Accounting for uncertainty in health economic decision models by using model averaging

Summary.  Health economic decision models are subject to considerable uncertainty, much of which arises from choices between several plausible model structures, e.g. choices of covariates in a regression model. Such structural uncertainty is rarely accounted for formally in decision models but can be addressed by model averaging. We discuss the most common methods of averaging models and the principles underlying them. We apply them to a comparison of two surgical techniques for repairing abdominal aortic aneurysms. In model averaging, competing models are usually either weighted by using an asymptotically consistent model assessment criterion, such as the Bayesian information criterion, or a measure of predictive ability, such as Akaike's information criterion. We argue that the predictive approach is more suitable when modelling the complex underlying processes of interest in health economics, such as individual disease progression and response to treatment.     

Autoregressive model selection based on a prediction perspective

The autoregressive (AR) model is a popular method for fitting and prediction in analyzing time-dependent data, where selecting an accurate model among considered orders is a crucial issue. Two commonly used selection criteria are the Akaike information criterion and the Bayesian information criterion. However, the two criteria are known to suffer potential problems regarding overfit and underfit, respectively. Therefore, using them would perform well in some situations, but poorly in others. In this paper, we propose a new criterion in terms of the prediction perspective based on the concept of generalized degrees of freedom for AR model selection. We derive an approximately unbiased estimator of mean-squared prediction errors based on a data perturbation technique for selecting the order parameter, where the estimation uncertainty involved in a modeling procedure is considered. Some numerical experiments are performed to illustrate the superiority of the proposed method over some commonly used order selection criteria. Finally, the methodology is applied to a real data example to predict the weekly rate of return on the stock price of Taiwan Semiconductor Manufacturing Company and the results indicate that the proposed method is satisfactory.     

Model selection and model averaging for semiparametric partially linear models with missing data

We study model selection and model averaging in semiparametric partially linear models with missing responses. An imputation method is used to estimate the linear regression coefficients and the nonparametric function. We show that the corresponding estimators of the linear regression coefficients are asymptotically normal. Then a focused information criterion and frequentist model average estimators are proposed and their theoretical properties are established. Simulation studies are performed to demonstrate the superiority of the proposed methods over the existing strategies in terms of mean squared error and coverage probability. Finally, the approach is applied to a real data case.     

Forecasting time series with missing data using Holt's model

This paper deals with the prediction of time series with missing data using an alternative formulation for Holt's model with additive errors. This formulation simplifies both the calculus of maximum likelihood estimators of all the unknowns in the model and the calculus of point forecasts. In the presence of missing data, the EM algorithm is used to obtain maximum likelihood estimates and point forecasts. Based on this application we propose a leave-one-out algorithm for the data transformation selection problem which allows us to analyse Holt's model with multiplicative errors. Some numerical results show the performance of these procedures for obtaining robust forecasts.     

Bayes model averaging with selection of regressors

Summary. When a number of distinct models contend for use in prediction, the choice of a single model can offer rather unstable predictions. In regression, stochastic search variable selection with Bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors. Here we look at Bayes model averaging incorporating variable selection for prediction. This offers similar mean-square errors of prediction but with a vastly reduced predictor space. This can greatly aid the interpretation of the model. It also reduces the cost if measured variables have costs. The development here uses decision theory in the context of the multivariate general linear model. In passing, this reduced predictor space Bayes model averaging is contrasted with single-model approximations. A fast algorithm for updating regressions in the Markov chain Monte Carlo searches for posterior inference is developed, allowing many more variables than observations to be contemplated. We discuss the merits of absolute rather than proportionate shrinkage in regression, especially when there are more variables than observations. The methodology is illustrated on a set of spectroscopic data used for measuring the amounts of different sugars in an aqueous solution.     

Adaptive order selection for autoregressive models

Autoregressive model is a popular method for analysing the time dependent data, where selection of order parameter is imperative. Two commonly used selection criteria are the Akaike information criterion (AIC) and the Bayesian information criterion (BIC), which are known to suffer the potential problems regarding overfit and underfit, respectively. To our knowledge, there does not exist a criterion in the literature that can satisfactorily perform under various situations. Therefore, in this paper, we focus on forecasting the future values of an observed time series and propose an adaptive idea to combine the advantages of AIC and BIC but to mitigate their weaknesses based on the concept of generalized degrees of freedom. Instead of applying a fixed criterion to select the order parameter, we propose an approximately unbiased estimator of mean squared prediction errors based on a data perturbation technique for fairly comparing between AIC and BIC. Then use the selected criterion to determine the final order parameter. Some numerical experiments are performed to show the superiority of the proposed method and a real data set of the retail price index of China from 1952 to 2008 is also applied for illustration.     

The performance of model averaged tail area confidence intervals

We investigate the exact coverage and expected length properties of the model averaged tail area (MATA) confidence interval proposed by Turek and Fletcher, CSDA, 2012, in the context of two nested, normal linear regression models. The simpler model is obtained by applying a single linear constraint on the regression parameter vector of the full model. For given length of response vector and nominal coverage of the MATA confidence interval, we consider all possible models of this type and all possible true parameter values, together with a wide class of design matrices and parameters of interest. Our results show that, while not ideal, MATA confidence intervals perform surprisingly well in our regression scenario, provided that we use the minimum weight within the class of weights that we consider on the simpler model.     

Time series forecasting with neural networks: a comparative study using the air line data

This case-study fits a variety of neural network (NN) models to the well-known air line data and compares the resulting forecasts with those obtained from the Box–Jenkins and Holt–Winters methods. Many potential problems in fitting NN models were revealed such as the possibility that the fitting routine may not converge or may converge to a local minimum. Moreover it was found that an NN model which fits well may give poor out-of-sample forecasts. Thus we think it is unwise to apply NN models blindly in 'black box' mode as has sometimes been suggested. Rather, the wise analyst needs to use traditional modelling skills to select a good NN model, e.g. to select appropriate lagged variables as the 'inputs'. The Bayesian information criterion is preferred to Akaike's information criterion for comparing different models. Methods of examining the response surface implied by an NN model are examined and compared with the results of alternative nonparametric procedures using generalized additive models and projection pursuit regression. The latter imposes less structure on the model and is arguably easier to understand.     

A model selection approach for the identification of quantitative trait loci in experimental crosses

Summary. We consider the problem of identifying the genetic loci (called quantitative trait loci (QTLs)) contributing to variation in a quantitative trait, with data on an experimental cross. A large number of different statistical approaches to this problem have been described; most make use of multiple tests of hypotheses, and many consider models allowing only a single QTL. We feel that the problem is best viewed as one of model selection. We discuss the use of model selection ideas to identify QTLs in experimental crosses. We focus on a back-cross experiment, with strictly additive QTLs, and concentrate on identifying QTLs, considering the estimation of their effects and precise locations of secondary importance. We present the results of a simulation study to compare the performances of the more prominent methods.