On responder analyses when a continuous variable is dichotomized and measurement error is present

In clinical studies results are often reported as proportions of responders, i.e. the proportion of subjects who fulfill a certain response criterion is reported, although the underlying variable of interest is continuous. In this paper, we consider the situation where a subject is defined as a responder if the (error-free) continuous measurements post-treatment are below a certain fraction of (error-free) continuous measurements obtained pre-treatment. Focus is on the one-sample case, but an extension to the two-sample case is also presented. The bias of different estimates for the proportion of responders is derived and compared. In addition, an asymptotically unbiased ML-type estimate for the proportion of responders is presented. The results are illustrated using data obtained in a clinical study investigating pre-menstrual dysphoric disorder (PMDD).     

Repeated significance tests for clinical trials with a fixed number of patients and variable follow-up

Group-sequential tests may be applied to trials in which the number of patients is fixed, a response variable is measured for each patient at successive follow-up visits, and the accumulated responses are compared across treatment groups. The standard theory is inapplicable because the increments in the accumulated responses are no longer independent. An adjustment can be made to allow for the ratio of between-patient to within-patient variance and for possible first-order autocorrelation. The method is illustrated by reference to a dental trial.     

Carbon-use efficiency in green sinks is increased when a blend of apoplastic fructose and glucose is available for uptake

Understanding how green sink strength is regulated in planta poses a difficult problem because non-structural carbohydrate (NSC) levels can have integrated, simultaneous feedback effects on photosynthesis, sugar uptake, and respiration that depend on specific NSC moieties. Photosynthetic gametophytes of the fern Ceratopteris richardii provide a simple land plant model to assess how different NSCs imported from the apoplast of intact plants affect green sink strength. Sink strength was quantified as the amount of exogenous sugar that plants grown in low light depleted from their liquid media, and the relative contributions of carbon assimilation by photosynthesis and sugar uptake was estimated from stable isotope analysis of plant dry mass. Gametophytes absorbed fructose and glucose with equal affinity when cultured on either hexose alone, or in the presence of an equimolar blend of both sugars. Plants also depleted sucrose from the surrounding media, although a portion of this disaccharide that was hydrolysed into fructose and glucose by putative cell wall invertase activity remained in the media. The δ(13)C in plant dry masses harvested from sugar treatments were all close to -18‰, indicating that 25-39% of total plant carbon was from C3 photosynthesis (δ(13)C=-29‰) and 61-75% was from uptake of exogenous sugars (δ(13)C=-11‰). Carbon-use efficiency (i.e. carbon accumulated/carbon depleted) was significantly improved when plants had a blend of exogenous sugars available compared with plants grown in a single hexose alone. Plants avoided complete down-regulation of photosynthesis even though a large excess of exogenous carbon fluxed through their cells.     

Feed efficiency of lactating Holstein cows is repeatable within diet but less reproducible when changing dietary starch and forage concentrations

Improving feed efficiency has become an important target for dairy farmers to produce more milk with fewer feed resources. With decreasing availability of arable land to produce feeds that are edible for human consumption, it will be important to increase the proportion of feeds in the diets for dairy cattle that are less edible for human consumption. The current research analyzed the ability of lactating dairy cows to maintain their feed efficiency when switching between a high starch diet (HS diet: 27% starch, 29% NDF, 47.1% forages on a DM basis) and a low starch diet (LS diet: 13% starch, 37% NDF, 66.4% forages on a DM basis). Sixty-two lactating Holstein cows (137 ± 23 days in milk (DIM) at the start of experiment), of which 29 were primiparous cows, were utilized in a crossover design with two 70-d experimental periods, including a 14-d adaption period for each. Feed efficiency was estimated as the individual deviation from the population average intercept in a mixed model predicting DM intake (DMI) with net energy in milk, maintenance and BW gain and loss. Repeatability was estimated within each diet by comparing feed efficiency estimated over the first 28-day period and the second 28-day period within each diet, using Pearson’s and intraclass correlations, and the estimation of error of repeatability. Similarly, reproducibility was estimated by comparing the second 28-day period of one diet with the first 28-day period of the other diet. Feed efficiency was less reproducible across diets than repeatable within the same diet. This was shown by lower intraclass correlations (0.399) across diets compared to that in the HS diet (0.587) and LS diet (0.806), as well as a lower Pearson’s correlation coefficient (0.418) across diets compared to that in the HS diet (0.630) and LS diet (0.809). In addition, the estimation of error of repeatability was higher (0.830 kg DM/d) across diets compared to that in the HS diet (0.761 kg DM/d) and LS diet (0.504 kg DM/d). This means that the feed efficiency of dairy cows is more likely to change after a diet change than over subsequent lactation stages. Other determinants, such as digestive processes, need to be further investigated to determine its effects on estimating feed efficiency.     

