Robust and efficient design of experiments for the Monod model

In this paper the problem of designing experiments for the Monod model, which is frequently used in microbiology, is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are local optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular, standardized maximin D- and E-optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor of two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model.     

Robustness and Efficiency of D‐optimal Experimental Designs in a Growth Problem

To assess tree growth, for example in diameter, a forester typically measures the trees at regular time points. We call such designs equidistant. In this paper we look at the robustness and efficiency of several experimental designs, using the D‐optimality criterion, in a case study of diameter growth in cork oaks. We compare D‐optimal designs (unrestricted and replication‐free) with equidistant designs. We further compare designs in different experimental regions. Results indicate that the experimental region should be adequate to the problem, and that D‐optimal designs are substantially more efficient than equidistant designs, even under parameter mis‐specification.     

Maximin D-optimal designs for longitudinal mixed effects models

In this article, the optimal selection and allocation of time points in repeated measures experiments is considered. D-optimal cohort designs are computed numerically for the first- and second-degree polynomial models with random intercept, random slope, and first-order autoregressive serial correlations. Because the optimal designs are locally optimal, it is proposed to use a maximin criterion. It is shown that, for a large class of symmetric designs, the smallest relative efficiency over the model parameter space is substantial.     

Adaptive two-stage designs for single-arm phase IIA cancer clinical trials

The main purpose of a phase IIA trial of a new anticancer therapy is to determine whether the therapy has sufficient promise against a specific type of tumor to warrant its further development. The therapy will be rejected for further investigation if the true response rate is less than some uninteresting level and the test of hypothesis is powered at a specific target response rate. Two-stage designs are commonly used for this situation. However, in many situations investigators often express concern about uncertainty in targeting the alternative hypothesis to study power at the planning stage. In this article, motivated by a real example, we propose a strategy for adaptive two-stage designs that will use the information at the first stage of the study to either reject the therapy or continue testing with either an optimistic or a skeptic target response rate, while the type I error rate is controlled. We also introduce new optimal criteria to reduce the expected total sample size.     

Sequential designs for ordinal phase I clinical trials

Sequential designs for phase I clinical trials which incorporate maximum likelihood estimates (MLE) as data accrue are inherently problematic because of limited data for estimation early on. We address this problem for small phase I clinical trials with ordinal responses. In particular, we explore the problem of the nonexistence of the MLE of the logistic parameters under a proportional odds model with one predictor. We incorporate the probability of an undetermined MLE as a restriction, as well as ethical considerations, into a proposed sequential optimal approach, which consists of a start‐up design, a follow‐on design and a sequential dose‐finding design. Comparisons with nonparametric sequential designs are also performed based on simulation studies with parameters drawn from a real data set.     

The interactive effects of competition and predation risk on dispersal in an insect

Dispersal dynamics have significant consequences for ecological and evolutionary processes. Previous work has demonstrated that dispersal can be context-dependent. However, factors affecting dispersal are typically considered in isolation, despite the probability that individuals make dispersal decisions in response to multiple, possibly interacting factors. We examined whether two ecological factors, predation risk and intraspecific competition, have interactive effects on dispersal dynamics. We performed a factorial experiment in mesocosms using backswimmers (Notonecta undulata), flight-capable, semi-aquatic insects. Emigration rates increased with density, and increased with predation risk at intermediate densities; however, predation had minimal effects on emigration at high and low densities. Our results indicate that factorial experiments may be required to understand dispersal dynamics under realistic ecological conditions.     

Directed walk designs for dose-response problems with competing failure modes

We examine adaptive allocation designs for the problem of determining the optimal therapeutic dose for subjects in early-phase clinical trials. A subject can fail due to lack of efficacy or due to a toxic reaction. Successful subjects will have both a positive response and no toxic side effects. Thus, we seek to maximize the product of the nontoxicity and efficacy dose-response curves. We are interested in sampling rules that perform well along several criteria, including the ethical criterion that, as often as possible, experimental subjects be treated at or close to the maximum in question. Statistically, we wish to identify the optimum dose with high probability at the close of the experiment. Here, we propose designs that combine new allocation policies, directed walks, with new smoothed shape-constrained curve-fitting techniques. These are compared with a variety of other curve-fitting techniques and with up-and-down and equal allocation rules.     

