Improved two‐stage group sequential procedures for testing a secondary endpoint after the primary endpoint achieves significance

In two‐stage group sequential trials with a primary and a secondary endpoint, the overall type I error rate for the primary endpoint is often controlled by an α‐level boundary, such as an O'Brien‐Fleming or Pocock boundary. Following a hierarchical testing sequence, the secondary endpoint is tested only if the primary endpoint achieves statistical significance either at an interim analysis or at the final analysis. To control the type I error rate for the secondary endpoint, this is tested using a Bonferroni procedure or any α‐level group sequential method. In comparison with marginal testing, there is an overall power loss for the test of the secondary endpoint since a claim of a positive result depends on the significance of the primary endpoint in the hierarchical testing sequence. We propose two group sequential testing procedures with improved secondary power: the improved Bonferroni procedure and the improved Pocock procedure. The proposed procedures use the correlation between the interim and final statistics for the secondary endpoint while applying graphical approaches to transfer the significance level from the primary endpoint to the secondary endpoint. The procedures control the familywise error rate (FWER) strongly by construction and this is confirmed via simulation. We also compare the proposed procedures with other commonly used group sequential procedures in terms of control of the FWER and the power of rejecting the secondary hypothesis. An example is provided to illustrate the procedures.     

Estimating the prevalence of two or more diseases using outcomes from multiplex group testing

When screening a population for infectious diseases, pooling individual specimens (e.g., blood, swabs, urine, etc.) can provide enormous cost savings when compared to testing specimens individually. In the biostatistics literature, testing pools of specimens is commonly known as group testing or pooled testing. Although estimating a population-level prevalence with group testing data has received a large amount of attention, most of this work has focused on applications involving a single disease, such as human immunodeficiency virus. Modern methods of screening now involve testing pools and individuals for multiple diseases simultaneously through the use of multiplex assays. Hou et al. (2017, Biometrics, 73, 656–665) and Hou et al. (2020, Biostatistics, 21, 417–431) recently proposed group testing protocols for multiplex assays and derived relevant case identification characteristics, including the expected number of tests and those which quantify classification accuracy. In this article, we describe Bayesian methods to estimate population-level disease probabilities from implementing these protocols or any other multiplex group testing protocol which might be carried out in practice. Our estimation methods can be used with multiplex assays for two or more diseases while incorporating the possibility of test misclassification for each disease. We use chlamydia and gonorrhea testing data collected at the State Hygienic Laboratory at the University of Iowa to illustrate our work. We also provide an online R resource practitioners can use to implement the methods in this article.     

Cost analysis in choosing group size when group testing for Potato virus Y in the presence of classification errors

In many areas of the world, Potato virus Y (PVY) is one of the most economically important disease problems in seed potatoes. In Taiwan, generation 2 (G2) class certified seed potatoes are required by law to be free of detectable levels of PVY. To meet this standard, it is necessary to perform accurate tests at a reasonable cost. We used a two‐stage testing design involving group testing which was performed in Taiwan's Seed Improvement and Propagation Station to identify plants infected with PVY. At the first stage of this two‐stage testing design, plants are tested in groups. The second stage involves no retesting for negative test groups and exhaustive testing of all constituent individual samples from positive test groups. In order to minimise costs while meeting government standards, it is imperative to estimate optimal group size. However, because of limited test accuracy, classification errors for diagnostic tests are inevitable; to get a more accurate estimate, it is necessary to adjust for these errors. Therefore, this paper describes an analysis of diagnostic test data in which specimens are grouped for batched testing to offset costs. The optimal batch size is determined by various cost parameters as well as test sensitivity, specificity and disease prevalence. Here, the Bayesian method is employed to deal with uncertainty in these parameters. Moreover, we developed a computer program to determine optimal group size for PVY tests such that the expected cost is minimised even when using imperfect diagnostic tests of pooled samples. Results from this research show that, compared with error free testing, when the presence of diagnostic testing errors is taken into account, the optimal group size becomes smaller. Higher diagnostic testing costs, lower costs of false negatives or smaller prevalence can all lead to a larger optimal group size. Regarding the effects of sensitivity and specificity, optimal group size increases as sensitivity increases; however, specificity has little effect on determining optimal group size. From our simulated study, it is apparent that the Bayesian method can truly update the prior information to more closely approximate the intrinsic characteristics of the parameters of interest. We believe that the results of this study will be useful in the implementation of seed potato certification programmes, particularly those which require zero tolerance for quarantine diseases in certified tubers.     