Monogamy when there is potential for polygyny: tests of multiple hypotheses in a group-living fish

Monogamy within social groups where there exists a high potentialfor polygyny poses a challenge to our understanding of matingsystem evolution. Specifically, the traditional explanationthat monogamy evolves due to wide female dispersion, affordingmales little opportunity to defend multiple females, cannotapply. Instead, monogamy in groups potentially arises becausefemales compete for breeding resources such as breeding sites,food, and paternal care. We conducted manipulative experimentsto determine whether females compete over limiting resourceswithin groups of the obligate coral-dwelling goby, Paragobiodonxanthosomus (Gobiidae). Breeding females behaved aggressivelytoward individuals of their own sex and evicted subordinatefemales that were large and mature from the group. Experimentalremoval of nest sites caused breeding partners to breed in alternativenest sites, demonstrating that nest site limitation was notthe cause of female competition. Supplemental feeding resultedin an increase in the fecundity of breeding females but no maturationof subordinate females, demonstrating that food-limited femalefecundity was a likely cause of female competition. Finally,supplemental feeding of breeding pairs demonstrated that thedifference in eggs hatched by fed versus unfed males was lessthan the difference in eggs laid by fed versus unfed females,suggesting that paternal care limitation might also drive femalecompetition. These results suggest that competition over foodand possibly paternal care selects for dominant, breeding femalesto suppress the maturation of subordinate females to minimizecompetition. Monogamy in association with group living is thereforelikely to have evolved because female competition prevents malesfrom utilizing the potential for polygyny.     

Optimal designs when the variance is a function of the mean

We develop locally D-optimal designs for nonlinear models when the variance of the response is a function of its mean. Using the two-parameter Michaelis-Menten model as an example, we show that the optimal design depends on both the type of heteroscedasticity and the magnitude of the variation. In addition, our results suggest that the homoscedastic D-optimal design has high efficiency under a broad class of heteroscedastic patterns and that it is fairly insensitive to nominal values of the parameters.     

Dynamics of neutral and selected alleles when the offspring distribution is skewed

We analyze the dynamics of two alternative alleles in a simple model of a population that allows for large family sizes in the distribution of offspring number. This population model was first introduced by Eldon and Wakeley, who described the backward-time genealogical relationships among sampled individuals, assuming neutrality. We study the corresponding forward-time dynamics of allele frequencies, with or without selection. We derive a continuum approximation, analogous to Kimura's diffusion approximation, and we describe three distinct regimes of behavior that correspond to distinct regimes in the coalescent processes of Eldon and Wakeley. We demonstrate that the effect of selection is strongly amplified in the Eldon-Wakeley model, compared to the Wright-Fisher model with the same variance effective population size. Remarkably, an advantageous allele can even be guaranteed to fix in the Eldon-Wakeley model, despite the presence of genetic drift. We compute the selection coefficient required for such behavior in populations of Pacific oysters, based on estimates of their family sizes. Our analysis underscores that populations with the same effective population size may nevertheless experience radically different forms of genetic drift, depending on the reproductive mechanism, with significant consequences for the resulting allele dynamics.     

