Olga Julià

Second-order functions are the simplest correlations between flow cytometric light scatter and bacterial diameter

Second-order mathematical relationships between bacterial cell diameter determined by electric particle analyser and flow cytometric forward light scatter in axenic cultures are obtained and discussed. Since it is technically impossible today to obtain both measurements for each individual cell, standard regression techniques cannot be applied. To overcome this limitation, we assume that these two parameters are related by a monotone increasing function that enables their mathematical relationships to be studied. Our conclusion is that forward light scatter data cannot be linearly transformed into bacterial size values by an accurate and universal function. However, second-order relationships seem to be the simplest satisfactory relationships between cell diameter and forward light scatter in eubacteria.

Statistical analysis and biological interpretation of the flow cytometric heterogeneity observed in bacterial axenic cultures

Histogram comparison and meaningful statistics in flow cytometry is probably the most widely encountered mathematical problem in flow cytometry. Ideally, a test for determining the statistical equality or difference of flow cytometric distributions will identify the significant differences or similarities of the obtained histograms. This situation is of particular interest when flow cytometry is used to study the heterogeneity of axenic bacterial populations. We have statistically measured the heterogeneity of successive cytometric measures, the modifications produced after 20 transfers from the same culture, and the differences between 20 subcultures of identical origin. The heterogeneity of the bacterial populations and the similarity of the obtained 360 histograms were analysed by standard statistical methods. We have studied bacterial axenic cultures in order to detect, quantify and interpret their cytometric heterogeneity, and to assess intrinsic differences and differences produced by laboratory manipulations. We concluded that the standard axenic cultures have a considerable intrinsic cellular and molecular heterogeneity. We suggest that the heterogeneity we have detected basically has two origins: cell size diversity and cell cycle variations.

Empirical study of correlated survival times for recurrent events with proportional hazards margins and the effect of correlation and censoring

BackgroundIn longitudinal studies where subjects experience recurrent incidents over a period of time, such as respiratory infections, fever or diarrhea, statistical methods are required to take into account the within-subject correlation.MethodsFor repeated events data with censored failure, the independent increment (AG), marginal (WLW) and conditional (PWP) models are three multiple failure models that generalize Cox’s proportional hazard model. In this paper, we revise the efficiency, accuracy and robustness of all three models under simulated scenarios with varying degrees of within-subject correlation, censoring levels, maximum number of possible recurrences and sample size. We also study the methods performance on a real dataset from a cohort study with bronchial obstruction.ResultsWe find substantial differences between methods and there is not an optimal method. AG and PWP seem to be preferable to WLW for low correlation levels but the situation reverts for high correlations.ConclusionsAll methods are stable in front of censoring, worsen with increasing recurrence levels and share a bias problem which, among other consequences, makes asymptotic normal confidence intervals not fully reliable, although they are well developed theoretically.

SURVIVAL ANALYSIS FOR LEFT CENSORED DATA

A left censoring scheme is such that the random variable of interest, X, is only observed if it is greater than or equal to a left censoring variable L, otherwise L is observed. The analysis is then based on the pair of random variables (U, δ) where U = max(L, X) and δ = 1{L ≤ X}. The problem concerns the estimation of the survival function SX(t) = Pr{X > t} from a left censored sample where X is assumed to be independent of L. We derive a Left-Kaplan-Meier estimator, \(\hat{\textup{S}}_{\textup{X}}\), as a solution of a backward Doleans differential equation. It is proved that this Left-Kaplan-Meier estimator is self-consistent, thus a generalized maximum likelihood estimator. Following Efron’s (1967) technique for the case of a right-censored scheme, it is shown that the Left-Kaplan-Meier estimator is the same estimator you would obtain through a redistribution to the left algorithm. The consistency of the Left-Kaplan-Meier estimator is established. The influence curves corresponding to \(\hat{\textup{S}}_{\textup{X}}\), are calculated. This provides an alternative derivation of the asymptotic variance of \(\hat{\textup{S}}_{\textup{X}}\), (Reid, 1981). The asymptotic normality then follows through standard arguments.

The distribution of a double stochastic integral with respect to two independent brownian sheets

Let be two two-parameter independent Wiener processes. We compute the characteristic function of the stochastic integral and we give an expression for its moments

Skew-Laplace and Cell-Size Distribution in Microbial Axenic Cultures: Statistical Assessment and Biological Interpretation

We report a skew-Laplace statistical analysis of both flow cytometry scatters and cell size from microbial strains primarily grown in batch cultures, others in chemostat cultures and bacterial aquatic populations. Cytometry scatters best fit the skew-Laplace distribution while cell size as assessed by an electronic particle analyzer exhibited a moderate fitting. Unlike the cultures, the aquatic bacterial communities clearly do not fit to a skew-Laplace distribution. Due to its versatile nature, the skew-Laplace distribution approach offers an easy, efficient, and powerful tool for distribution of frequency analysis in tandem with the flow cytometric cell sorting.

Asymptotic properties of the left kaplan-meier estimator

The Kaplan -Meier estimator for left censored data is studied as the solution of a backward Doleans equation. The compact differentiability techniques are used to prove the strong consistency and the weak convergence of this estimator.

Assessment of survival during starvation ofEscherichia coli andKlebsiella pneumoniae in artificial urine: analysis of the kinetics of colony formation

A kinetic model of colony formation was proposed by Hattori, based on a count of the colonies that appear on a plate in successive short intervals of time. In this model, three parameters (λ,tr and N∞) are defined, which reflect the ability of a bacterium to yield colonies and allow us to described the dynamics of bacterial populations in soil and ofE. coli at different growth phases. In this paper we report a reparametrization of the kinetic model of colony formation, with the aim of facilitating more accurate calculation of λ andtr. Moreover, we observed that during the starvation ofE. coli andK. pneumoniae in urine, λ can be used to assess survival, since this parameter clearly decreases during starvation. Retardation time values (tr) were similar inE. coli andK. pneumoniae throughout the starvation experimental period.