covariance_commonControl {metagear}

Generates a sampling variance-covariance matrix for modeling dependencies among effect sizes due to sharing a common control.

Description

Generates K by K sampling variance-covariance (VCV) matrix that models the dependencies that arise due to using the same control group study parameters when estimating multiple effect sizes. This VCV matrix can then be used in meta-analysis. Currently only supports VCV calculation for log response ratios (see Lajeunesse 2011).

Usage

covariance_commonControl(
  aDataFrame,
  control_ID,
  X_t,
  SD_t,
  N_t,
  X_c,
  SD_c,
  N_c,
  metric = "RR"
)

Arguments

aDataFrame

A data frame containing columns with all study parameters used to estimate effect sizes (e.g., means, SD, N's for treatment and control groups). Must also contain a column that codes which effect sizes share a common control. See example below.

control_ID

Label of the column that codes groups of effect sizes that share the mean, SD, and N of a control group.

X_t

Column label for the means of (t)reatment group used to estimate the effect size.

SD_t

Column label for the standard deviations (SD) of the treatment group used to estimate the effect size.

N_t

Column label for the sample size (N) of the treatment group used to estimate the effect size.

X_c

Column label for the means of (c)ontrol group used to estimate the effect size.

SD_c

Column label for the standard deviations (SD) of the control group used to estimate the effect size.

N_c

Column label for the sample size (N) of the control group used to estimate the effect size.

metric

Option to designate which effect size metric for which the common control VCV matrix is to be estimated. Default is "RR" for log response ratio.

Value

A K by K sampling variance-covariance matrix and a data frame aligned with the block diagonal design of the sampling matrix.

Note

Response Ratio's (\mathit{RR}) with a comon control group

Following Lajeunesse (2011), when two (or more) reponse ratio (\mathit{RR}) effect sizes share a common control mean (\bar{X}_C), such as \mathit{RR}_{A,C}=ln(\bar{X}_A/\bar{X}_C) and \mathit{RR}_{B,C}=ln(\bar{X}_B/\bar{X}_C), then they share a sampling covariance of:

cov(\mathit{\mathit{RR}}_{A,C},~\mathit{RR}_{B,C})=\frac{(\mathit{SD}_C)^2}{N_C\bar{X}_C^2},

where the \mathit{SD} and N are the standard deviation and sample size of \bar{X}_C, respectively.

References

Lajeunesse, M.J. 2011. On the meta-analysis of response ratios for studies with correlated and multi-group designs. Ecology 92: 2049-2055.