Modified GEE and Goodness of the Marginal Fit (GOMF) Test with Correlated Binary Responses for Contingency Tables

This paper addresses testing the goodness of fit of models for marginal probabilities estimated by generalized estimating equations. We develop a modified version of generalized estimating equation and a goodness‐of‐fit test based on the fitted marginal means. The test statistic is easy to compute and has a simple reference distribution. Its performance is evaluated asymptotically and in small samples. It is also compared to the deviance and Pearson X² statistics. Example applications are given. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

S-Sample Smooth Goodness of Fit Testing: Rederivation and Monte Carlo Assessment

S-sample smooth goodness of fit tests may be constructed using components from one sample goodness of fit testing. Each sample could be assessed for consistency with a target distribution using these components, although that is not our objective here. Contrasts in the components may be used to assess consistency of the samples with each other. If all the samples are consistent, we could then conveniently perform a one-sample goodness of fit test for the target distribution. If the samples are not consistent, an LSD-type analysis can be performed on the one-sample components to identify where the differences between occur. This approach gives a detailed and informative scrutiny of the data.     

Goodness‐of‐fit tests for disorder detection in NGS experiments

Next‐generation sequencing (NGS) experiments are often performed in biomedical research nowadays, leading to methodological challenges related to the high‐dimensional and complex nature of the recorded data. In this work we review some of the issues that arise in disorder detection from NGS experiments, that is, when the focus is the detection of deletion and duplication disorders for homozygosity and heterozygosity in DNA sequencing. A statistical model to cope with guanine/cytosine bias and phasing and prephasing phenomena at base level is proposed, and a goodness‐of‐fit procedure for disorder detection is derived. The method combines the proper evaluation of local p‐values (one for each DNA base) with suitable corrections for multiple comparisons and the discrete nature of the p‐values. A global test for the detection of disorders in the whole DNA region is proposed too. The performance of the introduced procedures is investigated through simulations. A real data illustration is provided.     

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.     

Linkage of a RAPD marker with powdery mildew resistance <Emphasis Type="Italic">er-1</Emphasis> gene in <Emphasis Type="Italic">Pisum sativum</Emphasis> L.

The aim of this study was to investigate the inheritance of powdery mildew disease and to tag it with a DNA marker to utilize for the marker-assisted selection (MAS) breeding program. The powdery mildew resistant genotype Fallon ^er and susceptible genotype 11760-3 ^ER were selected from 177 genotypes by heavy infestation of germplasm with Erysiphe pisi through artificial inoculation The F₁ plants of the cross Fallon/11760-3 indicated the dominance of the susceptible allele, while F₂ plants segregated in 3: 1 ratio (susceptible: resistant) that fit for goodness of fitness by χ² (P > 0.07), indicating monogenic recessive inheritance for powdery mildew resistance in Pisum sativum. A novel RAPD marker OPB18 (5′-CCACAGCAGT-3′) was linked to the er-1 gene with 83% probability with a LOD score of 4.13, and was located at a distance of 11.2 cM from the er-1 gene.     

A coefficient of determination (R2) for generalized linear mixed models

Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R²) or the adjusted R² are well established for linear models, it is not obvious how such measures should be defined for generalized linear and mixed models. There are by now several proposals but no consensus has yet emerged as to the best unified approach in these settings. In particular, it is an open question how to best account for heteroscedasticity and for covariance among observations present in residual error or induced by random effects. This paper proposes a new approach that addresses this issue and is universally applicable for arbitrary variance‐covariance structures including spatial models and repeated measures. It is exemplified using three biological examples.     

