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Harrison DA, Ferrando-Vivas P, Shahin J, et al. Ensuring comparisons of health-care providers are fair: development and validation of risk prediction models for critically ill patients. Southampton (UK): NIHR Journals Library; 2015 Oct. (Health Services and Delivery Research, No. 3.41.)

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Ensuring comparisons of health-care providers are fair: development and validation of risk prediction models for critically ill patients.

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Appendix 2The new Intensive Care National Audit & Research Centre model: ICNARCH-2014

The raw data fields required for calculation of the new ICNARC model for predicting acute hospital mortality, ICNARCH-2014, are shown in Table 42 and the final model coefficients are provided in Table 43. For continuous predictors, coefficients are provided for the cubic spline base variables, calculated for each predictor as follows.

TABLE 42

TABLE 42

Raw data fields for the ICNARCH-2014 risk prediction model for acute hospital mortality

TABLE 43

TABLE 43

Final coefficients for the ICNARCH-2014 risk prediction model for acute hospital mortality

Restricted cubic splines with j knots (positioned at k1,. . .,kj) require (j − 1) base variables x1 to xj − 1 calculated from the continuous predictor x as:

x1=x.
(3)
xi+1=[max⁡((x−ki)3,0)−(kj−ki)×max⁡((x−kj−1)3,0)/(kj−kj−1)+(kj−1−ki)×max⁡((x−kj)3,0)/(kj−kj−1)]/(kj−k1)2;i=1,. . . ,j−2.
(4)

Right-restricted cubic splines with j knots (positioned at k1,. . ., kj) require (j + 1) base variables x1 to xj+ 1 calculated from the continuous predictor x as:

x1=−x.
(5)
xi+1=max⁡((ki−x)3,0); i=1, . . ., j.
(6)

The predicted log-odds of acute hospital mortality for patient i, li, are calculated by multiplying each coefficient from the preceding table by the value of the corresponding predictor variable and summing. The predicted risk of acute hospital mortality, pi, is calculated from the predicted log-odds by the inverse logit function:

pi=1/(1+exp⁡(−li)),
(7)

where exp() denotes the exponential function.

Copyright © Queen’s Printer and Controller of HMSO 2015. This work was produced by Harrison et al. under the terms of a commissioning contract issued by the Secretary of State for Health. This issue may be freely reproduced for the purposes of private research and study and extracts (or indeed, the full report) may be included in professional journals provided that suitable acknowledgement is made and the reproduction is not associated with any form of advertising. Applications for commercial reproduction should be addressed to: NIHR Journals Library, National Institute for Health Research, Evaluation, Trials and Studies Coordinating Centre, Alpha House, University of Southampton Science Park, Southampton SO16 7NS, UK.

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Bookshelf ID: NBK321612
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