Group testing regression model estimation when case identification is a goal

Group testing is frequently used to reduce the costs of screening a large number of individuals for infectious diseases or other binary characteristics in small prevalence situations. In many applications, the goals include both identifying individuals as positive or negative and estimating the probability of positivity. The identification aspect leads to additional tests being performed, known as “retests”, beyond those performed for initial groups of individuals. In this paper, we investigate how regression models can be fit to estimate the probability of positivity while also incorporating the extra information from these retests. We present simulation evidence showing that significant gains in efficiency occur by incorporating retesting information, and we further examine which testing protocols are the most efficient to use. Our investigations also demonstrate that some group testing protocols can actually lead to more efficient estimates than individual testing when diagnostic tests are imperfect. The proposed methods are applied retrospectively to chlamydia screening data from the Infertility Prevention Project. We demonstrate that significant cost savings could occur through the use of particular group testing protocols.     

Biases incurred from nonrandom repeat testing of haemoglobin levels in blood donors: Selective testing and its implications

To help prevent anaemia, it is a requisite for blood donors to undergo a haemoglobin test to ensure levels are not too low before donation. It is therefore important to have an accurate testing device and strategy to ensure donors are not being inappropriately bled. A recent study in blood donors used a selective testing strategy where if a donor's haemoglobin level is below the level required for donation, then another reading is taken and if this occurs again, a third and final reading is used. This strategy can reduce the average number of readings required per donor compared to taking three measurements for all donors. However, the final decision‐making measurement will on average be higher than a single measurement. In this paper, a selective testing strategy is compared against other strategies. Individual‐level biases are derived for the selective strategy and are shown to depend on how close a donor's true haemoglobin level is to the donation threshold and the magnitude of error in the testing device. A simulation study was conducted using the distribution of haemoglobin levels from a large donor population to investigate the effects different strategies have on population performance. We consider scenarios based on varying the measurement device bias and error, including differential biases that depend on the underlying haemoglobin level. Discriminatory performance is shown to be affected when using the selective testing strategies, especially when measurement error is large and when differential bias is present in the device. We recommend that the average of a number of readings should be used in preference to selective testing strategies if multiple measurements are available.     

Do evolutionary constraints on thermal performance manifest at different organizational scales?

The two foremost hypotheses on the evolutionary constraints on an organism's thermal sensitivity – the hotter‐is‐better expectation, and the specialist–generalist trade‐off – have received mixed support from empirical studies testing for their existence. Could these conflicting results reflect confusion regarding the organizational level (i.e. species > population > individual) at which these constraints should manifest? We propose that these evolutionary constraints should manifest at different organizational levels because of differences in their underlying causes and requirements. The hotter‐is‐better expectation should only manifest across separate evolutionary units (e.g. species, populations), and not within populations. The specialist–generalist trade‐off, by contrast, should manifest within as well as between separate evolutionary units. We measured the thermal sensitivity of sprint performance for 440 rainforest sun skinks (Lampropholis coggeri) representing 10 populations, and used the resulting performance curves to test for evidence for the hypothesized constraints at two organizational levels: (i) across populations and (ii) within populations. As predicted, the hotter‐is‐better expectation was evident only at the across‐population level, whereas the specialist–generalist trade‐off was evident within, as well as across, populations. Our results suggest that, depending on the processes that drive them, evolutionary constraints can manifest at different organizational levels. Consideration of these underlying processes, and the organizational level at which a constraint should manifest, may help resolve conflicting empirical results.     

Informative Dorfman screening

Since the early 1940s, group testing (pooled testing) has been used to reduce costs in a variety of applications, including infectious disease screening, drug discovery, and genetics. In such applications, the goal is often to classify individuals as positive or negative using initial group testing results and the subsequent process of decoding of positive pools. Many decoding algorithms have been proposed, but most fail to acknowledge, and to further exploit, the heterogeneous nature of the individuals being screened. In this article, we use individuals' risk probabilities to formulate new informative decoding algorithms that implement Dorfman retesting in a heterogeneous population. We introduce the concept of "thresholding" to classify individuals as "high" or "low risk," so that separate, risk-specific algorithms may be used, while simultaneously identifying pool sizes that minimize the expected number of tests. When compared to competing algorithms which treat the population as homogeneous, we show that significant gains in testing efficiency can be realized with virtually no loss in screening accuracy. An important additional benefit is that our new procedures are easy to implement. We apply our methods to chlamydia and gonorrhea data collected recently in Nebraska as part of the Infertility Prevention Project.     

