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.

Designs for phase I clinical trials with multiple courses of subjects at different doses

The goal of this article is to provide a new design framework and its corresponding estimation for phase I trials. Existing phase I designs assign each subject to one dose level based on responses from previous subjects. Yet it is possible that subjects with neither toxicity nor efficacy responses can be treated at higher dose levels, and their subsequent responses to higher doses will provide more information. In addition, for some trials, it might be possible to obtain multiple responses (repeated measures) from a subject at different dose levels. In this article, a nonparametric estimation method is developed for such studies. We also explore how the designs of multiple doses per subject can be implemented to improve design efficiency. The gain of efficiency from "single dose per subject" to "multiple doses per subject" is evaluated for several scenarios. Our numerical study shows that using "multiple doses per subject" and the proposed estimation method together increases the efficiency substantially.

Induced smoothing for rank regression with censored survival times

Adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies. However, for only one simple weighting scheme, Gehan or Wilcoxon weights, are estimating equations guaranteed to be monotone in parameter components, and even in this case are step functions, requiring the equivalent of linear programming for computation. The lack of smoothness makes standard error or covariance matrix estimation even more difficult. An induced smoothing technique overcame these difficulties in various problems involving monotone but pure jump estimating equations, including conventional rank regression. The present paper applies induced smoothing to the Gehan-Wilcoxon weighted rank regression for the accelerated failure time model, for the more difficult case of survival time data subject to censoring, where the inapplicability of permutation arguments necessitates a new method of estimating null variance of estimating functions. Smooth monotone parameter estimation and rapid, reliable standard error or covariance matrix estimation is obtained.

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.

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.

Estimating equations with nonignorably missing response data

Troxel, Lipsitz, and Brennan (1997, Biometrics 53, 857-869) considered parameter estimation from survey data with nonignorable nonresponse and proposed weighted estimating equations to remove the biases in the complete-case analysis that ignores missing observations. This paper suggests two alternative modifications for unbiased estimation of regression parameters when a binary outcome is potentially observed at successive time points. The weighting approach of Robins, Rotnitzky, and Zhao (1995, Journal of the American Statistical Association 90, 106-121) is also modified to obtain unbiased estimating functions. The suggested estimating functions are unbiased only when the missingness probability is correctly specified, and misspecification of the missingness model will result in biases in the estimates. Simulation studies are carried out to assess the performance of different methods when the covariate is binary or normal. For the simulation models used, the relative efficiency of the two new methods to the weighting methods is about 3.0 for the slope parameter and about 2.0 for the intercept parameter when the covariate is continuous and the missingness probability is correctly specified. All methods produce substantial biases in the estimates when the missingness model is misspecified or underspecified. Analysis of data from a medical survey illustrates the use and possible differences of these estimating functions.

Estimating the efficiency of a small beam trawl for sampling tiger prawns Penaeus esculentus and P. semisulcatus in seagrass by removal experiments

The efficiency with which a small beam trawl (1 x 0.5 m mouth) sampled postlarvae and juveniles of tiger prawns Penaeus esculentus and P, semisulcatus at night was estimated in 3 tropical seagrass communities (dominated by Thalassia hemprichii, Syringodium isoetifolium and Enhalus acoroides, respectively) in the shallow waters of the Gulf of Carpentaria in northern Australia. An area of seagrass (40 x 3 m) was enclosed by a net and the beam trawl was repeatedly hand-hauled over the substrate. Net efficiency (q) was calculated using 4 methods: the unweighted Leslie, weighted Leslie, DeLury and Maximum-likelihood (ML) methods. The Maximum-likelihood is the preferred method for estimating efficiency because it makes the fewest assumptions and is not affected by zero catches. The major difference in net efficiencies was between postlarvae (mean ML q +/- 95% confidence limits = 0.66 +/- 0.16) and juveniles of both species (mean q for juveniles in water less than or equal to 1.0 m deep = 0.47 +/- 0.05), i.e. the beam trawl was more efficient at capturing postlarvae than juveniles. There was little difference in net efficiency for P, esculentus between seagrass types (T, hemprichii versus S. isoetifolium), even though the biomass and morphologies of seagrass in these communities differed greatly (biomasses were 54 and 204 g m(-2), respectively). The efficiency of the net appeared to be the same for juveniles of the 2 species in shallow water, but was lower for juvenile P, semisulcatus at high tide when the water was deeper (1.6 to 1.9 m) (0.35 +/- 0.08). The lower efficiency near the time of high tide is possibly because the prawns are more active at high than low tide, and can also escape above the net. Factors affecting net efficiency and alternative methods of estimating net efficiency are discussed.

Method for comparing the capture efficiency of benthic sampling devices

Traditional comparisons between the capture efficiency of sampling devices have generally looked at the absolute differences between devices. We recommend that the signal-to-noise ratio be used when comparing the capture efficiency of benthic sampling devices. Using the signal-to-noise ratio rather than the absolute difference has the advantages that the variance is taken into account when determining how important the difference is, the hypothesis and minimum detectable difference can be made identical for all taxa, it is independent of the units used for measurement, and the sample-size calculation is independent of the variance. This new technique is illustrated by comparing the capture efficiency of a 0.05 m(2) van Veen grab and an airlift suction device, using samples taken from Heron and One Tree lagoons, Australia.

