Defective regression models for cure rate modeling with interval‐censored data

Regression models in survival analysis are most commonly applied for right‐censored survival data. In some situations, the time to the event is not exactly observed, although it is known that the event occurred between two observed times. In practice, the moment of observation is frequently taken as the event occurrence time, and the interval‐censored mechanism is ignored. We present a cure rate defective model for interval‐censored event‐time data. The defective distribution is characterized by a density function whose integration assumes a value less than one when the parameter domain differs from the usual domain. We use the Gompertz and inverse Gaussian defective distributions to model data containing cured elements and estimate parameters using the maximum likelihood estimation procedure. We evaluate the performance of the proposed models using Monte Carlo simulation studies. Practical relevance of the models is illustrated by applying datasets on ovarian cancer recurrence and oral lesions in children after liver transplantation, both of which were derived from studies performed at A.C. Camargo Cancer Center in São Paulo, Brazil.     

Self‐assembly of short peptides composed of only aliphatic amino acids and a combination of aromatic and aliphatic amino acids

The morphology of structures formed by the self‐assembly of short N‐terminal t‐butyloxycarbonyl (Boc) and C‐terminal methyl ester (OMe) protected and Boc‐deprotected hydrophobic peptide esters was investigated. We have observed that Boc‐protected peptide esters composed of either only aliphatic hydrophobic amino acids or aliphatic hydrophobic amino acids in combination with aromatic amino acids, formed highly organized structures, when dried from methanol solutions. Transmission and scanning electron microscopic images of the peptides Boc‐Ile‐Ile‐OMe, Boc‐Phe‐Phe‐Phe‐Ile‐Ile‐OMe and Boc‐Trp‐Ile‐Ile‐OMe showed nanotubular structures. Removal of the Boc group resulted in disruption of the ability to form tubular structures though spherical aggregates were formed. Both Boc‐Leu‐Ile‐Ile‐OMe and H‐Leu‐Ile‐Ile‐OMe formed only spherical nanostructures. Dynamic light scattering studies showed that aggregates of varying dimensions were present in solution suggesting that self‐assembly into ordered structures is facilitated by aggregation in solution. Fourier transform infrared spectroscopy and circular dichroism spectroscopy data show that although all four of the protected peptides adopt well‐defined tertiary structures, upon removal of the Boc group, only H‐Phe‐Phe‐Phe‐Ile‐Ile‐OMe had the ability to adopt β‐structure. Our results indicate that hydrophobic interaction is a very important determinant for self‐assembly and presence of charged and aromatic amino acids in a peptide is not necessary for self‐assembly. Copyright © 2012 European Peptide Society and John Wiley & Sons, Ltd.     

Bayesian Predictive Probability Functions for Count Data that are Subject to Misclassification

We develop three Bayesian predictive probability functions based on data in the form of a double sample. One Bayesian predictive probability function is for predicting the true unobservable count of interest in a future sample for a Poisson model with data subject to misclassification and two Bayesian predictive probability functions for predicting the number of misclassified counts in a current observable fallible count for an event of interest. We formulate a Gibbs sampler to calculate prediction intervals for these three unobservable random variables and apply our new predictive models to calculate prediction intervals for a real‐data example. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymmetric regression models with limited responses with an application to antibody response to vaccine

We develop regression models for limited and censored data based on the mixture between the log‐power‐normal and Bernoulli‐type distributions. A likelihood‐based approach is implemented for parameter estimation and a small‐scale simulation study is conducted to evaluate parameter recovery, with emphasis on bias estimation. The main conclusion is that the approach is very much satisfactory for moderate and large sample sizes. A real data example, the safety and immunogenecity study of measles vaccine in Haiti, is presented to illustrate how different models can be used to fit this type of data. As shown, the asymmetric models considered seem to present the best fit for the data set under study, revealing significance of the explanatory variable sex, which is not found significant with the log‐normal model.     

Rapid calculation of the solution scattering profile from a macromolecule of known structure

If one expands the structure factor equation in spherical coordinates, rotational averaging of the molecular Fourier transform, which leads directly to the solution scattering profile, is greatly simplified. It becomes a projection in the polar and azimuthal angular variables. The profile is given by I(R) = 1/2 infinity sigma n = 0 n sigma m = 0 epsilon mNm,n magnitude of Gm,n(R) 2 where Gm,n(R) = sigma jfjYm,n(theta j, phi j)jn(2 pi rjR) The index j runs over all atoms; r, theta, phi are atomic coordinates and epsilon and N are constants; the Ym,n are complex spherical harmonics, and jn are spherical Bessel functions; R = 2 sin theta/lambda. The effects of solvent have been modeled by subtracting from each protein atom a properly weighted water. Hydrogens have been included by using scattering curves fj derived from the spherical averaging of protein atoms with their attached hydrogens. This approach may also be satisfactory for neutron scattering. Published scattering profiles for lysozyme and BPTI have been accurately matched in less than one-tenth the time required by other methods. Separate, adjustable temperature factors for the protein, solvent waters, and bound waters are used, and appear to be needed. In the case of BPTI, as suggested by NMR observations, the observed diffraction pattern was much better accounted for by including only 4 tightly bound waters rather than the roughly 60 seen by crystallography.     

