Semi‐Markov Models with Phase‐Type Sojourn Distributions

Summary Continuous‐time multistate models are widely used for categorical response data, particularly in the modeling of chronic diseases. However, inference is difficult when the process is only observed at discrete time points, with no information about the times or types of events between observation times, unless a Markov assumption is made. This assumption can be limiting as rates of transition between disease states might instead depend on the time since entry into the current state. Such a formulation results in a semi‐Markov model. We show that the computational problems associated with fitting semi‐Markov models to panel‐observed data can be alleviated by considering a class of semi‐Markov models with phase‐type sojourn distributions. This allows methods for hidden Markov models to be applied. In addition, extensions to models where observed states are subject to classification error are given. The methodology is demonstrated on a dataset relating to development of bronchiolitis obliterans syndrome in post‐lung‐transplantation patients.     

A Bayesian Chi‐Squared Goodness‐of‐Fit Test for Censored Data Models

Summary We propose a Bayesian chi‐squared model diagnostic for analysis of data subject to censoring. The test statistic has the form of Pearson's chi‐squared test statistic and is easy to calculate from standard output of Markov chain Monte Carlo algorithms. The key innovation of this diagnostic is that it is based only on observed failure times. Because it does not rely on the imputation of failure times for observations that have been censored, we show that under heavy censoring it can have higher power for detecting model departures than a comparable test based on the complete data. In a simulation study, we show that tests based on this diagnostic exhibit comparable power and better nominal Type I error rates than a commonly used alternative test proposed by Akritas (1988, Journal of the American Statistical Association 83, 222–230). An important advantage of the proposed diagnostic is that it can be applied to a broad class of censored data models, including generalized linear models and other models with nonidentically distributed and nonadditive error structures. We illustrate the proposed model diagnostic for testing the adequacy of two parametric survival models for Space Shuttle main engine failures.     

High‐resolution structures of collagen‐like peptides [(Pro‐Pro‐Gly)4‐Xaa‐Yaa‐Gly‐(Pro‐Pro‐Gly)4]: Implications for triple‐helix hydration and Hyp(X) puckering

Structures of (Pro‐Pro‐Gly)₄‐Xaa‐Yaa‐Gly‐(Pro‐Pro‐Gly)₄ (ppg9‐XYG) where (Xaa, Yaa) = (Pro, Hyp), (Hyp, Pro) or (Hyp, Hyp) were analyzed at high resolution using synchrotron radiation. Molecular and crystal structures of these peptides are very similar to those of the (Pro‐Pro‐Gly)₉ peptide. The results obtained in this study, together with those obtained from related compounds, indicated the puckering propensity of the Hyp in the X position: (1) Hyp(X) residues involved in the Hyp(X):Pro(Y) stacking pairs prefer the down‐puckering conformation, as in ppg9‐OPG, and ppg9‐OOG; (2) Hyp(X) residues involved in the Hyp(X):Hyp(Y) stacking pairs prefer the up‐puckering conformation if there is no specific reason to adopt the down‐puckering conformation. Water molecules in these peptide crystals are classified into two groups, the 1st and 2nd hydration waters. Water molecules in the 1st hydration group have direct hydrogen bonds with peptide oxygen atoms, whereas those in the 2nd hydration group do not. Compared with globular proteins, the number of water molecules in the 2nd hydration shell of the ppg9‐XYG peptides is very large, likely due to the unique rod‐like molecular structure of collagen model peptides. In the collagen helix, the amino acid residues in the X and Y positions must protrude outside of the triple helix, which forces even the hydrophobic side chains, such as Pro, to be exposed to the surrounding water molecules. Therefore, most of the waters in the 2nd hydration shell are covering hydrophobic Pro side chains by forming clathrate structures. © 2009 Wiley Periodicals, Inc. Biopolymers 91: 361–372, 2009. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com     

Inverse‐probability‐of‐treatment weighted estimation of causal parameters in the presence of error‐contaminated and time‐dependent confounders

Inverse‐probability‐of‐treatment weighted (IPTW) estimation has been widely used to consistently estimate the causal parameters in marginal structural models, with time‐dependent confounding effects adjusted for. Just like other causal inference methods, the validity of IPTW estimation typically requires the crucial condition that all variables are precisely measured. However, this condition, is often violated in practice due to various reasons. It has been well documented that ignoring measurement error often leads to biased inference results. In this paper, we consider the IPTW estimation of the causal parameters in marginal structural models in the presence of error‐contaminated and time‐dependent confounders. We explore several methods to correct for the effects of measurement error on the estimation of causal parameters. Numerical studies are reported to assess the finite sample performance of the proposed methods.     

