Revisiting proportion estimators

Proportion estimators are quite frequently used in many application areas. The conventional proportion estimator (number of events divided by sample size) encounters a number of problems when the data are sparse as will be demonstrated in various settings. The problem of estimating its variance when sample sizes become small is rarely addressed in a satisfying framework. Specifically, we have in mind applications like the weighted risk difference in multicenter trials or stratifying risk ratio estimators (to adjust for potential confounders) in epidemiological studies. It is suggested to estimate p using the parametric family (see PDF for character) and p(1 - p) using (see PDF for character), where (see PDF for character). We investigate the estimation problem of choosing c 0 from various perspectives including minimizing the average mean squared error of (see PDF for character), average bias and average mean squared error of (see PDF for character). The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be independent of n and equals c = 1. The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be dependent of n with limiting value c = 0.833. This might justifiy to use a near-optimal value of c = 1 in practice which also turns out to be beneficial when constructing confidence intervals of the form (see PDF for character).

Estimators in capture-recapture studies with two sources

This paper investigates the applications of capture-recapture methods to human populations. Capture-recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln-Petersen estimator and its modified version, the Chapman estimator, Chao's lower bound estimator, the Zelterman's estimator, McKendrick's moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao's estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao's and Chapman's estimator. Results indicate that Chao's estimator is less biased than Chapman's estimator unless both sources are independent. Chao's estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

Active-control trials with binary data: a comparison of methods for testing superiority or non-inferiority using the odds ratio

This paper considers methods for testing for superiority or non-inferiority in active-control trials with binary data, when the relative treatment effect is expressed as an odds ratio. Three asymptotic tests for the log-odds ratio based on the unconditional binary likelihood are presented, namely the likelihood ratio, Wald and score tests. All three tests can be implemented straightforwardly in standard statistical software packages, as can the corresponding confidence intervals. Simulations indicate that the three alternatives are similar in terms of the Type I error, with values close to the nominal level. However, when the non-inferiority margin becomes large, the score test slightly exceeds the nominal level. In general, the highest power is obtained from the score test, although all three tests are similar and the observed differences in power are not of practical importance. Copyright (C) 2007 John Wiley & Sons, Ltd.

Phyloclimatic modeling: Combining phylogenetics and bioclimatic modeling

We investigate the impact of past climates on plant diversification by tracking the "footprint" of climate change on a phylogenetic tree. Diversity within the cosmopolitan carnivorous plant genus Drosera (Droseraceae) is focused within Mediterranean climate regions. We explore whether this diversity is temporally linked to Mediterranean-type climatic shifts of the mid-Miocene and whether climate preferences are conservative over phylogenetic timescales. Phyloclimatic modeling combines environmental niche (bioclimatic) modeling with phylogenetics in order to study evolutionary patterns in relation to climate change. We present the largest and most complete such example to date using Drosera. The bioclimatic models of extant species demonstrate clear phylogenetic patterns; this is particularly evident for the tuberous sundews from southwestern Australia (subgenus Ergaleium). We employ a method for establishing confidence intervals of node ages on a phylogeny using replicates from a Bayesian phylogenetic analysis. This chronogram shows that many clades, including subgenus Ergaleium and section Bryastrum, diversified during the establishment of the Mediterranean-type climate. Ancestral reconstructions of bioclimatic models demonstrate a pattern of preference for this climate type within these groups. Ancestral bioclimatic models are projected into palaeo-climate reconstructions for the time periods indicated by the chronogram. We present two such examples that each generate plausible estimates of ancestral lineage distribution, which are similar to their current distributions. This is the first study to attempt bioclimatic projections on evolutionary time scales. The sundews appear to have diversified in response to local climate development. Some groups are specialized for Mediterranean climates, others show wide-ranging generalism. This demonstrates that Phyloclimatic modeling could be repeated for other plant groups and is fundamental to the understanding of evolutionary responses to climate change.

