Standard score

Summary

In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores. It is calculated by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This process of converting a raw score into a standard score is called standardizing or normalizing (however, "normalizing" can refer to many types of ratios; see Normalization for more). Standard scores are most commonly called z-scores; the two terms may be used interchangeably, as they are in this article. Other equivalent terms in use include z-value, z-statistic, normal score, standardized variable and pull in high energy physics. Computing a z-score requires knowledge of the mean and standard devi

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https://en.wikipedia.org/wiki/Standard_score

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Microarray gene expression data sets are jointly analyzed to increase statistical power. They could either be merged together or analyzed by meta-analysis. For a given ensemble of data sets, it cannot be foreseen which of these paradigms, merging or meta-analysis, works better. In this article, three joint analysis methods, Z-score normalization, ComBat and the inverse normal method (meta-analysis) were selected for survival prognosis and risk assessment of breast cancer patients. The methods were applied to eight microarray gene expression data sets, totaling 1324 patients with two clinical endpoints, overall survival and relapse-free survival. The performance derived from the joint analysis methods was evaluated using Cox regression for survival analysis and independent validation used as bias estimation. Overall, Z-score normalization had a better performance than ComBat and meta-analysis. Higher Area Under the Receiver Operating Characteristic curve and hazard ratio were also obtained when independent validation was used as bias estimation. With a lower time and memory complexity, Z-score normalization is a simple method for joint analysis of microarray gene expression data sets. The derived findings suggest further assessment of this method in future survival prediction and cancer classification applications.

Oxford Univ Press2016

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Purpose To exploit the improved comparability and hardware independency of quantitative MRI, databases of MR physical parameters in healthy tissue are required, to which tissue properties of patients can be compared. In this work, normative values for longitudinal and transverse relaxation times in the brain were established and tested in single-subject comparisons for detection of abnormal relaxation times. Methods Relaxometry maps of the brain were acquired from 52 healthy volunteers. After spatially normalizing the volumes into a common space, T-1 and T-2 inter-subject variability within the healthy cohort was modeled voxel-wise. A method for a single-subject comparison against the atlases was developed by computing z-scores with respect to the established healthy norms. The comparison was applied to two multiple sclerosis and one clinically isolated syndrome cases for a proof of concept. Results The established atlases exhibit a low variation in white matter structures (median RMSE of models equal to 32 ms for T-1 and 4 ms for T-2), indicating that relaxation times are in a narrow range for normal tissues. The proposed method for single-subject comparison detected relaxation time deviations from healthy norms in the example patient data sets. Relaxation times were found to be increased in brain lesions (mean z-scores >5). Moreover, subtle and confluent differences (z-scores similar to 2-4) were observed in clinically plausible regions (between lesions, corpus callosum). Conclusions Brain T-1 and T-2 quantitative norms were derived voxel-wise with low variability in healthy tissue. Example patient deviation maps demonstrated good sensitivity of the atlases for detecting relaxation time alterations.

WILEY2019

Effect heterogeneity and variable selection for standardizing causal effects to a target population

Mats Julius Stensrud

The participants in randomized trials and other studies used for causal inference are often not representative of the populations seen by clinical decision-makers. To account for differences between populations, researchers may consider standardizing results to a target population. We discuss several different types of homogeneity conditions that are relevant for standardization: Homogeneity of effect measures, homogeneity of counterfactual outcome state transition parameters, and homogeneity of counterfactual distributions. Each of these conditions can be used to show that a particular standardization procedure will result in an unbiased estimate of the effect in the target population, given assumptions about the relevant scientific context. We compare and contrast the homogeneity conditions, in particular their implications for selection of covariates for standardization and their implications for how to compute the standardized causal effect in the target population. While some of the recently developed counterfactual approaches to generalizability rely upon homogeneity conditions that avoid many of the problems associated with traditional approaches, they often require adjustment for a large (and possibly unfeasible) set of covariates.

2019