Bias-corrected Akaike Information Criterion Research Articles

Smoothing Lexis diagrams using kernel functions: A contemporary approach.

Lexis diagrams are rectangular arrays of event rates indexed by age and period. Analysis of Lexis diagrams is a cornerstone of cancer surveillance research. Typically, population-based descriptive studies analyze multiple Lexis diagrams defined by sex, tumor characteristics, race/ethnicity, geographic region, etc. Inevitably the amount of information per Lexis diminishes with increasing stratification. Several methods have been proposed to smooth observed Lexis diagrams up front to clarify salient patterns and improve summary estimates of averages, gradients, and trends. In this article, we develop a novel bivariate kernel-based smoother that incorporates two key innovations. First, for any given kernel, we calculate its singular values decomposition, and select an optimal truncation point-the number of leading singular vectors to retain-based on the bias-corrected Akaike information criterion. Second, we model-average over a panel of candidate kernels with diverse shapes and bandwidths. The truncated model averaging approach is fast, automatic, has excellent performance, and provides a variance-covariance matrix that takes model selection into account. We present an in-depth case study (invasive estrogen receptor-negative breast cancer incidence among non-Hispanic white women in the United States) and simulate operating characteristics for 20 representative cancers. The truncated model averaging approach consistently outperforms any fixed kernel. Our results support the routine use of the truncated model averaging approach in descriptive studies of cancer.

Comparing the structure-function relationship between the visual fields measured with variational Bayes linear regression and SITA standard.

We recently constructed an algorithm to measure visual field (VF) using the variational Bayes linear regression (VBLR). This algorithm enabled a faster VF measurement than the Swedish interactive thresholding algorithm (SITA) standard while maintaining the test-retest reproducibility (Murata H, et al. Br J Ophthalmol 2021). The current study aimed to compare the structure-function relationship between the SITA standard and VBLR. In 78 eyes of 56 patients with primary open-angle glaucoma, VF measurements were conducted using both SITA standard and VBLR VF, as well as spectral-domain optical coherence tomography. The structure-function relationship was investigated between visual sensitivity and circumpapillary retinal nerve fiber layer in the whole VF. This analysis was repeated for each of the 12 sectors (30 degrees). The strength of the structure-function relationship was evaluated using the second-order bias-corrected Akaike Information Criterion (AICc) index. In the whole VF, AICc values of SITA standard and VBLR were 601.6 and 597.3, respectively. The relative likelihood that VBLR had a better structure-function relationship than the SITA standard was 88.2% (when the entire field was averaged) or 99.9% (when all test points were analyzed in the pointwise manner). With the sector-wise analysis, SITA standard had a better structure-function relationship than VBLR in 1 sector (Superior sector in the retina), whereas VBLR had a better structure-function relationship than SITA standard in 4 sectors (Supero-Nasal, Infero-Nasal, Inferior, and Infero-Temporal sectors) with >95% relative likelihood. Although it depends on locations and similar between SITA standard and VBLR-VF, but VBLR-VF had a better structure-function relationship than the SITA standard overall.

Bi-exponential modelling of W^{^{prime}} reconstitution kinetics in trained cyclists