The adaptive significance of temperature-dependent sex determination: experimental tests with a short-lived lizard

Abstract Why is the sex of many reptiles determined by the temperatures that these animals experience during embryogenesis, rather than by their genes? The Charnov‐Bull model suggests that temperature‐dependent sex determination (TSD) can enhance maternal fitness relative to genotypic sex determination (GSD) if offspring traits affect fitness differently for sons versus daughters and nest temperatures either determine or predict those offspring traits. Although potential pathways for such effects have attracted much speculation, empirical tests largely have been precluded by logistical constraints (i.e., long life spans and late maturation of most TSD reptiles). We experimentally tested four differential fitness models within the Charnov‐Bull framework, using a short‐lived, early‐maturing Australian lizard (Amphibolurus muricatus) with TSD. Eggs from wild‐caught females were incubated at a range of thermal regimes, and the resultant hatchlings raised in large outdoor enclosures. We applied an aromatase inhibitor to half the eggs to override thermal effects on sex determination, thus decoupling sex and incubation temperature. Based on relationships between incubation temperatures, hatching dates, morphology, growth, and survival of hatchlings in their first season, we were able to reject three of the four differential fitness models. First, matching offspring sex to egg size was not plausible because the relationship between egg (offspring) size and fitness was similar in the two sexes. Second, sex differences in optimal incubation temperatures were not evident, because (1) although incubation temperature influenced offspring phenotypes and growth, it did so in similar ways in sons versus daughters, and (2) the relationship between phenotypic traits and fitness was similar in the two sexes, at least during preadult life. We were unable to reject a fourth model, in which TSD enhances offspring fitness by generating seasonal shifts in offspring sex ratio: that is, TSD allows overproduction of daughters (the sex likely to benefit most from early hatching) early in the nesting season. In keeping with this model, hatching early in the season massively enhanced body size at the beginning of the first winter, albeit with a significant decline in probability of survival. Thus, the timing of hatching is likely to influence reproductive success in this short‐lived, early maturing species; and this effect may well differ between the sexes.     

Influence of trial duration on the bias of the estimated treatment effect in clinical trials when individual heterogeneity is ignored

In randomized clinical trials where the times to event of two treatment groups are compared under a proportional hazards assumption, it has been established that omitting prognostic factors from the model entails an underestimation of the hazards ratio. Heterogeneity due to unobserved covariates in cancer patient populations is a concern since genomic investigations have revealed molecular and clinical heterogeneity in these populations. In HIV prevention trials, heterogeneity is unavoidable and has been shown to decrease the treatment effect over time. This article assesses the influence of trial duration on the bias of the estimated hazards ratio resulting from omitting covariates from the Cox analysis. The true model is defined by including an unobserved random frailty term in the individual hazard that reflects the omitted covariate. Three frailty distributions are investigated: gamma, log‐normal, and binary, and the asymptotic bias of the hazards ratio estimator is calculated. We show that the attenuation of the treatment effect resulting from unobserved heterogeneity strongly increases with trial duration, especially for continuous frailties that are likely to reflect omitted covariates, as they are often encountered in practice. The possibility of interpreting the long‐term decrease in treatment effects as a bias induced by heterogeneity and trial duration is illustrated by a trial in oncology where adjuvant chemotherapy in stage 1B NSCLC was investigated.     

A causal proportional hazards estimator for the effect of treatment actually received in a randomized trial with all-or-nothing compliance

Survival data from randomized trials are most often analyzed in a proportional hazards (PH) framework that follows the intention-to-treat (ITT) principle. When not all the patients on the experimental arm actually receive the assigned treatment, the ITT-estimator mixes its effect on treatment compliers with its absence of effect on noncompliers. The structural accelerated failure time (SAFT) models of Robins and Tsiatis are designed to consistently estimate causal effects on the treated, without direct assumptions about the compliance selection mechanism. The traditional PH-model, however, has not yet led to such causal interpretation. In this article, we examine a PH-model of treatment effect on the treated subgroup. While potential treatment compliance is unobserved in the control arm, we derive an estimating equation for the Compliers PROPortional Hazards Effect of Treatment (C-PROPHET). The jackknife is used for bias correction and variance estimation. The method is applied to data from a recently finished clinical trial in cancer patients with liver metastases.     

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.     

