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Meta-regression analysis for 2-group proportion ratios

Source: R/meta_model.R
meta.lm.propratio2.Rd

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a 2-group log proportion ratio. The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity. The exponentiated slope estimate for a predictor variable describes a multiplicative change in the proportion ratio associated with a 1-unit increase in that predictor variable, controlling for all other predictor variables in the model.

For more details, see Section 3.4 of Bonett (2021, Volume 5).

Usage

meta.lm.propratio2(alpha, f1, f2, n1, n2, X)

Arguments

alpha

alpha level for 1-alpha confidence

f1

vector of group 1 frequency counts

f2

vector of group 2 frequency counts

n1

vector of group 1 sample sizes

n2

vector of group 2 sample sizes

X

matrix of predictor values

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

  • Estimate - OLS estimate

  • SE - standard error

  • z - z-value

  • p - p-value

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

  • exp(Estimate) - the exponentiated estimate

  • exp(LL) - lower limit of the exponentiated confidence interval

  • exp(UL) - upper limit of the exponentiated confidence interval

References

Price RM, Bonett DG (2008). “Confidence intervals for a ratio of two independent binomial proportions.” Statistics in Medicine, 27(26), 5497–5508. ISSN 02776715, doi:10.1002/sim.3376 .

Bonett DG (2021). Statistical Methods for Psychologists, Vol 1-5, https://dgbonett.sites.ucsc.edu/.

Examples

n1 <- c(204, 201, 932, 130, 77)
n2 <- c(106, 103, 415, 132, 83)
f1 <- c(24, 40, 93, 14, 5)
f2 <- c(12, 9, 28, 3, 1)
x1 <- c(4, 4, 5, 3, 26)
x2 <- c(1, 1, 1, 0, 0)
X <- matrix(cbind(x1, x2), 5, 2)
meta.lm.propratio2(.05, f1, f2, n1, n2, X)
#>         Estimate         SE      z     p          LL         UL exp(Estimate)
#> b0  1.4924887636 0.69172794  2.158 0.031  0.13672691 2.84825062     4.4481522
#> b1  0.0005759509 0.04999884  0.012 0.990 -0.09741998 0.09857188     1.0005761
#> b2 -1.0837844594 0.59448206 -1.823 0.068 -2.24894789 0.08137897     0.3383128
#>      exp(LL)   exp(UL)
#> b0 1.1465150 17.257565
#> b1 0.9071749  1.103594
#> b2 0.1055102  1.084782

# Should return:
#         Estimate         SE      z     p          LL         UL
# b0  1.4924887636 0.69172794  2.158 0.031  0.13672691 2.84825062
# b1  0.0005759509 0.04999884  0.012 0.991 -0.09741998 0.09857188
# b2 -1.0837844594 0.59448206 -1.823 0.068 -2.24894789 0.08137897
#     exp(Estimate)   exp(LL)   exp(UL)
# b0      4.4481522 1.1465150 17.257565
# b1      1.0005761 0.9071749  1.103594
# b2      0.3383128 0.1055102  1.084782