PurposeThe aim of this study was to investigate the individual W^{^{prime}} reconstitution kinetics of trained cyclists following repeated bouts of incremental ramp exercise, and to determine an optimal mathematical model to describe W^{^{prime}} reconstitution.MethodsTen trained cyclists (age 41 ± 10 years; mass 73.4 ± 9.9 kg; dot{V}{text{O}}_{2max } 58.6 ± 7.1 mL kg min−1) completed three incremental ramps (20 W min−1) to the limit of tolerance with varying recovery durations (15–360 s) on 5–9 occasions. W^{^{prime}} reconstitution was measured following the first and second recovery periods against which mono-exponential and bi-exponential models were compared with adjusted R2 and bias-corrected Akaike information criterion (AICc).ResultsA bi-exponential model outperformed the mono-exponential model of W^{^{prime}} reconstitution (AICc 30.2 versus 72.2), fitting group mean data well (adjR2 = 0.999) for the first recovery when optimised with parameters of fast component (FC) amplitude = 50.67%; slow component (SC) amplitude = 49.33%; time constant (τ)FC = 21.5 s; τSC = 388 s. Following the second recovery, W′ reconstitution reduced by 9.1 ± 7.3%, at 180 s and 8.2 ± 9.8% at 240 s resulting in an increase in the modelled τSC to 716 s with τFC unchanged. Individual bi-exponential models also fit well (adjR2 = 0.978 ± 0.017) with large individual parameter variations (FC amplitude 47.7 ± 17.8%; first recovery: (τ)FC = 22.0 ± 11.8 s; (τ)SC = 377 ± 100 s; second recovery: (τ)FC = 16.3.0 ± 6.6 s; (τ)SC = 549 ± 226 s).ConclusionsW′ reconstitution kinetics were best described by a bi-exponential model consisting of distinct fast and slow phases. The amplitudes of the FC and SC remained unchanged with repeated bouts, with a slowing of W′ reconstitution confined to an increase in the time constant of the slow component.

Enhancing capacity planning through forecasting: An integrated tool for maintenance of complex product systems

Despite the extensive amount of data generated and stored during the maintenance capacity planning process, Maintenance, Repair, and Overhaul (MRO) organizations have yet to explore their full potential in forecasting the required capacity to face future and unprecedented maintenance interventions. This paper explores the integration of time series forecasting capabilities in a tool for maintenance capacity planning of complex product systems (CoPS), intended to value data that is routinely generated and stored, but often disregarded by MROs. State space formulations with multiplicative errors for the simple exponential smoothing (SES), Holt’s linear method (HLM), additive Holt-Winters (AHW), and multiplicative Holt-Winters (MHW) are assessed using real data, comprised of 171 maintenance projects collected from a major Portuguese aircraft MRO. A state space formulation of the MHW, selected using the bias-corrected Akaike information criterion (AICc), is integrated in a Decision Support System (DSS) for capacity planning with probabilistic inference capabilities and used to forecast the workload probability distribution of a future and unprecedent maintenance intervention. The developed tool is validated by comparing forecasted values with workloads of a particular maintenance intervention and with a model simulating current forecasting practices employed by MROs.

MSGP-LASSO: An improved multi-stage genetic programming model for streamflow prediction

This paper presents the development and verification of a new multi-stage genetic programming (MSGP) technique, called MSGP-LASSO, which was applied for univariate streamflow forecasting in the Sedre River, an intermittent river in Turkey. The MSGP-LASSO is a practical and cost-neutral improvement over classic genetic programming (GP) that increases modelling accuracy, while decreasing its complexity by coupling the MSGP and multiple regression LASSO methods. The new model uses average mutual information to identify the optimum lags, and root mean-square technique to minimize forecasting error. Based on Nash-Sutcliffe efficiency and bias-corrected Akaike information criterion, MSGP-LASSO is superior to GP, multigene GP, MSGP, and hybrid MSGP-least-square models. It is explicit and promising for real-life applications.

Estimating Forest Productivity Using Site Characteristics, Multipoint Measures, and a Nonparametric Approach

Abstract Understanding the productivity of forestland is essential in sustainable management of forest ecosystems. The most common measure of site productivity is breast height–age site index (BHASI). BHASI has limitations as a productivity measure and can compound error in predictive models. We explored the accuracy of productivity predictions using an alternative productivity measure (10-meter site index) and a nonparametric approach. An orthogonal sampling design ensured samples were collected across the range of conditions known to influence Douglas-fir (Pseudotsuga menziesii var. glauca) height-growth rates. Using climate, soil, and topographic data along with 10-meter site index measurements, we compared five possible models to estimate forest productivity. Model parameters, performance, and predictions were compared. Twelve validation sites were used to test the accuracy of model predictions. Model performance was significantly improved when smoothing span values were optimized and elevation was added as a predictor. A four-predictor nonparametric model with a bias-corrected Akaike information criterion–optimized smoothing span value produced the most accurate results and was used to produce forest productivity maps for the study area. The low resolution of currently available climatic data and the complex nature of the study area landscape necessitate a topographic variable for accurate productivity predictions. Study Implications Defining and understanding forest productivity is of interest to a wide variety of natural resource professionals including ecologists, climate change experts, forest biometricians, and forest managers. A new method of defining forest productivity using multipoint height-age pairs at 10 and 20 meters and calculated growth rates combined with an appropriate landscape-scale stratification and a nonparametric approach provides accurate productivity estimates. This method is more widely applicable and more precise for specific locations than previous productivity estimation methods. Better productivity and tree growth information will provide more accurate estimates of future forest condition and structure.

