Estimation of the parameter uncertainty resulting from bounded-error data

A procedure is described for characterizing the set of all parameter vectors that are consistent with data corrupted by a bounded noise. The method applies to any parametric model that can be simulated on a computer when upper and lower bounds for the noise are known a priori. The convergence properties of the associated estimator are considered, as well as its behavior in the presence of outliers. To illustrate the versatility of the technique, problems are considered where (i) the set of the true values of the parameter vector does not reduce to a singleton, (ii) the model is not uniquely identifiable, (iii) the hypotheses on the noise bounds are not satisfied, and (iv) the data contain a majority of outliers.     

Modeling pilus structures from sparse data

Bacterial Type II secretion systems (T2SS) and type IV pili (T4P) biogenesis machineries share the ability to assemble thin filaments from pilin protein subunits in the plasma membrane. Here we describe in detail the calculation strategy that served to determine a detailed atomic model of the T2SS pilus from Klebsiella oxytoca (Campos et al., PNAS 2010). The strategy is based on molecular modeling with generalized distance restraints and experimental validation (salt bridge charge inversion; double cysteine substitution and crosslinking). It does not require directly fitting structures into an envelope obtained from electron microscopy, but relies on lower resolution information, in particular the symmetry parameters of the helix forming the pilus. We validate the strategy with T4P where either a higher resolution structure is available (for the gonococcal (GC) pilus from Neisseria gonorrhoeae), or where we can compare our results to additional experimental data (for Vibrio cholerae TCP). The models are of sufficient precision to compare the architecture of the different pili in detail.     

Accuracy of femur reconstruction from sparse geometric data using a statistical shape model

Sparse geometric information from limited field-of-view medical images is often used to reconstruct the femur in biomechanical models of the hip and knee. However, the full femur geometry is needed to establish boundary conditions such as muscle attachment sites and joint axes which define the orientation of joint loads. Statistical shape models have been used to estimate the geometry of the full femur from varying amounts of sparse geometric information. However, the effect that different amounts of sparse data have on reconstruction accuracy has not been systematically assessed. In this study, we compared shape model and linear scaling reconstruction of the full femur surface from varying proportions of proximal and distal partial femur geometry in combination with morphometric and landmark data. We quantified reconstruction error in terms of surface-to-surface error as well as deviations in the reconstructed femur’s anatomical coordinate system which is important for biomechanical models. Using a partial proximal femur surface, mean shape model-based reconstruction surface error was 1.8 mm with 0.15° or less anatomic axis error, compared to 19.1 mm and 2.7–5.6° for linear scaling. Similar results were found when using a partial distal surface. However, varying amounts of proximal or distal partial surface data had a negligible effect on reconstruction accuracy. Our results show that given an appropriate set of sparse geometric data, a shape model can reconstruct full femur geometry with far greater accuracy than simple scaling.     

Estimation in regression models for longitudinal binary data with outcome-dependent follow-up

In many observational studies, individuals are measured repeatedly over time, although not necessarily at a set of pre-specified occasions. Instead, individuals may be measured at irregular intervals, with those having a history of poorer health outcomes being measured with somewhat greater frequency and regularity. In this paper, we consider likelihood-based estimation of the regression parameters in marginal models for longitudinal binary data when the follow-up times are not fixed by design, but can depend on previous outcomes. In particular, we consider assumptions regarding the follow-up time process that result in the likelihood function separating into two components: one for the follow-up time process, the other for the outcome measurement process. The practical implication of this separation is that the follow-up time process can be ignored when making likelihood-based inferences about the marginal regression model parameters. That is, maximum likelihood (ML) estimation of the regression parameters relating the probability of success at a given time to covariates does not require that a model for the distribution of follow-up times be specified. However, to obtain consistent parameter estimates, the multinomial distribution for the vector of repeated binary outcomes must be correctly specified. In general, ML estimation requires specification of all higher-order moments and the likelihood for a marginal model can be intractable except in cases where the number of repeated measurements is relatively small. To circumvent these difficulties, we propose a pseudolikelihood for estimation of the marginal model parameters. The pseudolikelihood uses a linear approximation for the conditional distribution of the response at any occasion, given the history of previous responses. The appeal of this approximation is that the conditional distributions are functions of the first two moments of the binary responses only. When the follow-up times depend only on the previous outcome, the pseudolikelihood requires correct specification of the conditional distribution of the current outcome given the outcome at the previous occasion only. Results from a simulation study and a study of asymptotic bias are presented. Finally, we illustrate the main results using data from a longitudinal observational study that explored the cardiotoxic effects of doxorubicin chemotherapy for the treatment of acute lymphoblastic leukemia in children.     

