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Statistical methodology: IV. Analysis of variance, analysis of covariance, and multivariate analysis of variance.

Medical research frequently involves the statistical comparison of >2 groups, often using data obtained through the application of complex experimental designs. Fortunately, inferential statistical methodologies exist to address these situations. Analysis of variance (ANOVA) in its many forms is used to simultaneously test the equality of all groups in a study. One-way (with 1 independent variable), 2-way (with 2 independent variables), and repeated-measures (patients serve as their own controls) ANOVAs are forms of this technique. Each form has been developed to analyze data from a specific experimental design. Analysis of covariance (ANCOVA) allows the researcher to control for confounding variables that may influence the response of the dependent variable. Finally, multivariate analysis of variance (MANOVA) evaluates the simultaneous responses of multiple dependent variables to > or = 1 independent variable. Whereas ANOVA is the correct alternative to statistically inappropriate multiple t-tests, MANOVA is the correct alternative to statistically inappropriate multiple univariate ANOVA calculations. Use of each of these statistical methods requires an appropriate experimental design and data meeting a number of assumptions. When used properly, each of these methods provides a powerful statistical analysis technique.

Analysis of Variance↗

Variance analysis. Part I, Extending flexible budget variance analysis to acuity.

The author reviews the concepts of flexible budget variance analysis, including the price, quantity, and volume variances generated by that technique. He also introduces the concept of acuity variance and provides direction on how such a variance measure can be calculated. Part II in this two-part series on variance analysis will look at how personal computers can be useful in the variance analysis process.

Analysis of Variance↗

Innovations in case flow analysis: using midlier variance analysis.

This article presents the use of midlier and case flow analysis during a retrospective chart review to study the costs of hospital length of stay. The results showed that considerable savings can be realized by using these methods for one group of patients with the same diagnosis. We were able to redefine and track patients during their pre-, peri-, and postoperative period and estimated the time and cost opportunities for work flow improvement. We concluded that considerable savings are possible by extending the analysis to patients in other DRG groups.

Analysis of Variance↗

Read-noise characterization of focal plane array detectors via mean-variance analysis.

Mean-variance analysis is described as a method for characterization of the read-noise and gain of focal plane array (FPA) detectors, including charge-coupled devices (CCDs), charge-injection devices (CIDs), and complementary metal-oxide-semiconductor (CMOS) multiplexers (infrared arrays). Practical FPA detector characterization is outlined. The nondestructive readout capability available in some CIDs and FPA devices is discussed as a means for signal-to-noise ratio improvement. Derivations of the equations are fully presented to unify understanding of this method by the spectroscopic community.

Algorithms↗

Helping financial analysts communicate variance analysis.

Healthcare organizations often use variance analysis to explain variation between planned and actual costs and charges. This type of analysis is becoming even more common as healthcare executives work to improve efficiency, to set priorities for organizational improvement as part of strategic planning, and to explain costs and charges to interested groups such as purchasers and payers. Variance analysis produces data that must be presented in a format useful to senior executives. An effective format would express the data in a visual summary that is simple enough to be readily understood and detailed enough to provide valuable information.

Analysis of Variance↗

Components of variance analysis of data produced in a national quality-control survey of radioimmunoassays of thyroxin, triiodothyronine, thyrotropin, prolactin, and progesterone.

Data collected in a collaborative survey for radioimmunoassays have been studied by using analysis of variance to estimate the within-kit (CVw.kit) and the between-kit (CVb.kit) components of the total variability (CVT). This analysis has been applied to the results for triiodothyronine, thyroxin, thyrotropin, prolactin, and progesterone produced by 80-150 laboratories that assayed blind, replicate samples. Total variability was lowest in the thyroxin assay (CVT = 10.9%), associated with a very close between-kit agreement (CVb.kit = 4.0%); in the triiodothyronine assay, on the other hand, the large between-kit component (CVb.kit = 10.1%) increased the total variability to 16.1%. In the prolactin assay the CVT of 19.3% included 17.5% CVw.kit and 8.1% CVb.kit. Assays for thyrotropin and progesterone involve analyses of two pools at different hormone concentrations. The CVb.kit component was very high in the low-concentration pool, both for thyrotropin (25.1%) and progesterone (45.2%); in the higher-concentration pool it decreased to 8.3% for thyrotropin but remained high (21.6%) for progesterone. Applying analysis of variance to the triiodothyronine and thyroxin data obtained by different laboratories using the same kit showed that most kits yielded significantly different measurements when used in different laboratories.

