SPSS Syntax for Combining Results of Principal Component Analysis of Multiply Imputed Data Sets using Generalized Procrustes Analysis.
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ABSTRACT:
SUBMITTER: van Wingerde B
PROVIDER: S-EPMC8042555 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:BackgroundNormalization is essential in dual-labelled microarray data analysis to remove non-biological variations and systematic biases. Many normalization methods have been used to remove such biases within slides (Global, Lowess) and across slides (Scale, Quantile and VSN). However, all these popular approaches have critical assumptions about data distribution, which is often not valid in practice.ResultsIn this study, we propose a novel assumption-free normalization method based on the Generalized Procrustes Analysis (GPA) algorithm. Using experimental and simulated normal microarray data and boutique array data, we systemically evaluate the ability of the GPA method in normalization compared with six other popular normalization methods including Global, Lowess, Scale, Quantile, VSN, and one boutique array-specific housekeeping gene method. The assessment of these methods is based on three different empirical criteria: across-slide variability, the Kolmogorov-Smirnov (K-S) statistic and the mean square error (MSE). Compared with other methods, the GPA method performs effectively and consistently better in reducing across-slide variability and removing systematic bias.ConclusionThe GPA method is an effective normalization approach for microarray data analysis. In particular, it is free from the statistical and biological assumptions inherent in other normalization methods that are often difficult to validate. Therefore, the GPA method has a major advantage in that it can be applied to diverse types of array sets, especially to the boutique array where the majority of genes may be differentially expressed.
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Project description:BackgroundAssessing disparities in injury is crucial for injury prevention and for evaluating injury prevention strategies, but efforts have been hampered by missing data. This study aimed to show the utility and reliability of the injury surveillance system as a trustworthy resource for examining disparities by generating multiple imputed companion datasets.MethodsWe employed data from the National Electronic Injury Surveillance System-All Injury Program (NEISS-AIP) for the period 2014-2018. A comprehensive simulation study was conducted to identify the appropriate strategy for addressing missing data limitations in NEISS-AIP. To evaluate the imputation performance more quantitatively, a new method based on Brier Skill Score (BSS) was developed to assess the accuracy of predictions by different approaches. We selected the multiple imputations by fully conditional specification (FCS MI) to generate the imputed companion data to NEISS-AIP 2014-2018. We further assessed health disparities systematically in nonfatal assault injuries treated in U.S. hospital emergency departments (EDs) by race and ethnicity, location of injury and sex.ResultsWe found for the first time that significantly higher age-adjusted nonfatal assault injury rates for ED visits per 100,000 population occurred among non-Hispanic Black persons (1306.8, 95% Confidence Interval [CI]: 660.1 - 1953.5), in public settings (286.3, 95% CI: 183.2 - 389.4) and for males (603.5, 95% CI: 409.4 - 797.5). We also observed similar trends in age-adjusted rates (AARs) by different subgroups for non-Hispanic Black persons, injuries occurring in public settings, and for males: AARs of nonfatal assault injury increased significantly from 2014 through 2017, then declined significantly in 2018.ConclusionsNonfatal assault injury imposes significant health care costs and productivity losses for millions of people each year. This study is the first to specifically look at health disparities in nonfatal assault injuries using multiply imputed companion data. Understanding how disparities differ by various groups may lead to the development of more effective initiatives to prevent such injury.
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Project description:In prognostic studies, the lasso technique is attractive since it improves the quality of predictions by shrinking regression coefficients, compared to predictions based on a model fitted via unpenalized maximum likelihood. Since some coefficients are set to zero, parsimony is achieved as well. It is unclear whether the performance of a model fitted using the lasso still shows some optimism. Bootstrap methods have been advocated to quantify optimism and generalize model performance to new subjects. It is unclear how resampling should be performed in the presence of multiply imputed data.The data were based on a cohort of Chronic Obstructive Pulmonary Disease patients. We constructed models to predict Chronic Respiratory Questionnaire dyspnea 6 months ahead. Optimism of the lasso model was investigated by comparing 4 approaches of handling multiply imputed data in the bootstrap procedure, using the study data and simulated data sets. In the first 3 approaches, data sets that had been completed via multiple imputation (MI) were resampled, while the fourth approach resampled the incomplete data set and then performed MI.The discriminative model performance of the lasso was optimistic. There was suboptimal calibration due to over-shrinkage. The estimate of optimism was sensitive to the choice of handling imputed data in the bootstrap resampling procedure. Resampling the completed data sets underestimates optimism, especially if, within a bootstrap step, selected individuals differ over the imputed data sets. Incorporating the MI procedure in the validation yields estimates of optimism that are closer to the true value, albeit slightly too larger.Performance of prognostic models constructed using the lasso technique can be optimistic as well. Results of the internal validation are sensitive to how bootstrap resampling is performed.
