A Note on the Linearly and Quadratically Weighted Kappa Coefficients

Analysis of the Weighted Kappa and Its Maximum with Markov Moves

In this paper, the notion of Markov move from algebraic statistics is used to analyze the weighted kappa indices in rater agreement problems. In particular, the problem of the maximum kappa and its dependence on the choice of the weighting schemes are discussed. The Markov moves are also used in a simulated annealing algorithm to actually find the configuration of maximum agreement.

Bowel movement frequency and risks of major vascular and non-vascular diseases: a population-based cohort study among Chinese adults

OBJECTIVE

The application of bowel movement frequency (BMF) in primary care is limited by the lack of solid evidence about the associations of BMF with health outcomes apart from Parkinson's disease and colorectal cancer. We examined the prospective associations of BMF with major vascular and non-vascular diseases outside the digestive system.

DESIGN

Population-based prospective cohort study.

SETTING

The China Kadoorie Biobank in which participants from 10 geographically diverse areas across China were enrolled between 2004 and 2008.

PARTICIPANTS

487 198 participants aged 30 to 79 years without cancer, heart disease or stroke at baseline were included and followed up for a median of 10 years. The usual BMF was self-reported once at baseline.

PRIMARY AND SECONDARY OUTCOME MEASURES

Incident events of predefined major vascular and non-vascular diseases.

RESULTS

In multivariable-adjusted analyses, participants having bowel movements 'more than once a day' had higher risks of ischaemic heart disease (IHD), heart failure, chronic obstructive pulmonary disease, type 2 diabetes mellitus and chronic kidney disease (CKD) when compared with the reference group ('once a day'). The respective HRs (95% CIs) were 1.12 (1.09 to 1.16), 1.33 (1.22 to 1.46), 1.28 (1.22 to 1.36), 1.20 (1.15 to 1.26) and 1.15 (1.07 to 1.24). The lowest BMF ('less than three times a week') was also associated with higher risks of IHD, major coronary events, ischaemic stroke and CKD. The respective HRs were 1.07 (1.02 to 1.12), 1.22 (1.10 to 1.36), 1.11 (1.05 to 1.16) and 1.20 (1.07 to 1.35).

CONCLUSION

BMF was associated with future risks of multiple vascular and non-vascular diseases. The integration of BMF assessment and health counselling into primary care should be considered.

An Alternative Interpretation of the Linearly Weighted Kappa Coefficients for Ordinal Data

When two (or more) observers are independently categorizing a set of observations, Cohen's kappa has become the most notable measure of interobserver agreement. When the categories are ordinal, a weighted form of kappa becomes desirable. The two most popular weighting schemes are the quadratic weights and linear weights. Quadratic weights have been justified by the fact that the corresponding weighted kappa is asymptotically equivalent to an intraclass correlation coefficient. This paper deals with linear weights and shows that the corresponding weighted kappa is equivalent to the unweighted kappa when cumulative probabilities are substituted for probabilities. A numerical example is provided.