metarate: Meta-analysis of single incidence rates

In meta: General Package for Meta-Analysis

Meta-analysis of single incidence rates

Description

Calculation of an overall incidence rate from studies reporting a single incidence rate. Inverse variance method and generalised linear mixed model (GLMM) are available for pooling. For GLMMs, the rma.glmm function from R package metafor (Viechtbauer 2010) is called internally.

Usage

metarate(
  event,
  time,
  studlab,
  data = NULL,
  subset = NULL,
  exclude = NULL,
  cluster = NULL,
  rho = 0,
  n = NULL,
  method = "Inverse",
  sm = gs("smrate"),
  incr = gs("incr"),
  method.incr = gs("method.incr"),
  method.ci = gs("method.ci.rate"),
  level = gs("level"),
  common = gs("common"),
  random = gs("random") | !is.null(tau.preset),
  overall = common | random,
  overall.hetstat = if (is.null(gs("overall.hetstat"))) common | random else
    gs("overall.hetstat"),
  prediction = gs("prediction") | !missing(method.predict),
  method.tau,
  method.tau.ci = gs("method.tau.ci"),
  level.hetstat = gs("level.hetstat"),
  tau.preset = NULL,
  TE.tau = NULL,
  tau.common = gs("tau.common"),
  method.I2 = gs("method.I2"),
  level.ma = gs("level.ma"),
  method.random.ci = gs("method.random.ci"),
  adhoc.hakn.ci = gs("adhoc.hakn.ci"),
  level.predict = gs("level.predict"),
  method.predict = gs("method.predict"),
  adhoc.hakn.pi = gs("adhoc.hakn.pi"),
  seed.predict = NULL,
  null.effect = NA,
  method.bias = gs("method.bias"),
  backtransf = gs("backtransf"),
  irscale = 1,
  irunit = "person-years",
  text.common = gs("text.common"),
  text.random = gs("text.random"),
  text.predict = gs("text.predict"),
  text.w.common = gs("text.w.common"),
  text.w.random = gs("text.w.random"),
  title = gs("title"),
  complab = gs("complab"),
  outclab = "",
  label.left = gs("label.left"),
  label.right = gs("label.right"),
  col.label.left = gs("col.label.left"),
  col.label.right = gs("col.label.right"),
  subgroup,
  subgroup.name = NULL,
  print.subgroup.name = gs("print.subgroup.name"),
  sep.subgroup = gs("sep.subgroup"),
  test.subgroup = gs("test.subgroup"),
  prediction.subgroup = gs("prediction.subgroup"),
  seed.predict.subgroup = NULL,
  byvar,
  hakn,
  adhoc.hakn,
  keepdata = gs("keepdata"),
  warn = gs("warn"),
  warn.deprecated = gs("warn.deprecated"),
  control = NULL,
  ...
)