Accounting for tagging‐to‐harvest mortality in a Brownie tag‐recovery model by incorporating radio‐telemetry data

The Brownie tag‐recovery model is useful for estimating harvest rates but assumes all tagged individuals survive to the first hunting season; otherwise, mortality between time of tagging and the hunting season will cause the Brownie estimator to be negatively biased. Alternatively, fitting animals with radio transmitters can be used to accurately estimate harvest rate but may be more costly. We developed a joint model to estimate harvest and annual survival rates that combines known‐fate data from animals fitted with transmitters to estimate the probability of surviving the period from capture to the first hunting season, and data from reward‐tagged animals in a Brownie tag‐recovery model. We evaluated bias and precision of the joint estimator, and how to optimally allocate effort between animals fitted with radio transmitters and inexpensive ear tags or leg bands. Tagging‐to‐harvest survival rates from >20 individuals with radio transmitters combined with 50–100 reward tags resulted in an unbiased and precise estimator of harvest rates. In addition, the joint model can test whether transmitters affect an individual's probability of being harvested. We illustrate application of the model using data from wild turkey, Meleagris gallapavo, to estimate harvest rates, and data from white‐tailed deer, Odocoileus virginianus, to evaluate whether the presence of a visible radio transmitter is related to the probability of a deer being harvested. The joint known‐fate tag‐recovery model eliminates the requirement to capture and mark animals immediately prior to the hunting season to obtain accurate and precise estimates of harvest rate. In addition, the joint model can assess whether marking animals with radio transmitters affects the individual's probability of being harvested, caused by hunter selectivity or changes in a marked animal's behavior.     

Hotspots of uncertainty in land‐use and land‐cover change projections: a global‐scale model comparison

Model‐based global projections of future land‐use and land‐cover (LULC) change are frequently used in environmental assessments to study the impact of LULC change on environmental services and to provide decision support for policy. These projections are characterized by a high uncertainty in terms of quantity and allocation of projected changes, which can severely impact the results of environmental assessments. In this study, we identify hotspots of uncertainty, based on 43 simulations from 11 global‐scale LULC change models representing a wide range of assumptions of future biophysical and socioeconomic conditions. We attribute components of uncertainty to input data, model structure, scenario storyline and a residual term, based on a regression analysis and analysis of variance. From this diverse set of models and scenarios, we find that the uncertainty varies, depending on the region and the LULC type under consideration. Hotspots of uncertainty appear mainly at the edges of globally important biomes (e.g., boreal and tropical forests). Our results indicate that an important source of uncertainty in forest and pasture areas originates from different input data applied in the models. Cropland, in contrast, is more consistent among the starting conditions, while variation in the projections gradually increases over time due to diverse scenario assumptions and different modeling approaches. Comparisons at the grid cell level indicate that disagreement is mainly related to LULC type definitions and the individual model allocation schemes. We conclude that improving the quality and consistency of observational data utilized in the modeling process and improving the allocation mechanisms of LULC change models remain important challenges. Current LULC representation in environmental assessments might miss the uncertainty arising from the diversity of LULC change modeling approaches, and many studies ignore the uncertainty in LULC projections in assessments of LULC change impacts on climate, water resources or biodiversity.     

