Approximation of Bayesian predictive p-values with regression ABC

In the Bayesian framework a standard approach to model criticism is to compare some function of the observed data to a reference predictive distribution. The result of the comparison can be summarized in the form of a p-value, and it's well known that computation of some kinds of Bayesian predictive p-values can be challenging. The use of regression adjustment approximate Bayesian computation (ABC) methods is explored for this task. Two problems are considered. The first is the calibration of posterior predictive p-values so that they are uniformly distributed under some reference distribution for the data. Computation is difficult because the calibration process requires repeated approximation of the posterior for different data sets under the reference distribution. The second problem considered is approximation of distributions of prior predictive p-values for the purpose of choosing weakly informative priors in the case where the model checking statistic is expensive to compute. Here the computation is difficult because of the need to repeatedly sample from a prior predictive distribution for different values of a prior hyperparameter. In both these problems we argue that high accuracy in the computations is not required, which makes fast approximations such as regression adjustment ABC very useful. We illustrate our methods with several samples.

Bayesian P-splines with a multiplicative term in EMG trace data

A method is proposed to describe force or compound muscle action potential (CMAP) trace data collected in an electromyography study for motor unit number estimation (MUNE). Experimental data was collected using incre- mental stimulation at multiple durations. However, stimulus information, vital for alternate MUNE methods, is not comparable for multiple duration data and therefore previous methods of MUNE (Ridall et al., 2006, 2007) cannot be used with any reliability. Hypothesised ring combinations of motor units are mod- elled using a multiplicative factor and Bayesian P-spline formulation. The model describes the process for force and CMAP in a meaningful way.

Consistency errors in p-values reported in Spanish psychology journals

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Incongruence between test statistics and P values in medical papers

Given an observed test statistic and its degrees of freedom, one may compute the observed P value with most statistical packages. It is unknown to what extent test statistics and P values are congruent in published medical papers. Methods: We checked the congruence of statistical results reported in all the papers of volumes 409–412 of Nature (2001) and a random sample of 63 results from volumes 322–323 of BMJ (2001). We also tested whether the frequencies of the last digit of a sample of 610 test statistics deviated from a uniform distribution (i.e., equally probable digits).Results: 11.6% (21 of 181) and 11.1% (7 of 63) of the statistical results published in Nature and BMJ respectively during 2001 were incongruent, probably mostly due to rounding, transcription, or type-setting errors. At least one such error appeared in 38% and 25% of the papers of Nature and BMJ, respectively. In 12% of the cases, the significance level might change one or more orders of magnitude. The frequencies of the last digit of statistics deviated from the uniform distribution and suggested digit preference in rounding and reporting.Conclusions: this incongruence of test statistics and P values is another example that statistical practice is generally poor, even in the most renowned scientific journals, and that quality of papers should be more controlled and valued

Appropriateness of reporting statistical results in orthodontics: the dominance of P values over confidence intervals

The purpose of this study was to search the orthodontic literature and determine the frequency of reporting of confidence intervals (CIs) in orthodontic journals with an impact factor. The six latest issues of the American Journal of Orthodontics and Dentofacial Orthopedics, the European Journal of Orthodontics, and the Angle Orthodontist were hand searched and the reporting of CIs, P values, and implementation of univariate or multivariate statistical analyses were recorded. Additionally, studies were classified according to the type/design as cross-sectional, case-control, cohort, and clinical trials, and according to the subject of the study as growth/genetics, behaviour/psychology, diagnosis/treatment, and biomaterials/biomechanics. The data were analyzed using descriptive statistics followed by univariate examination of statistical associations, logistic regression, and multivariate modelling. CI reporting was very limited and was recorded in only 6 per cent of the included published studies. CI reporting was independent of journal, study area, and design. Studies that used multivariate statistical analyses had a higher probability of reporting CIs compared with those using univariate statistical analyses. Misunderstanding of the use of P values and CIs may have important implications in implementation of research findings in clinical practice.

