Improved Prediction Intervals Research Articles

Ultrasound-based gestational-age estimation in late pregnancy.

ABSTRACTObjectiveAccurate gestational‐age (GA) estimation, preferably by ultrasound measurement of fetal crown–rump length before 14 weeks' gestation, is an important component of high‐quality antenatal care. The objective of this study was to determine how GA can best be estimated by fetal ultrasound for women who present for the first time late in pregnancy with uncertain or unknown menstrual dates.MethodsINTERGROWTH‐21st was a large, prospective, multicenter, population‐based project performed in eight geographically defined urban populations. One of its principal components, the Fetal Growth Longitudinal Study, aimed to develop international fetal growth standards. Each participant had their certain menstrual dates confirmed by first‐trimester ultrasound examination. Fetal head circumference (HC), biparietal diameter (BPD), occipitofrontal diameter (OFD), abdominal circumference (AC) and femur length (FL) were measured every 5 weeks from 14 weeks' gestation until delivery. For each participant, a single, randomly selected ultrasound examination was used to explore all candidate biometric variables and permutations to build models to predict GA. Regression equations were ranked based upon minimization of the mean prediction error, goodness of fit and model complexity. An automated machine learning algorithm, the Genetic Algorithm, was adapted to evaluate > 64 000 potential polynomial equations as predictors.ResultsOf the 4607 eligible women, 4321 (94%) had a pregnancy without major complications and delivered a live singleton without congenital malformations. After other exclusions (missing measurements in GA window and outliers), the final sample comprised 4229 women. Two skeletal measures, HC and FL, produced the best GA prediction, given by the equation loge(GA) = 0.03243 × (loge(HC))2 + 0.001644 × FL × loge(HC) + 3.813. When FL was not available, the best equation based on HC alone was loge(GA) = 0.05970 × (loge(HC))2 + 0.000000006409 × (HC)3 + 3.3258. The estimated uncertainty of GA prediction (half width 95% interval) was 6–7 days at 14 weeks' gestation, 12–14 days at 26 weeks' gestation and > 14 days in the third trimester. The addition of FL to the HC model led to improved prediction intervals compared with using HC alone, but no further improvement in prediction was afforded by adding AC, BPD or OFD. Equations that included other measurements (BPD, OFD and AC) did not perform better.ConclusionsAmong women initiating antenatal care late in pregnancy, a single set of ultrasound measurements combining HC and FL in the second trimester can be used to estimate GA with reasonable accuracy. We recommend this tool for underserved populations but considerable efforts should be implemented to improve early initiation of antenatal care worldwide. © 2016 Authors. Ultrasound in Obstetrics & Gynecology published by John Wiley & Sons Ltd on behalf of International Society of Ultrasound in Obstetrics and Gynecology.

Improved prediction intervals in heteroscedastic mixed-effects models

Prediction intervals are developed for the best linear unbiased predictor under heteroscedastic mixed models using the generalized pivotal quantity approach. The superiority of the proposed intervals, over widely used REML based intervals, is established via a simulation study.

Shorter nonparametric prediction intervals for an order statistic from a future sample

Abstract Standard nonparametric prediction intervals for a future order statistic are obtained by taking the interval between two order statistics of the initial sample. We obtain improved prediction intervals by taking the shortest of two or more standard intervals.

Model-free model-fitting and predictive distributions

The problem of prediction is revisited with a view towards going beyond the typical nonparametric setting and reaching a fully model-free environment for predictive inference, i.e., point predictors and predictive intervals. A basic principle of model-free prediction is laid out based on the notion of transforming a given setup into one that is easier to work with, namely i.i.d. or Gaussian. As an application, the problem of nonparametric regression is addressed in detail; the model-free predictors are worked out, and shown to be applicable under minimal assumptions. Interestingly, model-free prediction in regression is a totally automatic technique that does not necessitate the search for an optimal data transformation before model fitting. The resulting model-free predictive distributions and intervals are compared to their corresponding model-based analogs, and the use of cross-validation is extensively discussed. As an aside, improved prediction intervals in linear regression are also obtained.

Closed Form Prediction Intervals Applied for Disease Counts

The prediction interval is an important tool in medical applications for predicting the number of times a disease will occur in a population. The performance of the existing prediction intervals, however, is unsatisfactory when the true proportion is near a boundary. Since the true proportion can be very small in real applications, in this article, we propose improved prediction intervals with better coverage probability than the existing methods. Their predictive distributions are compared in terms of the Kullback–Leibler distance and the intervals are compared using a hearing screening medical example.

The asymptotic efficiency of improved prediction intervals

We consider the Barndorff-Nielsen and Cox (1994, p. 319) method of modifying an estimative prediction interval to obtain an improved prediction interval with better conditional coverage properties. The parameter estimator, on which this improved interval is based, is assumed to have the same asymptotic distribution as the conditional maximum likelihood estimator. This improved interval depends strongly on the asymptotic conditional bias of this estimator, which can be very sensitive to small changes in this estimator. We show, however, that the asymptotic efficiency of this improved prediction interval does not depend on this bias.

Improved Prediction Intervals and Distribution Functions

Abstract. The plug‐in solution is usually not entirely adequate for computing prediction intervals, as their coverage probability may differ substantially from the nominal value. Prediction intervals with improved coverage probability can be defined by adjusting the plug‐in ones, using rather complicated asymptotic procedures or suitable simulation techniques. Other approaches are based on the concept of predictive likelihood for a future random variable. The contribution of this paper is the definition of a relatively simple predictive distribution function giving improved prediction intervals. This distribution function is specified as a first‐order unbiased modification of the plug‐in predictive distribution function based on the constrained maximum likelihood estimator. Applications of the results to the Gaussian and the generalized extreme‐value distributions are presented.

A simple procedure for computing improved prediction intervals for autoregressive models

Abstract. This article concerns the construction of prediction intervals for time series models. The estimative or plug-in solution is usually not entirely adequate, since the (conditional) coverage probability may differ substantially from the nominal value. Prediction intervals with improved (conditional) coverage probability can be defined by adjusting the estimative ones, using rather complicated asymptotic procedures or suitable simulation techniques. This article extends to Markov process models a recent result by Vidoni, which defines a relatively simple predictive distribution function, giving improved prediction limits as quantiles. This new solution is fruitfully considered in the challenging context of prediction for time-series models, with particular regard to AR and ARCH processes.

Improved prediction intervals for stochastic process models

Abstract. This paper reviews some recent results on the construction of improved prediction limits for time series models and presents a simple solution based on a fully conditional approach. A prediction limit, expressed as a modification of the estimative one, is obtained so that its conditional and unconditional coverage probability equals the target value to third‐order accuracy. Although the specification of the ancillary statistic is not required, it respects the conditionality principle, to the relevant order of approximation. Moreover, the corresponding predictive density is specified in a relatively simple closed form. Simple examples show the usefulness of this conditional approach to prediction.

Prediction and calibration in generalized linear models

This paper concerns prediction and calibration in generalized linear models. A new predictive procedure, giving improved prediction intervals, is briefly reviewed and further theoretical results, useful for calculations, are presented. Indeed, the calibration problem is faced within the classical approach and a suitable solution is obtained by inverting the associated improved prediction procedure. This calibration technique gives accurate confidence regions and it constitutes a substantial improvement over both the estimative solution and the naive solution, which involves, even for non-linear and non-normal models, the results available for the linear Gaussian case. Finally, some useful explicit formulae for the construction of prediction and calibration intervals are presented, with regard to generalized linear models with alternative error terms and link functions.