An extended regression approach to estimating loads and their uncertainties in Great Barrier Reef catchments

There are numerous load estimation methods available, some of which are captured in various online tools. However, most estimators are subject to large biases statistically, and their associated uncertainties are often not reported. This makes interpretation difficult and the estimation of trends or determination of optimal sampling regimes impossible to assess. In this paper, we first propose two indices for measuring the extent of sampling bias, and then provide steps for obtaining reliable load estimates by minimizing the biases and making use of possible predictive variables. The load estimation procedure can be summarized by the following four steps: - (i) output the flow rates at regular time intervals (e.g. 10 minutes) using a time series model that captures all the peak flows; - (ii) output the predicted flow rates as in (i) at the concentration sampling times, if the corresponding flow rates are not collected; - (iii) establish a predictive model for the concentration data, which incorporates all possible predictor variables and output the predicted concentrations at the regular time intervals as in (i), and; - (iv) obtain the sum of all the products of the predicted flow and the predicted concentration over the regular time intervals to represent an estimate of the load. The key step to this approach is in the development of an appropriate predictive model for concentration. This is achieved using a generalized regression (rating-curve) approach with additional predictors that capture unique features in the flow data, namely the concept of the first flush, the location of the event on the hydrograph (e.g. rise or fall) and cumulative discounted flow. The latter may be thought of as a measure of constituent exhaustion occurring during flood events. The model also has the capacity to accommodate autocorrelation in model errors which are the result of intensive sampling during floods. Incorporating this additional information can significantly improve the predictability of concentration, and ultimately the precision with which the pollutant load is estimated. We also provide a measure of the standard error of the load estimate which incorporates model, spatial and/or temporal errors. This method also has the capacity to incorporate measurement error incurred through the sampling of flow. We illustrate this approach using the concentrations of total suspended sediment (TSS) and nitrogen oxide (NOx) and gauged flow data from the Burdekin River, a catchment delivering to the Great Barrier Reef. The sampling biases for NOx concentrations range from 2 to 10 times indicating severe biases. As we expect, the traditional average and extrapolation methods produce much higher estimates than those when bias in sampling is taken into account.

Working-correlation-structure identification in generalized estimating equations

Selecting an appropriate working correlation structure is pertinent to clustered data analysis using generalized estimating equations (GEE) because an inappropriate choice will lead to inefficient parameter estimation. We investigate the well-known criterion of QIC for selecting a working correlation Structure. and have found that performance of the QIC is deteriorated by a term that is theoretically independent of the correlation structures but has to be estimated with an error. This leads LIS to propose a correlation information criterion (CIC) that substantially improves the QIC performance. Extensive simulation studies indicate that the CIC has remarkable improvement in selecting the correct correlation structures. We also illustrate our findings using a data set from the Madras Longitudinal Schizophrenia Study.

Novel Mass Spectrometric Analysis Methods for Anabolic Androgenic Steroids in Sports Drug Testing

