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Santaguida PL, Balion C, Hunt D, et al. Diagnosis, Prognosis, and Treatment of Impaired Glucose Tolerance and Impaired Fasting Glucose. Rockville (MD): Agency for Healthcare Research and Quality (US); 2005 Sep. (Evidence Reports/Technology Assessments, No. 128.)

• This publication is provided for historical reference only and the information may be out of date.

This publication is provided for historical reference only and the information may be out of date.

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# Appendix G. Calculations

Section A: Calculation of kappa coefficient and confidence intervals (CI)

The simple kappa coefficient is calculated as:

where

and

The Variance and CI are calculated as follows:

where

and

Section B: Calculation of annualized relative risk, annualized risk for the exposed (IFG or IGT) and the normal glucose groups

Calculation of relative risk (RR t) at time t would be as follows:

where

= Calculated Risk in Exposed Group at time t (or i.e. in Male) and calculated as:

= Calculated Risk in Control Group at time t (or i.e. in Female)

and can be calculated as:

is Observed Risk after T period in Exposed Group

is Observed Risk after T period in Control Group

thus

where

T= Observed duration of study (0.5 to 18 years).

t= Up to one year study duration.

Section C: Calculation of 95% confidence intervals (CI) for the unadjusted annualized RR

Where:

Section D: Calculation and test of heterogeneity (Q) and the pooled estimate of RR{36574}:

Where k is the number of studies being combined, RR i is the relative risk estimate in ithStudy,

is the weighted estimator of relative risk, and W i is the weight attached to that study (the reciprocal of the variance of the ith study, varRR i).

Q is approximately distributed as a X 2 distribution with k- 1 degrees of freedom under H 0

Fixed effects model

Random effect model

and

Further, define

The estimated component of variance due to inter-study variation in effect size,, is calculated as:

and

Adjusted weights for each of the studies is calculated as

The mean relative risk estimate of all studies can then be computed by:

The variance of this estimate is calculated as:

U.S. Department of Health and Human Services

Mike Leavitt, Secretary

Office of Public Health and Science

Richard H. Carmona, M.D., M.P.H., F.A.C.S., Surgeon General of the United States

Agency for Healthcare Research and Quality

Carolyn M. Clancy, M.D., Director

Bookshelf ID: NBK37933