Trend in Pacific walrus (Odobenus rosmarus divergens) tusk asymmetry, 1990–2014

We used the basal circumference of Pacific walrus (Odobenus rosmarus divergens) tusks (upper canine teeth, n = 21,068 pairs) to estimate fluctuating asymmetry (FA1 index) from 1990 to 2014. The mean difference in circumference between paired tusks was ?0.006 (SEM = 0.002) cm and approximately normally distributed. Measurement error was 0.6 (0.02)%, similar between biologists and lay persons (P = 0.83), and ≤15% of FA1. Tusk FA1 was greatest in 1990 then declined by 56% (P = 0.0001) through 2014. Male and female trends differed (P = 0.0001) and male FA1 was 40% greater (P = 0.0001) and the rate of decline 28% steeper (P = 0.3) than females. A quartic polynomial model (r² = 0.66, w_i = 0.685) fit the trend for female data better than simpler forms, whereas a linear model (r² = 0.55, w_i = 0.693) was a better fit for male data. Walrus tusk FA1 reflected periods when the population was stressed due to food limitations and then recovered, and perhaps when females began to experience the loss of preferred sea ice habitat in summer and FA1 is an easily monitored indicator. More work is needed to confirm the link between FA1, individual fitness, and adaptive potential.     

An adjusted coefficient of determination (R2) for generalized linear mixed models in one go

The coefficient of determination (R²) is a common measure of goodness of fit for linear models. Various proposals have been made for extension of this measure to generalized linear and mixed models. When the model has random effects or correlated residual effects, the observed responses are correlated. This paper proposes a new coefficient of determination for this setting that accounts for any such correlation. A key advantage of the proposed method is that it only requires the fit of the model under consideration, with no need to also fit a null model. Also, the approach entails a bias correction in the estimator assessing the variance explained by fixed effects. Three examples are used to illustrate new measure. A simulation shows that the proposed estimator of the new coefficient of determination has only minimal bias.     

REVERSIBILITY IN EVOLUTION: A MAXIMUM LIKELIHOOD APPROACH TO CHARACTER GAIN/LOSS BIAS IN PHYLOGENIES

Statistical methods are used to test the hypothesis that rate of gain is equal to rate of loss for a single character on a cladogram. Ancestral character states are used as input for maximum likelihood (ML) rate estimation. Two markovian models of character evolution are considered: one has equality of rate across branches; the other permits variation in rate according to predetermined weights for branches. ML estimates are derived for both models, and their properties in large and small trees are investigated. Bias and error are significant in small trees. Error is greatest for characters in which rate of gain is low, and is greater for the loss estimate than for the gain estimate. Likelihood ratio (LR) tests of the null hypothesis of equality of gain/loss rate are derived, and their properties investigated. The distribution of -2 log LR is close to χ² with 1 df with as few as 32 taxa. However, the power of the test is low unless the character is evolving rapidly. Methods for increasing power are examined, including selection of rapidly evolving subsets of characters, and pooling across characters. A goodness of fit test is presented to determine if pooling is justified. An example using published restriction site data on the Asteraceae demonstrates significant deviation from the null model in the direction predicted on the basis of the molecular biology of restriction enzyme site recognition, but only for one large subset of the data in which pooling is warranted.     

Dual-substrate inhibition kinetic studies for recombinant human interferon gamma producing Pichia pastoris

Pichia pastoris is considered as one of the prominent host extensively used as a platform for heterologous protein production. In the present study, the growth inhibition kinetics of recombinant P. pastoris expressing human interferon gamma was studied under different initial substrate concentrations of gluconate (10–100?g?L^?1) and methanol (2–50?g?L^?1) in modified FM22 medium. The highest specific growth rate of 0.0206 and 0.019?hr^?1 was observed at 60?g?L^?1 of gluconate and 10?g?L^?1 of methanol, respectively. Various three- and four-parametric Monod-variant models were chosen to analyze the inhibition kinetics. The model parameters as well as goodness of fit were estimated using nonlinear regression analysis. The three-parameter Haldane model was found to be best fit for both gluconate (R²?=?0.95) and methanol substrate (R²?=?0.96). The parameter sensitivity analysis revealed that µ_max, K_i, and K_s are the most sensitive parameters for both methanol and gluconate. Different substrate inhibition models were fitted to the growth kinetic data and the additive form of double Webb model was found to be the best to explain the growth kinetics of recombinant P. pastoris.     