Visualizing the dynamic change of Ocular Response Analyzer waveform using Variational Autoencoder in association with the peripapillary retinal arteries angle

The aim of the current study is to identify possible new Ocular Response Analyzer (ORA) waveform parameters related to changes of retinal structure/deformation, as measured by the peripapillary retinal arteries angle (PRAA), using a generative deep learning method of variational autoencoder (VAE). Fifty-four eyes of 52 subjects were enrolled. The PRAA was calculated from fundus photographs and was used to train a VAE model. By analyzing the ORA waveform reconstructed (noise filtered) using VAE, a novel ORA waveform parameter (Monot1-2), was introduced, representing the change in monotonicity between the first and second applanation peak of the waveform. The variables mostly related to the PRAA were identified from a set of 41 variables including age, axial length (AL), keratometry, ORA corneal hysteresis, ORA corneal resistant factor, 35 well established ORA waveform parameters, and Monot1-2, using a model selection method based on the second-order bias-corrected Akaike information criterion. The optimal model for PRAA was the AL and six ORA waveform parameters, including Monot1-2. This optimal model was significantly better than the model without Monot1-2 (p = 0.0031, ANOVA). The current study suggested the value of a generative deep learning approach in discovering new useful parameters that may have clinical relevance.

Association between optic nerve head morphology in open-angle glaucoma and corneal biomechanical parameters measured with Corvis ST.

To investigate associations between Corvis ST-measured corneal biomechanical parameters and glaucomatous optic nerve head (ONH) morphology. In total, 118 eyes of 70 patients with open-angle glaucoma were examined in this retrospective cross-sectional study. We measured Heidelberg retina tomograph and Corvis ST values in all eyes. We used the linear mixed model in four sectors (temporal superior, TS; temporal inferior, TI; nasal superior, NS; and nasal inferior, NI) to detect associations between six ONH-related parameters and 14 Corvis ST-related parameters, controlling for age, intraocular pressure, axial length, and central corneal thickness. We calculated the ONH temporal and nasal sector vertical asymmetries (TS-TI and NS-NI asymmetries) and identified the optimal linear mixed models to describe them using model selection with the second-order bias corrected Akaike Information Criterion. The Corvis ST A2 velocity was negatively associated with the rim volume in the NS sector (p < 0.05). The optimal model for TS-TI asymmetry was TS-TI asymmetry = - 3.22 + 0.15 × HC time + 0.88 × HC deflection amplitude, whereas that for NS-NI asymmetry was 0.49-0.048 × axial length - 2.45 × A2 velocity. Glaucomatous ONH superior-inferior asymmetries were associated with biomechanical properties measured with Corvis ST. Eyes with superior-dominant rim volume reduction of ONH were associated with small deformations and slow recovery of the cornea.

Correlation Between the Myopic Retinal Deformation and Corneal Biomechanical Characteristics Measured With the Corvis ST Tonometry.