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Project description:Penalized regression methods are used in many biomedical applications for variable selection and simultaneous coefficient estimation. However, missing data complicates the implementation of these methods, particularly when missingness is handled using multiple imputation. Applying a variable selection algorithm on each imputed dataset will likely lead to different sets of selected predictors. This paper considers a general class of penalized objective functions which, by construction, force selection of the same variables across imputed datasets. By pooling objective functions across imputations, optimization is then performed jointly over all imputed datasets rather than separately for each dataset. We consider two objective function formulations that exist in the literature, which we will refer to as "stacked" and "grouped" objective functions. Building on existing work, we (a) derive and implement efficient cyclic coordinate descent and majorization-minimization optimization algorithms for continuous and binary outcome data, (b) incorporate adaptive shrinkage penalties, (c) compare these methods through simulation, and (d) develop an R package miselect. Simulations demonstrate that the "stacked" approaches are more computationally efficient and have better estimation and selection properties. We apply these methods to data from the University of Michigan ALS Patients Biorepository aiming to identify the association between environmental pollutants and ALS risk. Supplementary materials are available online.
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Project description:This manuscript considers regression models for generalized, multilevel functional responses: functions are generalized in that they follow an exponential family distribution and multilevel in that they are clustered within groups or subjects. This data structure is increasingly common across scientific domains and is exemplified by our motivating example, in which binary curves indicating physical activity or inactivity are observed for nearly 600 subjects over 5 days. We use a generalized linear model to incorporate scalar covariates into the mean structure, and decompose subject-specific and subject-day-specific deviations using multilevel functional principal components analysis. Thus, functional fixed effects are estimated while accounting for within-function and within-subject correlations, and major directions of variability within and between subjects are identified. Fixed effect coefficient functions and principal component basis functions are estimated using penalized splines; model parameters are estimated in a Bayesian framework using Stan, a programming language that implements a Hamiltonian Monte Carlo sampler. Simulations designed to mimic the application have good estimation and inferential properties with reasonable computation times for moderate datasets, in both cross-sectional and multilevel scenarios; code is publicly available. In the application we identify effects of age and BMI on the time-specific change in probability of being active over a 24-hour period; in addition, the principal components analysis identifies the patterns of activity that distinguish subjects and days within subjects.
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Project description:Whenever statistical analyses are applied to multiply imputed datasets, specific formulas are needed to combine the results into one overall analysis, also called combination rules. In the context of regression analysis, combination rules for the unstandardized regression coefficients, the t-tests of the regression coefficients, and the F-tests for testing [Formula: see text] for significance have long been established. However, there is still no general agreement on how to combine the point estimators of [Formula: see text] in multiple regression applied to multiply imputed datasets. Additionally, no combination rules for standardized regression coefficients and their confidence intervals seem to have been developed at all. In the current article, two sets of combination rules for the standardized regression coefficients and their confidence intervals are proposed, and their statistical properties are discussed. Additionally, two improved point estimators of [Formula: see text] in multiply imputed data are proposed, which in their computation use the pooled standardized regression coefficients. Simulations show that the proposed pooled standardized coefficients produce only small bias and that their 95% confidence intervals produce coverage close to the theoretical 95%. Furthermore, the simulations show that the newly proposed pooled estimates for [Formula: see text] are less biased than two earlier proposed pooled estimates.
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Project description:Many approaches for variable selection with multiply imputed data in the development of a prognostic model have been proposed. However, no method prevails as uniformly best. We conducted a simulation study with a binary outcome and a logistic regression model to compare two classes of variable selection methods in the presence of MI data: (I) Model selection on bootstrap data, using backward elimination based on AIC or lasso, and fit the final model based on the most frequently (e.g. ≥50% ) selected variables over all MI and bootstrap data sets; (II) Model selection on original MI data, using lasso. The final model is obtained by (i) averaging estimates of variables that were selected in any MI data set or (ii) in 50% of the MI data; (iii) performing lasso on the stacked MI data, and (iv) as in (iii) but using individual weights as determined by the fraction of missingness. In all lasso models, we used both the optimal penalty and the 1-se rule. We considered recalibrating models to correct for overshrinkage due to the suboptimal penalty by refitting the linear predictor or all individual variables. We applied the methods on a real dataset of 951 adult patients with tuberculous meningitis to predict mortality within nine months. Overall, applying lasso selection with the 1-se penalty shows the best performance, both in approach I and II. Stacking MI data is an attractive approach because it does not require choosing a selection threshold when combining results from separate MI data sets.
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Project description:This Teaching Resource provides lecture notes, slides, and a problem set for a series of lectures from a course entitled "Systems Biology: Biomedical Modeling." The materials are a lecture introducing the mathematical concepts behind principal components analysis (PCA). The lecture describes how to handle large data sets with correlation methods and unsupervised clustering with this popular method of analysis, PCA.
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