An Improved Goodness of Fit Statistic for Probability Prediction Models

We consider the general case of probability prediction models having two or more outcomes and propose an adjusted χ² statistic which can be used to assess the goodness of fit of these models. We present a simulation study to show that our proposed statistic has an approximate χ² distribution under the null hypothesis. Two applications are provided to illustrate the use of the new statistic. The first application examines the fit of a logistic regression model using both the proposed statistic and the popular Hosmer-Lemeshow statistic and we compare and contrast these two methods. The second application evaluates the goodness of fit of a polychotomous regression model.     

Drying of Pomegranate Arils and Selection of a Suitable Drying Model

The drying characteristics of pomegranate arils were investigated in temperature range of 50–70 °C. The increase in drying air temperature resulted in a decrease in drying time. The drying rate was found to increase with temperature, thereby reducing the total drying time. Thirteen drying models were evaluated in the kinetics research. The goodness of fit of the proposed models was evaluated by using the determination of coefficient (R ² ), mean relative percent error (P), reduced chi-square (χ ²), and root means square error (RMSE). The Midilli et al. model showed a better fit to experimental drying data as compared to other models. Effective moisture diffusivity (D _eff) ranged from 9.447 × 10⁻¹¹ to 3.481 × 10⁻¹⁰ m²/s as calculated by the Fick’s second law of diffusion. The temperature dependence of the value of effective moisture diffusivity followed an Arrhenius-type relationship. The activation energy for the moisture diffusion was determined to be 60.34 kJ/mol.     

Polymorphism in a casein fraction of sows' milk

Polyacrylamide vertical gel electrophoresis was used to separate the caseins of sows' milk. Polymorphism was found in a region of the gels designated Cn₃. The Cn₃ polymorphism consists of two bands which appear to be controlled by two codominant alleles designated Cn ₃ ^A and Cn ₃ ^B . Homozygotes possess one band and heterozygotes posses both bands of equal intensity giving the following phenotypes: Cn₃A, Cn₃AB, and Cn₃B. A chi-square test for goodness of fit of the observed phenotypes to that expected by the Hardy-Weinberg equilibrium formula and a segregation analysis of eight matings involving 19 female progeny conform to the hypothesis that the Cn₃ polymorphism is controlled by two codominant autosomal alleles. Further family studies will be necessary to confirm the genetic control of the Cn₃ polymorphism.Deceased.     

RAC1mutation is not a predictive biomarker for PI3’‐kinase‐β‐selective pathway‐targeted therapy

Mutational activation of RAC1 is detected in ~7% of cutaneous melanoma, with the most frequent mutation (RAC1^C85T) encoding for RAC1^P29S. RAC1^P29S is a fast‐cycling GTPase that leads to accumulation of RAC1^P29S‐GTP, which has potentially pleiotropic regulatory functions in melanoma cell signaling and biology. However, the precise mechanism by which mutationally activated RAC1^P29S propagates its pro‐tumorigenic effects remains unclear. RAC1‐GTP is reported to activate the beta isoform of PI3’‐kinase (PIK3CB/PI3Kβ) leading to downstream activation of PI3’‐lipid signaling. Hence, we employed both genetic and isoform‐selective pharmacological inhibitors to test if RAC1^P29S propagates its oncogenic signaling in melanoma through PI3Kβ. We observed that RAC1^P29S‐expressing melanoma cells were largely insensitive to inhibitors of PI3Kβ. Furthermore, RAC1^P29S melanoma cell lines showed variable sensitivity to pan‐class 1 (α/β/γ/δ) PI3’‐kinase inhibitors, suggesting that RAC1‐mutated melanoma cells may not rely on PI3’‐lipid signaling for their proliferation. Lastly, we observed that RAC1^P29S‐expressing cell lines also showed variable sensitivity to pharmacological inhibition of the RAC1 → PAK1 signaling pathway, questioning the relevance of inhibitors of this pathway for the treatment of patients with RAC1‐mutated melanoma.     