Spherical body formation in the spirochaete Brachyspira hyodysenteriae

When cultures of Brachyspira hyodysenteriae were grown under a wide range of in vitro conditions, at least 1% of the cells formed spherical bodies different to the normal helical form. This percentage increased considerably in aging cultures or following their incubation in caramelized media. Spherical body formation was initiated from a terminal localized swelling of the outer sheath followed by a retraction of the protoplasmic cylinder into the resulting swollen vesicle. As this occurred, the periplasmic flagella seemed to unwind from the protoplasmic cylinder. Once retracted, the protoplasmic cylinder was found to be wrapped in an organized manner around the inner surface of the membrane of the swollen vesicle. Although most were 2-3 microm in diameter, some much larger spherical bodies (6-12 microm diameter) were occasionally seen, with a corresponding increase in the visible number of peripheral protoplasmic cylinder cross-sections. Spherical bodies from older cultures did not contain protoplasmic cylinders arranged around the periphery, but instead were characterized by the presence of a centrally located, electron-dense body c. 0.5-0.8 mum in diameter. Brachyspira hyodysenteriae spherical bodies differ in both their structural organization and probable method of formation from similar structures described in other spirochaete genera.     

Influence of cell equivalent spherical diameter on the growth rate and cell density of marine phytoplankton

The maximal growth rates (μ_max) of 8 species of marine phytoplankton were studied in detail. A Logistic growth model was used to describe the growth process of phytoplankton and the averaged plotting correlation coefficient was 1.00 ± 0.01 (mean ± standard deviation). The size distribution of phytoplankton could be well represented by single or combined Gaussian distribution functions. The size distribution of phytoplankton was investigated by daily analysis, and the variation of the median equivalent spherical diameter (MESD) was recorded. The size of algal cells varied throughout the process of population growth, and the size distribution characteristic of the two species of pyrrophytes investigated also changed during the growth process. The relation between maximum growth rate and MESD could be expressed by the equation μ_max = a * MESD^b (where μ_max is the maximum specific growth rate, MESD is the median equivalent spherical diameter, and a and b are constants equal to 2.10 × 10⁵ and − 1.15, respectively), estimated by nonlinear regression analysis with the allometric function. The dependence of maximum cell density on algal MESD was also investigated and the relationship B_f = 1.56 × 10⁷ MESD^− 1.20 was obtained (where B_f is the maximum cell density).     

On Bivariate Cumulative Damage Models With Application

Bivariate cumulative damage models are proposed where the responses given the damages are independent random variables. The bivariate damage process can be either bivariate Poisson or bivariate gamma. A bivariate continuous cumulative damage model is investigated in which the responses given the damages have gamma distributions. In this case evaluation of the joint density function and bivariate tail probability function is facilitated by expanding the gamma distributions of the conditional responses by Laguerre polynomials. This approach also leads to evaluation of associated survival models. Moments and estimating equations are discussed. In addition, a bivariate discrete cumulative damage model is investigated in which the responses given the damages have a distribution chosen from a class that includes the negative binomial, the Neyman Type‐A, the Polya‐Aeppli, and the Lagrangian Poisson. Probabilities are obtained from recursive formulas which do not involve cancellation error as all quantities are non‐negative. Moments and estimating equations are presented for these models also. The continuous and the discrete models are applied to describe the rise of systolic and diastolic blood pressure with age.     

Studies on Ca2+-channel distribution in maturation arrested mouse oocyte

The present study was carried out to identify the existence of voltage-dependent Ca2+-channels (P/Q-, N-, and L-type) and their distributional differences in germinal vesicle (GV) and GV breakdown (GVBD)-arrested mouse oocytes which includes GVBD to telophase I of meiosis I and matured oocytes (MII, metaphase of meiosis II) by using the immunocytochemical method and a confocal laser scanning microscope. (1) Comparison between follicular oocytes (GV) and GV-arrested oocytes after 17 hr of in vitro culture. In follicular oocytes, P/Q-, N-, L (anti-alpha1C anti-alpha1D)-type Ca2+-channels showed both localized and uniform staining. In contrast, GV-arrested oocytes, after in vitro culture for 17 hr, showed no presence of Ca2+-channels in most oocytes. (2) Comparison between GVBD oocytes after culture in vitro for 3 hr and GVBD-arrested oocytes after culture in vitro for 17 hr. In GVBD oocytes, P/Q-, N-, L (anti-1C, anti-alpha1D)-type Ca2+-channels showed both localized and uniform staining. In contrast, in GVBD-arrested oocytes, none of the three types of Ca2+-channels were identified in 72-86% of oocytes. The present study demonstrates that in most GVBD-arrested oocytes that do not mature to MII, there is no Ca2+-channel identified. Therefore, most of the GVBD-arrested oocytes seem to have defects in Ca2+-channel expression/translation. Also, distributional changes of Ca2+-channels take place depending on the maturation progress in GV oocytes and MII stage oocytes (ovulated and 17 hr cultured MII stage oocytes). In addition, we found evidence that a functional voltage-dependent Ca2+-channel (L-type) exists in mouse oocytes (ovulated and cultured MII staged oocytes by a confocal laser scanning microscope).     

