Mixed-model of ANOVA for measurement reproducibility in proteomics

This work is a statistical analysis of reproducibility of a MALDI-TOF mass spectrometry experiment. Its aim is to evaluate measurement variability and compare peak intensities from two types of MALDI-TOF platforms. We compared and commented on the abilities of Principal Component Analysis and mixed-model analysis of variance to evaluate the biological variability and the technical variability of peak intensities in different patients. The properties and hypotheses of both methods are summarized and applied to spectra from plasma of patients with Hodgkin lymphoma. Principal Component Analysis checks rapidly the balance between the two variabilities; however, a mixed-model analysis of variance is necessary to quantify the biological and technical components of the experimental variance as well as their interactions and to split the total variance into between-subjects and within-subject components. The latter method helped to assess the reproducibility of measurements from two MALDI-TOF platforms and to decompose the technical variability according to the experimental design.     

Hypothesis testing in semiparametric additive mixed models

We consider testing whether the nonparametric function in a semiparametric additive mixed model is a simple fixed degree polynomial, for example, a simple linear function. This test provides a goodness-of-fit test for checking parametric models against nonparametric models. It is based on the mixed-model representation of the smoothing spline estimator of the nonparametric function and the variance component score test by treating the inverse of the smoothing parameter as an extra variance component. We also consider testing the equivalence of two nonparametric functions in semiparametric additive mixed models for two groups, such as treatment and placebo groups. The proposed tests are applied to data from an epidemiological study and a clinical trial and their performance is evaluated through simulations.     

Metapopulation dynamics with quasi-local competition

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.     

Gestational mutations and carcinogenesis

We present a mathematical formulation to evaluate the effects of gestational mutations on cancer risk. The hazard or incidence function of cancer is expressed in terms of the Probability Generating Function (PGF) of the number of normal and mutated cells at birth. Using Filtered Poisson Process Theory, we obtain the PGF for several models for the accumulation of gestational mutations. In particular, we develop expressions for the hazard function when one or two successive mutations could occur during gestation. We also calculate the hazard when the background gestational mutation rates are increased due to exposure to mutagens, such as prenatal radiation. To illustrate the use of our models, we apply them to colorectal cancer in the SEER database. We find that the proportion of cancer risk attributable to developmental mutations depends on age and that it could be quite significant when gestational mutation rates are high. The analysis of the SEER data also shows that gestational mutations could contribute to inter-individual variations in colorectal cancer risk.     

Lanchester's attrition models and fights among social animals

Lanchester's models of attrition during warfare have servedas the basis for several predictions about conflicts betweengroups of animals. These models and their extensions describerates of mortality during battles as functions of the numberand fighting abilities of individuals in each group, allowinganalysis of the determinants of group strength and of the cumulativenumbers of casualties. We propose modifications to Lanchester'smodels to improve their applicability to social animals. Inparticular, we suggest that the per-capita mortality rate ofa group is a decreasing function of the fighting abilities ofits members, that the mortality rate is an increasing functionof the number of individuals in both groups, and that therewill often be diminishing returns for increasing numerical advantage.Models incorporating these assumptions predict that the abilityof social animals to win fights depends less on group size andmore on individual prowess than under Lanchester's originalmodels. We discuss how data on casualties can be used to distinguishamong alternative attrition models.