Biometrics and Psychometrics: Origins, Commonalities and Differences

Starting with the common origins of biometrics and psychometrics at the beginning of the twentieth century, the paper compares and contrasts subsequent developments, informed by the author's 35 years at Rothamsted Experimental Station followed by a period with the data theory group in Leiden and thereafter. Although the methods used by biometricians and psychometricians have much in common, there are important differences arising from the different fields of study. Similar differences arise wherever data are generated and may be regarded as a major driving force in the development of statistical ideas

Further optimization of the reliability of the 28-joint disease activity score in patients with early rheumatoid arthritis

BACKGROUND: The 28-joint Disease Activity Score (DAS28) combines scores on a 28-tender and swollen joint count (TJC28 and SJC28), a patient-reported measure for general health (GH), and an inflammatory marker (either the erythrocyte sedimentation rate [ESR] or the C-reactive protein [CRP]) into a composite measure of disease activity in rheumatoid arthritis (RA). This study examined the reliability of the DAS28 in patients with early RA using principles from generalizability theory and evaluated whether it could be increased by adjusting individual DAS28 component weights. METHODS: Patients were drawn from the DREAM registry and classified into a "fast response" group (N = 466) and "slow response" group (N = 80), depending on their pace of reaching remission. Composite reliabilities of the DAS28-ESR and DAS28-CRP were determined with the individual components' reliability, weights, variances, error variances, correlations and covariances. Weight optimization was performed by minimizing the error variance of the index. RESULTS: Composite reliabilities of 0.85 and 0.86 were found for the DAS28-ESR and DAS28-CRP, respectively, and were approximately equal across patients groups. Component reliabilities, however, varied widely both within and between sub-groups, ranging from 0.614 for GH ("slow response" group) to 0.912 for ESR ("fast response" group). Weight optimization increased composite reliability even further. In the total and "fast response" groups, this was achieved mostly by decreasing the weight of the TJC28 and GH. In the "slow response" group, though, the weights of the TJC28 and SJC28 were increased, while those of the inflammatory markers and GH were substantially decreased. CONCLUSIONS: The DAS28-ESR and the DAS28-CRP are reliable instruments for assessing disease activity in early RA and reliability can be increased even further by adjusting component weights. Given the low reliability and weightings of the general health component across subgroups it is recommended to explore alternative patient-reported outcome measures for inclusion in the DAS28

Applications of quadratic minimisation problems in statistics

Albers et al. (2010) showed that the problem minx(x-t)'A(x-t) subject to x'Bx+2b'x=k where A is positive definite or positive semi-definite has a unique computable solution. Here, several statistical applications of this problem are shown to generate special cases of the general problem that may all be handled within a general unifying methodology. These include non-trivial considerations that arise when (i) A and/or B are not of full rank and (ii) where B is indefinite. General canonical forms for A and B that underpin the minimisation methodology give insight into structure that informs understanding

Applications of quadratic minimisation problems in statistics

Albers et al. (2010) [2] showed that the problem subject to where  is positive definite or positive semi-definite has a unique computable solution. Here, several statistical applications of this problem are shown to generate special cases of the general problem that may all be handled within a general unifying methodology. These include non-trivial considerations that arise when (i)  and/or  are not of full rank and (ii) where  is indefinite. General canonical forms for  and  that underpin the minimisation methodology give insight into structure that informs understanding.Canonical analysis Constraints Constrained regression Hardy-Weinberg Minimisation Optimal scaling Procrustes analysis Quadratic forms Ratios Reduced rank Splines