Analysis of Variance↗

Variance analysis for care path outcomes management.

Variance analysis and monitoring procedures of clinical care path interventions and outcomes are discussed with the objective of modifying suboptimal care paths into optimal pathways. These critical care paths will contain value-added interventions that contribute significantly to the achievement of measurable outcomes. Care path variables are defined and measurement considerations are presented. Variance analysis procedures, measures, and uses are discussed that facilitate outcomes management and continuous quality improvement.

Analysis of Variance↗

Budget variance analysis using RVUs.

This article details the use of the variance analysis as management tool to evaluate the financial health of the practice. A common financial tool for administrators has been a simple calculation measuring the difference between actual financials vs. budget financials. Standard cost accounting provides a methodology known as variance analysis to better understand the actual vs. budgeted financial streams. The standard variance analysis has been modified by applying relative value units (RVUs) as standards for the practice.

Accounting↗

[Variance analysis of Cd2+, Zn2+, and Mn2+ effect on membrane Na+,K(+)-ATPase activity of loach embryos].

The evaluation of influences Cd2+, Zn2+, Mn2+ in concentrations 10(-6), 10(-5), 10(-4) M (factor of dose) on the Na+, K(+)-ATP-ase activity in the early period of development (60-330 min.) of loach embryos (time factor) using one- and two-factor analysis of variance has been performed. It has been detected, that the changes of enzyme activity are mainly caused by action of the explored cations and do not depend on time of embryos development. The most influence on activity in the indicated period of embryos development of loach renders Cd2+ in concentration 10(-4) M, relative value of its influence being 95.7% (p = 0.01). Substantial concentration dependence of the Na+, K(+)-ATP-ase activity is exposed to the action of each of cations. The values of the influence of their concentration changes during the studied period of development differ insignificantly for all cations and make 76.2-77.5% (p < 0.01).

Analysis of Variance↗

Variance analysis applied to a stroke pathway: how this can improve efficiency of healthcare delivery.

INTRODUCTION: Stroke is a complicated disease that requires a multidisciplinary approach for its management. We postulated that variance analysis applied to a stroke pathway, by identifying major problem areas and encouraging timely corrective actions, would lead to more efficient healthcare delivery to hospitalised stroke patients. MATERIALS AND METHODS: Prospectively collected variance data from consecutive stroke patients discharged from a tertiary hospital in Singapore during a 3-month period in 2000 were used to identify the major variances causing increased length of stay. These were compared and contrasted to variance data collected during the same 3-month period in the subsequent year (2001), after the implementation of stroke pathway and the availability of monthly variance analysis reports. Patient characteristics and outcome measures were also compared between the two study periods. RESULTS: The four major variances that accounted for increased length of stay were, in descending order of the number of patients affected, awaiting bed availability in step-down facilities, delay in head computed tomographic scan performance, awaiting family's decision on discharge plan and incomplete application submitted to step-down facilities. After implementation of the stroke pathway with ongoing variance analysis, all four variances showed different extent of improvements. There were no significant differences in patient characteristics between the two study periods, whereas the average length of stay significantly diminished in the late study period with a trend for decreased in-hospital mortality, compared to the early study period. CONCLUSION: Variance analysis applied in the context of a stroke pathway was effective in identifying major variances causing increased length of stay. This allowed targeted intervention to improve efficiency of healthcare delivery to stroke patients.

Aged↗

An experimental bias-variance analysis of SVM ensembles based on resampling techniques.

Recently, bias-variance decomposition of error has been used as a tool to study the behavior of learning algorithms and to develop new ensemble methods well suited to the bias-variance characteristics of base learners. We propose methods and procedures, based on Domingo's unified bias-variance theory, to evaluate and quantitatively measure the bias-variance decomposition of error in ensembles of learning machines. We apply these methods to study and compare the bias-variance characteristics of single support vector machines (SVMs) and ensembles of SVMs based on resampling techniques, and their relationships with the cardinality of the training samples. In particular, we present an experimental bias-variance analysis of bagged and random aggregated ensembles of SVMs in order to verify their theoretical variance reduction properties. The experimental bias-variance analysis quantitatively characterizes the relationships between bagging and random aggregating, and explains the reasons why ensembles built on small subsamples of the data work with large databases. Our analysis also suggests new directions for research to improve on classical bagging.

