Two-stage Predictor Research Articles

Bias in estimating the causal hazard ratio when using two-stage instrumental variable methods.

Two-stage instrumental variable methods are commonly used to estimate the causal effects of treatments on survival in the presence of measured and unmeasured confounding. Two-stage residual inclusion (2SRI) has been the method of choice over two-stage predictor substitution (2SPS) in clinical studies. We directly compare the bias in the causal hazard ratio estimated by these two methods. Under a principal stratification framework, we derive a closed-form solution for asymptotic bias of the causal hazard ratio among compliers for both the 2SPS and 2SRI methods when survival time follows the Weibull distribution with random censoring. When there is no unmeasured confounding and no always takers, our analytic results show that 2SRI is generally asymptotically unbiased, but 2SPS is not. However, when there is substantial unmeasured confounding, 2SPS performs better than 2SRI with respect to bias under certain scenarios. We use extensive simulation studies to confirm the analytic results from our closed-form solutions. We apply these two methods to prostate cancer treatment data from Surveillance, Epidemiology and End Results-Medicare and compare these 2SRI and 2SPS estimates with results from two published randomized trials.

MetaPSICOV: combining coevolution methods for accurate prediction of contacts and long range hydrogen bonding in proteins.

Motivation: Recent developments of statistical techniques to infer direct evolutionary couplings between residue pairs have rendered covariation-based contact prediction a viable means for accurate 3D modelling of proteins, with no information other than the sequence required. To extend the usefulness of contact prediction, we have designed a new meta-predictor (MetaPSICOV) which combines three distinct approaches for inferring covariation signals from multiple sequence alignments, considers a broad range of other sequence-derived features and, uniquely, a range of metrics which describe both the local and global quality of the input multiple sequence alignment. Finally, we use a two-stage predictor, where the second stage filters the output of the first stage. This two-stage predictor is additionally evaluated on its ability to accurately predict the long range network of hydrogen bonds, including correctly assigning the donor and acceptor residues.Results: Using the original PSICOV benchmark set of 150 protein families, MetaPSICOV achieves a mean precision of 0.54 for top-L predicted long range contacts—around 60% higher than PSICOV, and around 40% better than CCMpred. In de novo protein structure prediction using FRAGFOLD, MetaPSICOV is able to improve the TM-scores of models by a median of 0.05 compared with PSICOV. Lastly, for predicting long range hydrogen bonding, MetaPSICOV-HB achieves a precision of 0.69 for the top-L/10 hydrogen bonds compared with just 0.26 for the baseline MetaPSICOV.Availability and implementation: MetaPSICOV is available as a freely available web server at http://bioinf.cs.ucl.ac.uk/MetaPSICOV. Raw data (predicted contact lists and 3D models) and source code can be downloaded from http://bioinf.cs.ucl.ac.uk/downloads/MetaPSICOV.Contact: d.t.jones@ucl.ac.ukSupplementary information: Supplementary data are available at Bioinformatics online.

MULTI SCALE TIME SERIES PREDICTION FOR INTRUSION DETECTION

We propose an anomaly-based network intrusion detection system, which analyzes traffic features to det ect anomalies. The proposed system can be used both in online as well as off-line mode for detecting devia tions from the expected behavior. Although our approach uses network packet or flow data, it is general enou gh to be adaptable for use with any other network vari able, which may be used as a signal for anomaly detection. It differs from most existing approaches in its use of wavelet transform for generating dif ferent time scales for a signal and using these scales as an input to a two-stage neural network predictor. T he predictor predicts the expected signal value and la bels considerable deviations from this value as anomalies. The primary contribution of our work would be to empirically evaluate the effectiveness of multi resolution analysis as an input to neural net work prediction engine specifically for the purpose of intrusion detection. The role of Intrusion Detectio n Systems (IDSs), as special-purpose devices to detect anomalies and attacks in a network, is becom ing more important. First, anomaly-based methods cannot achieve an outstanding performance without a comprehensive labeled and up-to-date training set with all different attack types, which is very costly and time-consuming to create if not impossib le. Second, efficient and effective fusion of several d etection technologies becomes a big challenge for building an operational hybrid intrusion detection system. Keyword: Anomaly Detection, Two-Stage Neural Network Predictor, Multi-Resolution Analysis

Simulation study of instrumental variable approaches with an application to a study of the antidiabetic effect of bezafibrate