An ecological framework of neophobia: from cells to organisms to populations

Neophobia is the fear of novel stimuli or situations. This phenotype has recently received much ecological attention, primarily in the context of decision making. Here, we explore neophobia across biological levels of organisation, first describing types of neophobia among animals and the underlying causes of neophobia, highlighting high levels of risk and uncertainty as key drivers. We place neophobia in the framework of Error Management Theory and Signal Detection Theory, showing how increases in overall risk and uncertainty can lead to costly non‐responses towards novel threats unless individuals lower their response threshold and become neophobic. We then discuss how neophobic behaviour translates into population and evolutionary consequences before introducing neophobia‐like processes at the cellular level, where some phenomena such as allergy and autoimmunity can parallel neophobic behaviour. Finally, we discuss neophobia attenuation, considering how a sudden change in the environment from dangerous to safe can lead to problematic over‐responses (i.e. the ‘maladaptive defensive carry‐over’ hypothesis), and discuss treatment methods for such over‐responses. We anticipate that bridging the concept of neophobia with a process‐centered perspective can facilitate a transfer of insight across organisational levels.     

Ecology,environment and evolutionary history influence genetic structure in five mammal species from the Italian Alps

The identification and evaluation of the ecological and environmental factors shaping patterns of natural genetic variation are fundamental goals of population and conservation genetics. Many studies focus on factors affecting single species, but it is also important to test whether some influential biotic and abiotic factors are common drivers of genetic diversity across species, or if species or species groups are each affected by different forces; a multi‐species analysis is necessary for this. Here we analysed the molecular variation from five mammal species (roe deer, red deer, chamois, mountain hare and European brown hare) at mtDNA and microsatellite loci from the eastern Italian Alps. We use phylogeographical and landscape‐level analyses to test the relative influence of large‐scale geographical history and contemporary environmental characteristics of the landscape on genetic diversity and differentiation. We found: (1) all study species except brown hare are strongly differentiated into two main groups, located west and east of a major river valley; (2) significant correlations between levels of within‐population diversity at both mtDNA and microsatellite loci, and several landscape features such as alpine grassland, water courses and anthropized areas. We conclude that heterogeneous landscape has some influence on within‐population diversity, but biogeographical history has probably had the stronger influence on current genetic patterns, despite an apparently large dispersal potential of certain species. However, our results for brown hare show that management actions such as stocking may alter these large‐scale patterns.     

Use of binomial group testing in tests of hypotheses for classification or quantitative covariables

In group testing, the test unit consists of a group of individuals. If the group test is positive, then one or more individuals in the group are assumed to be positive. A group observation in binomial group testing can be, say, the test result (positive or negative) for a pool of blood samples that come from several different individuals. It has been shown that, when the proportion (p) of infected individuals is low, group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of those infected. We extend the potential applications of group testing to hypothesis-testing problems wherein one wants to test for a relationship between p and a classification or quantitative covariable. Asymptotic relative efficiencies (AREs) of tests based on group testing versus the usual individual testing are obtained. The Pitman ARE strongly favors group testing in many cases. Small-sample results from simulation studies are given and are consistent with the large-sample (asymptotic) findings. We illustrate the potential advantages of group testing in hypothesis testing using HIV-1 seroprevalence data.     

Mid‐P confidence intervals for group testing based on the total number of positive groups

In the estimation of proportions by group testing, unequal sized groups results in an ambiguous ordering of the sample space, which complicates the construction of exact confidence intervals. The total number of positive groups is shown to be a suitable statistic for ordering outcomes, provided its ties are broken by the MLE. We propose an interval estimation method based on this quantity, with a mid‐P correction. Coverage is evaluated using group testing problems in plant disease assessment and virus transmission by insect vectors. The proposed method provides good coverage in a range of situations, and compares favorably with existing exact methods.     

Boom‐bust dynamics in biological invasions: towards an improved application of the concept

Boom‐bust dynamics – the rise of a population to outbreak levels, followed by a dramatic decline – have been associated with biological invasions and offered as a reason not to manage troublesome invaders. However, boom‐bust dynamics rarely have been critically defined, analyzed, or interpreted. Here, we define boom‐bust dynamics and provide specific suggestions for improving the application of the boom‐bust concept. Boom‐bust dynamics can arise from many causes, some closely associated with invasions, but others occurring across a wide range of ecological settings, especially when environmental conditions are changing rapidly. As a result, it is difficult to infer cause or predict future trajectories merely by observing the dynamic. We use tests with simulated data to show that a common metric for detecting and describing boom‐bust dynamics, decline from an observed peak to a subsequent trough, tends to severely overestimate the frequency and severity of busts, and should be used cautiously if at all. We review and test other metrics that are better suited to describe boom‐bust dynamics. Understanding the frequency and importance of boom‐bust dynamics requires empirical studies of large, representative, long‐term data sets that use clear definitions of boom‐bust, appropriate analytical methods, and careful interpretations.     