PurposeWe previously reported that the retinal deformation due to myopia was represented by the peripapillary retinal arteries angle (PRAA). In this study, we investigated the relationship between the PRAA and biomechanical properties measured with Corvis ST (CST) tonometry.MethodsThirty-four normative eyes of 34 subjects who underwent CST measurement were enrolled. The PRAA was calculated from a fundus photograph. Variables related to the PRAA were identified from age, axial length, spherical equivalent refractive error, and 10 CST parameters using model selection with the second-order bias-corrected Akaike information criterion index.ResultsThe PRAA was best described with axial length (coefficient = −5.66, P < 0.0001), maximum deflection amplitude (mm; coefficient = 130.5, P = 0.0004), and deflection amplitude ratio (DA ratio) 2 mm (coefficient = −25.8, P = 0.0032), where mm was the amount of the maximum corneal apex movement and DA ratio 2 mm was the ratio between the deformation amplitudes at the apex and 2 mm away from the apex. The optimal model was significantly better than the model only with axial length (P = 0.0014, analysis of variance).ConclusionsThe PRAA was significantly better described with the CST parameters compared to the axial length model only; eyes with small PRAA (larger myopic retinal deformation) showed narrow and shallow maximum corneal deflection.Translational RelevanceThe Corvis ST parameters, which represents corneal biomechanical characteristics, were associated with myopic retinal deformation.

Relationship Between the Shift of the Retinal Artery Associated With Myopia and Ocular Response Analyzer Waveform Parameters.

PurposeWe have recently reported that the retinal stretch due to myopia is closely related to the peripapillary retinal arteries angle (PRAA) (Yamashita et al., Invest Ophthalmol Vis Sci 2013;54:5481–5488). The purpose of the current study was to investigate the relationship between retinal artery position and Ocular Response Analyzer (ORA) waveform parameters.MethodsIn 43 eyes of 41 healthy subjects, ORA measurements were carried out and the PRAA was calculated from fundus photographs. Then, the variables related to PRAA were identified from 40 variables of age, axial length (AL), keratometry, ORA corneal hysteresis (CH), ORA corneal resistant factor (CRF), and 35 ORA waveform parameters, using the Lasso regression and model selection with the second-order bias-corrected Akaike information criterion index.ResultsThe optimal model for PRAA included AL, CRF, and three ORA waveform parameters (aindex, w2, and slew1). This optimal model was significantly better than the model with AL-only, the model only with AL and CH, and the model only with AL and CRF (P < 0.0001, P < 0.0001, P < 0.0001, respectively; analysis of variance).ConclusionsThe PRAA was significantly better represented by using AL and ORA parameters including waveform parameters, compared with AL alone, with AL and CH alone, and with AL and CRF alone.Translational RelevanceORA waveform, which represents corneal biomechanical properties, was associated with myopic retinal stretch.

Development of a Novel Corneal Concavity Shape Parameter and Its Association with Glaucomatous Visual Field Progression

To develop a novel Corvis ST (Oculus Co. Ltd, Wetzlar, Germany) corneal concavity shape parameter (concavity shape index [CSI]) and investigate its association with glaucomatous visual field (VF) progression. Retrospective longitudinal study. A total of 103 eyes with primary open-angle glaucoma in 68 patients with 8 reliable VFs using the Humphrey Field Analyzer (HFA) (Carl Zeiss Meditec Inc, Dublin, CA). The mean total deviation (mTD) of the 52 test points in the 24-2 HFA test pattern was calculated for each VF, and the mTD progression rate was determined. A Corvis ST measurement was performed, and CSI was calculated as the ratio of (peak distance× curvature radius at the time of highest concavity [HC] state) to (the deflection amplitude at the time of HC× curvature radius at the undeformed state). The association between mTD progression rate and CSI, as well as other variables (including age, intraocular pressure, corneal hysteresis [CH], and 35 standard Corvis ST parameters), was investigated using the linear mixed model. The optimal linear mixed model to describe mTD progression rate was selected using the Random Forest method followed by variable selection using the second order bias corrected Akaike Information Criterion (AICc) index. Optimal linear mixed models for the mTD progression rate, as determined by AICc index. Univariate analysis revealed mTD progression rate was significantly associated with CSI (P=0.0042), CH, HC radius, A1 deflection length, max inverse radius, and integrated radius. The optimal model to describe mTD progression rate included CSI, max inverse radius, Ambrósio rational thickness horizontal, and age (AICc= 41.59). A novel corneal concavity shape parameter, CSI, was closely related to glaucomatous VF progression.