Modelling climate‐change‐induced nonlinear thresholds in cephalopod population dynamics

A significant global challenge lies in our current inability to anticipate, and therefore prepare for, critical ecological thresholds (i.e. tipping points in ecosystems). This deficit stems largely from an inadequate understanding of the many complex interactions between species and the environment at the ecosystem level, and the paucity of mechanistic models relating environment to population dynamics at the species level. In marine ecosystems, abundant, short‐lived and fast‐growing species such as anchovies or squids, consistently function as ‘keystone’ groups whose population dynamics affect entire ecosystems. Increasing exploitation coupled with climate change impacts has the potential to affect these ecological groups and consequently, the entire marine ecosystem. There are currently very few models that predict the impact of climate change on these keystone groups. Here we use a combination of individual‐based bioenergetics and stage‐structured population models to characterize the fundamental capacity of cephalopods to respond to climate change. We demonstrate the potential for, and mechanisms behind, two unfavourable climate‐change‐induced thresholds in future population dynamics. Although one threshold was the direct consequence of a decrease in incubation time caused by ocean warming, the other threshold was linked to survivorship, implying the possibility of management through a modification of fishing mortality. Additional substantive changes in phenology were also predicted, with a possible loss in population resilience. Our results demonstrate the feasibility of predicting complex nonlinear dynamics with a reasonably simplistic mechanistic model, and highlight the necessity of developing such approaches for other species if attempts to moderate the impact of climate change on natural resources are to be effective.     

A goodness‐of‐fit test for occupancy models with correlated within‐season revisits

Occupancy modeling is important for exploring species distribution patterns and for conservation monitoring. Within this framework, explicit attention is given to species detection probabilities estimated from replicate surveys to sample units. A central assumption is that replicate surveys are independent Bernoulli trials, but this assumption becomes untenable when ecologists serially deploy remote cameras and acoustic recording devices over days and weeks to survey rare and elusive animals. Proposed solutions involve modifying the detection‐level component of the model (e.g., first‐order Markov covariate). Evaluating whether a model sufficiently accounts for correlation is imperative, but clear guidance for practitioners is lacking. Currently, an omnibus goodness‐of‐fit test using a chi‐square discrepancy measure on unique detection histories is available for occupancy models (MacKenzie and Bailey, Journal of Agricultural, Biological, and Environmental Statistics, 9, 2004, 300; hereafter, MacKenzie–Bailey test). We propose a join count summary measure adapted from spatial statistics to directly assess correlation after fitting a model. We motivate our work with a dataset of multinight bat call recordings from a pilot study for the North American Bat Monitoring Program. We found in simulations that our join count test was more reliable than the MacKenzie–Bailey test for detecting inadequacy of a model that assumed independence, particularly when serial correlation was low to moderate. A model that included a Markov‐structured detection‐level covariate produced unbiased occupancy estimates except in the presence of strong serial correlation and a revisit design consisting only of temporal replicates. When applied to two common bat species, our approach illustrates that sophisticated models do not guarantee adequate fit to real data, underscoring the importance of model assessment. Our join count test provides a widely applicable goodness‐of‐fit test and specifically evaluates occupancy model lack of fit related to correlation among detections within a sample unit. Our diagnostic tool is available for practitioners that serially deploy survey equipment as a way to achieve cost savings.     

Crystal structure of the collagen model peptide (Pro‐Pro‐Gly)4‐Hyp‐Asp‐Gly‐(Pro‐Pro‐Gly)4 at 1.0 Å resolution

The single‐crystal structure of the collagen‐like peptide (Pro‐Pro‐Gly)₄‐Hyp‐Asp‐Gly‐(Pro‐Pro‐Gly)₄, was analyzed at 1.02 Å resolution. The overall average helical twist (θ = 49.6°) suggests that this peptide adopts a 7/2 triple‐helical structure and that its conformation is very similar to that of (Gly‐Pro‐Hyp)₉, which has the typical repeating sequence in collagen. High‐resolution studies on other collagen‐like peptides have shown that imino acid‐rich sequences preferentially adopt a 7/2 triple‐helical structure (θ = 51.4°), whereas imino acid‐lean sequences adopt relaxed conformations (θ < 51.4°). The guest Gly‐Hyp‐Asp sequence in the present peptide, however, has a large helical twist (θ = 61.1°), whereas that of the host Pro‐Pro‐Gly sequence is small (θ = 46.7°), indicating that the relationship between the helical conformation and the amino acid sequence of such peptides is complex. In the present structure, a strong intermolecular hydrogen bond between two Asp residues on the A and B strands might induce the large helical twist of the guest sequence; this is compensated by a reduced helical twist in the host, so that an overall 7/2‐helical symmetry is maintained. The Asp residue in the C strand might interact electrostatically with the N‐terminus of an adjacent molecule, causing axial displacement, reminiscent of the D‐staggered structure in fibrous collagens. © 2013 Wiley Periodicals, Inc. Biopolymers 99: 436–447, 2013.     

