early-life traits.     

Relationship of current management practices to movements of Piping Plover broods in an Atlantic Coast population

Mobility of precocial chicks facilitates self-feeding and escape from predators, but also allows chicks to move into potentially dangerous areas. At Cape Hatteras National Seashore and Pea Island National Wildlife Refuge, North Carolina, precocial Piping Plovers (Charadrius melodus) are managed with vehicle and pedestrian exclusion buffers to reduce potential anthropogenic disturbance and mortality. From 2015 to 2018, we monitored 23 broods from hatching until fledging age (25 days), and recorded brood locations, chick behavior, and potentially disruptive predators, people, or vehicles. We estimated straight-line hourly movement rates relative to brood habitat selection, behavior, and potential disturbance stimuli, daily movement distances, and 95% minimum convex polygon home range areas of broods through the pre-fledging period. Daily brood movements , range = 0–327.3 m/d) varied by age and year. Hourly movements also varied , range = 0.04–1450.9 m/h), but were not well described by the factors we tested. Daily and hourly movements were generally shorter than current management buffer sizes, broods were always observed within protective buffers, and were rarely disturbed by human activity or possible predators. Home range sizes of broods ( increased as broods aged. Our results show that movements by plover broods can be variable and relatively unpredictable across temporal and spatial scales, but the low rate of brood disturbance suggests effective management of anthropogenic disturbance. We recommend that under current conditions, regular monitoring by managers should continue to ensure that the size and location of implemented buffers track actual brood use without exposing broods to risks from human beach users.