Correlation between elastic energy stored in an eye and visual field progression in glaucoma.

PurposeTo investigate whether the elastic energy stored in an eyeball at highest concavity (highest concavity energy; HCE), calculated with Corivs ST (CST, OCULUS), correlates with glaucomatous visual field (VF) progression.Methods108 eyes from 70 primary open angle-glaucoma patients were studied. The HCE was calculated using CST parameters. For each eye, the mean total deviation (mTD) of the 52 test points in the 24–2 Humphrey Field Analyzer test pattern was calculated and the mTD progression rate was determined from eight reliable VFs. Eyes were subdivided into: subgroups with low- or high-whole eye motion maximal length (WEM-d) and subgroups with short- or long-time taken to reach WEM-d (WEM-t), as measured with CST. The associations between mTD progression rate and HCE and other ocular/systemic parameters including age, Goldmann applanation tonometry based-intraocular pressure [GAT-IOP], and corneal hysteresis [CH] from the Ocular Response Analyzer (ORA®, Reichert) were investigated using the linear mixed model. The optimal model to describe mTD progression rate was selected from all possible combinations according to the second order bias corrected Akaike Information Criterion index.ResultsOptimal models to describe mTD progression rate included: CH in the model for all eyes, age and HCE in the model for the WEM-d low group, HCE in the model for the WEM-t short group, mean GAT-IOP in the model for the WEM-d high group, and age in the model for the WEM-t long-group.ConclusionsHCE was associated with glaucomatous VF progression in eyes with minimal whole eye motion (low WEM-d and WEM-t subgroups).

The Relationship between the Waveform Parameters from the Ocular Response Analyzer and the Progression of Glaucoma

To investigate the usefulness of waveform parameters measured with the Ocular Response Analyzer (Reichert Ophthalmic Instruments, Depew, NY) in assessing the progression of glaucomatous visual field (VF). Observational cross-sectional study. One hundred and one eyes with primary open-angle glaucoma in 68 patients with 8 reliable VFs using the Humphrey Field Analyzer (Carl Zeiss Meditec, Inc., Dublin, CA). The mean of total deviation (mTD) value of the 52 test points in the 24-2 Humphrey Field Analyzer VF test pattern was calculated, and the progression rate of mTD was determined using 8 VFs. Ocular Response Analyzer measurement was performed 3 times in the same day, and the average values of the 3 measurements were used in the analysis. Then, the optimal linear mixed model was selected using 7 parameters: age, mean and standard deviation of intraocular pressure with the Goldmann applanation tonometry during the observation period, central corneal thickness, axial length, mTD in the initial VF, and corneal hysteresis (CH) other than waveform parameters, henceforth known as the basic model. In addition, using the 37 waveform parameters, the optimal model for the mTD progression rate was identified, according to the second-order bias-corrected Akaike information criterion (AICc) index, using 15 preselected waveform parameters with the least absolute shrinkage and selection operator regression (henceforth known as the waveform model). Optimal linear mixed models for the mTD progression rate, as determined by AICc index. The mean ± standard deviation mTD progression rate was -0.25±0.31 dB/year. The basic model was mTD progression rate= -0.94+ 0.075× CH (AICc= 46.71). The waveform model was mTD progression rate= 1.25 - 0.066× path2 - 0.000099× p2area+ 0.0021× mslew2 (AICc= 44.95). The relative likelihood of the latter model being the optimal model was 6.23 times greater than that of the former model. Ocular Response Analyzer waveform parameters were correlated significantly with glaucomatous VF progression and showed a stronger than correlation with VF progression than CH.

Using CorvisST tonometry to assess glaucoma progression.

