The Representative Soil Sampling Scheme of England and Wales: a statistical analysis of topsoil nutrient status and pH between 1971 and 2001

The Representative Soil Sampling Scheme of England and Wales has recorded information on the soil of agricultural land in England and Wales since 1969. It is a valuable source of information about the soil in the context of monitoring for sustainable agricultural development. Changes in soil nutrient status and pH were examined over the period 1971-2001. Several methods of statistical analysis were applied to data from the surveys during this period. The main focus here is on the data for 1971, 1981, 1991 and 2001. The results of examining change over time in general show that levels of potassium in the soil have increased, those of magnesium have remained fairly constant, those of phosphorus have declined and pH has changed little. Future sampling needs have been assessed in the context of monitoring, to determine the mean at a given level of confidence and tolerable error and to detect change in the mean over time at these same levels over periods of 5 and 10 years. The results of a non-hierarchical multivariate classification suggest that England and Wales could be stratified to optimize future sampling and analysis. To monitor soil quality and health more generally than for agriculture, more of the country should be sampled and a wider range of properties recorded.

An Assessment of the Recent Past and Future Climate Change, Glacier Retreat, and Runoff in the Caucasus Region Using Dynamical and Statistical Downscaling and HBV-ETH Hydrological Model

The paper discusses the observed and projected warming in the Caucasus region and its implications for glacier melt and runoff. A strong positive trend in summer air temperatures of 0.05 degrees C a(-1) is observed in the high-altitude areas providing for a strong glacier melt and continuous decline in glacier mass balance. A warming of 4-7 degrees C and 3-5 degrees C is projected for the summer months in 2071-2100 under the A2 and B2 emission scenarios respectively, suggesting that enhanced glacier melt can be expected. The expected changes in winter precipitation will not compensate for the summer melt and glacier retreat is likely to continue. However, a projected small increase in both winter and summer precipitation combined with the enhanced glacier melt will result in increased summer runoff in the currently glaciated region of the Caucasus (independent of whether the region is glaciated at the end of the twenty-first century) by more than 50% compared with the baseline period.

Self-play: statistical significance

Heinz recently completed a comprehensive experiment in self-play using the FRITZ chess engine to establish the ‘decreasing returns’ hypothesis with specific levels of statistical confidence. This note revisits the results and recalculates the confidence levels of this and other hypotheses. These appear to be better than Heinz’ initial analysis suggests.

Diagnosis of variability and trends in a global precipitation dataset using a physically motivated statistical model

A physically motivated statistical model is used to diagnose variability and trends in wintertime ( October - March) Global Precipitation Climatology Project (GPCP) pentad (5-day mean) precipitation. Quasi-geostrophic theory suggests that extratropical precipitation amounts should depend multiplicatively on the pressure gradient, saturation specific humidity, and the meridional temperature gradient. This physical insight has been used to guide the development of a suitable statistical model for precipitation using a mixture of generalized linear models: a logistic model for the binary occurrence of precipitation and a Gamma distribution model for the wet day precipitation amount. The statistical model allows for the investigation of the role of each factor in determining variations and long-term trends. Saturation specific humidity q(s) has a generally negative effect on global precipitation occurrence and with the tropical wet pentad precipitation amount, but has a positive relationship with the pentad precipitation amount at mid- and high latitudes. The North Atlantic Oscillation, a proxy for the meridional temperature gradient, is also found to have a statistically significant positive effect on precipitation over much of the Atlantic region. Residual time trends in wet pentad precipitation are extremely sensitive to the choice of the wet pentad threshold because of increasing trends in low-amplitude precipitation pentads; too low a choice of threshold can lead to a spurious decreasing trend in wet pentad precipitation amounts. However, for not too small thresholds, it is found that the meridional temperature gradient is an important factor for explaining part of the long-term trend in Atlantic precipitation.

Self-play: statistical significance

Heinz recently completed a comprehensive experiment in self-play using the FRITZ chess engine to establish the ‘decreasing returns’ hypothesis with specific levels of statistical confidence. This note revisits the results and recalculates the confidence levels of this and other hypotheses. These appear to be better than Heinz’ initial analysis suggests.