Reporting of statistical results in prosthodontic and implantology journals: p values or confidence intervals?

PURPOSE Confidence intervals (CIs) are integral to the interpretation of the precision and clinical relevance of research findings. The aim of this study was to ascertain the frequency of reporting of CIs in leading prosthodontic and dental implantology journals and to explore possible factors associated with improved reporting. MATERIALS AND METHODS Thirty issues of nine journals in prosthodontics and implant dentistry were accessed, covering the years 2005 to 2012: The Journal of Prosthetic Dentistry, Journal of Oral Rehabilitation, The International Journal of Prosthodontics, The International Journal of Periodontics & Restorative Dentistry, Clinical Oral Implants Research, Clinical Implant Dentistry and Related Research, The International Journal of Oral & Maxillofacial Implants, Implant Dentistry, and Journal of Dentistry. Articles were screened and the reporting of CIs and P values recorded. Other information including study design, region of authorship, involvement of methodologists, and ethical approval was also obtained. Univariable and multivariable logistic regression was used to identify characteristics associated with reporting of CIs. RESULTS Interrater agreement for the data extraction performed was excellent (kappa = 0.88; 95% CI: 0.87 to 0.89). CI reporting was limited, with mean reporting across journals of 14%. CI reporting was associated with journal type, study design, and involvement of a methodologist or statistician. CONCLUSIONS Reporting of CI in implant dentistry and prosthodontic journals requires improvement. Improved reporting will aid appraisal of the clinical relevance of research findings by providing a range of values within which the effect size lies, thus giving the end user the opportunity to interpret the results in relation to clinical practice.

On the hydrophobicity of peptides:comparing empirical predictions of peptide log P values

Peptides are of great therapeutic potential as vaccines and drugs. Knowledge of physicochemical descriptors, including the partition coefficient logP, is useful for the development of predictive Quantitative Structure-Activity Relationships (QSARs). We have investigated the accuracy of available programs for the prediction of logP values for peptides with known experimental values obtained from the literature. Eight prediction programs were tested, of which seven programs were fragment-based methods: XLogP, LogKow, PLogP, ACDLogP, AlogP, Interactive Analysis's LogP and MlogP; and one program used a whole molecule approach: QikProp. The predictive accuracy of the programs was assessed using r(2) values, with ALogP being the most effective (r( 2) = 0.822) and MLogP the least (r(2) = 0.090). We also examined three distinct types of peptide structure: blocked, unblocked, and cyclic. For each study (all peptides, blocked, unblocked and cyclic peptides) the performance of programs rated from best to worse is as follows: all peptides - ALogP, QikProp, PLogP, XLogP, IALogP, LogKow, ACDLogP, and MlogP; blocked peptides - PLogP, XLogP, ACDLogP, IALogP, LogKow, QikProp, ALogP, and MLogP; unblocked peptides - QikProp, IALogP, ALogP, ACDLogP, MLogP, XLogP, LogKow and PLogP; cyclic peptides - LogKow, ALogP, XLogP, MLogP, QikProp, ACDLogP, IALogP. In summary, all programs gave better predictions for blocked peptides, while, in general, logP values for cyclic peptides were under-predicted and those of unblocked peptides were over-predicted.

Hypothesis test for changes in variance using a statistic based in P-values in a time series of normal independent observations.

The present work proposes a Hypothesis Test to detect a shift in the variance of a series of independent normal observations using a statistic based on the p-values of the F distribution. Since the probability distribution function of this statistic is intractable, critical values were we estimated numerically through extensive simulation. A regression approach was used to simplify the quantile evaluation and extrapolation. The power of the test was simulated using Monte Carlo simulation, and the results were compared with the Chen test (1997) to prove its efficiency. Time series analysts might find the test useful to address homoscedasticity studies were at most one change might be involved.