Comparative evaluation of a new effective population size estimator based on approximate Bayesian computation

We describe and evaluate a new estimator of the effective population size (N-e), a critical parameter in evolutionary and conservation biology. This new "SummStat" N-e. estimator is based upon the use of summary statistics in an approximate Bayesian computation framework to infer N-e. Simulations of a Wright-Fisher population with known N-e show that the SummStat estimator is useful across a realistic range of individuals and loci sampled, generations between samples, and N-e values. We also address the paucity of information about the relative performance of N-e estimators by comparing the SUMMStat estimator to two recently developed likelihood-based estimators and a traditional moment-based estimator. The SummStat estimator is the least biased of the four estimators compared. In 32 of 36 parameter combinations investigated rising initial allele frequencies drawn from a Dirichlet distribution, it has the lowest bias. The relative mean square error (RMSE) of the SummStat estimator was generally intermediate to the others. All of the estimators had RMSE > 1 when small samples (n = 20, five loci) were collected a generation apart. In contrast, when samples were separated by three or more generations and Ne less than or equal to 50, the SummStat and likelihood-based estimators all had greatly reduced RMSE. Under the conditions simulated, SummStat confidence intervals were more conservative than the likelihood-based estimators and more likely to include true N-e. The greatest strength of the SummStat estimator is its flexible structure. This flexibility allows it to incorporate any, potentially informative summary statistic from Population genetic data.

A comparison of the relative toxicity of bone meal and other P sources used as remedial treatments to the earthworm Eisenia fetida

It has been suggested that sources of P could be used to remediate metal-contaminated soil. The toxicity of four potential P sources, potassium hydrogen phosphate (PHP), triple superphosphate (TSP), rock phosphate (RP) and raw bone meal (RBM) to Eisenia fetida was determined. The concentration of P that is statistically likely to kill 50% of the population (LC50) for PHP, TSP and RBM was determined in OECD acute toxicity tests. 14 day LC50s expressed as bulk P concentration lay in the range 3319–4272 mg kg−1 for PHP, 3107–3590 mg kg−1 for TSP and 1782–2196 mg kg−1 for RBM (ranges present the 95% confidence intervals). For PHP and TSP mortality was significantly impacted by the electrical conductivity of the treated soils. No consistent relationship existed between mortality and electrical conductivity, soil pH and available (Olsen) P across the PHP, TSP and RBM amendment types. In RP toxicity tests mortality was low and it was not possible to determine a LC50 value. Incineration of bone meal at temperatures between 200 and 300 ◦C, pre-washing the bone meal, co-amendment with 5% green waste compost and delaying introduction of earthworms after bone meal amendments by 21 days or more led to significant reductions in the bone meal toxicity. These results are consistent with the toxicity being associated with the release and/or degradation of a soluble organic component present in raw bone meal. Bone meal can be used as an earthworm-friendly remedial amendment in metal-contaminated soils but initial additions may have a negative effect on any earthworms surviving in the contaminated soil before the organic component in the bone meal degrades in the soil.

The REFLEX project: Comparing different algorithms and implementations for the inversion of a terrestrial ecosystem model against eddy covariance data

We describe a model-data fusion (MDF) inter-comparison project (REFLEX), which compared various algorithms for estimating carbon (C) model parameters consistent with both measured carbon fluxes and states and a simple C model. Participants were provided with the model and with both synthetic net ecosystem exchange (NEE) of CO2 and leaf area index (LAI) data, generated from the model with added noise, and observed NEE and LAI data from two eddy covariance sites. Participants endeavoured to estimate model parameters and states consistent with the model for all cases over the two years for which data were provided, and generate predictions for one additional year without observations. Nine participants contributed results using Metropolis algorithms, Kalman filters and a genetic algorithm. For the synthetic data case, parameter estimates compared well with the true values. The results of the analyses indicated that parameters linked directly to gross primary production (GPP) and ecosystem respiration, such as those related to foliage allocation and turnover, or temperature sensitivity of heterotrophic respiration, were best constrained and characterised. Poorly estimated parameters were those related to the allocation to and turnover of fine root/wood pools. Estimates of confidence intervals varied among algorithms, but several algorithms successfully located the true values of annual fluxes from synthetic experiments within relatively narrow 90% confidence intervals, achieving >80% success rate and mean NEE confidence intervals <110 gC m−2 year−1 for the synthetic case. Annual C flux estimates generated by participants generally agreed with gap-filling approaches using half-hourly data. The estimation of ecosystem respiration and GPP through MDF agreed well with outputs from partitioning studies using half-hourly data. Confidence limits on annual NEE increased by an average of 88% in the prediction year compared to the previous year, when data were available. Confidence intervals on annual NEE increased by 30% when observed data were used instead of synthetic data, reflecting and quantifying the addition of model error. Finally, our analyses indicated that incorporating additional constraints, using data on C pools (wood, soil and fine roots) would help to reduce uncertainties for model parameters poorly served by eddy covariance data.

