Discovery and replication of gene influences on brain structure using LASSO regression

We implemented least absolute shrinkage and selection operator (LASSO) regression to evaluate gene effects in genome-wide association studies (GWAS) of brain images, using an MRI-derived temporal lobe volume measure from 729 subjects scanned as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI). Sparse groups of SNPs in individual genes were selected by LASSO, which identifies efficient sets of variants influencing the data. These SNPs were considered jointly when assessing their association with neuroimaging measures. We discovered 22 genes that passed genome-wide significance for influencing temporal lobe volume. This was a substantially greater number of significant genes compared to those found with standard, univariate GWAS. These top genes are all expressed in the brain and include genes previously related to brain function or neuropsychiatric disorders such as MACROD2, SORCS2, GRIN2B, MAGI2, NPAS3, CLSTN2, GABRG3, NRXN3, PRKAG2, GAS7, RBFOX1, ADARB2, CHD4, and CDH13. The top genes we identified with this method also displayed significant and widespread post hoc effects on voxelwise, tensor-based morphometry (TBM) maps of the temporal lobes. The most significantly associated gene was an autism susceptibility gene known as MACROD2.We were able to successfully replicate the effect of the MACROD2 gene in an independent cohort of 564 young, Australian healthy adult twins and siblings scanned with MRI (mean age: 23.8±2.2 SD years). Our approach powerfully complements univariate techniques in detecting influences of genes on the living brain.

Rank regression for analyzing ordinal qualitative data for treatment comparison

Ordinal qualitative data are often collected for phenotypical measurements in plant pathology and other biological sciences. Statistical methods, such as t tests or analysis of variance, are usually used to analyze ordinal data when comparing two groups or multiple groups. However, the underlying assumptions such as normality and homogeneous variances are often violated for qualitative data. To this end, we investigated an alternative methodology, rank regression, for analyzing the ordinal data. The rank-based methods are essentially based on pairwise comparisons and, therefore, can deal with qualitative data naturally. They require neither normality assumption nor data transformation. Apart from robustness against outliers and high efficiency, the rank regression can also incorporate covariate effects in the same way as the ordinary regression. By reanalyzing a data set from a wheat Fusarium crown rot study, we illustrated the use of the rank regression methodology and demonstrated that the rank regression models appear to be more appropriate and sensible for analyzing nonnormal data and data with outliers.

Efficient estimation for rank-based regression with clustered data

Rank-based inference is widely used because of its robustness. This article provides optimal rank-based estimating functions in analysis of clustered data with random cluster effects. The extensive simulation studies carried out to evaluate the performance of the proposed method demonstrate that it is robust to outliers and is highly efficient given the existence of strong cluster correlations. The performance of the proposed method is satisfactory even when the correlation structure is misspecified, or when heteroscedasticity in variance is present. Finally, a real dataset is analyzed for illustration.

Rank regression for accelerated failure time model with clustered and censored data

For clustered survival data, the traditional Gehan-type estimator is asymptotically equivalent to using only the between-cluster ranks, and the within-cluster ranks are ignored. The contribution of this paper is two fold: - (i) incorporating within-cluster ranks in censored data analysis, and; - (ii) applying the induced smoothing of Brown and Wang (2005, Biometrika) for computational convenience. Asymptotic properties of the resulting estimating functions are given. We also carry out numerical studies to assess the performance of the proposed approach and conclude that the proposed approach can lead to much improved estimators when strong clustering effects exist. A dataset from a litter-matched tumorigenesis experiment is used for illustration.

Rank regression analysis of correlated water quality data from South East Queensland

With growing population and fast urbanization in Australia, it is a challenging task to maintain our water quality. It is essential to develop an appropriate statistical methodology in analyzing water quality data in order to draw valid conclusions and hence provide useful advices in water management. This paper is to develop robust rank-based procedures for analyzing nonnormally distributed data collected over time at different sites. To take account of temporal correlations of the observations within sites, we consider the optimally combined estimating functions proposed by Wang and Zhu (Biometrika, 93:459-464, 2006) which leads to more efficient parameter estimation. Furthermore, we apply the induced smoothing method to reduce the computational burden. Smoothing leads to easy calculation of the parameter estimates and their variance-covariance matrix. Analysis of water quality data from Total Iron and Total Cyanophytes shows the differences between the traditional generalized linear mixed models and rank regression models. Our analysis also demonstrates the advantages of the rank regression models for analyzing nonnormal data.

Nonparametric rank regression for analyzing water quality concentration data with multiple detection limits

Environmental data usually include measurements, such as water quality data, which fall below detection limits, because of limitations of the instruments or of certain analytical methods used. The fact that some responses are not detected needs to be properly taken into account in statistical analysis of such data. However, it is well-known that it is challenging to analyze a data set with detection limits, and we often have to rely on the traditional parametric methods or simple imputation methods. Distributional assumptions can lead to biased inference and justification of distributions is often not possible when the data are correlated and there is a large proportion of data below detection limits. The extent of bias is usually unknown. To draw valid conclusions and hence provide useful advice for environmental management authorities, it is essential to develop and apply an appropriate statistical methodology. This paper proposes rank-based procedures for analyzing non-normally distributed data collected at different sites over a period of time in the presence of multiple detection limits. To take account of temporal correlations within each site, we propose an optimal linear combination of estimating functions and apply the induced smoothing method to reduce the computational burden. Finally, we apply the proposed method to the water quality data collected at Susquehanna River Basin in United States of America, which dearly demonstrates the advantages of the rank regression models.

