Patty Solomon

Correlates of retention on the South Australian Methadone Program 1981–91

Objectives: To investigate correlates of retention on the South Australian Methadone Program during 1981–91.

Components of variance

Abstract Components of variance have a long history and find application in all areas of scientific investigation. This review introduces components of variance and their importance firstly by examples on blood pressure, proteomic data, breath analysers and esophageal pH monitoring devices. We then present an intuitive geometric representation of analysis of variance and explain how the components of variance can be estimated from the analysis of variance table. We conclude by suggesting practice points for studies which incorporate components of variance, and recommend commonly used statistical software to undertake such analysis.

Comparing Score-Based Methods for Estimating Bayesian Networks Using the Kullback–Leibler Divergence

We recently proposed two methods for estimating Bayesian networks from high-dimensional non-independent and identically distributed data containing exogenous variables and random effects (Kasza et al., 2012). The first method is fully Bayesian, and the second is “residual”-based, accounting for the effects of the exogenous variables by utilizing the notion of restricted maximum likelihood. We describe the methods and compare their performance using the Kullback–Leibler divergence, which provides a natural framework for comparing posterior distributions. In applications where the exogenous variables are not of primary interest, we show that the potential loss of information about parameters of interest is typically small.

Informed baseline subtraction of proteomic mass spectrometry data aided by a novel sliding window algorithm

BackgroundProteomic matrix-assisted laser desorption/ionisation (MALDI) linear time-of-flight (TOF) mass spectrometry (MS) may be used to produce protein profiles from biological samples with the aim of discovering biomarkers for disease. However, the raw protein profiles suffer from several sources of bias or systematic variation which need to be removed via pre-processing before meaningful downstream analysis of the data can be undertaken. Baseline subtraction, an early pre-processing step that removes the non-peptide signal from the spectra, is complicated by the following: (i) each spectrum has, on average, wider peaks for peptides with higher mass-to-charge ratios (m/z), and (ii) the time-consuming and error-prone trial-and-error process for optimising the baseline subtraction input arguments. With reference to the aforementioned complications, we present an automated pipeline that includes (i) a novel ‘continuous’ line segment algorithm that efficiently operates over data with a transformed m/z-axis to remove the relationship between peptide mass and peak width, and (ii) an input-free algorithm to estimate peak widths on the transformed m/z scale.ResultsThe automated baseline subtraction method was deployed on six publicly available proteomic MS datasets using six different m/z-axis transformations. Optimality of the automated baseline subtraction pipeline was assessed quantitatively using the mean absolute scaled error (MASE) when compared to a gold-standard baseline subtracted signal. Several of the transformations investigated were able to reduce, if not entirely remove, the peak width and peak location relationship resulting in near-optimal baseline subtraction using the automated pipeline. The proposed novel ‘continuous’ line segment algorithm is shown to far outperform naive sliding window algorithms with regard to the computational time required. The improvement in computational time was at least four-fold on real MALDI TOF-MS data and at least an order of magnitude on many simulated datasets.ConclusionsThe advantages of the proposed pipeline include informed and data specific input arguments for baseline subtraction methods, the avoidance of time-intensive and subjective piecewise baseline subtraction, and the ability to automate baseline subtraction completely. Moreover, individual steps can be adopted as stand-alone routines.

A Descriptive Model for Microbial Population Dynamics in a Copper Sulphide Bioleaching Heap with Spatial and Physicochemical Considerations

A descriptive mathematical model is a valuable tool that can help understand the relationship between the heap leaching process at the Escondida mine in Chile, the microbial community that participates in the process, and the physical characteristics of the heap, such as the arrangement and the mineral composition of the individual leaching strips. However, the bioleaching process at Escondida is a system, which presents many challenges to modelling. The main challenges relate to heaps design and mineral characteristics, the complex interactions between biological and physicochemical parameters, and the unexpected changes in the heaps operational conditions. The heap is sampled periodically and more than 20 variables, including 16S rRNA gene copy number for 16 different microorganisms, are recorded. The data exhibit complex behaviour, including variable dynamics between strips, systematic differences between lifts of the heap, and spatial and temporal correlations. In this work, we develop a non-linear descriptive model for the microbial population trajectory along the leaching cycle and across the different strips. The parameterisation of the model considers the different dynamics between lifts, and strip specific parameters characterise the behaviour of data from individual strips. The parameterisation also allows for spatial correlation by incorporating the effect of adjacent strips on the microbial population trajectory. The model is found to provide a good fit to the data and captures its behaviour across strips. Residuals showed no systematic patterns of departure between the observed and modelled response. The R2 values ranged from 0.53 to 0.71, indicating a reasonable level of predictive power.

Variance Calculations for Quantitative Real-Time PCR Experiments with Multiple Levels of Replication

Heap bioleaching is an established technology for recovering copper from low-grade sulphide ores. Recently, genetics-based approaches have been employed to characterize mineral-processing bacteria. In these approaches, data analysis is a key issue. Consequently, it is of fundamental importance to provide adequate mathematical models and statistical tools to draw reliable conclusions. The present work relates to current studies of the consortium of organisms inhabiting the bioleaching heap of the Escondida mine in Northern Chile. These studies aim to describe and understand the relationship between the dynamics of the community and the performance of the industrial process. Here, we consider a series of quantitative real-time polymerase chain reaction (PCR) experiments performed to quantify six different microorganisms at various stages of the bioleaching cycle. Establishing the reliability of the data obtained by real-time PCR requires the estimation of the error variance at several different levels. The results obtained show that the sampling component of the error variance is the dominant source of variability for most microorganisms. An estimate for the proportional reduction in residual standard deviation from the use of extraction and real-time PCR triplicates was found to range from 3% to 27% for the different organisms. This result suggests that triplicate assays would produce only a modest reduction in error variance compared to more frequent sampling from the heap.