Predicting treatment effect from surrogate endpoints and historical trials: an extrapolation involving probabilities of a binary outcome or survival to a specific time

Using multiple historical trials with surrogate and true endpoints, we consider various models to predict the effect of treatment on a true endpoint in a target trial in which only a surrogate endpoint is observed. This predicted result is computed using (1) a prediction model (mixture, linear, or principal stratification) estimated from historical trials and the surrogate endpoint of the target trial and (2) a random extrapolation error estimated from successively leaving out each trial among the historical trials. The method applies to either binary outcomes or survival to a particular time that is computed from censored survival data. We compute a 95% confidence interval for the predicted result and validate its coverage using simulation. To summarize the additional uncertainty from using a predicted instead of true result for the estimated treatment effect, we compute its multiplier of standard error. Software is available for download.     

Estimation and interpretation of incidence rate difference for recurrent events when the estimation model is misspecified

Recurrent events data are common in experimental and observational studies. It is often of interest to estimate the effect of an intervention on the incidence rate of the recurrent events. The incidence rate difference is a useful measure of intervention effect. A weighted least squares estimator of the incidence rate difference for recurrent events was recently proposed for an additive rate model in which both the baseline incidence rate and the covariate effects were constant over time. In this article, we relax this model assumption and examine the properties of the estimator under the additive and multiplicative rate models assumption in which the baseline incidence rate and covariate effects may vary over time. We show analytically and numerically that the estimator gives an appropriate summary measure of the time‐varying covariate effects. In particular, when the underlying covariate effects are additive and time‐varying, the estimator consistently estimates the weighted average of the covariate effects over time. When the underlying covariate effects are multiplicative and time‐varying, and if there is only one binary covariate indicating the intervention status, the estimator consistently estimates the weighted average of the underlying incidence rate difference between the intervention and control groups over time. We illustrate the method with data from a randomized vaccine trial.     

Estimation and inference for the causal effect of receiving treatment on a multinomial outcome

Summary .  This article considers the analysis of two-arm randomized trials with noncompliance, which have a multinomial outcome. We first define the causal effect in these trials as some function of outcome distributions of compliers with and without treatment (e.g., the complier average causal effect, the measure of stochastic superiority of treatment over control for compliers), then estimate the causal effect with the likelihood method. Next, based on the likelihood-ratio (LR) statistic, we test those functions of or the equality of the outcome distributions of compliers with and without treatment. Although the corresponding LR statistic follows a chi-squared  (χ²)  distribution asymptotically when the true values of parameters are in the interior of the parameter space under the null, its asymptotic distribution is not  χ²  when the true values of parameters are on the boundary of the parameter space under the null. Therefore, we propose a bootstrap/double bootstrap version of a LR test for the causal effect in these trials. The methods are illustrated by an analysis of data from a randomized trial of an encouragement intervention to improve adherence to prescribed depression treatments among depressed elderly patients in primary care practices.     

Parental provisioning in a variable environment: Evaluation of three foraging currencies and a state variable model

We estimated the reproductive success of black terns (Chlidonias niger) based on three optimal foraging currencies (maximizing the net rate of energy intake, daily delivery rate, and efficiency, respectively) and a state variable model. There was a broad range of capture intervals (the time required for the parent to capture a single prey) when the flight speeds predicted by the three currencies were so high that they resulted in daily provisioning costs which parents could not fully recover through self-feeding. Whenever the efficiency currency produced higher estimates of reproductive success, parents lost comparatively less weight than when they foraged as rate-maximizers. If parents did not experience any weight loss, the net rate and efficiency currencies made equivalent fitness projections. However, both of these currencies provided lower fitness returns than daily delivery rate at longer capture intervals. There were a number of capture intervals when estimates of reproductive success from the state variable model and at least one of the foraging currencies were equal. Provisioning behaviour under the state variable model was much more flexible and parents were therefore able to reduce their self-feeding rate on days when food was particularly scarce, thereby increasing the total delivery to the nest. This resulted in higher fitness returns than was possible under the foraging currencies. Our results suggest that efficiency-maximizing is more likely to provide fitness returns that are equivalent to the state variable model in comparison with the rate-maximizing alternatives. Furthermore, only the efficiency currency and the state variable model made predictions of flight speed that were similar to speeds measured in black tern parents provisioning young at natural nests.     