An improved methodology for the recovery of Zea mays and other large crop pollen, with implications for environmental archaeology in the Neotropics

We present a simple sieving methodology to aid the recovery of large cultigen pollen grains, such as maize (Zea mays L.), manioc (Manihot esculenta Crantz), and sweet potato (Ipomoea batatas L.), among others, for the detection of food production using fossil pollen analysis of lake sediments in the tropical Americas. The new methodology was tested on three large study lakes located next to known and/or excavated pre-Columbian archaeological sites in South and Central America. Five paired samples, one treated by sieving, the other prepared using standard methodology, were compared for each of the three sites. Using the new methodology, chemically digested sediment samples were passed through a 53 µm sieve, and the residue was retained, mounted in silicone oil, and counted for large cultigen pollen grains. The filtrate was mounted and analysed for pollen according to standard palynological procedures. Zea mays (L.) was recovered from the sediments of all three study lakes using the sieving technique, where no cultigen pollen had been previously recorded using the standard methodology. Confidence intervals demonstrate there is no significant difference in pollen assemblages between the sieved versus unsieved samples. Equal numbers of exotic Lycopodium spores added to both the filtrate and residue of the sieved samples allow for direct comparison of cultigen pollen abundance with the standard terrestrial pollen count. Our technique enables the isolation and rapid scanning for maize and other cultigen pollen in lake sediments, which, in conjunction with charcoal and pollen records, is key to determining land-use patterns and the environmental impact of pre-Columbian societies.

Simple uncertainty frameworks for selecting weighting schemes and interpreting multimodel ensemble climate change experiments

Future climate change projections are often derived from ensembles of simulations from multiple global circulation models using heuristic weighting schemes. This study provides a more rigorous justification for this by introducing a nested family of three simple analysis of variance frameworks. Statistical frameworks are essential in order to quantify the uncertainty associated with the estimate of the mean climate change response. The most general framework yields the “one model, one vote” weighting scheme often used in climate projection. However, a simpler additive framework is found to be preferable when the climate change response is not strongly model dependent. In such situations, the weighted multimodel mean may be interpreted as an estimate of the actual climate response, even in the presence of shared model biases. Statistical significance tests are derived to choose the most appropriate framework for specific multimodel ensemble data. The framework assumptions are explicit and can be checked using simple tests and graphical techniques. The frameworks can be used to test for evidence of nonzero climate response and to construct confidence intervals for the size of the response. The methodology is illustrated by application to North Atlantic storm track data from the Coupled Model Intercomparison Project phase 5 (CMIP5) multimodel ensemble. Despite large variations in the historical storm tracks, the cyclone frequency climate change response is not found to be model dependent over most of the region. This gives high confidence in the response estimates. Statistically significant decreases in cyclone frequency are found on the flanks of the North Atlantic storm track and in the Mediterranean basin.