British Nutrition Foundation annual lecture: chips with everything? Nutritional genomics and the application of diet in disease prevention

The development of high throughput techniques ('chip' technology) for measurement of gene expression and gene polymorphisms (genomics), and techniques for measuring global protein expression (proteomics) and metabolite profile (metabolomics) are revolutionising life science research, including research in human nutrition. In particular, the ability to undertake large-scale genotyping and to identify gene polymorphisms that determine risk of chronic disease (candidate genes) could enable definition of an individual's risk at an early age. However, the search for candidate genes has proven to be more complex, and their identification more elusive, than previously thought. This is largely due to the fact that much of the variability in risk results from interactions between the genome and environmental exposures. Whilst the former is now very well defined via the Human Genome Project, the latter (e.g. diet, toxins, physical activity) are poorly characterised, resulting in inability to account for their confounding effects in most large-scale candidate gene studies. The polygenic nature of most chronic diseases offers further complexity, requiring very large studies to disentangle relatively weak impacts of large numbers of potential 'risk' genes. The efficacy of diet as a preventative strategy could also be considerably increased by better information concerning gene polymorphisms that determine variability in responsiveness to specific diet and nutrient changes. Much of the limited available data are based on retrospective genotyping using stored samples from previously conducted intervention trials. Prospective studies are now needed to provide data that can be used as the basis for provision of individualised dietary advice and development of food products that optimise disease prevention. Application of the new technologies in nutrition research offers considerable potential for development of new knowledge and could greatly advance the role of diet as a preventative disease strategy in the 21st century. Given the potential economic and social benefits offered, funding for research in this area needs greater recognition, and a stronger strategic focus, than is presently the case. Application of genomics in human health offers considerable ethical and societal as well as scientific challenges. Economic determinants of health care provision are more likely to resolve such issues than scientific developments or altruistic concerns for human health.

Statistical methods for examining genetic influences of resistance to anti-epileptic drugs

It is generally accepted that genetics may be an important factor in explaining the variation between patients’ responses to certain drugs. However, identification and confirmation of the responsible genetic variants is proving to be a challenge in many cases. A number of difficulties that maybe encountered in pursuit of these variants, such as non-replication of a true effect, population structure and selection bias, can be mitigated or at least reduced by appropriate statistical methodology. Another major statistical challenge facing pharmacogenetics studies is trying to detect possibly small polygenic effects using large volumes of genetic data, while controlling the number of false positive signals. Here we review statistical design and analysis options available for investigations of genetic resistance to anti-epileptic drugs.

Statistical downscaling of river flows

An extensive statistical ‘downscaling’ study is done to relate large-scale climate information from a general circulation model (GCM) to local-scale river flows in SW France for 51 gauging stations ranging from nival (snow-dominated) to pluvial (rainfall-dominated) river-systems. This study helps to select the appropriate statistical method at a given spatial and temporal scale to downscale hydrology for future climate change impact assessment of hydrological resources. The four proposed statistical downscaling models use large-scale predictors (derived from climate model outputs or reanalysis data) that characterize precipitation and evaporation processes in the hydrological cycle to estimate summary flow statistics. The four statistical models used are generalized linear (GLM) and additive (GAM) models, aggregated boosted trees (ABT) and multi-layer perceptron neural networks (ANN). These four models were each applied at two different spatial scales, namely at that of a single flow-gauging station (local downscaling) and that of a group of flow-gauging stations having the same hydrological behaviour (regional downscaling). For each statistical model and each spatial resolution, three temporal resolutions were considered, namely the daily mean flows, the summary statistics of fortnightly flows and a daily ‘integrated approach’. The results show that flow sensitivity to atmospheric factors is significantly different between nival and pluvial hydrological systems which are mainly influenced, respectively, by shortwave solar radiations and atmospheric temperature. The non-linear models (i.e. GAM, ABT and ANN) performed better than the linear GLM when simulating fortnightly flow percentiles. The aggregated boosted trees method showed higher and less variable R2 values to downscale the hydrological variability in both nival and pluvial regimes. Based on GCM cnrm-cm3 and scenarios A2 and A1B, future relative changes of fortnightly median flows were projected based on the regional downscaling approach. The results suggest a global decrease of flow in both pluvial and nival regimes, especially in spring, summer and autumn, whatever the considered scenario. The discussion considers the performance of each statistical method for downscaling flow at different spatial and temporal scales as well as the relationship between atmospheric processes and flow variability.