PurposeTo investigate the utility of the Corneal Visualization Scheimpflug Technology instrument (CST) to assess the progression of visual field (VF) damage in primary open angle glaucoma patients.MethodA total of 75 eyes from 111 patients with primary open-angle glaucoma were investigated. All patients underwent at least nine VF measurements with the Humphrey Field Analyzer, CST measurements, axial length (AL), central corneal thickness (CCT) and intraocular pressure (IOP) with Goldmann applanation tonometry (GAT). Mean total deviation (mTD) progression rates of the eight VFs, excluding the first VF, were calculated and the association between progression rate and the other listed measurements was analyzed using linear regression, and the optimal to describe mTD progression rate was selected based on the second order bias corrected Akaike Information Criterion (AICc) index.ResultsVF progression was described best in a model that included CST parameters as well as other ocular measurements. The optimal linear model to describe mTD progression rate was given by the equation: -8.9–0.068 x mean GAT + 0.68 x A1 time + 0.31 x A2 time -0.39 x A2 length– 1.26 x highest deformation amplitude.ConclusionCST measurements are useful when assessing VF progression in glaucoma patients. In particular, careful consideration should be given to patients where: (i) an eye is observed to be applanated fast in the first and second applanations, (ii) the applanated area is wide in the second applanation and (iii) the indentation is deep at the maximum deformation, since these eyes appear to be at greater risk of VF progression.

Toward a theory of energetically optimal body size in growing animals.

Our objective was to formulate a general and useful model of the energy economy of the growing animal. We developed a theory that the respiratory energy per unit of size reaches a minimum at a particular point, when the marginal respiratory heat production rate is equal to the average rate. This occurs at what we defined as the energetically optimal size for the animal. The relationship between heat production rate and size was found to be well described by a cubic function in which heat production rate accelerates as the animal approaches and then exceeds its optimal size. Reanalysis of energetics data from the literature often detected cubic curvature in the relationship between heat production rate and body size of fish, rats, chickens, goats, sheep, swine, cattle, and horses. This finding was consistent with the theory for 13 of 17 data sets. The bias-corrected Akaike information criterion indicated that the cubic equation modeled the influence of the size of a growing animal on its heat production rate better than a power function for 11 of 17 data sets. Changes in the sizes and specific heat production rates of metabolically active internal organs, and body composition and tissue turnover rates were found to explain notable portions of the expected increase in heat production rate as animals approached and then exceeded their energetically optimum size. Accelerating maintenance costs in this region decrease net energy available for productive functions. Energetically and economically optimum size criteria were also compared.

Local tumor control probability modeling of primary and secondary lung tumors in stereotactic body radiotherapy

Background and purposeTo evaluate whether local tumor control probability (TCP) in stereotactic body radiotherapy (SBRT) varies between lung metastases of different primary cancer sites and between primary non-small cell lung cancer (NSCLC) and secondary lung tumors. Materials and methodsA retrospective multi-institutional (n=22) database of 399 patients with stage I NSCLC and 397 patients with 525 lung metastases was analyzed. Irradiation doses were converted to biologically effective doses (BED). Logistic regression was used for local tumor control probability (TCP) modeling and the second-order bias corrected Akaike Information Criterion was used for model comparison. ResultsAfter median follow-up of 19months and 16months (n.s.), local tumor control was observed in 87.7% and 86.7% of the primary and secondary lung tumors (n.s.), respectively. A strong dose–response relationship was observed in the primary NSCLC and metastatic cohort but dose–response relationships were not significantly different: the TCD90 (dose to achieve 90% TCP; BED of maximum planning target volume dose) estimates were 176Gy (151–223) and 160Gy (123–237) (n.s.), respectively. The dose–response relationship was not influenced by the primary cancer site within the metastatic cohort. ConclusionsDose–response relationships for local tumor control in SBRT were not different between lung metastases of various primary cancer sites and between primary NSCLC and lung metastases.