Quantifying the effects of host discrimination on egg‐laying decision of the cowpea seed beetle,Callosobruchus maculatus

Many parasitic and endophagous insect species are capable of discriminating among the quality of their hosts. However, there is no appropriate way to quantify their discrimination performance. In this study, we quantified how oviposition of the cowpea seed beetle, Callosobruchus maculatus (Fabricius) (Coleoptera: Bruchidae), was affected by the relative contributions of both egg number and host size discrimination. The effect of egg density and resource heterogeneity on these discrimination performances was also explored. Egg‐distribution predictions were made by combining time‐dependent available resource fitness (egg discrimination) and host weight factors (size discrimination). The χ² test was then used for goodness‐of‐fit testing. The effects of both egg and size discrimination on oviposition in environments with different levels of resource heterogeneity were compared. It was found that host size, rather than the number of eggs on the host, plays a larger role in the egg‐laying decision for most individual seed beetles, especially when egg density is high. Host size discrimination behavior was reinforced when the beetles experienced increasing resource heterogeneity, but the performance might reach a plateau. This is the first quantitative evaluation of the effect of host discrimination on egg‐laying decisions of seed beetles.     

A novel enzymatic microreactor with Aspergillus oryzae β‐galactosidase immobilized on silicon dioxide nanosprings

The use of silicon dioxide (SiO₂) nanosprings as supports for immobilized enzymes in a continuous microreactor is described. A nanospring mat (2.2 cm² × 60 μm thick) was functionalized with γ‐aminopropyltriethoxysilane, then treated with N‐succinimidyl‐3‐(2‐pyridyldithio)‐propionate (SPDP) and dithiothreitol (DTT) to produce surface thiol (? SH) groups. SPDP‐modified β‐galactosidase from Aspergillus oryzae was immobilized on the thiolated nanosprings by reversible disulfide linkages. The enzyme‐coated nanospring mat was placed into a 175‐μm high microchannel, with the mat partially occluding the channel. The kinetics and steady‐state conversion of hydrolysis of o‐nitrophenyl β‐D ‐galactosylpyranoside at various substrate flow rates and concentrations were measured. Substantial flow was observed through the nanosprings, for which the Darcy permeability κ ≈ 3 × 10^?6 cm². A simple, one‐parameter numerical model coupling Navier‐Stokes and Darcy flow with a pseudo‐first‐order reaction was used to fit the experimental data. Simulated reactor performance was sensitive to changes in κ and the height of the nanospring mat. Permeabilities lower than 10^?8 cm² practically eliminated convective flow through the nanosprings, and substantially decreased conversion. Increasing the height of the mat increased conversion in simulations, but requires more enzymes and could cause sealing issues if grown above channel walls. Preliminary results indicate that in situ regeneration by reduction with DTT and incubation with SPDP‐modified β‐galactosidase is possible. Nanosprings provide high solvent‐accessible surface area with good permeability and mechanical stability, can be patterned into existing microdevices, and are amenable to immobilization of biomolecules. Nanosprings offer a novel and useful support for enzymatic microreactors, biosensors, and lab‐on‐chip devices. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