An integrated model of an open-pit coal mine: Improving energy efficiency decisions

This article contributes an original integrated model of an open-pit coal mine for supporting energy-efficient decisions. Mixed integer linear programming is used to formulate a general integrated model of the operational energy consumption of four common open-pit coal mining subsystems: excavation and haulage, stockpiles, processing plants and belt conveyors. Mines are represented as connected instances of the four subsystems, in a flow sheet manner, which are then fitted to data provided by the mine operators. Solving the integrated model ensures the subsystems’ operations are synchronised and whole-of-mine energy efficiency is encouraged. An investigation on a case study of an open-pit coal mine is conducted to validate the proposed methodology. Opportunities are presented for using the model to aid energy-efficient decision-making at various levels of a mine, and future work to improve the approach is described.

Design and Development of an In-Vehicle Human Machine Interface to Improve Fuel Efficiency & Safety

Road transport plays a significant role in various industries and mobility services around the globe and has a vital impact on our daily lives. However it also has serious impacts on both public health and the environment. In-vehicle feedback systems are a relatively new approach to encouraging driver behaviour change for improving fuel efficiency and safety in automotive environments. While many studies claim that the adoption of eco-driving practices, such as eco-driving training programs and in-vehicle feedback to drivers, has the potential to improve fuel efficiency, limited research has integrated safety and eco-driving. Therefore, this research seeks to use human factors related theories and practices to inform the design and evaluation of an in-vehicle Human Machine Interface (HMI) providing real-time driver feedback with the aim of improving both fuel efficiency and safety.

Implementation of parallel tridiagonal solvers for a heterogeneous computing environment

Tridiagonal diagonally dominant linear systems arise in many scientific and engineering applications. The standard Thomas algorithm for solving such systems is inherently serial forming a bottleneck in computation. Algorithms such as cyclic reduction and SPIKE reduce a single large tridiagonal system into multiple small independent systems which can be solved in parallel. We have developed portable cyclic reduction and SPIKE algorithm OpenCL implementations with the intent to target a range of co-processors in a heterogeneous computing environment including Field Programmable Gate Arrays (FPGAs), Graphics Processing Units (GPUs) and other multi-core processors. In this paper, we evaluate these designs in the context of solver performance, resource efficiency and numerical accuracy.

Using rowers’ perceptions of on-water stroke success to evaluate sculling catch efficiency variables via a boat instrumentation system

Aim An effective catch in sculling is a critical determinant of boat velocity. This study used rowers’ performance-based judgments to compare three measures of catch slip efficiency. Two questions were addressed: (1) would rower-judged Yes strokes be faster than No strokes? and (2) which method of quantifying catch slip best reflected these judgements? Methods Eight single scullers performed two 10-min blocks of sub maximal on-water rowing at 20 strokes per minute. Every 30 s, rowers reported either Yes or No about the quality of their stroke at the catch. Results It was found that Yes strokes identified by rowers had, on average, a moderate effect advantage over No strokes with a standardised effect size of 0.43. In addition, a quicker time to positive acceleration best reflected the change in performance; where the standardised mean difference score of 0.57 for time to positive acceleration was larger than the scores of 0.47 for time to PowerLine force, and 0.35 for time to 30% peak pin force catch slip measures. For all eight rowers, Yes strokes corresponded to time to positive acceleration occurring earlier than No strokes. Conclusion Rower judgements about successful strokes was linked to achieving a quicker time to positive acceleration, and may be of the most value in achieving a higher average boat velocity.

Influence of organic amendments on greenhouse gas emissions and N use efficiency in sub-tropical cropping systems

This thesis investigated the impact of organic sources of nutrients on greenhouse gas emissions (carbon dioxide, nitrous oxide and methane), nitrogen use efficiency and biomass production in subtropical cropping soils. The study was conducted in two main soil types in subtropical ecosystems, sandy loam soil and clay soil, with a variety of organic materials from agro-industrial residues and crop residues. It is important for recycling of agro-industrial residues and agricultural residues and the mitigation of greenhouse gas emissions and nitrogen use efficiency.

Rice husk biochar and crop residue amendment in subtropical cropping soils: Effect on biomass production, nitrogen use efficiency and greenhouse gas emissions

We investigated the effect of maize residues and rice husk biochar on biomass production, fertiliser nitrogen recovery (FNR) and nitrous oxide (N2O) emissions for three different subtropical cropping soils. Maize residues at two rates (0 and 10 t ha−1) combined with three rates (0, 15 and 30 t ha-1) of rice husk biochar were added to three soil types in a pot trial with maize plants. Soil N2O emissions were monitored with static chambers for 91 days. Isotopic 15N-labelled urea was applied to the treatments without added crop residues to measure the FNR. Crop residue incorporation significantly reduced N uptake in all treatments but did not affect overall FNR. Rice husk biochar amendment had no effect on plant growth and N uptake but significantly reduced N2O and carbon dioxide (CO2) emissions in two of the three soils. The incorporation of crop residues had a contrasting effect on soil N2O emissions depending on the mineral N status of the soil. The study shows that effects of crop residues depend on soil properties at the time of application. Adding crop residues with a high C/N ratio to soil can immobilise N in the soil profile and hence reduce N uptake and/or total biomass production. Crop residue incorporation can either stimulate or reduce N2O emissions depending on the mineral N content of the soil. Crop residues pyrolysed to biochar can potentially stabilise native soil C (negative priming) and reduce N2O emissions from cropping soils thus providing climate change mitigation potential beyond the biochar C storage in soils. Incorporation of crop residues as an approach to recycle organic materials and reduce synthetic N fertiliser use in agricultural production requires a thorough evaluation, both in terms of biomass production and greenhouse gas emissions.