Bayesian versus frequentist statistical inference for investi gating a one-off cancer cluster reported to a health department

Background The problem of silent multiple comparisons is one of the most difficult statistical problems faced by scientists. It is a particular problem for investigating a one-off cancer cluster reported to a health department because any one of hundreds, or possibly thousands, of neighbourhoods, schools, or workplaces could have reported a cluster, which could have been for any one of several types of cancer or any one of several time periods. Methods This paper contrasts the frequentist approach with a Bayesian approach for dealing with silent multiple comparisons in the context of a one-off cluster reported to a health department. Two published cluster investigations were re-analysed using the Dunn-Sidak method to adjust frequentist p-values and confidence intervals for silent multiple comparisons. Bayesian methods were based on the Gamma distribution. Results Bayesian analysis with non-informative priors produced results similar to the frequentist analysis, and suggested that both clusters represented a statistical excess. In the frequentist framework, the statistical significance of both clusters was extremely sensitive to the number of silent multiple comparisons, which can only ever be a subjective "guesstimate". The Bayesian approach is also subjective: whether there is an apparent statistical excess depends on the specified prior. Conclusion In cluster investigations, the frequentist approach is just as subjective as the Bayesian approach, but the Bayesian approach is less ambitious in that it treats the analysis as a synthesis of data and personal judgements (possibly poor ones), rather than objective reality. Bayesian analysis is (arguably) a useful tool to support complicated decision-making, because it makes the uncertainty associated with silent multiple comparisons explicit.

Statistical hypothesis testing and common misinterpretations: should we abandon p-value in forensic science applications?

Many people regard the concept of hypothesis testing as fundamental to inferential statistics. Various schools of thought, in particular frequentist and Bayesian, have promoted radically different solutions for taking a decision about the plausibility of competing hypotheses. Comprehensive philosophical comparisons about their advantages and drawbacks are widely available and continue to span over large debates in the literature. More recently, controversial discussion was initiated by an editorial decision of a scientific journal [1] to refuse any paper submitted for publication containing null hypothesis testing procedures. Since the large majority of papers published in forensic journals propose the evaluation of statistical evidence based on the so called p-values, it is of interest to expose the discussion of this journal's decision within the forensic science community. This paper aims to provide forensic science researchers with a primer on the main concepts and their implications for making informed methodological choices.