β‐Cell Function and Insulin Sensitivity in Adolescents From an OGTT

Given the increase in the incidence of insulin resistance, obesity, and type 2 diabetes in children and adolescents, it would be of paramount importance to assess quantitative indices of insulin secretion and action during a physiological perturbation, such as a meal or an oral glucose‐tolerance test (OGTT). A minimal model method is proposed to measure quantitative indices of insulin secretion and action in adolescents from an oral test. A 7 h, 21‐sample OGTT was performed in 11 adolescents. The C‐peptide minimal model was identified on C‐peptide and glucose data to quantify indices of β‐cell function: static φ_s and dynamic φ_d responsivity to glucose from which total responsivity φ was also measured. The glucose minimal model was identified on glucose and insulin data to estimate insulin sensitivity, S_I, which was compared to a reference measure, S_I^ref, provided by a tracer method. Disposition indices, which adjust insulin secretion for insulin action, were then calculated. Indices of β‐cell function were φ_s = 51.35 ± 8.89 × 10^?9min^?1, φ_d = 1,392 ± 258 × 10^?9, and φ = 82.09 ± 17.70 × 10^?9min^?1. Insulin sensitivity was S_I = 14.19 ± 2.73 × 10^?4, not significantly different from S_I^ref = 14.96 ± 3.04 × 10^?4 dl/kg·min per µU/ml, and well correlated: r = 0.98, P < 0.0001, thus indicating that S_I can be accurately measured from an oral test. Disposition indices were DI_s = 1,040 ± 201 × 10^?14 dl/kg/min² per pmol/l, DI_d = 33,178 ± 10,720 × 10^?14 dl/kg/min per pmol/l, DI = 1,844 ± 522 × 10^?14 dl/kg/min² per pmol/l. Virtually the same minimal model assessment was obtained with a reduced 3 h, 9‐sample protocol. OGTT interpreted with C‐peptide and glucose minimal model has the potential to provide novel insight regarding the regulation of glucose metabolism in adolescents, and to evaluate the effect of obesity and interventions such as diet and exercise.     

Does Circadian and Seasonal Variation in Occurrence of Acute Aortic Dissection Influence in‐Hospital Outcomes?

The risk of acute aortic dissection (AAD) exhibits chronobiological variations with peak onset in the morning and in winter. However, it is not known whether the time of day or season of the year of the AAD affects clinical outcomes. We studied 1,032 patients enrolled in the International Registry of Acute Aortic Dissection from January 1997 to December 2001. For circadian and seasonal analysis, the time and date of symptom onset were available for 741 and 1,007 patients, respectively, and were grouped into four 6 h periods (morning, afternoon, evening, and night) and four seasons (winter, spring, summer, and autumn). The χ² test for goodness of fit was used to evaluate non‐uniformity of the time of day and time of year for critical in‐hospital clinical events, including death. While highest incidence of AAD occurred in the morning and winter, clinical events (including mortality) were similar during the four different periods of the 24 h (χ²=1.9, p=0.60) and seasonal (χ²=1.2, p=0.75) periods.     

Syntheses,Receptor Bindings,in vitro and in vivo Stabilities and Biodistributions of DOTA‐Neurotensin(8–13) Derivatives Containing β‐Amino Acid Residues – A Lesson about the Importance of Animal Experiments

Neurotensin(8–13) (NTS(8–13)) analogs with C‐ and/or N‐terminal β‐amino acid residues and three DOTA derivatives thereof have been synthesized (i.e., 1 – 6 ). A virtual docking experiment showed almost perfect fit of one of the 1,4,7,10‐tetraazacyclododecane‐1,4,7,10‐tetraacetic acid (DOTA) derivatives, 6a , into a crystallographically identified receptor NTSR1 (Fig. 1). The affinities for the receptors of the NTS analogs and derivatives are low, when determined with cell‐membrane homogenates, while, with NTSR1‐exhibiting cancer tissues, affinities in the single‐digit nanomolar range can be observed (Table 2). Most of the β‐amino acid‐containing NTS(8–13) analogs (Table 1 and Fig. 2), including the ⁶⁸Ga complexes of the DOTA‐substituted ones ( 6 ; Figs. 2 and 5), are stable for ca. 1 h in human serum and plasma, and in murine plasma. The biodistributions of two ⁶⁸Ga complexes (of 6a and 6b ) in HT29 tumor‐bearing nude mice, in the absence and in the presence of a blocking compound, after 10, 30, and 60 min (Figs. 3 and 4) lead to the conclusion that the amount of specifically bound radioligand is rather low. This was confirmed by PET‐imaging experiments with the tumor‐bearing mice (Fig. 6). Comparison of the in vitro plasma stability (after 1 h) with the ex vivo blood content (after 10–15 min) of the two ⁶⁸Ga complexes shows that they are rapidly cleaved in the animals (Fig. 5).