On Parametric Confidence Intervals for the Cost‐Effectiveness Ratio

When comparing two competing interventions, confidence intervals for cost‐effectiveness ratios (CERs) provide information on the uncertainty in their point estimates. Techniques for constructing these confidence intervals are much debated. We provide a formal comparison of the Fieller, symmetric and Bonferroni methods for constructing confidence intervals for the CER using only the joint asymptotic distribution of the incremental cost and incremental effectiveness of the two interventions being compared. We prove the existence of a finite interval under the Fieller method when the incremental effectiveness is statistically significant. When this difference is not significant the Fieller method yields an unbounded confidence interval. The Fieller interval is always wider than the symmetric interval, but the latter is an approximation to the Fieller interval when the incremental effectiveness is highly significant. The Bonferroni method is shown to produce the widest interval. Because it accounts for the likely correlation between cost and effectiveness measures, and the intuitively appealing relationship between the existence of a bounded interval and the significance of the incremental effectiveness, the Fieller interval is to be preferred in reporting a confidence interval for the CER.     

Maintenance of low sodium and high potassium levels in cells and in tendon/collagen

Mammalian cells have a higher concentration of potassium and a lower concentration of sodium than their extracellular environment. The mechanisms responsible for the unequal distribution of these ions are commonly ascribed to the presence of an energy requiring plasma membrane ATPase pump, and the presence of membrane channels that pass one ion selectively, while excluding others. This report deals with other mechanisms that might explain this heterogeneous distribution of ions. To study other mechanisms, we turned to a non-living system, specifically tendon/collagen to eliminate the contribution of the membrane pump and channels. A simple gravimetric method was designed to measure solute accumulation or exclusion during rehydration of a well-washed, carefully dried and well-characterized protein specimen (tendon/collagen). Exposure to physiological salt concentrations resulted in selective exclusion of Na+ over K+, whereas exposure to low-salt concentration resulted in accumulation of these solutes. It is postulated that this solute redistribution occurs in all hydrated proteins and is partially responsible for the heterogeneous solute distribution in cells presently assigned to pump and channel mechanisms. Physical and thermodynamic mechanisms are offered to explain the observed heterogeneous solute distributions.     

An 'unconditional-like' structure for the conditional estimator of odds ratio from 2 x 2 tables

In the estimation of the odds ratio (OR), the conditional maximum-likelihood estimate (cMLE) is preferred to the more readily computed unconditional one (uMLE). However, the exact cMLE does not have a closed form to help divine it from the uMLE or to understand in what circumstances the difference between the two is appreciable. Here, the cMLE is shown to have the same 'ratio of cross-products' structure as its unconditional counterpart, but with two of the cell frequencies augmented, so as to shrink the unconditional estimator towards unity. The augmentation involves a factor, similar to the finite population correction, derived from the minimum of the marginal totals.     

A beta‐binomial mixed‐effects model approach for analysing longitudinal discrete and bounded outcomes

Patient‐reported outcomes (PROs) are currently being increasingly used as primary outcome measures in observational and experimental studies since they inform clinicians and researchers about the health‐status of patients and generate data to facilitate improved care. PROs usually appear as discrete and bounded with U, J, or inverse J shapes, and hence, exponential family members offer inadequate distributional fits. The beta‐binomial distribution has been proposed in the literature to fit PROs. However, the fact that the beta‐binomial distribution does not belong to the exponential family limits its applicability in the regression model context, and classical estimation approaches are not straightforward. Moreover, PROs are usually measured in a longitudinal framework in which individuals are followed up for a certain period. Hence, each individual obtains several scores of the PRO over time, which leads to the repeated measures and defines the correlation structure in the data. In this work, we have developed and proposed an estimation procedure for the analysis of correlated discrete and bounded outcomes, particularly PROs, by a beta‐binomial mixed‐effects model. Additionally, we have implemented the methodology in the PROreg package in R. Because there are similar approaches in the literature to address the same issue, this work also incorporates a comparison study between our proposal and alternative methodologies commonly implemented in R and shows the superior performance of our estimation procedure. This paper was motivated by the analysis of the health‐status of patients with chronic obstructive pulmonary disease, where the main objective is the assessment of risk factors that may affect the evolution of the disease. The application of the proposed approach in the study leads to clinically relevant results.     