Estimation of hominoid phylogeny from a DNA hybridization data set

Summary Analysis of the expanded data set of Sibley and Ahlquist (1987) on primate phylogeny using a maximum likelihood mixed model analysis of variance method shows that there is significant evidence for resolving theHomo-Pan-Gorilla trifurcation in favor of aHomo-Pan clade. The resulting tree is close to that estimated by Sibley and Ahlquist (1984). The mixed model can be used to test a number of hypotheses about the existence of components of variance and the linearity of the relationship between branch length and expected distance. No evidence is found that there is a variance component for extract, or for the individual from which the extract was taken. A variance component for experiment does seem to exist, presumably arising as a result of error of measurement of the common standard from which all values in the same experiment were substracted. There is significant evidence that the relationship between total branch length between species and their expected distances is nonlinear, or else that the measurement error on larger distances is greater than on smaller ones. Allowing for the nonlinearity might cause one to infer the time of distant common ancestors as less remote than the measured hybridization values would imply if used directly.     

Biologically-informed neural networks guide mechanistic modeling from sparse experimental data

Biologically-informed neural networks (BINNs), an extension of physics-informed neural networks [1], are introduced and used to discover the underlying dynamics of biological systems from sparse experimental data. In the present work, BINNs are trained in a supervised learning framework to approximate in vitro cell biology assay experiments while respecting a generalized form of the governing reaction-diffusion partial differential equation (PDE). By allowing the diffusion and reaction terms to be multilayer perceptrons (MLPs), the nonlinear forms of these terms can be learned while simultaneously converging to the solution of the governing PDE. Further, the trained MLPs are used to guide the selection of biologically interpretable mechanistic forms of the PDE terms which provides new insights into the biological and physical mechanisms that govern the dynamics of the observed system. The method is evaluated on sparse real-world data from wound healing assays with varying initial cell densities [2].     

Estimation of spermarche from longitudinal spermaturia data

A number of studies have dealt with determination of the age at onset of sperm emission (spermarche), based on observations of first occurrence of spermatozoa in urine. A major problem in this connection is the intermittent occurrence of sperm-negative urine samples after the achievement of spermarche. We have here considered an empirical Bayes approach for handling the probability of a sperm-positive urine sample after spermarche. The investigation was inspired by a concrete longitudinal study concerning 40 Scottish boys, which is used for illustration throughout. In this study, the urine was tested for spermatozoa from well before spermarche and every 3 months thereafter for at most 7 years. Some of the boys left the study earlier and techniques for handling such censoring were also developed.     

Estimation of penetrance from twin data.

A simple method for estimating the gene frequency p and the penetrance value K from data on polymorphic monogenic characteristics on monozygotic twin pairs is presented. In spite of the method here presented having limited value because the results it yields cannot be evaluated on their own, the estimates of p and K it provides can be indirectly tested by comparing them to the ones obtained in familial aggregates through classical segregation analysis or by using the latter to calculate the expected proportions of dominant-dominant, dominant-recessive and recessive-recessive monozygotic twin pairs. When the method is applied to data on tongue-rolling ability published in the literature, a good agreement is observed between twin and familial estimates, thus indicating that the method is reliable and that it can be used as an ancillary way of corroborating or otherwise evidence of monogenic autosomal dominant mechanism inferred from the analysis of familial data.     

Estimation of growth parameters from multiple-recapture data

This article develops a method for analysis of growth data with multiple recaptures when the initial ages for all individuals are unknown. The existing approaches either impute the initial ages or model them as random effects. Assumptions about the initial age are not verifiable because all the initial ages are unknown. We present an alternative approach that treats all the lengths including the length at first capture as correlated repeated measures for each individual. Optimal estimating equations are developed using the generalized estimating equations approach that only requires the first two moment assumptions. Explicit expressions for estimation of both mean growth parameters and variance components are given to minimize the computational complexity. Simulation studies indicate that the proposed method works well. Two real data sets are analyzed for illustration, one from whelks (Dicathais aegaota) and the other from southern rock lobster (Jasus edwardsii) in South Australia.     

Estimation of heritability from varietal trials data

We present the estimation of heritabilities of an observed trait in situations where evaluation of several pure breeding lines is performed in a trial at a single location and in trials from several locations. For the single location situation, we evaluate exact confidence intervals, the probability of invalid estimates, and the percentage points of the distribution of heritability. Simulations were performed to numerically verify the results. Additionally, approximations to the bias and standard error of the estimate were obtained and are presented along with their simulated values and coefficients of skewness and kurtosis. For trials in several locations, explicit expressions for exact values of confidence limits are not available. Further, one would require knowledge of one more parameter, represented by the ratio of genotype x environment (G x E) interaction variance to error variance, in addition to the number of genotypes, replication and true heritability value. Approximations were made for bias and the standard error of estimates of heritability. The evaluation of the distribution of heritability and its moments was recognized as a problem of the linear function of an independent chi-square. The methods have been illustrated by data from experiments on grain and straw yield of 64 barley genotypes evaluated at three locations.     

