A default prior for regression coefficients

When the sample size is not too small, M-estimators of regression coefficients are approximately normal and unbiased. This leads to the familiar frequentist inference in terms of normality-based confidence intervals and p-values. From a Bayesian perspective, use of the (improper) uniform prior yields matching results in the sense that posterior quantiles agree with one-sided confidence bounds. For this, and various other reasons, the uniform prior is often considered objective or non-informative. In spite of this, we argue that the uniform prior is not suitable as a default prior for inference about a regression coefficient in the context of the bio-medical and social sciences. We propose that a more suitable default choice is the normal distribution with mean zero and standard deviation equal to the standard error of the M-estimator. We base this recommendation on two arguments. First, we show that this prior is non-informative for inference about the sign of the regression coefficient. Secondly, we show that this prior agrees well with a meta-analysis of 50 articles from the MEDLINE database

The statistical properties of RCTs and a proposal for shrinkage

We abstract the concept of a randomized controlled trial as a triple (β,b,s) , where β is the primary efficacy parameter, b the estimate, and s the standard error ( s>0 ). If the parameter β is either a difference of means, a log odds ratio or a log hazard ratio, then it is reasonable to assume that b is unbiased and normally distributed. This then allows us to estimate the joint distribution of the z-value z=b/s and the signal-to-noise ratio SNR=β/s from a sample of pairs (bi,si) . We have collected 23 551 such pairs from the Cochrane database. We note that there are many statistical quantities that depend on (β,b,s) only through the pair (z,SNR) . We start by determining the estimated distribution of the achieved power. In particular, we estimate the median achieved power to be only 13%. We also consider the exaggeration ratio which is the factor by which the magnitude of β is overestimated. We find that if the estimate is just significant at the 5% level, we would expect it to overestimate the true effect by a factor of 1.7. This exaggeration is sometimes referred to as the winner's curse and it is undoubtedly to a considerable extent responsible for disappointing replication results. For this reason, we believe it is important to shrink the unbiased estimator, and we propose a method for doing so. We show that our shrinkage estimator successfully addresses the exaggeration. As an example, we re-analyze the ANDROMEDA-SHOCK trial. Keywords: Cochrane review; achieved power; exaggeration; randomized controlled trial; type M error

Detecting DNA regulatory motifs by incorporating positional trends in information content

On the basis of the observation that conserved positions in transcription factor binding sites are often clustered together, we propose a simple extension to the model-based motif discovery methods. We assign position-specific prior distributions to the frequency parameters of the model, penalizing deviations from a specified conservation profile. Examples with both simulated and real data show that this extension helps discover motifs as the data become noisier or when there is a competing false motif

Measuring Traffic

A traffic performance measurement system, PeMS, currently functions as a statewide repository for traffic data gathered by thousands of automatic sensors. It has integrated data collection, processing and communications infrastructure with data storage and analytical tools. In this paper, we discuss statistical issues that have emerged as we attempt to process a data stream of 2 GB per day of wildly varying quality. In particular, we focus on detecting sensor malfunction, imputation of missing or bad data, estimation of velocity and forecasting of travel times on freeway networks.Comment: Published in at http://dx.doi.org/10.1214/07-STS238 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Effect of COVID vaccination on monthly migraine days:a longitudinal cohort study

BACKGROUND: This longitudinal cohort study aimed to investigate changes in migraine-related outcomes following COVID-19 infection and vaccination. METHODS: We identified 547 clinically diagnosed migraine patients from the Leiden Headache Center who kept a headache E-diary during the COVID-19 pandemic (February 2020 to August 2022). We sent a questionnaire to register their COVID-19 infection and/or vaccination dates. After applying inclusion criteria, n = 59 participants could be included in the infection analysis and n = 147 could be included in the vaccination analysis. Primary outcome was the change in monthly migraine days (MMD) between 1 month prior and 1 month post COVID-19 infection or vaccination. Secondary outcome variables were change in monthly headache days (MHD) and monthly acute medication days (MAMD). RESULTS:Vaccination against COVID-19 was associated with an increase in MMD (1.06; 95% confidence interval [CI] = 0.57-1.55; p &lt; 0.001), MHD (1.52; 95% CI = 0.91-2.14; p &lt; 0.001) and MAMD (0.72; 95% CI = 0.33-1.12; p &lt; 0.001) in the first month post-vaccination. COVID-19 infection solely increased the number of MAMD (1.11; 95% CI = 0.10-1.62; p &lt; 0.027), but no statistically significant differences in MMD or MHD were observed. CONCLUSIONS: Our findings imply that vaccination against COVID-19 is associated with an increase in migraine, indicating a possible role of inflammatory mediators in migraine pathophysiology.</p

Depression and treatment with anti-calcitonin gene related peptide (CGRP) (ligand or receptor) antibodies for migraine

Background and purpose: The aim was to evaluate the effect of anti-calcitonin gene related peptide (CGRP) (ligand or receptor) antibodies on depressive symptoms in subjects with migraine and to determine whether depressive symptoms predict treatment response. Methods: Patients with migraine treated with erenumab and fremanezumab at the Leiden Headache Centre completed daily E-headache diaries. A control group was included. Depressive symptoms were assessed using the Hospital Anxiety and Depression Scale (HADS) and the Center for Epidemiological Studies Depression Scale (CES-D) questionnaires at baseline (T0) and after 3 months (T1). First, the effect of treatment on the reduction in HADS-D and CES-D scores was assessed, with reduction in depression scores as the dependent variable and reduction in monthly migraine days (MMD) and treatment with anti-CGRP medication as independent variables. Second, depression as a predictor of treatment response was investigated, using the absolute reduction in MMD as a dependent variable and age, gender, MMD, active depression, impact, stress and locus of control scores as independent variables. Results: In total, n = 108 patients were treated with erenumab, n = 90 with fremanezumab and n = 68 were without active treatment. Treatment with anti-CGRP medication was positively associated with a reduction in the HADS-D (β = 1.65, p = 0.01) compared to control, independent of MMD reduction. However, the same effect was not found for the CES-D (β = 2.15, p = 0.21). Active depression predicted poorer response to erenumab (p = 0.02) but not to fremanezumab (p = 0.09). Conclusion: Anti-CGRP (ligand or receptor) monoclonals lead to improvement of depressive symptoms in individuals with migraine, independent of migraine reduction. Depression may predict treatment response to erenumab but not to fremanezumab.</p