Predicting the century‐long post‐fire responses of reptiles

Aim We examined the century‐long post‐fire responses of reptiles to (1) determine the time‐scales over which fauna – fire relationships occur, (2) assess the capacity of a conceptual model to predict faunal response to fire, and (3) investigate the degree to which models of fauna – fire relationships can predict species occurrence and are transferable across space. Location A 104,000 km² area in the semi‐arid Murray Mallee region of south‐eastern Australia. Methods We surveyed reptiles at 280 sites across a century‐long post‐fire chronosequence. We developed generalized additive mixed models (GAMMs) of the relationship between time since fire and the occurrence of 17 species in two subregions, and compared modelled responses with predictions derived from the conceptual model. The predictive capacity of GAMMs was then assessed (1) within the subregion the model was developed and (2) when transferred into a novel subregion. Results Eleven species displayed a significant relationship with time‐since‐fire, with changes in species probability of occurrence continuing up to 100 years post‐fire. Predictions of the timing of species post‐fire peak in occurrence were accurate for 9 of 13 species models for which a significant fire response was detected, but little success was achieved in predicting the shape of a species' response. GAMMs predicted species occurrence more accurately when applied within the subregion in which they were developed than when transferred into a novel subregion, primarily due to some species responding to fire more strongly in one part of their geographic range. Main conclusions Fire influences the occurrence of reptiles in semi‐arid ecosystems over century‐long time frames. Habitat‐use conceptual models have value in predicting the peak occurrence of species following fire, particularly for species with distributions strongly shaped by fire. Species relationships with fire can differ across their geographic range, probably associated with variation in climatic influences on post‐fire succession and the consequent provision of habitat resources.     

Antibody‐ and aptamer‐strategies for GvHD prevention

Prevention of Graft‐versus‐Host‐Disease (GvHD) by preserved Graft‐versus‐Leukaemia (GvL) effect is one of the major obstacles following allogeneic haematopoietic stem cell transplantation. Currently used drugs are associated with side effects and were not able to separate GvHD from the GvL‐effect because of general T‐cell suppression. This review focuses on murine models for GvHD and currently available treatment options involving antibodies and applications for the therapeutic use of aptamers as well as strategies for targeting immune responses by allogenic antigens.     

A joint model for longitudinal continuous and time‐to‐event outcomes with direct marginal interpretation

Joint modeling of various longitudinal sequences has received quite a bit of attention in recent times. This paper proposes a so‐called marginalized joint model for longitudinal continuous and repeated time‐to‐event outcomes on the one hand and a marginalized joint model for bivariate repeated time‐to‐event outcomes on the other. The model has several appealing features. It flexibly allows for association among measurements of the same outcome at different occasions as well as among measurements on different outcomes recorded at the same time. The model also accommodates overdispersion. The time‐to‐event outcomes are allowed to be censored. While the model builds upon the generalized linear mixed model framework, it is such that model parameters enjoy a direct marginal interpretation. All of these features have been considered before, but here we bring them together in a unified, flexible framework. The model framework's properties are scrutinized using a simulation study. The models are applied to data from a chronic heart failure study and to a so‐called comet assay, encountered in preclinical research. Almost surprisingly, the models can be fitted relatively easily using standard statistical software.     

Continental‐scale tree‐ring‐based projection of Douglas‐fir growth: Testing the limits of space‐for‐time substitution

