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.

Effects of variance-function misspecification in analysis of longitudinal data

The approach of generalized estimating equations (GEE) is based on the framework of generalized linear models but allows for specification of a working matrix for modeling within-subject correlations. The variance is often assumed to be a known function of the mean. This article investigates the impacts of misspecifying the variance function on estimators of the mean parameters for quantitative responses. Our numerical studies indicate that (1) correct specification of the variance function can improve the estimation efficiency even if the correlation structure is misspecified; (2) misspecification of the variance function impacts much more on estimators for within-cluster covariates than for cluster-level covariates; and (3) if the variance function is misspecified, correct choice of the correlation structure may not necessarily improve estimation efficiency. We illustrate impacts of different variance functions using a real data set from cow growth.

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.

Error bounds for calculation of the Gittins indices

For a wide class of semi-Markov decision processes the optimal policies are expressible in terms of the Gittins indices, which have been found useful in sequential clinical trials and pharmaceutical research planning. In general, the indices can be approximated via calibration based on dynamic programming of finite horizon. This paper provides some results on the accuracy of such approximations, and, in particular, gives the error bounds for some well known processes (Bernoulli reward processes, normal reward processes and exponential target processes).

Application of commercially available, low-cost, miniaturised NIR spectrometers to the assessment of the sugar content of intact fruit

Recent decreases in costs, and improvements in performance, of silicon array detectors open a range of potential applications of relevance to plant physiologists, associated with spectral analysis in the visible and short-wave near infra-red (far-red) spectrum. The performance characteristics of three commercially available ‘miniature’ spectrometers based on silicon array detectors operating in the 650–1050-nm spectral region (MMS1 from Zeiss, S2000 from Ocean Optics, and FICS from Oriel, operated with a Larry detector) were compared with respect to the application of non-invasive prediction of sugar content of fruit using near infra-red spectroscopy (NIRS). The FICS–Larry gave the best wavelength resolution; however, the narrow slit and small pixel size of the charge-coupled device detector resulted in a very low sensitivity, and this instrumentation was not considered further. Wavelength resolution was poor with the MMS1 relative to the S2000 (e.g. full width at half maximum of the 912 nm Hg peak, 13 and 2 nm for the MMS1 and S2000, respectively), but the large pixel height of the array used in the MMS1 gave it sensitivity comparable to the S2000. The signal-to-signal standard error ratio of spectra was greater by an order of magnitude with the MMS1, relative to the S2000, at both near saturation and low light levels. Calibrations were developed using reflectance spectra of filter paper soaked in range of concentrations (0–20% w/v) of sucrose, using a modified partial least squares procedure. Calibrations developed with the MMS1 were superior to those developed using the S2000 (e.g. coefficient of correlation of 0.90 and 0.62, and standard error of cross-validation of 1.9 and 5.4%, respectively), indicating the importance of high signal to noise ratio over wavelength resolution to calibration accuracy. The design of a bench top assembly using the MMS1 for the non-invasive assessment of mesocarp sugar content of (intact) melon fruit is reported in terms of light source and angle between detector and light source, and optimisation of math treatment (derivative condition and smoothing function).

Influence of environmental and instrumental variables on the non-invasive prediction of Brix in pineapple using near infrared spectroscopy

The Brix content of pineapple fruit can be non-invasively predicted from the second derivative of near infrared reflectance spectra. Correlations obtained using a NIRSystems 6500 spectrophotometer through multiple linear regression and modified partial least squares analyses using a post-dispersive configuration were comparable with that from a pre-dispersive configuration in terms of accuracy (e.g. coefficient of determination, R2, 0.73; standard error of cross validation, SECV, 1.01°Brix). The effective depth of sample assessed was slightly greater using the post-dispersive technique (about 20 mm for pineapple fruit), as expected in relation to the higher incident light intensity, relative to the pre-dispersive configuration. The effect of such environmental variables as temperature, humidity and external light, and instrumental variables such as the number of scans averaged to form a spectrum, were considered with respect to the accuracy and precision of the measurement of absorbance at 876 nm, as a key term in the calibration for Brix, and predicted Brix. The application of post-dispersive near infrared technology to in-line assessment of intact fruit in a packing shed environment is discussed.