Algorithms↗

Questions to ask: implementing a system for clinical pathway variance analysis.

Although it is agreed that there is a need for clinical pathway variance analysis, methods for creating a system are less well defined. To help others down this path, we have developed a list of questions around four core issues: data collection, data entry and analysis, data reporting, and organizational support. Our goal is to identify key questions related to variance management and provide a framework for clinical pathway variance analysis.

Analysis of Variance↗

Sub-angstrom conformational changes of a single molecule captured by AFM variance analysis.

A system's equilibrium variance can be analyzed to probe its underlying dynamics at higher resolution. Here, using single-molecule atomic-force microscope techniques, we show how the variance in the length of a single dextran molecule can be used to establish thermodynamic equilibrium and to detect conformational changes not directly observable with other methods. Dextran is comprised of a chain of pyranose rings that each undergoes an Angstrom-scale transition from a chair to boat conformation under a stretching force. Our analysis of the variance of the molecule's fluctuations verifies equilibrium throughout the force-extension curve, consistent with the expected thermodynamic ensemble. This validates further analysis of the variance in the transition region, which reveals an intermediate conformation between the chair and the boat on the sub-Angstrom scale. Our test of thermal equilibrium as well as our variance analysis can be readily extended to a wide variety of molecules, including proteins.

Analysis of Variance↗

Variance analysis in clinical pathways for total hip and knee joint arthroplasty.

Clinical pathways are being increasingly used for daily patient care. The pathways consist of a sequence of critical treatment events matched to the patient's recovery. Variance analysis identifies deviations from the pathway and can be used for quality improvement and clinical audit. The aim of this study is to analyse the variances from clinical pathways in two common elective orthopaedic operations. A prospective variance analysis was performed from the clinical pathways of all patients undergoing total hip and total knee arthroplasty over a 12 month period. Variances were categorised according to their source and then further divided into serious and non-serious variances. A total of 65 patients underwent total knee replacement during the study. Eleven serious variances were recorded in eight of these patients (12.3%) with a surprisingly high number of cardiac events. A total of 52 patients underwent total hip replacement with nine serious variances recorded in seven of these patients (13.5%). Clinical pathways can be used as a means of incorporating evidence-based medicine into clinical practice. Variance analysis of the pathways can be utilised as a process of quality control and to improve patient outcomes. Serious variances within this study were higher than anticipated.

Adult↗

Multi-locus penetrance variance analysis method for association study in complex diseases.

Common heritable diseases often result from the action of several different genes, each of which contributes to the total observed variability in the disease trait. Traditional single-locus association approaches rely heavily on the marginal effects of single-locus and tend to ignore the multigenic nature of complex diseases. The increasing request for localizing genes underlying traits in multi-gene diseases has led to the development of some statistical methods. In this study, we develop a multi-locus analysis method - multi-locus penetrance variance analysis (MPVA), and conduct systematical simulation studies to evaluate its performance. Our results show that compared with other multi-locus methods, MPVA has some advantage in detecting complicated interactions under different epistatic models, and its performance is stable and robust.

Analysis of Variance↗

Outcomes assessment of total hip and total knee arthroplasty: critical pathways, variance analysis, and continuous quality improvement.

Using critical pathways, with variance analysis and continuous quality improvement techniques to refine the pathways, the efficiency of total hip and total knee surgeries in one academic health center was maximized. Using a retrospective cohort study design, complications, readmissions, morbidity/mortality, and function scores were examined in two groups of patients attended by the same surgeon for the year before and the year after the implementation of an outcomes management program. The length of stay was reduced by 57% for knee patients and by 46% for hip patients. Hospital costs were reduced 11% for all knees and 38% for hips. Complications were also significantly reduced. There was no statistically significant difference between pre- or postoperative knee or hip outcome scores. The program resulted in significant savings without adversely affecting overall outcome.

Aged↗

Variance analysis of error in selected ion monitoring assays using various internal standards. A practical study case.

This study contains a practical application of variance analysis for the evaluation of precision in selected ion monitoring using stable isotope variants or chemically related compounds as internal standards. Variance analysis is applied to determine the relative contributions of the errors due to long-term and short-term effects of instrument stability. The technique allows the resolution of variance due to sample manipulation from that introduced by the gas chromatography mass spectrometry instrumentation. This provides an objective measure of potential internal standards. Evaluation of the dependency of these errors upon concentration indicates appropriate weighing factors to be applied for regression analysis.

Analysis of Variance↗