A graphical method for finding maximin efficiency designs

We consider the problem of designing an experiment when there are two competing optimality criteria. Designs that maximize the minimum efficiencies under the two criteria are proposed along with a graphical method for finding these maximin designs.     

Test‐compatible confidence intervals for adaptive two‐stage single‐arm designs with binary endpoint

Inference after two‐stage single‐arm designs with binary endpoint is challenging due to the nonunique ordering of the sampling space in multistage designs. We illustrate the problem of specifying test‐compatible confidence intervals for designs with nonconstant second‐stage sample size and present two approaches that guarantee confidence intervals consistent with the test decision. Firstly, we extend the well‐known Clopper–Pearson approach of inverting a family of two‐sided hypothesis tests from the group‐sequential case to designs with fully adaptive sample size. Test compatibility is achieved by using a sample space ordering that is derived from a test‐compatible estimator. The resulting confidence intervals tend to be conservative but assure the nominal coverage probability. In order to assess the possibility of further improving these confidence intervals, we pursue a direct optimization approach minimizing the mean width of the confidence intervals. While the latter approach produces more stable coverage probabilities, it is also slightly anti‐conservative and yields only negligible improvements in mean width. We conclude that the Clopper–Pearson‐type confidence intervals based on a test‐compatible estimator are the best choice if the nominal coverage probability is not to be undershot and compatibility of test decision and confidence interval is to be preserved.     

Gyro-scope: an individual-based computer model to forecast gyrodactylid infections on fish hosts

Individual-based computer models (IBM) feature prominently in current theoretical ecology but have only been applied in a small number of parasitological studies. Here we designed an IBM to simulate the infection dynamics of gyrodactylid parasites and immune defence of na?ve hosts (i.e. fish previously not exposed to these parasites). We compared the results of the model with empirical data from guppies (Poecilia reticulata) infected with Gyrodactylus parasites. The laboratory experiments on guppies showed that larger fish acquired a heavier parasite load at the peak of the infection. The survival probability declined with increased body size and no fish survived a parasite load of 80 or more worms in this experiment (i.e. lethal load). The model was a good predictor of the Gyrodactylus infection dynamics of guppies and the model output was congruent with previously published data on Gyrodactylus salaris infections of salmon (Salmo salar). Computer simulations indicated that the infections persisted longer on larger hosts and that the parasite load increased exponentially with the body size of the host. Simulations furthermore predicted that the parasite load of fish with a standard length in excess of 17mm (i.e. the size of adult guppies) reached a lethal load. This suggests that in the conditions of the experiment, the immune defence of na?ve guppies can offer moderate protection against gyrodactylid infections to juveniles, but not to na?ve adult guppies. The model is a useful tool to forecast the development of gyrodactylid infections on single hosts and make predictions about optimal life history strategies of parasites.     

Bayesian enrichment strategies for randomized discontinuation trials

We propose optimal choice of the design parameters for random discontinuation designs (RDD) using a Bayesian decision-theoretic approach. We consider applications of RDDs to oncology phase II studies evaluating activity of cytostatic agents. The design consists of two stages. The preliminary open-label stage treats all patients with the new agent and identifies a possibly sensitive subpopulation. The subsequent second stage randomizes, treats, follows, and compares outcomes among patients in the identified subgroup, with randomization to either the new or a control treatment. Several tuning parameters characterize the design: the number of patients in the trial, the duration of the preliminary stage, and the duration of follow-up after randomization. We define a probability model for tumor growth, specify a suitable utility function, and develop a computational procedure for selecting the optimal tuning parameters.     