A central challenge in global change research is the projection of the future behavior of a system based upon past observations. Tree‐ring data have been used increasingly over the last decade to project tree growth and forest ecosystem vulnerability under future climate conditions. But how can the response of tree growth to past climate variation predict the future, when the future does not look like the past? Space‐for‐time substitution (SFTS) is one way to overcome the problem of extrapolation: the response at a given location in a warmer future is assumed to follow the response at a warmer location today. Here we evaluated an SFTS approach to projecting future growth of Douglas‐fir (Pseudotsuga menziesii), a species that occupies an exceptionally large environmental space in North America. We fit a hierarchical mixed‐effects model to capture ring‐width variability in response to spatial and temporal variation in climate. We found opposing gradients for productivity and climate sensitivity with highest growth rates and weakest response to interannual climate variation in the mesic coastal part of Douglas‐fir's range; narrower rings and stronger climate sensitivity occurred across the semi‐arid interior. Ring‐width response to spatial versus temporal temperature variation was opposite in sign, suggesting that spatial variation in productivity, caused by local adaptation and other slow processes, cannot be used to anticipate changes in productivity caused by rapid climate change. We thus substituted only climate sensitivities when projecting future tree growth. Growth declines were projected across much of Douglas‐fir's distribution, with largest relative decreases in the semiarid U.S. Interior West and smallest in the mesic Pacific Northwest. We further highlight the strengths of mixed‐effects modeling for reviving a conceptual cornerstone of dendroecology, Cook's 1987 aggregate growth model, and the great potential to use tree‐ring networks and results as a calibration target for next‐generation vegetation models.     

Variable selection in Bayesian generalized linear‐mixed models: An illustration using candidate gene case‐control association studies

The problem of variable selection in the generalized linear‐mixed models (GLMMs) is pervasive in statistical practice. For the purpose of variable selection, many methodologies for determining the best subset of explanatory variables currently exist according to the model complexity and differences between applications. In this paper, we develop a “higher posterior probability model with bootstrap” (HPMB) approach to select explanatory variables without fitting all possible GLMMs involving a small or moderate number of explanatory variables. Furthermore, to save computational load, we propose an efficient approximation approach with Laplace's method and Taylor's expansion to approximate intractable integrals in GLMMs. Simulation studies and an application of HapMap data provide evidence that this selection approach is computationally feasible and reliable for exploring true candidate genes and gene–gene associations, after adjusting for complex structures among clusters.     

Heterogeneous treatment effects in stratified clinical trials with time‐to‐event endpoints

When analyzing clinical trials with a stratified population, homogeneity of treatment effects is a common assumption in survival analysis. However, in the context of recent developments in clinical trial design, which aim to test multiple targeted therapies in corresponding subpopulations simultaneously, the assumption that there is no treatment‐by‐stratum interaction seems inappropriate. It becomes an issue if the expected sample size of the strata makes it unfeasible to analyze the trial arms individually. Alternatively, one might choose as primary aim to prove efficacy of the overall (targeted) treatment strategy. When testing for the overall treatment effect, a violation of the no‐interaction assumption renders it necessary to deviate from standard methods that rely on this assumption. We investigate the performance of different methods for sample size calculation and data analysis under heterogeneous treatment effects. The commonly used sample size formula by Schoenfeld is compared to another formula by Lachin and Foulkes, and to an extension of Schoenfeld's formula allowing for stratification. Beyond the widely used (stratified) Cox model, we explore the lognormal shared frailty model, and a two‐step analysis approach as potential alternatives that attempt to adjust for interstrata heterogeneity. We carry out a simulation study for a trial with three strata and violations of the no‐interaction assumption. The extension of Schoenfeld's formula to heterogeneous strata effects provides the most reliable sample size with respect to desired versus actual power. The two‐step analysis and frailty model prove to be more robust against loss of power caused by heterogeneous treatment effects than the stratified Cox model and should be preferred in such situations.     

Lipid‐Bilayer Permeation of Drug‐Like Compounds

Lipid‐bilayer permeation is determinant for the disposition of xenobiotics in the body. It controls the pharmacokinetic behavior of drugs and is, in many cases, a prerequisite for intracellular targeting. Permeation of in vivo barriers is in general predicted from lipophilicity and related parameters. This article goes beyond the empirical correlations, and elucidates the processes and their interplay determining bilayer permeation. A flip‐flop model for bilayer permeation, which considers the partitioning rate constants beside the translocation rate constants, is compared with the diffusion model based on Fick's first law. According to the flip‐flop model, the ratios of aqueous volumes to barrier area can determine whether partitioning or translocation is rate‐limiting. The flip‐flop model allows permeation of anions and cations, and expands our understanding of pH‐dependent permeation kinetics. Some experimental evidences for ion‐controlled permeation at pH 7 are also included in this work.