Statistical mechanics analysis of sparse data

Inferential structure determination uses Bayesian theory to combine experimental data with prior structural knowledge into a posterior probability distribution over protein conformational space. The posterior distribution encodes everything one can say objectively about the native structure in the light of the available data and additional prior assumptions and can be searched for structural representatives. Here an analogy is drawn between the posterior distribution and the canonical ensemble of statistical physics. A statistical mechanics analysis assesses the complexity of a structure calculation globally in terms of ensemble properties. Analogs of the free energy and density of states are introduced; partition functions evaluate the consistency of prior assumptions with data. Critical behavior is observed with dwindling restraint density, which impairs structure determination with too sparse data. However, prior distributions with improved realism ameliorate the situation by lowering the critical number of observations. An in-depth analysis of various experimentally accessible structural parameters and force field terms will facilitate a statistical approach to protein structure determination with sparse data that avoids bias as much as possible.     

De novo high-resolution protein structure determination from sparse spin-labeling EPR data

As many key proteins evade crystallization and remain too large for nuclear magnetic resonance spectroscopy, electron paramagnetic resonance (EPR) spectroscopy combined with site-directed spin labeling offers an alternative approach for obtaining structural information. Such information must be translated into geometric restraints to be used in computer simulations. Here, distances between spin labels are converted into distance ranges between beta carbons by using a "motion-on-a-cone" model, and a linear-correlation model links spin-label accessibility to the number of neighboring residues. This approach was tested on T4-lysozyme and alphaA-crystallin with the de novo structure prediction algorithm Rosetta. The results demonstrate the feasibility of obtaining highly accurate, atomic-detail models from EPR data by yielding 1.0 A and 2.6 A full-atom models, respectively. Distance restraints between amino acids far apart in sequence but close in space are most valuable for structure determination. The approach can be extended to other experimental techniques such as fluorescence spectroscopy, substituted cysteine accessibility method, or mutational studies.     

Macular auto-fluorescence is a follow-up parameter for cystoids macular edema

This study aimed to evaluate if macular autofluorescence(MAF) is a valuable, non-invasive follow-up parameter for cystoid macular edema. A total of 71 eyes(71 cases) with cystoid macular edema(CME) were included in the study. Macular pigment(MP) was evaluated using HRA2(infrared) IF and FA models. The density of MP was graded into three categories: without, partial, and normal amount of MP. A comparison was made between the baseline(before the first administration) level and at the fourth month, following three consecutive intravitreal lucentis injections every month. The morphology and distribution of MAF, and the density and distribution of MP were regarded as the main outcome measures. At the baseline visit, all eyes with CME had petaloid/irregular-shaped MAF in the macular area(100%). No MAF was detected in the control eyes(0). There was significant difference in MAF between the CME and normal groups(P=0.000). At the fourth monthly visit, normal levels of MP density without MAF was detected in 68 eyes(95.8%) with the best corrected spectacular visual acuity increasing to at least 1 line accordingly. We conclude that macular MAF can be used as a follow-up parameter for patients with CME. MP and MAF can indirectly reflect the fovea cone function.     

Estimation in Markov models from aggregate data

In this paper, situations in which individuals move through a finite set of states according to a continuous-time Markov process are considered. Only aggregate data are available: these consist of the number of individuals in each state at specified observation times. We develop conditional least squares and approximate maximum-likelihood-estimation procedures for time-homogeneous models, and extend the methods so that they can handle immigration of individuals into the system during observation. Asymptotic covariance estimates are presented, and some problems for future study are noted.     

Estimation of initial rate from discontinuous progress data

Abstract

When using discontinuous assay of reactions, initial rates are often estimated from a limited number of time points. There has been no detailed study of how best to do this. In this work, time courses were simulated by different theoretical equations (including strong product inhibition, first order, Michaelis–Menten and truly linear), but with random error addition to each data point. Various methods were tested to fit an initial rate to the data, and the result compared with the known “true” value. Fitting a simple quadratic generally gives initial rates as accurate as any other curve, and is better than a linear fit if there are about 8 or more time points. For fewer points a linear fit gives less variable and often more accurate rates. The absolute contribution to data point error has a major impact on rate accuracy, and often dominates that due to curvature, so that sampling to at least 10% conversion is preferred. The accuracy of a linear fit can be improved by methods that reject some later points based on curvature tests. Awareness of these effects can help avoid rate inaccuracies of 10% or more due to poor methods of data analysis.