Second-order bias-corrected AIC in multivariate normal linear models under non-normality

This paper deals with a bias correction of Akaike's information criterion (AIC) for selecting variables in multivariate normal linear regression models when the true distribution of observation is an unknown non-normal distribution. It is well known that the bias of AIC is , and there are a number of the first-order bias-corrected AICs which improve the bias to , where is the sample size. A new information criterion is proposed by slightly adjusting the first-order bias-corrected AIC. Although the adjustment is achieved by merely using constant coefficients, the bias of the new criterion is reduced to . Then, a variance of the new criterion is also improved. Through numerical experiments, we verify that our criterion is superior to others. The Canadian Journal of Statistics 39: 126–146; 2011 © 2011 Statistical Society of Canada Cet article traite de la correction du biais du critère d'information d'Akaike (AIC) lors de la sélection de variables dans des modèles de régression linéaires multidimensionnels normaux lorsque la vraie distribution des observations n'est pas connue, mais que nous savons qu'elle n'est pas normale. Il est bien connu que le biais de l'AIC est , et qu'il existe de nombreuses versions de l'AIC avec une correction de premier ordre pour le biais. Une fois corrigé, le biais est , où correspond la taille échantionnalle. Un nouveau critère d'information est proposé qui ajuste légèrement l'AIC avec une correction pour le biais de premier ordre. Même si cet ajustement est obtenu en utilisant des coefficients constants, le biais de ce nouveau critère est réduit . Par la suite, la variance du nouveau critère est aussi améliorée. À l'aide d'expériences numériques, nous vérifions que notre critère est supérieur aux autres. La revue canadienne de statistique 39: 126–146; 2011 © 2011 Société statistique du Canada

Time-Series Forecast Jointly Allowing the Unit-Root Detection and the Box–Cox Transformation

ABSTRACT An information-criterion-based model-selection method is presented for forecasting that allows for the unit-root detection and the Box–Cox transformation simultaneously. In this method, a battery of alternative models with and without unit root is considered changing the order of autoregressive process and the Box–Cox parameter, and the best model is selected using information criteria. Simulation results suggest that the Bayesian information criterion (BIC) outperforms the bias-corrected Akaike information criterion (AICc) and that the augmented Dickey–Fuller test performs worse in the case of incorrect data transformation. The results of forecasting quarterly time series of industrial production indicate that the BIC-based method outperforms the other conventional methods.

A new approach to correct the QT interval for changes in heart rate using a nonparametric regression model in beagle dogs

Introduction Over- and/or under-correction of QT intervals for changes in heart rate may lead to misleading conclusions and/or masking the potential of a drug to prolong the QT interval. This study examines a nonparametric regression model (Loess Smoother) to adjust the QT interval for differences in heart rate, with an improved fitness over a wide range of heart rates. Methods 240 sets of (QT, RR) observations collected from each of 8 conscious and non-treated beagle dogs were used as the materials for investigation. The fitness of the nonparametric regression model to the QT–RR relationship was compared with four models (individual linear regression, common linear regression, and Bazett's and Fridericia's correlation models) with reference to Akaike's Information Criterion (AIC). Residuals were visually assessed. Results The bias-corrected AIC of the nonparametric regression model was the best of the models examined in this study. Although the parametric models did not fit, the nonparametric regression model improved the fitting at both fast and slow heart rates. Discussion The nonparametric regression model is the more flexible method compared with the parametric method. The mathematical fit for linear regression models was unsatisfactory at both fast and slow heart rates, while the nonparametric regression model showed significant improvement at all heart rates in beagle dogs.

The weighted average information criterion for order selection in time series and regression models

We propose a consistent criterion for model order selection in the model identification phase of time series and regression, based on a weighted average of an asymptotically efficient selection criterion, AICC (bias-corrected Akaike information criterion) and a consistent selection criterion, BIC (Akaike's Bayesian modification of AIC). The weights attached to AICC and BIC are optimal choices from a natural class of possible weights, and are proportional to the model-complexity penalty term of AICC and BIC, respectively. Thus, the AICC part of the criterion receives most of the weight for small sample size n, and the BIC part receives the most weight for large n. It is shown that this weighted average criterion, WIC, is essentially equivalent to AICC for small n and to BIC for large n. An extensive simulation study comparing the performance of WIC with several popular criteria has been done. It clearly shows that WIC is a very reliable and practical criterion. In particular, for small n, WIC performs as well as AICC and outperforms other criteria, and for large n, WIC performs as well as BIC and outperforms other criteria. This demonstrates the overall strength of WIC.