Metabolic partitioning across individuals in ecological communities

The mechanistic origin and shape of body‐size distributions within communities are of considerable interest in ecology. A recently proposed light‐limitation model provides a good fit to the distribution of tree sizes in a tropical forest plot. The maximum entropy theory of ecology (METE) also predicts size distributions, but without explicit mechanistic assumptions, and thus its predictions should hold in ecosystems generally, regardless of whether they are light limited. A comparison of the form and success of the predictions of the model and the theory can provide insight into the role that mechanisms play in shaping patterns in macroecology. The prediction by the METE of the size distribution of organisms is remarkably similar in form to that of the model: power‐law behaviour in the size range where the light‐limitation model predicts a power law, and exponential behaviour in the size range where the model predicts an exponential tail. The METE prediction matches data widely, including data in ecosystems where light is not limiting. We show examples for three disparate communities: trees in a tropical forest plot; herbaceous plants in a treeless subalpine meadow; and island arthropods. We conclude that the success of METE's predicted form across systems, including those that are clearly not light limited, enriches our capacity to predict patterns in macroecology without making explicit mechanistic assumptions and provides a unified framework that can capture ubiquitous features of those patterns across diverse ecosystems governed by a variety of mechanisms.     

Modification of the degree of branching of a beta‐(1,3)‐glucan affects aggregation behavior and activity in an oxidative burst assay

Scleroglucan is a β‐(1,3)‐glucan which is highly branched at the 6‐position with a single glucose residue. Acid hydrolysis of a high molecular weight scleroglucan gave a medium molecular weight, freely soluble material. Linkage analysis by the partially methylated alditol acetate method showed that the solubilized material had 30% branching. When the material was subjected to partial Smith degradations, the percent branching was reduced accordingly to 12% or 17%. After the percent branching was reduced, the average molecular weight of the samples increased considerably, indicating the assembly of higher ordered aggregate structures. An aggregate number distribution analysis was applied to confirm the higher aggregated structures. These aggregated structures gave the material significantly enhanced activity in an in vitro oxidative burst assay compared to the highly branched material. © 2015 Wiley Periodicals, Inc. Biopolymers 103: 665–674, 2015.     

Cumulative Damage Survival Models for the Randomized Complete Block Design

A continuous time discrete state cumulative damage process {X(t), t ≥ 0} is considered, based on a non‐homogeneous Poisson hit‐count process and discrete distribution of damage per hit, which can be negative binomial, Neyman type A, Polya‐Aeppli or Lagrangian Poisson. Intensity functions considered for the Poisson process comprise a flexible three‐parameter family. The survival function is S(t) = P(X(t) ≤ L) where L is fixed. Individual variation is accounted for within the construction for the initial damage distribution {P(X(0) = x) | x = 0, 1, …,}. This distribution has an essential cut‐off before x = L and the distribution of L – X(0) may be considered a tolerance distribution. A multivariate extension appropriate for the randomized complete block design is developed by constructing dependence in the initial damage distributions. Our multivariate model is applied (via maximum likelihood) to litter‐matched tumorigenesis data for rats. The litter effect accounts for 5.9 percent of the variance of the individual effect. Cumulative damage hazard functions are compared to nonparametric hazard functions and to hazard functions obtained from the PVF‐Weibull frailty model. The cumulative damage model has greater dimensionality for interpretation compared to other models, owing principally to the intensity function part of the model.     

Estimation of distribution function in bivariate competing risk models

We consider lifetime data involving pairs of study individuals with more than one possible cause of failure for each individual. Non-parametric estimation of cause-specific distribution functions is considered under independent censoring. Properties of the estimators are discussed and an illustration of their application is given.     

The relation between the neutrality index for mitochondrial genes and the distribution of mutational effects on fitness

We explore factors affecting patterns of polymorphism and divergence (as captured by the neutrality index) at mammalian mitochondrial loci. To do this, we develop a population genetic model that incorporates a fraction of neutral amino acid sites, mutational bias, and a probability distribution of selection coefficients against new nonsynonymous mutations. We confirm, by reanalyzing publicly available datasets, that the mitochondrial cyt-b gene shows a broad range of neutrality indices across mammalian taxa, and explore the biological factors that can explain this observation. We find that observed patterns of differences in the neutrality index, polymorphism, and divergence are not caused by differences in mutational bias. They can, however, be explained by a combination of a small fraction of neutral amino acid sites, weak selection acting on most amino acid mutations, and differences in effective population size among taxa.