The feasibility of different modern analytical techniques for the mass spectrometric detection of anabolic androgenic steroids (AAS) in human urine was examined in order to enhance the prevalent analytics and to find reasonable strategies for effective sports drug testing. A comparative study of the sensitivity and specificity between gas chromatography (GC) combined with low (LRMS) and high resolution mass spectrometry (HRMS) in screening of AAS was carried out with four metabolites of methandienone. Measurements were done in selected ion monitoring mode with HRMS using a mass resolution of 5000. With HRMS the detection limits were considerably lower than with LRMS, enabling detection of steroids at low 0.2-0.5 ng/ml levels. However, also with HRMS, the biological background hampered the detection of some steroids. The applicability of liquid-phase microextraction (LPME) was studied with metabolites of fluoxymesterone, 4-chlorodehydromethyltestosterone, stanozolol and danazol. Factors affecting the extraction process were studied and a novel LPME method with in-fiber silylation was developed and validated for GC/MS analysis of the danazol metabolite. The method allowed precise, selective and sensitive analysis of the metabolite and enabled simultaneous filtration, extraction, enrichment and derivatization of the analyte from urine without any other steps in sample preparation. Liquid chromatographic/tandem mass spectrometric (LC/MS/MS) methods utilizing electrospray ionization (ESI), atmospheric pressure chemical ionization (APCI) and atmospheric pressure photoionization (APPI) were developed and applied for detection of oxandrolone and metabolites of stanozolol and 4-chlorodehydromethyltestosterone in urine. All methods exhibited high sensitivity and specificity. ESI showed, however, the best applicability, and a LC/ESI-MS/MS method for routine screening of nine 17-alkyl-substituted AAS was thus developed enabling fast and precise measurement of all analytes with detection limits below 2 ng/ml. The potential of chemometrics to resolve complex GC/MS data was demonstrated with samples prepared for AAS screening. Acquired full scan spectral data (m/z 40-700) were processed by the OSCAR algorithm (Optimization by Stepwise Constraints of Alternating Regression). The deconvolution process was able to dig out from a GC/MS run more than the double number of components as compared with the number of visible chromatographic peaks. Severely overlapping components, as well as components hidden in the chromatographic background could be isolated successfully. All studied techniques proved to be useful analytical tools to improve detection of AAS in urine. Superiority of different procedures is, however, compound-dependent and different techniques complement each other.

From Polymorph Screening to Dissolution Testing - Solid Phase Analysis during Pharmaceutical Development and Manufacturing

Solid materials can exist in different physical structures without a change in chemical composition. This phenomenon, known as polymorphism, has several implications on pharmaceutical development and manufacturing. Various solid forms of a drug can possess different physical and chemical properties, which may affect processing characteristics and stability, as well as the performance of a drug in the human body. Therefore, knowledge and control of the solid forms is fundamental to maintain safety and high quality of pharmaceuticals. During manufacture, harsh conditions can give rise to unexpected solid phase transformations and therefore change the behavior of the drug. Traditionally, pharmaceutical production has relied on time-consuming off-line analysis of production batches and finished products. This has led to poor understanding of processes and drug products. Therefore, new powerful methods that enable real time monitoring of pharmaceuticals during manufacturing processes are greatly needed. The aim of this thesis was to apply spectroscopic techniques to solid phase analysis within different stages of drug development and manufacturing, and thus, provide a molecular level insight into the behavior of active pharmaceutical ingredients (APIs) during processing. Applications to polymorph screening and different unit operations were developed and studied. A new approach to dissolution testing, which involves simultaneous measurement of drug concentration in the dissolution medium and in-situ solid phase analysis of the dissolving sample, was introduced and studied. Solid phase analysis was successfully performed during different stages, enabling a molecular level insight into the occurring phenomena. Near-infrared (NIR) spectroscopy was utilized in screening of polymorphs and processing-induced transformations (PITs). Polymorph screening was also studied with NIR and Raman spectroscopy in tandem. Quantitative solid phase analysis during fluidized bed drying was performed with in-line NIR and Raman spectroscopy and partial least squares (PLS) regression, and different dehydration mechanisms were studied using in-situ spectroscopy and partial least squares discriminant analysis (PLS-DA). In-situ solid phase analysis with Raman spectroscopy during dissolution testing enabled analysis of dissolution as a whole, and provided a scientific explanation for changes in the dissolution rate. It was concluded that the methods applied and studied provide better process understanding and knowledge of the drug products, and therefore, a way to achieve better quality.