Density‐dependent space use affects interpretation of camera trap detection rates

Camera traps (CTs) are an increasingly popular tool for wildlife survey and monitoring. Estimating relative abundance in unmarked species is often done using detection rate as an index of relative abundance, which assumes that detection rate has a positive linear relationship with true abundance. This assumption may be violated if movement behavior varies with density, but the degree to which movement behavior is density‐dependent across taxa is unclear. The potential confounding of population‐level relative abundance indices by movement would depend on how regularly, and by what magnitude, movement rate and home‐range size vary with density. We conducted a systematic review and meta‐analysis to quantify relationships between movement rate, home‐range size, and density, across terrestrial mammalian taxa. We then simulated animal movements and CT sampling to test the effect of contrasting movement scenarios on CT detection rate indices. Overall, movement rate and home‐range size were negatively correlated with density and positively correlated with one another. The strength of the relationships varied significantly between taxa and populations. In simulations, detection rates were related to true abundance but underestimated change, particularly for slower moving species with small home ranges. In situations where animal space use changes markedly with density, we estimate that up to thirty percent of a true change in relative abundance may be missed due to the confounding effect of movement, making trend estimation more difficult. The common assumption that movement remains constant across densities is therefore violated across a wide range of mammal species. When studying unmarked species using CT detection rates, researchers and managers should explicitly consider that such indices of relative abundance reflect both density and movement. Practitioners interpreting changes in camera detection rates should be aware that observed differences may be biased low relative to true changes in abundance. Further information on animal movement, or methods that do not depend on assumptions of density‐independent movement, may be required to make robust inferences on population trends.     

Obtaining Critical Values for Simultaneous Confidence Intervals and Multiple Testing

There are many situations where it is desired to make simultaneous tests or give simultaneous confidence intervals for linear combinations (contrasts) of population or treatment means. Somerville (1997, 1999) developed algorithms for calculating the critical values for a large class of simultaneous tests and simultaneous confidence intervals. Fortran 90 and SAS‐IML batch programs and interactive programs were developed. These programs calculate the critical values for 15 different simultaneous confidence interval procedures (and the corresponding simultaneous tests) and for arbitrary procedures where the user specifies a combination of one and two sided contrasts. The programs can also be used to obtain the constants for “step‐down” testing of multiple hypotheses. This paper gives examples of the use of the algorithms and programs and illustrates their versatility and generality. The designs need not be balanced, multiple covariates may be present and there may be many missing values. The use of multiple regression and dummy variables to obtain the required variance covariance matrix is illustrated. Under weak normality assumptions the methods are “exact” and make the use of approximate methods or “simulation” unnecessary.     

Interactive life‐history traits predict sensitivity of plants and animals to temporal autocorrelation

Temporal autocorrelation in demographic processes is an important aspect of population dynamics, but a comprehensive examination of its effects on different life‐history strategies is lacking. We use matrix population models from 454 plant and animal populations to simulate stochastic population growth rates (log λ_s) under different temporal autocorrelations in demographic rates , using simulated and observed covariation among rates. We then test for differences in sensitivities, or changes of log λ_s to changes in autocorrelation among two major axes of life‐history strategies, obtained from phylogenetically informed principal component analysis: the fast‐slow and reproductive‐strategy continua. Fast life histories exhibit highest sensitivities to simulated autocorrelation in demographic rates across reproductive strategies. Slow life histories are less sensitive to temporal autocorrelation, but their sensitivities increase among highly iteroparous species. We provide cross‐taxonomic evidence that changes in the autocorrelation of environmental variation may affect a wide range of species, depending on complex interactions of life‐history strategies.     

K‐Sample comparisons using propensity analysis

In this paper, we investigate K‐group comparisons on survival endpoints for observational studies. In clinical databases for observational studies, treatment for patients are chosen with probabilities varying depending on their baseline characteristics. This often results in noncomparable treatment groups because of imbalance in baseline characteristics of patients among treatment groups. In order to overcome this issue, we conduct propensity analysis and match the subjects with similar propensity scores across treatment groups or compare weighted group means (or weighted survival curves for censored outcome variables) using the inverse probability weighting (IPW). To this end, multinomial logistic regression has been a popular propensity analysis method to estimate the weights. We propose to use decision tree method as an alternative propensity analysis due to its simplicity and robustness. We also propose IPW rank statistics, called Dunnett‐type test and ANOVA‐type test, to compare 3 or more treatment groups on survival endpoints. Using simulations, we evaluate the finite sample performance of the weighted rank statistics combined with these propensity analysis methods. We demonstrate these methods with a real data example. The IPW method also allows us for unbiased estimation of population parameters of each treatment group. In this paper, we limit our discussions to survival outcomes, but all the methods can be easily modified for any type of outcomes, such as binary or continuous variables.     