Dorso-ventral asymmetric functions of teashirt in Drosophila eye development depend on spatial cues provided by early DV patterning genes

The teashirt (tsh) gene has dorso-ventral (DV) asymmetric functions in Drosophila eye development: promoting eye development in dorsal and suppressing eye development in ventral by Wingless mediated Homothorax (HTH) induction [Development 129 (2002) 4271]. We looked for DV spatial cues required by tsh for its asymmetric functions. The dorsal Iroquois-Complex (Iro-C) genes and Delta (Dl) are required and sufficient for the tsh dorsal functions. The ventral Serrate (Ser), but not fringe (fng) or Lobe (L), is required and sufficient for the tsh ventral function. We propose that DV asymmetric function of tsh represents a novel tier of DV pattern regulation, which takes place after the spatial expression patterns of early DV patterning genes are established in the eye.     

Prey selection and the functional response of sea stars (Asterias vulgaris Verrill) and rock crabs (Cancer irroratus Say) preying on juvenile sea scallops (Placopecten magellanicus (Gmelin)) and blue mussels (Mytilus edulis Linnaeus)

Predators in nature include an array of prey types in their diet, and often select certain types over others. We examined (i) prey selection by sea stars (Asterias vulgaris) and rock crabs (Cancer irroratus) when offered two prey types, juvenile sea scallops (Placopecten magellanicus) and blue mussels (Mytilus edulis), and (ii) the effect of prey density on predation, prey selection, and component behaviours. We quantified predation rates, behavioural components (proportion of time spent searching for prey, encounter probabilities) and various prey characteristics (shell strength, energy content per prey, handling time per prey) to identify mechanisms underlying predation patterns and to assess the contribution of active and passive prey selection to observed selection of prey. Sea stars strongly selected mussels over scallops, resulting from both active and passive selection. Active selection was associated with the probability of attack upon encounter; it was higher on mussels than on scallops. The probability of capture upon attack, associated with passive selection, was higher for mussels than for scallops, since mussels can not swim to escape predators. Sea stars consumed few scallops when mussels were present, and so did not have a functional response on scallops (the target prey). Rock crabs exhibited prey switching: they selected mussels when scallop density was very low, did not select a certain prey type when scallop density was intermediate, and selected scallops when scallop density was high relative to mussel density. The interplay between encounter rate (associated with passive selection) and probability of consumption upon capture (associated with both active and passive selection) explained observed selection by crabs. Scallops were encountered by crabs relatively more often and/or mussels less often than expected from random movements of animals at all scallop densities. However, the probability of consumption varied with scallop density: it was lower for scallops than mussels at low and intermediate scallop densities, but tended to be higher for scallops than mussels at high scallop densities. When mussels were absent, crabs did not have a functional response on scallops, but rather were at the plateau of the response. When mussels were present with scallops at relatively low density, crabs exhibited a type II functional response on scallops. Our results have implications for the provision of protective refuges for species of interest (i.e., scallops) released onto the sea bed, such as in population enhancement operations and bottom aquaculture.     

Conserved regulation of the Caenorhabditis elegans labial/Hox1 gene ceh-13

Caenorhabditis elegans contains a set of six cluster-type homeobox (Hox) genes that are required during larval development. Some of them, but unlike in flies not all of them, are also required during embryogenesis. It has been suggested that the control of the embryonic expression of the worm Hox genes might differ from that of other species by being regulated in a lineal rather than a regional mode. Here, we present a trans-species analysis of the cis-regulatory region of ceh-13, the worm ortholog of the Drosophila labial and the vertebrate Hox1 genes, and find that the molecular mechanisms that regulate its expression may be similar to what has been found in species that follow a regulative, non-cell-autonomous mode of development. We have identified two enhancer fragments that are involved in different aspects of the embryonic ceh-13 expression pattern. We show that important features of comma-stage expression depend on an autoregulatory input that requires ceh-13 and ceh-20 functions. Our data show that the molecular nature of Hox1 class gene autoregulation has been conserved between worms, flies, and vertebrates. The second regulatory sequence is sufficient to drive correct early embryonic expression of ceh-13. Interestingly, this enhancer fragment acts as a response element of the Wnt/WG signaling pathway in Drosophila embryos.     

