grl function

Approximating effective-counts as proposed by Greenland & Longnecker

Reconstructs the set of pseudo-numbers (or 'effective' numbers) of cases and non-cases consistent with the input data (log relative risks). The method was first proposed in 1992 by Greenland and Longnecker.

grl(y, v, cases, n, type, data, tol = 1e-05)

Arguments

• y: a vector, defining the (reported) log relative risks.
• v: a vector, defining the variances of the reported log relative risks.
• cases: a vector, defining the number of cases for each exposure level.
• n: a vector, defining the total number of subjects for each exposure level. For incidence-rate data n indicates the amount of person-time within each exposure level.
• type: a vector (or a character string), specifying the design of the study. Options are cc, ir, and ci, for case-control, incidence-rate, and cumulative incidence data, respectively.
• data: an optional data frame (or object coercible by as.data.frame to a data frame) containing the variables in the previous arguments.
• tol: define the tolerance.

Returns

The results are returned structured in a matrix

A	approximated number of effective cases.
N	approximated total number of effective subjects.

Details

The function reconstructs the effective counts corresponding to the multivariable adjusted log relative risks as well as their standard errors. A unique solution is guaranteed by keeping the margins of the table of pseudo-counts equal to the margins of the crude or unadjusted data (Greenland and Longnecker 1992). See the referenced article for a complete description of the algorithm implementation.

Examples

## Loading data
data("alcohol_cvd")

## Obtaining pseudo-counts for the first study (id = 1)
grl(y = logrr, v = I(se^2), cases = cases, n = n, type = type,
   data = subset(alcohol_cvd, id == 1))
   
## Obtaining pseudo-counts for all study
by(alcohol_cvd, alcohol_cvd$id, function(x)
   grl(y = logrr, v = I(se^2), cases = cases, n = n, type = type, data = x))

## Restructuring the previous results in a matrix
do.call("rbind", by(alcohol_cvd, alcohol_cvd$id, function(x)
   grl(y = logrr, v = I(se^2), cases = cases, n = n, type = type, data = x)))

References

Greenland, S., Longnecker, M. P. (1992). Methods for trend estimation from summarized dose-response data, with applications to meta-analysis. American journal of epidemiology, 135(11), 1301-1309.

Orsini, N., Li, R., Wolk, A., Khudyakov, P., Spiegelman, D. (2012). Meta-analysis for linear and nonlinear dose-response relations: examples, an evaluation of approximations, and software. American journal of epidemiology, 175(1), 66-73.

See Also

covar.logrr, hamling

Author(s)

Alessio Crippa, alessio.crippa@ki.se