A maximum likelihood approach for estimating growth from tag–recapture data

The Fabens method is commonly used to estimate growth parameters k and l infinity in the von Bertalanffy model from tag-recapture data. However, the Fabens method of estimation has an inherent bias when individual growth is variable. This paper presents an asymptotically unbiassed method using a maximum likelihood approach that takes account of individual variability in both maximum length and age-at-tagging. It is assumed that each individual's growth follows a von Bertalanffy curve with its own maximum length and age-at-tagging. The parameter k is assumed to be a constant to ensure that the mean growth follows a von Bertalanffy curve and to avoid overparameterization. Our method also makes more efficient use nf thp measurements at tno and recapture and includes diagnostic techniques for checking distributional assumptions. The method is reasonably robust and performs better than the Fabens method when individual growth differs from the von Bertalanffy relationship. When measurement error is negligible, the estimation involves maximizing the profile likelihood of one parameter only. The method is applied to tag-recapture data for the grooved tiger prawn (Penaeus semisulcatus) from the Gulf of Carpentaria, Australia.

A simple method for estimating growth parameters from multiple length-frequency data in presence of continuous recruitment

The extended recruitment season for short-lived species such as prawns biases the estimation of growth parameters from length-frequency data when conventional methods are used. We propose a simple method for overcoming this bias given a time series of length-frequency data. The difficulties arising from extended recruitment are eliminated by predicting the growth of the succeeding samples and the length increments of the recruits in previous samples. This method requires that some maximum size at recruitment can be specified. The advantages of this multiple length-frequency method are: it is simple to use; it requires only three parameters; no specific distributions need to be assumed; and the actual seasonal recruitment pattern does not have to be specified. We illustrate the new method with length-frequency data on the tiger prawn Penaeus esculentus from the north-western Gulf of Carpentaria, Australia.

Robust estimating functions and bias correction for longitudinal data analysis

Robust methods are useful in making reliable statistical inferences when there are small deviations from the model assumptions. The widely used method of the generalized estimating equations can be "robustified" by replacing the standardized residuals with the M-residuals. If the Pearson residuals are assumed to be unbiased from zero, parameter estimators from the robust approach are asymptotically biased when error distributions are not symmetric. We propose a distribution-free method for correcting this bias. Our extensive numerical studies show that the proposed method can reduce the bias substantially. Examples are given for illustration.

An optimal design for screening trials

Yao, Begg, and Livingston (1996, Biometrics 52, 992-1001) considered the optimal group size for testing a series of potentially therapeutic agents to identify a promising one as soon as possible for given error rates. The number of patients to be tested with each agent was fixed as the group size. We consider a sequential design that allows early acceptance and rejection, and we provide an optimal strategy to minimize the sample sizes (patients) required using Markov decision processes. The minimization is under the constraints of the two types (false positive and false negative) of error probabilities, with the Lagrangian multipliers corresponding to the cost parameters for the two types of errors. Numerical studies indicate that there can be a substantial reduction in the number of patients required.

Iterative estimating equations: Linear convergence and asymptotic properties

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity. Furthermore, we show that the limiting estimator is consistent and asymptotically efficient, as expected. The method applies to semiparametric regression models with unspecified covariances among the observations. In the special case of linear models, the procedure reduces to iterative reweighted least squares. Finite sample performance of the procedure is studied by simulations, and compared with other methods. A numerical example from a medical study is considered to illustrate the application of the method.

General ranked set sampling with cost considerations

Nahhas, Wolfe, and Chen (2002, Biometrics 58, 964-971) considered optimal set size for ranked set sampling (RSS) with fixed operational costs. This framework can be very useful in practice to determine whether RSS is beneficial and to obtain the optimal set size that minimizes the variance of the population estimator for a fixed total cost. In this article, we propose a scheme of general RSS in which more than one observation can be taken from each ranked set. This is shown to be more cost-effective in some cases when the cost of ranking is not so small. We demonstrate using the example in Nahhas, Wolfe, and Chen (2002, Biometrics 58, 964-971), by taking two or more observations from one set even with the optimal set size from the RSS design can be more beneficial.