Non-invasive assessment of pineapple and mango fruit quality using near infra-red spectroscopy

The potential of near infra-red (NIR) spectroscopy for non-invasive measurement of fruit quality of pineapple (Ananas comosus var. Smooth Cayenne) and mango (Magnifera indica var. Kensington) fruit was assessed. A remote reflectance fibre optic probe, placed in contact with the fruit skin surface in a light-proof box, was used to deliver monochromatic light to the fruit, and to collect NIR reflectance spectra (760–2500 nm). The probe illuminated and collected reflected radiation from an area of about 16 cm2. The NIR spectral attributes were correlated with pineapple juice Brix and with mango flesh dry matter (DM) measured from fruit flesh directly underlying the scanned area. The highest correlations for both fruit were found using the second derivative of the spectra (d2 log 1/R) and an additive calibration equation. Multiple linear regression (MLR) on pineapple fruit spectra (n = 85) gave a calibration equation using d2 log 1/R at wavelengths of 866, 760, 1232 and 832 nm with a multiple coefficient of determination (R2) of 0.75, and a standard error of calibration (SEC) of 1.21 °Brix. Modified partial least squares (MPLS) regression analysis yielded a calibration equation with R2 = 0.91, SEC = 0.69, and a standard error of cross validation (SECV) of 1.09 oBrix. For mango, MLR gave a calibration equation using d2 log 1/R at 904, 872, 1660 and 1516 nm with R2 = 0.90, and SEC = 0.85% DM and a bias of 0.39. Using MPLS analysis, a calibration equation with R2 = 0.98, SEC = 0.54 and SECV = 1.19 was obtained. We conclude that NIR technology offers the potential to assess fruit sweetness in intact whole pineapple and DM in mango fruit, respectively, to within 1° Brix and 1% DM, and could be used for the grading of fruit in fruit packing sheds.

Robustness of NIR calibrations for soluble solids in intact melon and pineapple

The soluble solids content of intact fruit can be measured non-invasively by near infrared spectroscopy, allowing “sweetness” grading of individual fruit. However, little information is available in the literature with respect to the robustness of such calibrations. We developed calibrations based on a restricted wavelength range (700–1100 nm), suitable for use with low-cost silicon detector systems, using a stepwise multiple linear regression routine. Calibrations for total soluble solids (°Brix) in intact pineapple fruit were not transferable between summer and winter growing seasons. A combined calibration (data of three harvest dates) validated reasonably well against a population set drawn from all harvest dates (r2 = 0.72, SEP = 1.84 °Brix). Calibrations for Brix in melon were transferable between two of the three varieties examined. However, a lack of robustness of calibration was indicated by poor validation within populations of fruit harvested at different times. Further work is planned to investigate the robustness of calibration across varieties, growing districts and seasons.

Assessment of quality defects in macadamia kernels using NIR spectroscopy

Spectral data were collected of intact and ground kernels using 3 instruments (using Si-PbS, Si, and InGaAs detectors), operating over different areas of the spectrum (between 400 and 2500 nm) and employing transmittance, interactance, and reflectance sample presentation strategies. Kernels were assessed on the basis of oil and water content, and with respect to the defect categories of insect damage, rancidity, discoloration, mould growth, germination, and decomposition. Predictive model performance statistics for oil content models were acceptable on all instruments (R2 > 0.98; RMSECV < 2.5%, which is similar to reference analysis error), although that for the instrument employing reflectance optics was inferior to models developed for the instruments employing transmission optics. The spectral positions for calibration coefficients were consistent with absorbance due to the third overtones of CH2 stretching. Calibration models for moisture content in ground samples were acceptable on all instruments (R2 > 0.97; RMSECV < 0.2%), whereas calibration models for intact kernels were relatively poor. Calibration coefficients were more highly weighted around 1360, 740 and 840 nm, consistent with absorbance due to overtones of O-H stretching and combination. Intact kernels with brown centres or rancidity could be discriminated from each other and from sound kernels using principal component analysis. Part kernels affected by insect damage, discoloration, mould growth, germination, and decomposition could be discriminated from sound kernels. However, discrimination among these defect categories was not distinct and could not be validated on an independent set. It is concluded that there is good potential for a low cost Si photodiode array instrument to be employed to identify some quality defects of intact macadamia kernels and to quantify oil and moisture content of kernels in the process laboratory and for oil content in-line. Further work is required to examine the robustness of predictive models across different populations, including growing districts, cultivars and times of harvest.

