Wilcoxon signed-rank test
The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used either to test the location of a set of samples or to compare the locations of two populations using a set of matched samples.[1] When applied to test the location of a set of samples, it serves the same purpose as the one-sample Student's t-test.[2] On a set of matched samples, it is a paired difference test like the paired Student's t-test (also known as the "t-test for matched pairs" or "t-test for dependent samples"). Unlike the Student's t-test, the Wilcoxon signed-rank test does not assume that the data is normally distributed. On a wide variety of data sets, it has greater statistical power than the Student's t-test and is more likely to produce a statistically significant result. The cost of this applicability is that it has less statistical power than the Student's t-test when the data is normally distributed.
Mann–Whitney U test
In statistics, the Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probability of Y being greater than X.
Calculation of sensitivity and specificity trade-offs for ZCoR
Estimation of Dementia Disease Severity
@article{lowe2012greater,
title={Greater precision when measuring dementia severity: establishing item parameters for the clinical dementia rating scale},
author={Lowe, Deborah A and Balsis, Steve and Miller, Tyler M and Benge, Jared F and Doody, Rachelle S},
journal={Dementia and geriatric cognitive disorders},
volume={34},
number={2},
pages={128--134},
year={2012},
publisher={Karger Publishers}
}
@article{hughes1982new,
title={A new clinical scale for the staging of dementia},
author={Hughes, Charles P and Berg, Leonard and Danziger, Warren and Coben, Lawrence A and Martin, Ronald L},
journal={The British journal of psychiatry},
volume={140},
number={6},
pages={566--572},
year={1982},
publisher={Cambridge University Press}
}
@article{liu2002performance,
title={Performance on the cognitive abilities screening instrument at different stages of Alzheimer’s disease},
author={Liu, Hsiu-Chih and Teng, Evelyn Lee and Lin, Ker-Neng and Chuang, Ya-Yun and Wang, Pei-Ning and Fuh, Jong-Ling and Liu, Chia-Yih},
journal={Dementia and geriatric cognitive disorders},
volume={13},
number={4},
pages={244--248},
year={2002},
publisher={Karger Publishers}
}
@article{nordlund2010cognitive,
title={Cognitive profiles of incipient dementia in the Goteborg MCI study},
author={Nordlund, Arto and Rolstad, Sindre and G{\"o}thlin, Mattias and Edman, {\AA}ke and Hansen, Stefan and Wallin, Anders},
journal={Dementia and geriatric cognitive disorders},
volume={30},
number={5},
pages={403--410},
year={2010},
publisher={Karger Publishers}
}
@article{park2007functional,
title={Is functional decline necessary for a diagnosis of Alzheimer’s disease?},
author={Park, Kyung Won and Pavlik, Valory N and Rountree, Susan D and Darby, Eveleen J and Doody, Rachelle S},
journal={Dementia and geriatric cognitive disorders},
volume={24},
number={5},
pages={375--379},
year={2007},
publisher={Karger Publishers}
}
@article{schwam2010cognition,
title={Cognition and function in Alzheimer’s disease: identifying the transitions from moderate to severe disease},
author={Schwam, Elias and Xu, Yikang},
journal={Dementia and geriatric cognitive disorders},
volume={29},
number={4},
pages={309--316},
year={2010},
publisher={Karger Publishers}
}
@article{yeh2011functional,
title={Functional disability profiles in amnestic mild cognitive impairment},
author={Yeh, Yen-Chi and Lin, Ker-Neng and Chen, Wei-Ta and Lin, Chi-Ying and Chen, Ting-Bin and Wang, Pei-Ning},
journal={Dementia and geriatric cognitive disorders},
volume={31},
number={3},
pages={225--232},
year={2011},
publisher={Karger Publishers}
}
@article{balsis2011dementia,
title={Dementia staging across three different methods},
author={Balsis, Steve and Miller, Tyler M and Benge, Jared F and Doody, Rachelle S},
journal={Dementia and geriatric cognitive disorders},
volume={31},
number={5},
pages={328--333},
year={2011},
publisher={Karger Publishers}
}
@article{lynch2006clinical,
title={The clinical dementia rating sum of box score in mild dementia},
author={Lynch, CA and Walsh, C and Blanco, A and Moran, M and Coen, RF and Walsh, JB and Lawlor, BA},
journal={Dementia and geriatric cognitive disorders},
volume={21},
number={1},
pages={40--43},
year={2006},
publisher={Karger Publishers}
}Determining dementia severity is critical when working with dementia patients, whether providing patient care, establishing the effectiveness of interventions, or conducting translational and clinical research. Depending on the degree of dementia severity of the patients (e.g. mild, moderate or severe), there will be differences in their specific symptom presentations and severities, behavioral and functional outcomes (e.g. aggression, mood disturbance, impairment in activities of daily living), and patterns of cognitive deficits~\cite{yeh2011functional,schwam2010cognition,park2007functional,nordlund2010cognitive,liu2002performance}. A variety of measures have been developed for determining dementia severity. One of the most widely used measures is the Clinical Dementia Rating Scale (CDR)~\cite{lowe2012greater,hughes1982new}. The CDR is comprised of six cognitive and functional domains: memory, orientation, judgment and problem solving, community affairs, home and hobbies, and personal care. Clinicians complete the CDR based on interview data from the patient and a collateral source (e.g. spouse, caregiver). According to classic scaling of the measure, the first five domains are scored on a five-point ordinal scale, where 0 = no impairment, 0.5 = questionable impairment, 1 = mild impairment, 2 = moderate impairment and 3 = severe impairment. The sixth domain (personal care) is scored on a four-point ordinal scale with possible scores of 0, 1, 2 or 3. To obatin a total score using the CDR, often memory is weighted as the primary domain and all other domains as secondary, which produces a coarse estimation of dementia severity~\cite{balsis2011dementia}, and patients with the same degree of dementia severity can sometimes be placed into different CDR stages. It is likely that these problems occur because the scoring algorithm for global CDR scores uses a weighting scheme that is not based on optimal psychometric principles. Another option is to use the sum of the boxes (SOB) scoring approach, in which all domains are weighted equally. The summed score serves as the total estimate of dementia severity, with possible total scores ranging from 0 to 18. Because of its larger range of possible values, the SOB approach is able to detect more subtlety dementia severity than the standard algorithm~\cite{lynch2006clinical}. An item response theory (IRT)-based scoring approach to the CDR has been recommended for increased precision when estimating dementia severity~\cite{lowe2012greater}, which takes into account the differential ability of each domain to predict and reflect the latent construct, $i.e.$, dementia severity.
ANOVA
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means.