Equal-tailed Intervals Research Articles

Seroprevalence of human herpes viruses in France, 2018–2022: a multilevel regression and poststratification approach

Background Information related to herpes simplex virus 1 and 2 (HSV-1 and 2), varicella-zoster virus (VZV), Epstein-Barr virus (EBV), and cytomegalovirus (CMV) seroprevalence in France is either lacking, incomplete, or outdated, despite their public health burden. Method We used routinely collected serological data between 2018 and 2022 to estimate HSV-1, HSV-2, VZV, EBV, and CMV seroprevalence in France. To account for demographic differences between our analytic samples and the French population and get estimates for sparsely sampled districts and age classes, we used a multilevel regression and poststratification approach combined with Bayesian model averaging via stacking weights. Results The observed seroprevalence (number of positive tests/number of tests) were 64.6% (93,294/144,424), 16.9% (24,316/144,159), 93.0% (141,419/152,084), 83.4% (63,199/75, 781), and 49.0% (23,276/47,525), respectively, for HSV-1, HSV-2, VZV, EBV, and CMV. Between 2018 and 2022, France had a model-based average (equal-tailed interval at 95%) expected seroprevalence equal to 61.1% (60.7,61.5), 14.5% (14.2,14.81), 89.5% (89.3,89.8), 85.6% (85.2,86.0), and 50.5% (49.3,51.7), respectively, for HSV-1, HSV-2, VZV, EBV, and CMV infections. We found an almost certain lower expected seroprevalence in Metropolitan France than in overseas territories for all viruses but VZV, for which it was almost certainly greater. The expected seroprevalences were likely greater among females for all viruses. Limitations Our results relied on the assumption that individuals were sampled at random conditionally to variables used to build the poststratification table. Implications The analysis highlights spatial and demographic patterns in seroprevalence that should be considered for designing tailored public health policies.

Fifty-year forecasts of daily smoking prevalence: can Australia reach 5% by 2030?

ObjectiveTo compare 50-year forecasts of Australian tobacco smoking rates in relation to trends in smoking initiation and cessation and in relation to a national target of ≤5% adult daily prevalence...

Bayesian Simultaneous Credible Intervals for Effect Measures from Multiple Markers

Inference from multiple markers is often encountered in biomedical research, especially when comparing treatments. Most common statistical methods rely on hypothesis testing with null hypothesis of no effect for each marker and methods based on closed testing for getting the combined p-value. This article proposes the use of simultaneous credible intervals obtained from the joint posterior distribution of effect measures of multiple markers for combined inference. The advantage of this method is that it finds the actual effect sizes and also allows different types of effect measures for various markers. We used equal tailed intervals and highest posterior density regions for effect measures of multiple markers. Simulation studies were carried out to examine frequentist properties of these simultaneous credible regions. These studies revealed that the inference based on simultaneous intervals can be different than the inference based on individual marker. The method is demonstrated through two case studies: (a) an observational study of wet age-related macular degeneration (wet-AMD); and (b) reanalysis of a randomized controlled trial for treatment of migraine. The wet-AMD observational study was the motivation for the present research.

Scoring interval forecasts: Equal-tailed, shortest, and modal interval

We consider different types of predictive intervals and ask whether they are elicitable, that is, are unique minimizers of a loss or scoring function in expectation. The equal-tailed interval is elicitable, with a rich class of suitable loss functions, though subject to translation invariance, or positive homogeneity and differentiability, the Winkler interval score becomes a unique choice. The modal interval also is elicitable, with a sole consistent scoring function, up to equivalence. However, the shortest interval fails to be elicitable relative to practically relevant classes of distributions. These results provide guidance in interval forecast evaluation and support recent choices of performance measures in forecast competitions.

Predicting Upper Limb Motor Impairment Recovery after Stroke: A Mixture Model.

ObjectiveSpontaneous recovery is an important determinant of upper extremity recovery after stroke and has been described by the 70% proportional recovery rule for the Fugl–Meyer motor upper extremity (FM‐UE) scale. However, this rule is criticized for overestimating the predictability of FM‐UE recovery. Our objectives were to develop a longitudinal mixture model of FM‐UE recovery, identify FM‐UE recovery subgroups, and internally validate the model predictions.MethodsWe developed an exponential recovery function with the following parameters: subgroup assignment probability, proportional recovery coefficient , time constant in weeks , and distribution of the initial FM‐UE scores. We fitted the model to FM‐UE measurements of 412 first‐ever ischemic stroke patients and cross‐validated endpoint predictions and FM‐UE recovery cluster assignment.ResultsThe model distinguished 5 subgroups with different recovery parameters (, , , , , , , , , ). Endpoint FM‐UE was predicted with a median absolute error of 4.8 (interquartile range [IQR] = 1.3–12.8) at 1 week poststroke and 4.2 (IQR = 1.3–9.8) at 2 weeks. Overall accuracy of assignment to the poor (subgroup 1), moderate (subgroups 2 and 3), and good (subgroups 4 and 5) FM‐UE recovery clusters was 0.79 (95% equal‐tailed interval [ETI] = 0.78–0.80) at 1 week poststroke and 0.81 (95% ETI = 0.80–0.82) at 2 weeks.InterpretationFM‐UE recovery reflects different subgroups, each with its own recovery profile. Cross‐validation indicates that FM‐UE endpoints and FM‐UE recovery clusters can be well predicted. Results will contribute to the understanding of upper limb recovery patterns in the first 6 months after stroke. ANN NEUROL 2020;87:383–393 Ann Neurol 2020;87:383–393