Use of electronic portal imaging devices for electron treatment verification

This study aims to help broaden the use of electronic portal imaging devices (EPIDs) for pre-treatment patient positioning verification, from photon-beam radiotherapy to photon- and electron-beam radiotherapy, by proposing and testing a method for acquiring clinicallyuseful EPID images of patient anatomy using electron beams, with a view to enabling and encouraging further research in this area. EPID images used in this study were acquired using all available beams from a linac configured to deliver electron beams with nominal energies of 6, 9, 12, 16 and 20 MeV, as well as photon beams with nominal energies of 6 and 10 MV. A widely-available heterogeneous, approximately-humanoid, thorax phantom was used, to provide an indication of the contrast and noise produced when imaging different types of tissue with comparatively realistic thicknesses. The acquired images were automatically calibrated, corrected for the effects of variations in the sensitivity of individual photodiodes, using a flood field image. For electron beam imaging, flood field EPID calibration images were acquired with and without the placement of blocks of water-equivalent plastic (with thicknesses approximately equal to the practical range of electrons in the plastic) placed upstream of the EPID, to filter out the primary electron beam, leaving only the bremsstrahlung photon signal. While the electron beam images acquired using a standard (unfiltered) flood field calibration were observed to be noisy and difficult to interpret, the electron beam images acquired using the filtered flood field calibration showed tissues and bony anatomy with levels of contrast and noise that were similar to the contrast and noise levels seen in the clinically acceptable photon beam EPID images. The best electron beam imaging results (highest contrast, signal-to-noise and contrast-to-noise ratios) were achieved when the images were acquired using the higher energy electron beams (16 and 20 MeV) when the EPID was calibrated using an intermediate (12 MeV) electron beam energy. These results demonstrate the feasibility of acquiring clinically-useful EPID images of patient anatomy using electron beams and suggest important avenues for future investigation, thus enabling and encouraging further research in this area. There is manifest potential for the EPID imaging method proposed in this work to lead to the clinical use of electron beam imaging for geometric verification of electron treatments in the future.

Robustness of NIR calibrations for assessing fruit quality

Predictive models based on near infra-red spectroscopy for the assessment of fruit internal quality attributes must exhibit a degree of robustness across the parameters of variety, district and time to be of practical use in fruit grading. At the time this thesis was initiated, while there were a number of published reports on the development of near infra-red based calibration models for the assessment of internal quality attributes of intact fruit, there were no reports of the reliability ("robustness") of such models across time, cultivars or growing regions. As existing published reports varied in instrumentation employed, a re-analysis of existing data was not possible. An instrument platform, based on partial transmittance optics, a halogen light source and (Zeiss MMS 1) detector operating in the short wavelength near infra-red region was developed for use in the assessment of intact fruit. This platform was used to assess populations of macadamia kernels, melons and mandarin fruit for total soluble solids, dry matter and oil concentration. Calibration procedures were optimised and robustness assessed across growing areas, time of harvest, season and variety. In general, global modified partial least squares regression (MPLS) calibration models based on derivatised absorbance data were better than either multiple linear regression or `local' MPLS models in the prediction of independent validation populations . Robustness was most affected by growing season, relative to the growing district or variety . Various calibration updating procedures were evaluated in terms of calibration robustness. Random selection of samples from the validation population for addition to the calibration population was equivalent to or better than other methods of sample addition (methods based on the Mahalanobis distance of samples from either the centroid of the population or neighbourhood samples). In these exercises the global Mahalanobis distance (GH) was calculated using the scores and loadings from the calibration population on the independent validation population. In practice, it is recommended that model predictive performance be monitored in terms of predicted sample GH, with model updating using as few as 10 samples from the new population undertaken when the average GH value exceeds 1 .0 .

Near infrared spectroscopy as a rapid tool to measure volatile aroma compounds in Riesling wine: Possibilities and limits

Volatile chemical compounds responsible for the aroma of wine are derived from a number of different biochemical and chemical pathways. These chemical compounds are formed during grape berry metabolism, crushing of the berries, fermentation processes (i.e. yeast and malolactic bacteria) and also from the ageing and storage of wine. Not surprisingly, there are a large number of chemical classes of compounds found in wine which are present at varying concentrations (ng L-1 to mg L-1), exhibit differing potencies, and have a broad range of volatilities and boiling points. The aim of this work was to investigate the potential use of near infrared (NIR) spectroscopy combined with chemometrics as a rapid and low-cost technique to measure volatile compounds in Riesling wines. Samples of commercial Riesling wine were analyzed using an NIR instrument and volatile compounds by gas chromatography (GC) coupled with selected ion monitoring mass spectrometry. Correlation between the NIR and GC data were developed using partial least-squares (PLS) regression with full cross validation (leave one out). Coefficients of determination in cross validation (R 2) and the standard error in cross validation (SECV) were 0.74 (SECV: 313.6 μg L−1) for esters, 0.90 (SECV: 20.9 μg L−1) for monoterpenes and 0.80 (SECV: 1658 ?g L-1) for short-chain fatty acids. This study has shown that volatile chemical compounds present in wine can be measured by NIR spectroscopy. Further development with larger data sets will be required to test the predictive ability of the NIR calibration models developed.