Arguments

event	Number of events.
time	Person time at risk.
studlab	An optional vector with study labels.
data	An optional data frame containing the study information, i.e., event and time.
subset	An optional vector specifying a subset of studies to be used.
exclude	An optional vector specifying studies to exclude from meta-analysis, however, to include in printouts and forest plots.
cluster	An optional vector specifying which estimates come from the same cluster resulting in the use of a three-level meta-analysis model.
rho	Assumed correlation of estimates within a cluster.
n	Number of observations.
method	A character string indicating which method is to be used for pooling of studies. One of "Inverse" and "GLMM", can be abbreviated.
sm	A character string indicating which summary measure ("IR", "IRLN", "IRS", or "IRFT") is to be used for pooling of studies, see Details.
incr	A numeric which is added to the event number of studies with zero events, i.e., studies with an incidence rate of 0.
method.incr	A character string indicating which continuity correction method should be used ("only0", "if0all", or "all"), see Details.
method.ci	A character string indicating whether to use approximate normal ("NAsm") or exact Poisson ("Poisson") confidence limits.
level	The level used to calculate confidence intervals for individual studies.
common	A logical indicating whether a common effect meta-analysis should be conducted.
random	A logical indicating whether a random effects meta-analysis should be conducted.
overall	A logical indicating whether overall summaries should be reported. This argument is useful in a meta-analysis with subgroups if overall results should not be reported.
overall.hetstat	A logical value indicating whether to print heterogeneity measures for overall treatment comparisons. This argument is useful in a meta-analysis with subgroups if heterogeneity statistics should only be printed on subgroup level.
prediction	A logical indicating whether a prediction interval should be printed.
method.tau	A character string indicating which method is used to estimate the between-study variance \tau^2 and its square root \tau (see meta-package).
method.tau.ci	A character string indicating which method is used to estimate the confidence interval of \tau^2 and \tau (see meta-package).
level.hetstat	The level used to calculate confidence intervals for heterogeneity statistics.
tau.preset	Prespecified value for the square root of the between-study variance \tau^2.
TE.tau	Overall treatment effect used to estimate the between-study variance tau-squared.
tau.common	A logical indicating whether tau-squared should be the same across subgroups.
method.I2	A character string indicating which method is used to estimate the heterogeneity statistic I^2. Either "Q" or "tau2", can be abbreviated (see meta-package).
level.ma	The level used to calculate confidence intervals for meta-analysis estimates.
method.random.ci	A character string indicating which method is used to calculate confidence interval and test statistic for random effects estimate (see meta-package).
adhoc.hakn.ci	A character string indicating whether an ad hoc variance correction should be applied in the case of an arbitrarily small Hartung-Knapp variance estimate (see meta-package).
level.predict	The level used to calculate prediction interval for a new study.
method.predict	A character string indicating which method is used to calculate a prediction interval (see meta-package).
adhoc.hakn.pi	A character string indicating whether an ad hoc variance correction should be applied for prediction interval (see meta-package).
seed.predict	A numeric value used as seed to calculate bootstrap prediction interval (see meta-package).
null.effect	A numeric value specifying the effect under the null hypothesis.
method.bias	A character string indicating which test is to be used. Either "Begg", "Egger", or "Thompson", can be abbreviated. See function metabias.
backtransf	A logical indicating whether results for transformed rates (argument sm != "IR") should be back transformed in printouts and plots. If TRUE (default), results will be presented as incidence rates; otherwise transformed rates will be shown.
irscale	A numeric defining a scaling factor for printing of rates.
irunit	A character string specifying the time unit used to calculate rates, e.g. person-years.
text.common	A character string used in printouts and forest plot to label the pooled common effect estimate.
text.random	A character string used in printouts and forest plot to label the pooled random effects estimate.
text.predict	A character string used in printouts and forest plot to label the prediction interval.
text.w.common	A character string used to label weights of common effect model.
text.w.random	A character string used to label weights of random effects model.
title	Title of meta-analysis / systematic review.
complab	Comparison label.
outclab	Outcome label.
label.left	Graph label on left side of null effect in forest plot.
label.right	Graph label on right side of null effect in forest plot.
col.label.left	The colour of the graph label on the left side of the null effect.
col.label.right	The colour of the graph label on the right side of the null effect.
subgroup	An optional vector to conduct a meta-analysis with subgroups.
subgroup.name	A character string with a name for the subgroup variable.
print.subgroup.name	A logical indicating whether the name of the subgroup variable should be printed in front of the group labels.
sep.subgroup	A character string defining the separator between name of subgroup variable and subgroup label.
test.subgroup	A logical value indicating whether to print results of test for subgroup differences.
prediction.subgroup	A logical indicating whether prediction intervals should be printed for subgroups.
seed.predict.subgroup	A numeric vector providing seeds to calculate bootstrap prediction intervals within subgroups. Must be of same length as the number of subgroups.
byvar	Deprecated argument (replaced by 'subgroup').
hakn	Deprecated argument (replaced by 'method.random.ci').
adhoc.hakn	Deprecated argument (replaced by 'adhoc.hakn.ci').
keepdata	A logical indicating whether original data (set) should be kept in meta object.
warn	A logical indicating whether the addition of incr to studies with zero events should result in a warning.
warn.deprecated	A logical indicating whether warnings should be printed if deprecated arguments are used.
control	An optional list to control the iterative process to estimate the between-study variance \tau^2. This argument is passed on to rma.uni or rma.glmm, respectively.
...	Additional arguments passed on to rma.glmm function and to catch deprecated arguments.