Unbiased estimating equations from working correlation models for irregularly timed repeated measures

The method of generalized estimating equation-, (GEEs) has been criticized recently for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. However, the feasibility and efficiency of GEE methods can be enhanced considerably by using flexible families of working correlation models. We propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance GEE. The supplementary estimating equations are obtained by differentiation of the Cholesky decomposition of the working correlation, or as score equations for decoupled Gaussian pseudolikelihood. The estimating equations are solved with computational effort equivalent to that required for a first-order GEE. Full details and analytic expressions are developed for a generalized Markovian model that was evaluated through simulation. Large-sample ".sandwich" standard errors for working correlation parameter estimates are derived and shown to have good performance. The proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children.

Analysing commercial catch and effort data from a penaeid trawl fishery: A comparison of linear models, mixed models, and generalised estimating equations approaches

Statistical methods are often used to analyse commercial catch and effort data to provide standardised fishing effort and/or a relative index of fish abundance for input into stock assessment models. Achieving reliable results has proved difficult in Australia's Northern Prawn Fishery (NPF), due to a combination of such factors as the biological characteristics of the animals, some aspects of the fleet dynamics, and the changes in fishing technology. For this set of data, we compared four modelling approaches (linear models, mixed models, generalised estimating equations, and generalised linear models) with respect to the outcomes of the standardised fishing effort or the relative index of abundance. We also varied the number and form of vessel covariates in the models. Within a subset of data from this fishery, modelling correlation structures did not alter the conclusions from simpler statistical models. The random-effects models also yielded similar results. This is because the estimators are all consistent even if the correlation structure is mis-specified, and the data set is very large. However, the standard errors from different models differed, suggesting that different methods have different statistical efficiency. We suggest that there is value in modelling the variance function and the correlation structure, to make valid and efficient statistical inferences and gain insight into the data. We found that fishing power was separable from the indices of prawn abundance only when we offset the impact of vessel characteristics at assumed values from external sources. This may be due to the large degree of confounding within the data, and the extreme temporal changes in certain aspects of individual vessels, the fleet and the fleet dynamics.

Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance

The method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations. We investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods. The asymptotic relative efficiency depends on three-features of the analysis, namely (i) the discrepancy between the working correlation structure and the unobservable true correlation structure, (ii) the method by which the correlation parameters are estimated and (iii) the 'design', by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes. Analytical and numerical studies of realistic data-analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency. Protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a 'Gaussian estimation' pseudolikelihood procedure is used with an AR(1) structure.

A generalized estimating equations approach for analysis of the impact of new technology on a trawl fishery

The article describes a generalized estimating equations approach that was used to investigate the impact of technology on vessel performance in a trawl fishery during 1988-96, while accounting for spatial and temporal correlations in the catch-effort data. Robust estimation of parameters in the presence of several levels of clustering depended more on the choice of cluster definition than on the choice of correlation structure within the cluster. Models with smaller cluster sizes produced stable results, while models with larger cluster sizes, that may have had complex within-cluster correlation structures and that had within-cluster covariates, produced estimates sensitive to the correlation structure. The preferred model arising from this dataset assumed that catches from a vessel were correlated in the same years and the same areas, but independent in different years and areas. The model that assumed catches from a vessel were correlated in all years and areas, equivalent to a random effects term for vessel, produced spurious results. This was an unexpected finding that highlighted the need to adopt a systematic strategy for modelling. The article proposes a modelling strategy of selecting the best cluster definition first, and the working correlation structure (within clusters) second. The article discusses the selection and interpretation of the model in the light of background knowledge of the data and utility of the model, and the potential for this modelling approach to apply in similar statistical situations.

A maximum-likelihood method for estimating natural mortality and catchability coefficient from catch-and-effort data

A simple stochastic model of a fish population subject to natural and fishing mortalities is described. The fishing effort is assumed to vary over different periods but to be constant within each period. A maximum-likelihood approach is developed for estimating natural mortality (M) and the catchability coefficient (q) simultaneously from catch-and-effort data. If there is not enough contrast in the data to provide reliable estimates of both M and q, as is often the case in practice, the method can be used to obtain the best possible values of q for a range of possible values of M. These techniques are illustrated with tiger prawn (Penaeus semisulcatus) data from the Northern Prawn Fishery of Australia.