Effect of polymorphisms in the PPARGC1A gene on body fat in Asian Indians

OBJECTIVE: To evaluate whether polymorphisms in the peroxisome proliferator-activated receptor-gamma coactivator-1 alpha (PPARGC1A) gene were related to body fat in Asian Indians. METHODS: Three polymorphisms of PPARGC1A gene, the Thr394Thr, Gly482Ser and +A2962G, were genotyped on 82 type 2 diabetic and 82 normal glucose tolerant (NGT) subjects randomly chosen from the Chennai Urban Rural Epidemiology Study using PCR-RFLP, and the nature of the variants were confirmed using direct sequencing. Linkage disequilibrium (LD) was estimated from the estimates of haplotypic frequencies using an expectation-maximization algorithm. Visceral, subcutaneous and total abdominal fat were measured using computed tomography, whereas dual X-ray absorptiometry was used to measure central abdominal and total body fat. RESULTS: None of the three polymorphisms studied were in LD. The genotype (0.59 vs 0.32, P=0.001) and allele (0.30 vs 0.17, P=0.007) frequencies of Thr394Thr polymorphism were significantly higher in type 2 diabetic subjects compared to those in NGT subjects. The odds ratio for diabetes (adjusted for age, sex and body mass index) for the susceptible genotype, XA (GA+AA) of Thr394Thr polymorphism, was 2.53 (95% confidence intervals: 1.30-5.04, P=0.009). Visceral and subcutaneous fat were significantly higher in NGT subjects with XA genotype of the Thr394Thr polymorphism compared to those with GG genotype (visceral fat: XA 148.2+/-46.9 vs GG 106.5+/-51.9 cm(2), P=0.001; subcutaneous fat: XA 271.8+/-167.1 vs GG 181.5+/-78.5 cm(2), P=0.001). Abdominal (XA 4521.9+/-1749.6 vs GG 3445.2+/-1443.4 g, P=0.004), central abdominal (XA 1689.0+/-524.0 vs GG 1228.5+/-438.7 g, P<0.0001) and non-abdominal fat (XA 18763.8+/-8789.4 vs GG 13160.4+/-4255.3 g, P<0.0001) were also significantly higher in the NGT subjects with XA genotype compared to those with GG genotype. The Gly482Ser and +A2962G polymorphisms were not associated with any of the body fat measures. CONCLUSION: Among Asian Indians, the Thr394Thr (G --> A) polymorphism is associated with increased total, visceral and subcutaneous body fat.

Peroxisome proliferator-activated receptor-gamma co-activator-1alpha (PGC-1alpha) gene polymorphisms and their relationship to Type 2 diabetes in Asian Indians

AIMS: The objective of the present investigation was to examine the relationship of three polymorphisms, Thr394Thr, Gly482Ser and +A2962G, of the peroxisome proliferator activated receptor-gamma co-activator-1 alpha (PGC-1alpha) gene with Type 2 diabetes in Asian Indians. METHODS: The study group comprised 515 Type 2 diabetic and 882 normal glucose tolerant subjects chosen from the Chennai Urban Rural Epidemiology Study, an ongoing population-based study in southern India. The three polymorphisms were genotyped using polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP). Haplotype frequencies were estimated using an expectation-maximization (EM) algorithm. Linkage disequilibrium was estimated from the estimates of haplotypic frequencies. RESULTS: The three polymorphisms studied were not in linkage disequilibrium. With respect to the Thr394Thr polymorphism, 20% of the Type 2 diabetic patients (103/515) had the GA genotype compared with 12% of the normal glucose tolerance (NGT) subjects (108/882) (P = 0.0004). The frequency of the A allele was also higher in Type 2 diabetic subjects (0.11) compared with NGT subjects (0.07) (P = 0.002). Regression analysis revealed the odds ratio for Type 2 diabetes for the susceptible genotype (XA) to be 1.683 (95% confidence intervals: 1.264-2.241, P = 0.0004). Age adjusted glycated haemoglobin (P = 0.003), serum cholesterol (P = 0.001) and low-density lipoprotein (LDL) cholesterol (P = 0.001) levels and systolic blood pressure (P = 0.001) were higher in the NGT subjects with the XA genotype compared with GG genotype. There were no differences in genotype or allelic distribution between the Type 2 diabetic and NGT subjects with respect to the Gly482Ser and +A2962G polymorphisms. CONCLUSIONS: The A allele of Thr394Thr (G --> A) polymorphism of the PGC-1 gene is associated with Type 2 diabetes in Asian Indian subjects and the XA genotype confers 1.6 times higher risk for Type 2 diabetes compared with the GG genotype in this population.

Associations between FTO genotype and total energy and macronutrients intake: a systematic review and meta-analysis

Risk variants of the fat-mass and obesity-associated (FTO) gene have been associated with increased obesity. However, the evidence for associations between FTO genotype and macronutrients intake has not been reviewed systematically. Our aim was to evaluate potential associations between FTO genotype and intakes of total energy, fat, carbohydrate and protein. We undertook a systematic literature search in Medline, Scopus, EMBASE and Cochrane of associations between macronutrients intake and FTO genotype in adults. Beta coefficients and confidence intervals were used for per-allele comparisons. Random-effects models assessed the pooled effect sizes. We identified 56 eligible studies reporting on 213 173 adults. For each copy of the FTO risk allele, individuals reported 6.46 kcal/day (95% CI: 10.76, 2.16) lower total energy intake (P=0.003). Total fat (P=0.028) and protein (P=0.006), but not carbohydrate intakes, were higher in those carrying the FTO risk allele. After adjustment for body weight, total energy intakes remained significantly lower in individuals with the FTO risk genotype (P=0.028). The FTO risk allele is associated with a lower reported total energy intake and with altered patterns of macronutrients intake. Although significant, these differences are small and further research is needed to determine whether the associations are independent of dietary misreporting.