Rank regression for analysis of clustered data: A natural induced smoothing approach

We consider rank regression for clustered data analysis and investigate the induced smoothing method for obtaining the asymptotic covariance matrices of the parameter estimators. We prove that the induced estimating functions are asymptotically unbiased and the resulting estimators are strongly consistent and asymptotically normal. The induced smoothing approach provides an effective way for obtaining asymptotic covariance matrices for between- and within-cluster estimators and for a combined estimator to take account of within-cluster correlations. We also carry out extensive simulation studies to assess the performance of different estimators. The proposed methodology is substantially Much faster in computation and more stable in numerical results than the existing methods. We apply the proposed methodology to a dataset from a randomized clinical trial.

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.

Statistical power calculation and sample size determination for environmental studies with data below detection limits

Power calculation and sample size determination are critical in designing environmental monitoring programs. The traditional approach based on comparing the mean values may become statistically inappropriate and even invalid when substantial proportions of the response values are below the detection limits or censored because strong distributional assumptions have to be made on the censored observations when implementing the traditional procedures. In this paper, we propose a quantile methodology that is robust to outliers and can also handle data with a substantial proportion of below-detection-limit observations without the need of imputing the censored values. As a demonstration, we applied the methods to a nutrient monitoring project, which is a part of the Perth Long-Term Ocean Outlet Monitoring Program. In this example, the sample size required by our quantile methodology is, in fact, smaller than that by the traditional t-test, illustrating the merit of our method.

Weighted rank regression for clustered data analysis

We consider ranked-based regression models for clustered data analysis. A weighted Wilcoxon rank method is proposed to take account of within-cluster correlations and varying cluster sizes. The asymptotic normality of the resulting estimators is established. A method to estimate covariance of the estimators is also given, which can bypass estimation of the density function. Simulation studies are carried out to compare different estimators for a number of scenarios on the correlation structure, presence/absence of outliers and different correlation values. The proposed methods appear to perform well, in particular, the one incorporating the correlation in the weighting achieves the highest efficiency and robustness against misspecification of correlation structure and outliers. A real example is provided for illustration.

Rank-based regression for analysis of repeated measures

We consider rank-based regression models for repeated measures. To account for possible withinsubject correlations, we decompose the total ranks into between- and within-subject ranks and obtain two different estimators based on between- and within-subject ranks. A simple perturbation method is then introduced to generate bootstrap replicates of the estimating functions and the parameter estimates. This provides a convenient way for combining the corresponding two types of estimating function for more efficient estimation.

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.

Efficient regression analysis with ranked-set sampling

This article is motivated by a lung cancer study where a regression model is involved and the response variable is too expensive to measure but the predictor variable can be measured easily with relatively negligible cost. This situation occurs quite often in medical studies, quantitative genetics, and ecological and environmental studies. In this article, by using the idea of ranked-set sampling (RSS), we develop sampling strategies that can reduce cost and increase efficiency of the regression analysis for the above-mentioned situation. The developed method is applied retrospectively to a lung cancer study. In the lung cancer study, the interest is to investigate the association between smoking status and three biomarkers: polyphenol DNA adducts, micronuclei, and sister chromatic exchanges. Optimal sampling schemes with different optimality criteria such as A-, D-, and integrated mean square error (IMSE)-optimality are considered in the application. With set size 10 in RSS, the improvement of the optimal schemes over simple random sampling (SRS) is great. For instance, by using the optimal scheme with IMSE-optimality, the IMSEs of the estimated regression functions for the three biomarkers are reduced to about half of those incurred by using SRS.

Land use regression model (LUR) for ultrafine particles in Brisbane

Traffic-related air pollution has been associated with a wide range of adverse health effects. One component of traffic emissions that has been receiving increasing attention is ultrafine particles(UFP, < 100 nm), which are of concern to human health due to their small diameters. Vehicles are the dominant source of UFP in urban environments. Small-scale variation in ultrafine particle number concentration (PNC) can be attributed to local changes in land use and road abundance. UFPs are also formed as a result of particle formation events. Modelling the spatial patterns in PNC is integral to understanding human UFP exposure and also provides insight into particle formation mechanisms that contribute to air pollution in urban environments. Land-use regression (LUR) is a technique that can use to improve the prediction of air pollution.

No evidence for association of ataxia-telangiectasia mutated gene T2119C and C3161G amino acid substitution variants with risk of breast cancer

Background There is evidence that certain mutations in the double-strand break repair pathway ataxia-telangiectasia mutated gene act in a dominant-negative manner to increase the risk of breast cancer. There are also some reports to suggest that the amino acid substitution variants T2119C Ser707Pro and C3161G Pro1054Arg may be associated with breast cancer risk. We investigate the breast cancer risk associated with these two nonconservative amino acid substitution variants using a large Australian population-based case–control study. Methods The polymorphisms were genotyped in more than 1300 cases and 600 controls using 5' exonuclease assays. Case–control analyses and genotype distributions were compared by logistic regression. Results The 2119C variant was rare, occurring at frequencies of 1.4 and 1.3% in cases and controls, respectively (P = 0.8). There was no difference in genotype distribution between cases and controls (P = 0.8), and the TC genotype was not associated with increased risk of breast cancer (adjusted odds ratio = 1.08, 95% confidence interval = 0.59–1.97, P = 0.8). Similarly, the 3161G variant was no more common in cases than in controls (2.9% versus 2.2%, P = 0.2), there was no difference in genotype distribution between cases and controls (P = 0.1), and the CG genotype was not associated with an increased risk of breast cancer (adjusted odds ratio = 1.30, 95% confidence interval = 0.85–1.98, P = 0.2). This lack of evidence for an association persisted within groups defined by the family history of breast cancer or by age. Conclusion The 2119C and 3161G amino acid substitution variants are not associated with moderate or high risks of breast cancer in Australian women.