Bootstrap confidence intervals for the contributions of individual variables to a Mahalanobis distance

ABSTRACTHotelling's and Mahalanobis distance are widely used in the statistical analysis of multivariate data. When either of these quantities is large, a natural question is: How do individual variables contribute to its size? The Garthwaite–Koch partition has been proposed as a means of assessing the contribution of each variable. This yields point estimates of each variable's contribution and here we consider bootstrap methods for forming interval estimates of these contributions. New bootstrap methods are proposed and compared with the percentile, bias-corrected percentile, non-studentized pivotal and studentized pivotal methods via a large simulation study. The new methods enable use of a broader range of pivotal quantities than with standard pivotal methods, including vector pivotal quantities. In the context considered here, this obviates the need for transformations and leads to intervals that have higher coverage, and yet are narrower, than intervals given by the standard pivotal methods. These results held both when the population distributions were multivariate normal and when they were skew with heavy tails. Both equal-tailed intervals and shortest intervals are constructed; the latter are particularly attractive when (as here) squared quantities are of interest.

Confidence distributions from likelihoods by median bias correction

By the modified directed likelihood, higher order accurate confidence limits for a scalar parameter are obtained from the likelihood. They are conveniently described in terms of a confidence distribution, that is a sample dependent distribution function on the parameter space. In this paper we explore a different route to accurate confidence limits via tail-symmetric confidence curves, that is curves that describe equal tailed intervals at any level. Instead of modifying the directed likelihood, we consider inversion of the log-likelihood ratio when evaluated at the median of the maximum likelihood estimator. This is shown to provide equal tailed intervals, and thus an exact confidence distribution, to the third-order of approximation in regular one-dimensional models. Median bias correction also provides an alternative approximation to the modified directed likelihood which holds up to the second order in exponential families.

Melanesian origin of Polynesian Y-chromosomes

In our recent Research Paper on the Melanesian origin of Polynesian Y-chromosomes, which appeared in the 19 October 2000 issue of Current Biology, we included published data on Y-chromosome haplotypes from the Cook Islands and coastal Papua New Guinea (Hurles et al., Am J Hum Genet 1998, 63:1793-1806). We have since been informed that the allelic designations for DYS19 in this paper are incorrect (Hurles et al., Am J Hum Genet, 2001, 68:298). We corrected and reanalyzed our data, with the result that three Polynesian Y-STR haplotypes from Hurles et al. (1998), all on the DYS390.3del/RPS4Y711T haplotype, are now identical to haplotypes observed in our sample of Polynesians. The number of DYS390.3del/RPS4Y711T Y-STR haplotypes is thus reduced from 39 to 36, and the demographic inferences (with associated 95% equal-tailed intervals) concerning this haplotype that were presented in Table 2 of the original paper should be as follows: initial effective population size in 1000 individuals, 0.31 (0.1; 0.97); population growth rate per generation × 10−3, 7.4 (1.0, 25.5); time of expansion in 1000 years, 4.25 (0.9; 15.6); time back to mrca in 1,000 years, 10.9 (4.7; 30.9). All references in the text to these particular demographic parameters should also be corrected. New versions of Figure 3a, Figure 4, Figure 5 are shown above. All other figures, tables, and analyses are not affected by this error, and none of our conclusions are altered.Figure 4Median-joining network of 36 Y-STR haplotypes from 75 individuals belonging to the DYS390.3del/RPS4Y711T haplotype. Circles, Y-STR haplotypes with the area proportional to the number of individuals; lines, mutation steps; parallel lines, identical mutations. Red haplotypes are from Polynesia, blue, from Melanesia, and yellow, from Indonesia. The scale bar indicates one mutationView Large Image Figure ViewerDownload Hi-res image Download (PPT)Figure 5Bayesian-based demographic data inferred from Y-STR variation associated with the DYS390.3del/RPS4Y711T haplotype (n = 75). Each panel shows the prior (dashed lines) and posterior (continuous lines) probability distribution of (a) the time of population expansion and (b) the time back to the mrca. Pr indicates probabilityView Large Image Figure ViewerDownload Hi-res image Download (PPT)

A Note on Shortest Prediction Intervals for Log-Linear Regression

In situations where the log transformation is used to make the assumptions of the ordinary linear regression model more reasonable, interval estimates for future observations are often desired in the scale of the original measurements. Common practice is to transfer the usual equal tail interval in the transformed scale back to the original scale. Conditions under which this procedure gives reasonably short intervals as compared with the shortest possible interval having the same content are derived, and a simple procedure that gives a reasonably short interval is suggested when it is not satisfactory. Primarily, a Bayesian point of view is taken.