Goodman and Kruskal's Gamma Coefficient for Ordinalized Bivariate Normal Distributions.

We consider a bivariate normal distribution with linear correlation [Formula: see text] whose random components are discretized according to two assigned sets of thresholds. On the resulting bivariate ordinal random variable, one can compute Goodman and Kruskal's gamma coefficient, [Formula: see text], which is a common measure of ordinal association. Given the known analytical monotonic relationship between Pearson's [Formula: see text] and Kendall's rank correlation [Formula: see text] for the bivariate normal distribution, and since in the continuous case, Kendall's [Formula: see text] coincides with Goodman and Kruskal's [Formula: see text], the change of this association measure before and after discretization is worth studying. We consider several experimental settings obtained by varying the two sets of thresholds, or, equivalently, the marginal distributions of the final ordinal variables. This study, confirming previous findings, shows how the gamma coefficient is always larger in absolute value than Kendall's rank correlation; this discrepancy lessens when the number of categories increases or, given the same number of categories, when using equally probable categories. Based on these results, a proposal is suggested to build a bivariate ordinal variable with assigned margins and Goodman and Kruskal's [Formula: see text] by ordinalizing a bivariate normal distribution. Illustrative examples employing artificial and real data are provided.

Enteral versus intravenous approach for the sedation of critically ill patients: a randomized and controlled trial.

BACKGROUND: ICU patients must be kept conscious, calm, and cooperative even during the critical phases of illness. Enteral administration of sedative drugs might avoid over sedation, and would be as adequate as intravenous administration in patients who are awake, with fewer side effects and lower costs. This study compares two sedation strategies, for early achievement and maintenance of the target light sedation. METHODS: This was a multicenter, single-blind, randomized and controlled trial carried out in 12 Italian ICUs, involving patients with expected mechanical ventilation duration > 72 h at ICU admission and predicted mortality > 12% (Simplified Acute Physiology Score II > 32 points) during the first 24 h on ICU. Patients were randomly assigned to receive intravenous (midazolam, propofol) or enteral (hydroxyzine, lorazepam, and melatonin) sedation. The primary outcome was percentage of work shifts with the patient having an observed Richmond Agitation-Sedation Scale (RASS) = target RASS ±1. Secondary outcomes were feasibility, delirium-free and coma-free days, costs of drugs, length of ICU and hospital stay, and ICU, hospital, and one-year mortality. RESULTS: There were 348 patients enrolled. There were no differences in the primary outcome: enteral 89.8% (74.1-100), intravenous 94.4% (78-100), p = 0.20. Enteral-treated patients had more protocol violations: n = 81 (46.6%) vs 7 (4.2%), p < 0.01; more self-extubations: n = 14 (8.1%) vs 4 (2.4%), p = 0.03; a lighter sedative target (RASS = 0): 93% (71-100) vs 83% (61-100), p < 0.01; and lower total drug costs: 2.39 (0.75-9.78) vs 4.15 (1.20-20.19) €/day with mechanical ventilation (p = 0.01). CONCLUSIONS: Although enteral sedation of critically ill patients is cheaper and permits a lighter sedation target, it is not superior to intravenous sedation for reaching the RASS target. TRIAL REGISTRATION: ClinicalTrials.gov, NCT01360346 . Registered on 25 March 2011.

Simulating Ordinal Data.

The increasing use of ordinal variables in different fields has led to the introduction of new statistical methods for their analysis. The performance of these methods needs to be investigated under a number of experimental conditions. Procedures to simulate from ordinal variables are then required. In this article, we deal with simulation from multivariate ordinal random variables. We propose a new procedure for generating samples from ordinal random variables with a prespecified correlation matrix and marginal distributions. Its features are examined and compared with those of its main competitors. A software implementation in R is also provided along with examples of its application.