We studied the application of the generalized structural mean model (GSMM) of instrumental variable (IV) methods in estimating treatment odds ratios (ORs) for binary outcomes in pharmacoepidemiologic studies and evaluated the bias of GSMM compared to other IV methods. Because of the bias of standard IV methods, including two-stage predictor substitution (2SPS) and two-stage residual inclusion (2SRI) with binary outcomes, we implemented another IV approach based on the GSMM of Vansteelandt and Goetghebeur. We performed simulations under the principal stratification setting and evaluated whether GSMM provides approximately unbiased estimates of the causal OR and compared its bias and mean squared error to that of 2SPS and 2SRI. We then applied different IV methods to a study comparing bezafibrate versus other fibrates on the risk of diabetes. Our simulations showed that unlike the standard logistic, 2SPS, and 2SRI procedures, our implementation of GSMM provides an approximately unbiased estimate of the causal OR even under unmeasured confounding. However, for the effect of bezafibrate versus other fibrates on the risk of diabetes, the GSMM and two-stage approaches yielded similarly attenuated and statistically non-significant OR estimates. The attenuation of the OR by the two-stage and GSMM IV approaches suggests unmeasured confounding, although violations of the IV assumptions or differences in the parameters estimated could be playing a role. The GSMM IV approach provides approximately unbiased adjustment for unmeasured confounding on binary outcomes when a valid IV is available.

Large-eddy simulation of natural convection in an asymmetrically-heated vertical parallel-plate channel: Assessment of subgrid-scale models

The performance of four different large-eddy simulation subgrid-scale models has been examined a posteriori for natural convection in an asymmetrically-heated vertical parallel-plate channel with a high aspect ratio. The compressible three-dimensional Favre-filtered mass, momentum and energy conservation equations have been closed using the Smagorinsky, dynamic, approximate localised dynamic and Vreman models. A two-stage predictor–corrector numerical methodology for low-Mach-number compressible flows was adopted to strongly couple the density with the Navier–Stokes equations. Based on the comparison with experimental data, it has been shown that the Smagorinsky model predicts inaccurate near-wall flow dynamics and delayed transitional behaviour while both dynamic procedures to compute the Smagorinsky model coefficient result in over prediction of wall temperatures, suggesting an under estimation of subgrid-scale dissipation. The time extrapolation procedure utilised in the approximate localised dynamic model has been shown to produce better adaptation towards the local flow behaviour when compared with the standard dynamic model. At the same time, time-averaged wall temperature and velocity field profiles have been well captured by the Vreman model, demonstrating its superiority when compared to the rest of the models.

Estimating cost‐offsets of new medications: Use of new antipsychotics and mental health costs for schizophrenia

Estimation of the effect of one treatment compared to another in the absence of randomization is a common problem in biostatistics. An increasingly popular approach involves instrumental variables—variables that are predictive of who received a treatment yet not directly predictive of the outcome. When treatment is binary, many estimators have been proposed: method-of-moments estimators using a two-stage least-squares procedure, generalized-method-of-moments estimators using two-stage predictor substitution or two-stage residual inclusion procedures, and likelihood-based latent variable approaches. The critical assumptions to the consistency of two-stage procedures and of the likelihood-based procedures differ. Because neither set of assumptions can be completely tested from the observed data alone, comparing the results from the different approaches is an important sensitivity analysis. We provide a general statistical framework for estimation of the casual effect of a binary treatment on a continuous outcome using simultaneous equations to specify models. A comparison of health care costs for adults with schizophrenia treated with newer atypical antipsychotics and those treated with conventional antipsychotic medications illustrates our methods. Surprisingly large differences in the results among the methods are investigated using a simulation study. Several new findings concerning the performance in terms of precision and robustness of each approach in different situations are obtained. We illustrate that in general supplemental information is needed to determine which analysis, if any, is trustworthy and reaffirm that comparing results from different approaches is a valuable sensitivity analysis. Copyright © 2011 John Wiley & Sons, Ltd.

Two‐stage instrumental variable methods for estimating the causal odds ratio: Analysis of bias

We present closed-form expressions of asymptotic bias for the causal odds ratio from two estimation approaches of instrumental variable logistic regression: (i) the two-stage predictor substitution (2SPS) method and (ii) the two-stage residual inclusion (2SRI) approach. Under the 2SPS approach, the first stage model yields the predicted value of treatment as a function of an instrument and covariates, and in the second stage model for the outcome, this predicted value replaces the observed value of treatment as a covariate. Under the 2SRI approach, the first stage is the same, but the residual term of the first stage regression is included in the second stage regression, retaining the observed treatment as a covariate. Our bias assessment is for a different context from that of Terza (J. Health Econ. 2008; 27(3):531-543), who focused on the causal odds ratio conditional on the unmeasured confounder, whereas we focus on the causal odds ratio among compliers under the principal stratification framework. Our closed-form bias results show that the 2SPS logistic regression generates asymptotically biased estimates of this causal odds ratio when there is no unmeasured confounding and that this bias increases with increasing unmeasured confounding. The 2SRI logistic regression is asymptotically unbiased when there is no unmeasured confounding, but when there is unmeasured confounding, there is bias and it increases with increasing unmeasured confounding. The closed-form bias results provide guidance for using these IV logistic regression methods. Our simulation results are consistent with our closed-form analytic results under different combinations of parameter settings.