Multiple testing in spatial epidemiology: a Bayesian approach

In this work we aim to propose a new approach for preliminary epidemiological studies on Standardized Mortality Ratios (SMR) collected in many spatial regions. A preliminary study on SMRs aims to formulate hypotheses to be investigated via individual epidemiological studies that avoid bias carried on by aggregated analyses. Starting from collecting disease counts and calculating expected disease counts by means of reference population disease rates, in each area an SMR is derived as the MLE under the Poisson assumption on each observation. Such estimators have high standard errors in small areas, i.e. where the expected count is low either because of the low population underlying the area or the rarity of the disease under study. Disease mapping models and other techniques for screening disease rates among the map aiming to detect anomalies and possible high-risk areas have been proposed in literature according to the classic and the Bayesian paradigm. Our proposal is approaching this issue by a decision-oriented method, which focus on multiple testing control, without however leaving the preliminary study perspective that an analysis on SMR indicators is asked to. We implement the control of the FDR, a quantity largely used to address multiple comparisons problems in the eld of microarray data analysis but which is not usually employed in disease mapping. Controlling the FDR means providing an estimate of the FDR for a set of rejected null hypotheses. The small areas issue arises diculties in applying traditional methods for FDR estimation, that are usually based only on the p-values knowledge (Benjamini and Hochberg, 1995; Storey, 2003). Tests evaluated by a traditional p-value provide weak power in small areas, where the expected number of disease cases is small. Moreover tests cannot be assumed as independent when spatial correlation between SMRs is expected, neither they are identical distributed when population underlying the map is heterogeneous. The Bayesian paradigm oers a way to overcome the inappropriateness of p-values based methods. Another peculiarity of the present work is to propose a hierarchical full Bayesian model for FDR estimation in testing many null hypothesis of absence of risk.We will use concepts of Bayesian models for disease mapping, referring in particular to the Besag York and Mollié model (1991) often used in practice for its exible prior assumption on the risks distribution across regions. The borrowing of strength between prior and likelihood typical of a hierarchical Bayesian model takes the advantage of evaluating a singular test (i.e. a test in a singular area) by means of all observations in the map under study, rather than just by means of the singular observation. This allows to improve the power test in small areas and addressing more appropriately the spatial correlation issue that suggests that relative risks are closer in spatially contiguous regions. The proposed model aims to estimate the FDR by means of the MCMC estimated posterior probabilities b i's of the null hypothesis (absence of risk) for each area. An estimate of the expected FDR conditional on data (\FDR) can be calculated in any set of b i's relative to areas declared at high-risk (where thenull hypothesis is rejected) by averaging the b i's themselves. The\FDR can be used to provide an easy decision rule for selecting high-risk areas, i.e. selecting as many as possible areas such that the\FDR is non-lower than a prexed value; we call them\FDR based decision (or selection) rules. The sensitivity and specicity of such rule depend on the accuracy of the FDR estimate, the over-estimation of FDR causing a loss of power and the under-estimation of FDR producing a loss of specicity. Moreover, our model has the interesting feature of still being able to provide an estimate of relative risk values as in the Besag York and Mollié model (1991). A simulation study to evaluate the model performance in FDR estimation accuracy, sensitivity and specificity of the decision rule, and goodness of estimation of relative risks, was set up. We chose a real map from which we generated several spatial scenarios whose counts of disease vary according to the spatial correlation degree, the size areas, the number of areas where the null hypothesis is true and the risk level in the latter areas. In summarizing simulation results we will always consider the FDR estimation in sets constituted by all b i's selected lower than a threshold t. We will show graphs of the\FDR and the true FDR (known by simulation) plotted against a threshold t to assess the FDR estimation. Varying the threshold we can learn which FDR values can be accurately estimated by the practitioner willing to apply the model (by the closeness between\FDR and true FDR). By plotting the calculated sensitivity and specicity (both known by simulation) vs the\FDR we can check the sensitivity and specicity of the corresponding\FDR based decision rules. For investigating the over-smoothing level of relative risk estimates we will compare box-plots of such estimates in high-risk areas (known by simulation), obtained by both our model and the classic Besag York Mollié model. All the summary tools are worked out for all simulated scenarios (in total 54 scenarios). Results show that FDR is well estimated (in the worst case we get an overestimation, hence a conservative FDR control) in small areas, low risk levels and spatially correlated risks scenarios, that are our primary aims. In such scenarios we have good estimates of the FDR for all values less or equal than 0.10. The sensitivity of\FDR based decision rules is generally low but specicity is high. In such scenario the use of\FDR = 0:05 or\FDR = 0:10 based selection rule can be suggested. In cases where the number of true alternative hypotheses (number of true high-risk areas) is small, also FDR = 0:15 values are well estimated, and \FDR = 0:15 based decision rules gains power maintaining an high specicity. On the other hand, in non-small areas and non-small risk level scenarios the FDR is under-estimated unless for very small values of it (much lower than 0.05); this resulting in a loss of specicity of a\FDR = 0:05 based decision rule. In such scenario\FDR = 0:05 or, even worse,\FDR = 0:1 based decision rules cannot be suggested because the true FDR is actually much higher. As regards the relative risk estimation, our model achieves almost the same results of the classic Besag York Molliè model. For this reason, our model is interesting for its ability to perform both the estimation of relative risk values and the FDR control, except for non-small areas and large risk level scenarios. A case of study is nally presented to show how the method can be used in epidemiology.