Differential activities of the core planar polarity proteins during Drosophila wing patterning

During planar polarity patterning of the Drosophila wing, a "core" group of planar polarity genes has been identified which acts downstream of global polarity cues to locally coordinate cell polarity and specify trichome production at distal cell edges. These genes encode protein products that assemble into asymmetric apicolateral complexes that straddle the proximodistal junctional region between adjacent cells. We have carried out detailed genetic analysis experiments, analysing the requirements of each complex component for planar polarity patterning. We find that the three transmembrane proteins at the core of the complex, Frizzled, Strabismus and Flamingo, are required earliest in development and are the only components needed for intercellular polarity signalling. Notably, cells that lack both Frizzled and Strabismus are unable to signal, revealing an absolute requirement for both proteins in cell-cell communication. In contrast the cytoplasmic components Dishevelled, Prickle and Diego are not needed for intercellular communication. These factors contribute to the cell-cell propagation of polarity, most likely by promotion of intracellular asymmetry. Interestingly, both local polarity propagation and trichome placement occur normally in mutant backgrounds where asymmetry of polarity protein distribution is undetectable, suggesting such asymmetry is not an absolute requirement for any of the functions of the core complex.     

Preference for outbred host plants and positive effects of inbreeding on egg survival in a specialist herbivore

Inbreeding can profoundly affect the interactions of plants with herbivores as well as with the natural enemies of the herbivores. We studied how plant inbreeding affects herbivore oviposition preference, and whether inbreeding of both plants and herbivores alters the probability of predation or parasitism of herbivore eggs. In a laboratory preference test with the specialist herbivore moth Abrostola asclepiadis and inbred and outbred Vincetoxicum hirundinaria plants, we discovered that herbivores preferred to oviposit on outbred plants. A field experiment with inbred and outbred plants that bore inbred or outbred herbivore eggs revealed that the eggs of the outbred herbivores were more likely to be lost by predation, parasitism or plant hypersensitive responses than inbred eggs. This difference did not lead to differences in the realized fecundity as the number of hatched larvae did not differ between inbred and outbred herbivores. Thus, the strength of inbreeding depression in herbivores decreases when their natural enemies are involved. Plant inbreeding did not alter the attraction of natural enemies of the eggs. We conclude that inbreeding can significantly alter the interactions of plants and herbivores at different life-history stages, and that some of these alterations are mediated by the natural enemies of the herbivores.     

Host plant and population determine the fitness costs of resistance to Bacillus thuringiensis

Novel adaptations often cause pleiotropic reductions in fitness. Under optimal conditions individual organisms may be able to compensate for, or reduce, these fitness costs. Declining environmental quality may therefore lead to larger costs. We investigated whether reduced plant quality would increase the fitness costs associated with resistance to Bacillus thuringiensis in two populations of the diamondback moth Plutella xylostella. We also measured the rate of decline in resistance on two host-plant (Brassica) species for one insect population (Karak). Population X plant species interactions determined the fitness costs in this study. Poor plant quality increased the fitness costs in terms of development time for both populations. However, fitness costs seen in larval survival did not always increase as plant quality declined. Both the fitness and the stability experiment indicated that fitness costs were higher on the most suitable plant for one population. Theoretically, if the fitness cost of a mutation interacts additively with environmental factors, the relative fitness of resistant insects will decrease with environmental quality. However, multiplicative costs do not necessarily increase with declining quality and may be harder to detect when fitness parameters are more subject to variation in poorer environments.     

Optimal designs for a multiresponse Emax model and efficient parameter estimation

The aim of dose finding studies is sometimes to estimate parameters in a fitted model. The precision of the parameter estimates should be as high as possible. This can be obtained by increasing the number of subjects in the study, N, choosing a good and efficient estimation approach, and by designing the dose finding study in an optimal way. Increasing the number of subjects is not always feasible because of increasing cost, time limitations, etc. In this paper, we assume fixed N and consider estimation approaches and study designs for multiresponse dose finding studies. We work with diabetes dose–response data and compare a system estimation approach that fits a multiresponse Emax model to the data to equation‐by‐equation estimation that fits uniresponse Emax models to the data. We then derive some optimal designs for estimating the parameters in the multi‐ and uniresponse Emax model and study the efficiency of these designs.