Characterisation of humidity dependence of a metal oxide semiconductor (MOS) sensor array using Partial Least Squares (PLS)

Metal oxide semiconductor (MOS) sensors are a class of chemical sensor that have potential for being a practical core sensor module for an electronic nose system in various environmental monitoring applications. However, the responses of these sensors may be affected by changes in humidity and this must be taken into consideration when developing calibration models. This paper characterises the humidity dependence of a sensor array which consists of 12 MOS sensors. The results were used to develop calibration models using partial least squares. Effects of humidity on the response of the sensor array and predictive ability of partial least squares are discussed. It is shown that partial least squares can provide proper calibration models to compensate for effects caused by changes in humidity.

Characterisation of humidity dependence of a metal oxide semiconductor sensor array using partial least squares

Metal oxide semiconductor (MOS) sensors are a class of chemical sensors that have potential for being a practical core sensor module for an electronic nose system in various environmental monitoring applications. However, the responses of these sensors may be affected by changes in humidity and this must be taken into consideration when developing calibration models. This paper characterises the humidity dependence of a sensor array which consists of 12 MOS sensors. The results were used to develop calibration models using partial least squares (PLS). Effects of humidity on the response of the sensor array and predictive ability of partial least squares are discussed. It is shown that partial least squares can provide proper calibration models to compensate for effects caused by changes in humidity. Special Issue: Selected Paper from the 12th International Symposium on Olfaction and Electronic Noses - ISOEN 2007, International Symposium on Olfaction and Electronic Noses.

Diet quality and liveweight gain of steers grazing Leucaena-grass pasture estimated with faecal near infrared reflectance spectroscopy (F.NIRS)

Three drafts of Bos indicus cross steers (initially 178-216 kg) grazed Leucaena-grass pasture [Leucaena leucocephala subspecies glabrata cv. Cunningham with green panic (Panicum maximum cv. trichoglume)] from late winter through to autumn during three consecutive years in the Burnett region of south-east Queensland. Measured daily weight gain (DWGActual) of the steers was generally 0.7-1.1 kg/day during the summer months. Estimated intakes of metabolisable energy and dry matter (DM) were calculated from feeding standards as the intakes required by the steers to grow at the DWGActual. Diet attributes were predicted from near infrared reflectance spectroscopy spectra of faeces (F.NIRS) using established calibration equations appropriate for northern Australian forages. Inclusion of some additional reference samples from cattle consuming Leucaena diets into F.NIRS calibrations based on grass and herbaceous legume-grass pastures improved prediction of the proportion of Leucaena in the diet. Mahalanobis distance values supported the hypothesis that the F.NIRS predictions of diet crude protein concentration and DM digestibility (DMD) were acceptable. F.NIRS indicated that the percentage of Leucaena in the diet varied widely (10-99%). Diet crude protein concentration and DMD were usually high, averaging 12.4 and 62%, respectively, and were related asymptotically to the percentage of Leucaena in the diet (R2 = 0.48 and 0.33, respectively). F.NIRS calibrations for DWG were not satisfactory to predict this variable from an individual faecal sample since the s.e. of prediction were 0.33-0.40 kg/day. Cumulative steer liveweight (LW) predicted from F.NIRS DWG calibrations, which had been previously developed with tropical grass and grass-herbaceous legume pastures, greatly overestimated the measured steer LW; therefore, these calibrations were not useful. Cumulative steer LW predicted from a modified F.NIRS DWG calibration, which included data from the present study, was strongly correlated (R2 = 0.95) with steer LW but overestimated LW by 19-31 kg after 8 months. Additional reference data are needed to develop robust F.NIRS calibrations to encompass the diversity of Leucaena pastures of northern Australia. In conclusion, the experiment demonstrated that F.NIRS could improve understanding of diet quality and nutrient intake of cattle grazing Leucaena-grass pasture, and the relationships between nutrient supply and cattle growth.