An Efficient Lossless Compression Scheme for Hyperspectral Images Using Two-Stage Prediction

In this letter, an efficient lossless compression scheme for hyperspectral images is presented. The proposed scheme uses a two-stage predictor. The stage-1 predictor takes advantage of spatial data correlation and formulates the derivation of a spectral domain predictor as a process of Wiener filtering. The stage-2 predictor takes the prediction from the stage-1 predictor as an initial value and conducts a backward pixel search (BPS) scheme on the current band for the final prediction value. Experimental results show that the BPS scheme, aimed at exploiting calibration-induced data correlation, is effective on Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) 1997 images where such artifacts are significant. The proposed work outperforms all other schemes under comparison in this category. For the newer Consultative Committee for Space Data Systems images where calibration-induced artifacts are minimized, the BPS scheme does not help, and the stage-1 predictor alone achieves better compression performance.

On efficient multistep non-linear time series prediction in chaotic diode resonator circuits by optimizing the combination of non-linear time series analysis and neural networks

An improved novel non-linear time series prediction method is presented based on optimizing the combination of non-linear signal analysis and deterministic chaos techniques with Artificial Neural Networks of the Multilayer Perceptron (MLP) type. The proposed methodology has been applied to the non-linear time series produced by a diode resonator chaotic circuit. Multisim is used to simulate the circuit and show the presence of chaos. The first stage of the proposed approach employs a non-linear time series analysis module applying the method proposed by Grasberger and Procaccia, involving estimation of the correlation and minimum embedding dimension as well as of the corresponding largest Lyapunov exponent in combination with a nearest neighbour-based non-linear signal predictor. The two previously mentioned modules are used to construct the first stage of a one-step/multistep predictor while a back-propagation MLP is involved in the second stage to enhance prediction results. The novelty of the proposed two-stage predictor lies on that the back-propagation MLP is employed as an error predictor of the nearest neighbour-based first-stage non-linear signal forecasting application following an efficient strategy for optimizing the combination of nearest neighbour prediction based on deterministic chaos techniques and MLP neural networks. This novel two-stage predictor is evaluated through an extensive experimental study and is favourably compared with rival approaches.

Two-stage residual inclusion estimation: Addressing endogeneity in health econometric modeling

The paper focuses on two estimation methods that have been widely used to address endogeneity in empirical research in health economics and health services research— two-stage predictor substitution (2SPS) and two-stage residual inclusion (2SRI). 2SPS is the rote extension (to nonlinear models) of the popular linear two-stage least squares estimator. The 2SRI estimator is similar except that in the second-stage regression, the endogenous variables are not replaced by first-stage predictors. Instead, first-stage residuals are included as additional regressors. In a generic parametric framework, we show that 2SRI is consistent and 2SPS is not. Results from a simulation study and an illustrative example also recommend against 2SPS and favor 2SRI. Our findings are important given that there are many prominent examples of the application of inconsistent 2SPS in the recent literature. This study can be used as a guide by future researchers in health economics who are confronted with endogeneity in their empirical work.

On MSE of EBLUP

We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976. Żadlo (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp 2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate to terms o(D−1) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D−1) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE and estimators of its MSE and their performance in Monte Carlo simulation study.

Quantitation of Promoter Methylation of Multiple Genes in Urine DNA and Bladder Cancer Detection

The noninvasive identification of bladder tumors may improve disease control and prevent disease progression. Aberrant promoter methylation (i.e., hypermethylation) is a major mechanism for silencing tumor suppressor genes and other cancer-associated genes in many human cancers, including bladder cancer. A quantitative fluorogenic real-time polymerase chain reaction (PCR) assay was used to examine primary tumor DNA and urine sediment DNA from 15 patients with bladder cancer and 25 control subjects for promoter hypermethylation of nine genes (APC, ARF, CDH1, GSTP1, MGMT, CDKN2A, RARbeta2, RASSF1A, and TIMP3) to identify potential biomarkers for bladder cancer. We then used these markers to examine urine sediment DNA samples from an additional 160 patients with bladder cancers of various stages and grades and from an additional 69 age-matched control subjects. Data were analyzed on the basis of a prediction model and were internally validated using a jacknife procedure. All statistical tests were two-sided. For all 15 patients with paired DNA samples, the promoter methylation pattern in urine matched that in the primary tumors. Four genes displayed 100% specificity. Of the 175 bladder cancer patients, 121 (69%, 95% confidence interval [CI] = 62% to 76%) displayed promoter methylation in at least one of these genes (CDKN2A, ARF, MGMT, and GSTP1), whereas all control subjects were negative for such methylation (100% specificity, 95% CI = 96% to 100%). A logistic prediction model using the methylation levels of all remaining five genes was developed and internally validated for subjects who were negative on the four-gene panel. This combined, two-stage predictor produced an internally validated ROC curve with an overall sensitivity of 82% (95% CI = 75 % to 87%) and specificity of 96% (95% CI = 90% to 99%). Testing a small panel of genes with the quantitative methylation-specific PCR assay in urine sediment DNA is a powerful noninvasive approach for the detection of bladder cancer. Larger independent confirmatory cohorts with longitudinal follow-up will be required in future studies to define the impact of this technology on early detection, prognosis, and disease monitoring before clinical application.