Statistical evaluation of an acute dermal toxicity test using the dermal fixed dose procedure

The conventional method for the assessment of acute dermal toxicity (OECD Test Guideline 402, 1987) uses death of animals as an endpoint to identify the median lethal dose (LD50). A new OECD Testing Guideline called the dermal fixed dose procedure (dermal FDP) is being prepared to provide an alternative to Test Guideline 402. In contrast to Test Guideline 402, the dermal FDP does not provide a point estimate of the LD50, but aims to identify that dose of the substance under investigation that causes clear signs of nonlethal toxicity. This is then used to assign classification according to the new Globally Harmonised System of Classification and Labelling scheme (GHS). The dermal FDP has been validated using statistical modelling rather than by in vivo testing. The statistical modelling approach enables calculation of the probability of each GHS classification and the expected numbers of deaths and animals used in the test for imaginary substances with a range of LD50 values and dose-response curve slopes. This paper describes the dermal FDP and reports the results from the statistical evaluation. It is shown that the procedure will be completed with considerably less death and suffering than guideline 402, and will classify substances either in the same or a more stringent GHS class than that assigned on the basis of the LD50 value.

Statistical evaluation of the fixed concentration procedure for acute inhalation toxicity assessment

The conventional method for the assessment of acute inhalation toxicity (OECD Test Guideline 403, 1981) uses death of animals as an endpoint to identify the median lethal concentration (LC50). A new OECD Testing Guideline called the Fixed Concentration Procedure (FCP) is being prepared to provide an alternative to Test Guideline 403. Unlike Test Guideline 403, the FCP does not provide a point estimate of the LC50, but aims to identify an airborne exposure level that causes clear signs of nonlethal toxicity. This is then used to assign classification according to the new Globally Harmonized System of Classification and Labelling scheme (GHS). The FCP has been validated using statistical simulation rather than byin vivo testing. The statistical simulation approach predicts the GHS classification outcome and the numbers of deaths and animals used in the test for imaginary substances with a range of LC50 values and dose response curve slopes. This paper describes the FCP and reports the results from the statistical simulation study assessing its properties. It is shown that the procedure will be completed with considerably less death and suffering than Test Guideline 403, and will classify substances either in the same or a more stringent GHS class than that assigned on the basis of the LC50 value.

A statistical evaluation of the fixed dose procedure

The fixed-dose procedure (FDP) was introduced as OECD Test Guideline 420 in 1992, as an alternative to the conventional median lethal dose (LD50) test for the assessment of acute oral toxicity (OECD Test Guideline 401). The FDP uses fewer animals and causes less suffering than the conventional test, while providing information on the acute toxicity to allow substances to be ranked according to the EU hazard classification system. Recently the FDP has been revised, with the aim of providing further reductions and refinements, and classification according to the criteria of the Globally Harmonized Hazard Classification and Labelling scheme (GHS). This paper describes the revised FDP and analyses its properties, as determined by a statistical modelling approach. The analysis shows that the revised FDP classifies substances for acute oral toxicity generally in the same, or a more stringent, hazard class as that based on the LD50 value, according to either the GHS or the EU classification scheme. The likelihood of achieving the same classification is greatest for substances with a steep dose-response curve and median toxic dose (TD50) close to the LD50. The revised FDP usually requires five or six animals with two or fewer dying as a result of treatment in most cases.

Statistical design and analysis of pharmacogenetic trials

Pharmacogenetic trials investigate the effect of genotype on treatment response. When there are two or more treatment groups and two or more genetic groups, investigation of gene-treatment interactions is of key interest. However, calculation of the power to detect such interactions is complicated because this depends not only on the treatment effect size within each genetic group, but also on the number of genetic groups, the size of each genetic group, and the type of genetic effect that is both present and tested for. The scale chosen to measure the magnitude of an interaction can also be problematic, especially for the binary case. Elston et al. proposed a test for detecting the presence of gene-treatment interactions for binary responses, and gave appropriate power calculations. This paper shows how the same approach can also be used for normally distributed responses. We also propose a method for analysing and performing sample size calculations based on a generalized linear model (GLM) approach. The power of the Elston et al. and GLM approaches are compared for the binary and normal case using several illustrative examples. While more sensitive to errors in model specification than the Elston et al. approach, the GLM approach is much more flexible and in many cases more powerful. Copyright © 2005 John Wiley & Sons, Ltd.

Statistical methods for ordered categorical data based on a constrained odds model

The proportional odds model provides a powerful tool for analysing ordered categorical data and setting sample size, although for many clinical trials its validity is questionable. The purpose of this paper is to present a new class of constrained odds models which includes the proportional odds model. The efficient score and Fisher's information are derived from the profile likelihood for the constrained odds model. These results are new even for the special case of proportional odds where the resulting statistics define the Mann-Whitney test. A strategy is described involving selecting one of these models in advance, requiring assumptions as strong as those underlying proportional odds, but allowing a choice of such models. The accuracy of the new procedure and its power are evaluated.