Using high-frequency water quality data to assess sampling strategies for the EU Water Framework Directive

The EU Water Framework Directive (WFD) requires that the ecological and chemical status of water bodies in Europe should be assessed, and action taken where possible to ensure that at least "good" quality is attained in each case by 2015. This paper is concerned with the accuracy and precision with which chemical status in rivers can be measured given certain sampling strategies, and how this can be improved. High-frequency (hourly) chemical data from four rivers in southern England were subsampled to simulate different sampling strategies for four parameters used for WFD classification: dissolved phosphorus, dissolved oxygen, pH and water temperature. These data sub-sets were then used to calculate the WFD classification for each site. Monthly sampling was less precise than weekly sampling, but the effect on WFD classification depended on the closeness of the range of concentrations to the class boundaries. In some cases, monthly sampling for a year could result in the same water body being assigned to three or four of the WFD classes with 95% confidence, due to random sampling effects, whereas with weekly sampling this was one or two classes for the same cases. In the most extreme case, the same water body could have been assigned to any of the five WFD quality classes. Weekly sampling considerably reduces the uncertainties compared to monthly sampling. The width of the weekly sampled confidence intervals was about 33% that of the monthly for P species and pH, about 50% for dissolved oxygen, and about 67% for water temperature. For water temperature, which is assessed as the 98th percentile in the UK, monthly sampling biases the mean downwards by about 1 °C compared to the true value, due to problems of assessing high percentiles with limited data. Low-frequency measurements will generally be unsuitable for assessing standards expressed as high percentiles. Confining sampling to the working week compared to all 7 days made little difference, but a modest improvement in precision could be obtained by sampling at the same time of day within a 3 h time window, and this is recommended. For parameters with a strong diel variation, such as dissolved oxygen, the value obtained, and thus possibly the WFD classification, can depend markedly on when in the cycle the sample was taken. Specifying this in the sampling regime would be a straightforward way to improve precision, but there needs to be agreement about how best to characterise risk in different types of river. These results suggest that in some cases it will be difficult to assign accurate WFD chemical classes or to detect likely trends using current sampling regimes, even for these largely groundwater-fed rivers. A more critical approach to sampling is needed to ensure that management actions are appropriate and supported by data.

Is it significant? Guidelines for reporting BCI performance

Recent growth in brain-computer interface (BCI) research has increased pressure to report improved performance. However, different research groups report performance in different ways. Hence, it is essential that evaluation procedures are valid and reported in sufficient detail. In this chapter we give an overview of available performance measures such as classification accuracy, cohen’s kappa, information transfer rate (ITR), and written symbol rate. We show how to distinguish results from chance level using confidence intervals for accuracy or kappa. Furthermore, we point out common pitfalls when moving from offline to online analysis and provide a guide on how to conduct statistical tests on (BCI) results.

Meta-analysis to integrate effect sizes within a paper: Possible misuse and Type-1 error inflation

In recent years an increasing number of papers have employed meta-analysis to integrate effect sizes of researchers’ own series of studies within a single paper (“internal meta-analysis”). Although this approach has the obvious advantage of obtaining narrower confidence intervals, we show that it could inadvertently inflate false-positive rates if researchers are motivated to use internal meta-analysis in order to obtain a significant overall effect. Specifically, if one decides whether to stop or continue a further replication experiment depending on the significance of the results in an internal meta-analysis, false-positive rates would increase beyond the nominal level. We conducted a set of Monte-Carlo simulations to demonstrate our argument, and provided a literature review to gauge awareness and prevalence of this issue. Furthermore, we made several recommendations when using internal meta-analysis to make a judgment on statistical significance.