Competition of pathogen strains leading to infection with variable infectivity and the effect of treatment

A model for the spread of two strains of a pathogen leading to an infection with variable infectivity is considered. The course of infection is described by two stages with different infectivity levels. The model is extended to account for treatment by including a third stage with different infectivity and survival for those treated. The contribution of each stage to incidence and prevalence is investigated and the effect of infectivity and survival on the basic reproduction ratio is examined. Standard equilibrium analysis is performed for both models, revealing that the successful strain is the one with highest reproduction ratio. If therapy, however, is more effective against the strain that wins in the absence of treatment and its reproduction ratio is sufficiently reduced, it might be outcompeted by the other strain after treatment becomes widely available. In this case, early introduction of treatment can prevent a major outbreak.     

Estimating abundance and population trends when detection is low and highly variable: A comparison of three methods for the Hermann's tortoise

Assessing population trends is a basic prerequisite to carrying out adequate conservation strategies. Selecting an appropriate method to monitor animal populations can be challenging, particularly for low-detection species such as reptiles. This study compares 3 detection-corrected abundance methods (capture–recapture, distance sampling, and N-mixture) used to assess population size of the threatened Hermann's tortoise. We used a single dataset of 432 adult tortoise observations collected at 118 sampling sites in the Plaine des Maures, southeastern France. We also used a dataset of 520 tortoise observations based on radiotelemetry data collected from 10 adult females to estimate and model the availability (g0) needed for distance sampling. We evaluated bias for N-mixture and capture–recapture, by using simulations based on different values of detection probabilities. Finally, we conducted a power analysis to estimate the ability of the 3 methods to detect changes in Hermann's tortoise abundances. The abundance estimations we obtained using distance sampling and N-mixture models were respectively 1.75 and 2.19 times less than those obtained using the capture–recapture method. Our results indicated that g0 was influenced by temperature variations and can differ for the same temperature on different days. Simulations showed that the N-mixture models provide unstable estimations for species with detection probabilities <0.5, whereas capture–recapture estimations were unbiased. Power analysis showed that none of the 3 methods were precise enough to detect slow population changes. We recommend that great care should be taken when implementing monitoring designs for species with large variation in activity rates and low detection probabilities. Although N-mixture models are easy to implement, we would not recommend using them in situations where the detection probability is very low at the risk of providing biased estimates. Among the 3 methods allowing estimation of tortoise abundances, capture–recapture should be preferred to assess population trends. © 2013 The Wildlife Society.     

Changes in the structure and function of northern Alaskan ecosystems when considering variable leaf‐out times across groupings of species in a dynamic vegetation model

The phenology of arctic ecosystems is driven primarily by abiotic forces, with temperature acting as the main determinant of growing season onset and leaf budburst in the spring. However, while the plant species in arctic ecosystems require differing amounts of accumulated heat for leaf‐out, dynamic vegetation models simulated over regional to global scales typically assume some average leaf‐out for all of the species within an ecosystem. Here, we make use of air temperature records and observations of spring leaf phenology collected across dominant groupings of species (dwarf birch shrubs, willow shrubs, other deciduous shrubs, grasses, sedges, and forbs) in arctic and boreal ecosystems in Alaska. We then parameterize a dynamic vegetation model based on these data for four types of tundra ecosystems (heath tundra, shrub tundra, wet sedge tundra, and tussock tundra), as well as ecotonal boreal white spruce forest, and perform model simulations for the years 1970–2100. Over the course of the model simulations, we found changes in ecosystem composition under this new phenology algorithm compared with simulations with the previous phenology algorithm. These changes were the result of the differential timing of leaf‐out, as well as the ability for the groupings of species to compete for nitrogen and light availability. Regionally, there were differences in the trends of the carbon pools and fluxes between the new phenology algorithm and the previous phenology algorithm, although these differences depended on the future climate scenario. These findings indicate the importance of leaf phenology data collection by species and across the various ecosystem types within the highly heterogeneous Arctic landscape, and that dynamic vegetation models should consider variation in leaf‐out by groupings of species within these ecosystems to make more accurate projections of future plant distributions and carbon cycling in Arctic regions.