Panmixia on a continental scale in a widely distributed colonial waterbird

Many highly mobile species, such as migratory birds, can move and disperse over long distances, yet exhibit high levels of population genetic structuring. Although movement capabilities may enable dispersal, gene flow may be restricted by behavioural constraints such as philopatry. In the present study, we examined patterns of genetic differentiation across the range of a highly mobile, colonial waterbird. American white pelicans (Pelecanus erythrorhynchos) breed across continental North America and are currently experiencing a range expansion, especially on the eastern range limit. To assess patterns of genetic structuring, we sampled 333 individuals from 19 colonies across their North American range. The use of ten variable microsatellite markers revealed high levels of allelic richness with no population differentiation. Both Bayesian and frequentist approaches to examining genetic structuring revealed a single panmictic population. We found no evidence of genetic structuring across the Continental Divide or between migratory and non‐migratory colonies. The lack of any genetic structure across the range indicates that, unlike other waterbirds with similar life‐history characteristics, extensive gene flow and presumably low philopatry appear to preclude genetic differentiation. The lack of population genetic structure in American white pelicans provides an example of range‐wide panmixia, a rare phenomenon in any terrestrial species. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 102 , 583–592.     

Approval policies for modifications to machine learning‐based software as a medical device: A study of bio‐creep

Successful deployment of machine learning algorithms in healthcare requires careful assessments of their performance and safety. To date, the FDA approves locked algorithms prior to marketing and requires future updates to undergo separate premarket reviews. However, this negates a key feature of machine learning—the ability to learn from a growing dataset and improve over time. This paper frames the design of an approval policy, which we refer to as an automatic algorithmic change protocol (aACP), as an online hypothesis testing problem. As this process has obvious analogy with noninferiority testing of new drugs, we investigate how repeated testing and adoption of modifications might lead to gradual deterioration in prediction accuracy, also known as “biocreep” in the drug development literature. We consider simple policies that one might consider but do not necessarily offer any error‐rate guarantees, as well as policies that do provide error‐rate control. For the latter, we define two online error‐rates appropriate for this context: bad approval count (BAC) and bad approval and benchmark ratios (BABR). We control these rates in the simple setting of a constant population and data source using policies aACP‐BAC and aACP‐BABR, which combine alpha‐investing, group‐sequential, and gate‐keeping methods. In simulation studies, bio‐creep regularly occurred when using policies with no error‐rate guarantees, whereas aACP‐BAC and aACP‐BABR controlled the rate of bio‐creep without substantially impacting our ability to approve beneficial modifications.     

Stability and synchrony across ecological hierarchies in heterogeneous metacommunities: linking theory to data

Understanding stability across ecological hierarchies is critical for landscape management in a changing world. Recent studies showed that synchrony among lower‐level components is key to scaling temporal stability across two hierarchical levels, whether spatial or organizational. But an extended framework that integrates both spatial scale and organizational level simultaneously is required to clarify the sources of ecosystem stability at large scales. However, such an extension is far from trivial when taking into account the spatial heterogeneities in real‐world ecosystems. In this paper, we develop a partitioning framework that bridges variability and synchrony measures across spatial scales and organizational levels in heterogeneous metacommunities. In this framework, metacommunity variability is expressed as the product of local‐scale population variability and two synchrony indices that capture the temporal coherence across species and space, respectively. We develop an R function ‘var.partition’ and apply it to five types of desert plant communities to illustrate our framework and test how diversity shapes synchrony and variability at different hierarchical levels. As the observation scale increased from local populations to metacommunities, the temporal variability of plant productivity was reduced mainly by factors that decreased species synchrony. Species synchrony decreased from local to regional scales, and spatial synchrony decreased from species to community levels. Local and regional species diversity were key factors that reduced species synchrony at the two scales. Moreover, beta diversity contributed to decreasing spatial synchrony among communities. We conclude that our new framework offers a valuable toolbox for future empirical studies to disentangle the mechanisms and pathways by which ecological factors influence stability at large scales.