Mean squared error of empirical predictor

The term ``empirical predictor'' refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML estimators are used for the second stage. We obtain second-order approximation to the MSE as well as an estimator of the MSE correct to the same order. The general results are applied to mixed linear models to obtain a second-order approximation to the MSE of the empirical best linear unbiased predictor (EBLUP) of a linear mixed effect and an estimator of the MSE of EBLUP whose bias is correct to second order. The general mixed linear model includes the mixed ANOVA model and the longitudinal model as special cases.

Prediction in a class of mixed models with two variance components

Abstract A best unbiased predictor (BUP) of an arbitrary linear combination of fixed and random effects in mixed linear models is available when the true values of the variance ratios are known. When the true values are unknown, a two-stage predictor, obtained from the BUP by replacing the true values by estimated values, can be used. In this article, exact mean squared errors of two-stage predictors are obtained for a class of mixed models with two variance components that includes the balanced one-way random model and other analysis-of-variance models with proportional frequencies and one balanced random factor.

Comparisons of Alternative Predictors under the Balanced One-Way Random Model

Abstract Prediction of an arbitrary linear combination of the random effects of a balanced one-way random model is investigated. Alternative two-stage predictors are compared on the basis of their conditional (on the random effects) and unconditional bias and mean squared errors. When the true value of the ratio of expected mean squares is known, there exists a best linear unbiased predictor (BLUP). When the true value is unknown, a two-stage predictor, obtained from the BLUP by replacing the true value with an estimated value, can be used. When the ratio of expected mean squares is estimated by maximum likelihood, Bayesian methods, or various related methods, a two-stage predictor is obtained whose properties compare favorably with, for example, those of the least squares predictor and the positive-part James—Stein predictor.

Self-tuning predictors with application to river flow prediction

The paper presents developments of recursive self-adaptive prediction algorithms, called ‘self-tuning predictors’, using some common estimation techniques, and their application to prediction of flow discharge of the river Tigris at Baghdad, Iraq. Four kinds of predictors, viz the least-square predictor, the minimum-variance predictor, a predictor using stochastic approximation, and a two-stage predictor, have been developed. Using available data for the River Tigris, prediction results have been obtained for the average daily discharge, the average monthly discharge and the average yearly discharge. In each type of prediction a number of models have been tried. The various prediction results are presented in graphical and in tabular forms for comparison.

A two-stage pole-zero predictor

A two-stage pole-zero predictor is proposed which is capable of predicting minimum phase Auto Regressive Moving Average (ARMA) processes accurately with a reduced number of parameters. This is achieved by cascading the classical predictor (lst stage), and the pole-zero recursive-like structure (2nd stage). The constraint on the order of the first stage is relaxed since the unknown process is actually represented by the parameters of the second stage. Computer simulations for both low- and high-order ARMA processes are given to demonstrate the excellent performance of the proposed technique.

Two-stage bias correction estimators based on generalized partitioning estimation method†

The generalized partitioning estimation method, which is well known in tho literature (for example, Lainiotis 1976), is applied to solve the bias correction filtering, predicting and amoothing problems for a linear continuous.time system with undisturbable bias subsystem. With tho aid of an initial dependent-type partitioning approach, it is shown that the Friedland (1969) elemental results con be readily extended to the more general case where the bias and the original states are mutually dependent at the initial time, and that two-stage bias correction predictors and smoothers can also be developed. Finally, the dual set of Chandrasekhar algorithms, which alleviates the computation burden for a bias correction fixed-interval smoother evolving forwards in time, is presented.

Two-stage predictor of air pollution adapted to daily fluctuation

The paper proposes a new statistical prediction system of air pollution which is developed by applying the multivariate analyses to the accumulated data. First, the data are classified into some clusters corresponding to the patterns of daily fluctuations and various regression models are prepared. Secondly, based on the above models, the following two-stage predictor is introduced; at the first stage a suitable model for the pattern of the predicted day is selected by the discriminant function with the qualitative and quantitative data, and at the second stage the coefficients of the selected one are determined for the prediction of concentration levels. Finally, results are shown that are obtained by applying this method to the prediction of the SO2 concentration levels one and two hours ahead.