Combining Information From Multiple Data Sources to Create Multivariable Risk Models: Illustration and Preliminary Assessment of a New Method

Samsa, Greg; Hu, Guizhou; Root, Martin

doi:10.1155/jbb.2005.113

Cited by 19 publications

(18 citation statements)

References 29 publications

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“…where X denotes the n p × design matrix of the independent variables, T X the transpose matrix of X and In Appendix A, we show that the estimated regression coefficients by this method are identical to the ones obtained by Samsa and coworkers [12]. In other words, we show that:…”

supporting

confidence: 71%

“…It is obvious that the estimate proposed by Samsa and coworkers [12] is just a re-parameterization of a well-known result and produces identical estimates.…”

mentioning

confidence: 83%

“…As we already discussed, Samsa and coworkers [12] did not provide an estimate for the covariance matrix, whereas Zhou and coworkers [13] provided a difficult to obtain estimate, using the delta method. However, the variance of a regression coefficient (let's say β i ) can be obtained relatively easily from summary statistics and it can be shown to be equal to:…”

Section: Variance-covariance Matrixmentioning

confidence: 98%

“…In Equation (4), the Pearson's correlation coefficient between x i and x j are denoted by r ij for 1 ≤ i, j ≤ p. The first approach for synthesis analysis was presented by Samsa and coworkers [12] who used Equation (2) and Equation (3) in order to calculate the estimates of Equation (1). In particular, the authors used a previously known result that relates β to the matrices A, S, where β is the p × 1 matrix of the regression coefficients 1 2 , , , p β β β  from the multivariate model of Equation (1), A is the p × 1 matrix of the regression coefficients of Equation (2), S is the p × 1 matrix of the standard deviations of the x i covariates and R x is given by Equation (4).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the Covariance of Regression Coefficients

Bagos¹,

Αδάμ²

2015

OJS

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In many applications, such as in multivariate meta-analysis or in the construction of multivariate models from summary statistics, the covariance of regression coefficients needs to be calculated without having access to individual patients' data. In this work, we derive an alternative analytic expression for the covariance matrix of the regression coefficients in a multiple linear regression model. In contrast to the well-known expressions which make use of the cross-product matrix and hence require access to individual data, we express the covariance matrix of the regression coefficients directly in terms of covariance matrix of the explanatory variables. In particular, we show that the covariance matrix of the regression coefficients can be calculated using the matrix of the partial correlation coefficients of the explanatory variables, which in turn can be calculated easily from the correlation matrix of the explanatory variables. This is very important since the covariance matrix of the explanatory variables can be easily obtained or imputed using data from the literature, without requiring access to individual data. Two important applications of the method are discussed, namely the multivariate meta-analysis of regression coefficients and the so-called synthesis analysis, and the aim of which is to combine in a single predictive model, information from different variables. The estimator proposed in this work can increase the usefulness of these methods providing better results, as seen by application in a publicly available dataset. Source code is provided in the Appendix and in http://www.compgen.org/tools/regression.

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supporting

confidence: 71%

“…It is obvious that the estimate proposed by Samsa and coworkers [12] is just a re-parameterization of a well-known result and produces identical estimates.…”

mentioning

confidence: 83%

Section: Variance-covariance Matrixmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Covariance of Regression Coefficients

Bagos¹,

Αδάμ²

2015

OJS

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“…[11,12]. Model parameter/data fusion implements a direct combination of the parameters of individual models [13,14]. The approach proposed in this work is included in this last category and explores the particular features of Bayesian inference mechanism.…”

Section: Introductionmentioning

confidence: 99%

Heart Rate Variability Applied to Short-Term Cardiovascular Event Risk Assessment

Paredes¹,

Rocha²,

Carvalho³

et al. 2013

ENG

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Cardiovascular disease (CVD) risk assessment is an important instrument to enhance the clinical decision in the daily practice as well as to improve the preventive health care promoting the transfer from the hospital to patient's home. Due to its importance, clinical guidelines recommend the use of risk scores to predict the risk of a cardiovascular disease event. Therefore, there are several well known risk assessment tools, unfortunately they present some limitations. This work addresses this problem with two different methodologies: 1) combination of risk assessment tools based on fusion of Bayesian classifiers complemented with genetic algorithm optimization; 2) personalization of risk assessment through the creation of groups of patients that maximize the performance of each risk assessment tool. This last approach is implemented based on subtractive clustering applied to a reduced-dimension space. Both methodologies were developed to short-term CVD risk prediction for patients with Acute Coronary Syndromes without ST segment elevation (ACS-NSTEMI). Two different real patients' datasets were considered to validate the developed strategies: 1) Santa Cruz Hospital, Portugal, N = 460 patients; 2) Leiria-Pombal Hospital Centre, Portugal, N = 99 patients. This work improved the performance in relation to current risk assessment tools reaching maximum values of sensitivity, specificity and geometric mean of, respectively, 80.0%, 82.9%, 81.5%. Besides this enhancement, the proposed methodologies allow the incorporation of new risk factors, deal with missing risk factors and avoid the selection of a single tool to be applied in the daily clinical practice. In spite of these achievements, the CVD risk assessment (patient stratification) should be improved. The incorporation of new risk factors recognized as clinically significant, namely parameters derived from heart rate variability (HRV), is introduced in this work. HRV is a strong and independent predictor of mortality in patients following acute myocardial infarction. The impact of HRV parameters in the characterization of coronary artery disease (CAD) patients will be conducted during hospitalization of these patients in the Leiria-Pombal Hospital Centre (LPHC).

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A multipoint method for meta‐analysis of genetic association studies

Bagos

Liakopoulos

2010

Genetic Epidemiology

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Meta-analyses of genetic association studies are usually performed using a single polymorphism at a time, even though in many cases the individual studies report results from partially overlapping sets of polymorphisms. We present here a multipoint (or multilocus) method for multivariate meta-analysis of published population-based case-control association studies. The method is derived by extending the general method for multivariate meta-analysis and allows for multivariate modelling of log(odds ratios (OR)) derived from several polymorphisms that are in linkage disequilibrium (LD). The method is presented in a genetic model-free approach, although it can also be used by assuming a genetic model of inheritance beforehand. Furthermore, the method is presented in a unified framework and is easily applied to both discrete outcomes (using the OR), as well as to meta-analyses of a continuous outcome (using the mean difference). The main innovation of the method is the analytical calculation of the within-studies covariances between estimates derived from linked polymorphisms. The only requirement is that of an external estimate for the degree of pairwise LD between the polymorphisms under study, which can be obtained from the same published studies, from the literature or from HapMap. Thus, the method is quite simple and fast, it can be extended to an arbitrary set of polymorphisms and can be fitted in nearly all statistical packages (Stata, R/Splus and SAS). Applications in two already published meta-analyses provide encouraging results concerning the robustness and the usefulness of the method and we expect that it would be widely used in the future.

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Combining Information From Multiple Data Sources to Create Multivariable Risk Models: Illustration and Preliminary Assessment of a New Method

Cited by 19 publications

References 29 publications

On the Covariance of Regression Coefficients

On the Covariance of Regression Coefficients

Heart Rate Variability Applied to Short-Term Cardiovascular Event Risk Assessment

A multipoint method for meta‐analysis of genetic association studies

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