Details

This function provides methods for common effect and random effects meta-analysis of single incidence rates to calculate an overall rate. Note, you should use R function metainc to compare incidence rates of pairwise comparisons instead of using metarate for each treatment arm separately which will break randomisation in randomised controlled trials.

The following transformations of incidence rates are implemented to calculate an overall rate:

• Log transformation (sm = "IRLN", default)

• Square root transformation (sm = "IRS")

• Freeman-Tukey Double arcsine transformation (sm = "IRFT")

• No transformation (sm = "IR")

List elements TE, TE.common, TE.random, etc., contain the transformed incidence rates. In printouts and plots these values are back transformed if argument backtransf = TRUE (default).

By default (argument method = "Inverse"), the inverse variance method (Borenstein et al., 2010) is used for pooling by calling metagen internally. A random intercept Poisson regression model (Stijnen et al., 2010) can be utilised instead with argument method = "GLMM" which calls the rma.glmm function from R package metafor.

A three-level random effects meta-analysis model (Van den Noortgate et al., 2013) is utilised if argument cluster is used and at least one cluster provides more than one estimate. Internally, rma.mv is called to conduct the analysis and weights.rma.mv with argument type = "rowsum" is used to calculate random effects weights.

Default settings are utilised for several arguments (assignments using gs function). These defaults can be changed for the current R session using the settings.meta function.

Furthermore, R function update.meta can be used to rerun a meta-analysis with different settings.

Continuity correction

Three approaches are available to apply a continuity correction:

• Only studies with a zero cell count (method.incr = "only0")

• All studies if at least one study has a zero cell count (method.incr = "if0all")

• All studies irrespective of zero cell counts (method.incr = "all")

If the summary measure (argument sm) is equal to "IR" or "IRLN", the continuity correction is applied if a study has zero events, i.e., an incidence rate of 0.

By default, 0.5 is used as continuity correction (argument incr). This continuity correction is used both to calculate individual study results with confidence limits and to conduct meta-analysis based on the inverse variance method.

For the Freeman-Tukey (Freeman & Tukey, 1950) and square root transformation as well as GLMMs no continuity correction is used.

Subgroup analysis

Argument subgroup can be used to conduct subgroup analysis for a categorical covariate. The metareg function can be used instead for more than one categorical covariate or continuous covariates.

Specify the null hypothesis of test for an overall effect

Argument null.effect can be used to specify the rate used under the null hypothesis in a test for an overall effect.

By default (null.effect = NA), no hypothesis test is conducted as it is unclear which value is a sensible choice for the data at hand. An overall rate of 2, for example, could be tested by setting argument null.effect = 2.

Note, all tests for an overall effect are two-sided with the alternative hypothesis that the effect is unequal to null.effect.

Exclusion of studies from meta-analysis

Arguments subset and exclude can be used to exclude studies from the meta-analysis. Studies are removed completely from the meta-analysis using argument subset, while excluded studies are shown in printouts and forest plots using argument exclude (see Examples in metagen). Meta-analysis results are the same for both arguments.

Presentation of meta-analysis results

Internally, both common effect and random effects models are calculated regardless of values choosen for arguments common and random. Accordingly, the estimate for the random effects model can be extracted from component TE.random of an object of class "meta" even if argument random = FALSE. However, all functions in R package meta will adequately consider the values for common and random. E.g. function print.meta will not print results for the random effects model if random = FALSE.

Argument irscale can be used to rescale rates, e.g. irscale = 1000 means that rates are expressed as events per 1000 time units, e.g. person-years. This is useful in situations with (very) low rates. Argument irunit can be used to specify the time unit used in individual studies (default: "person-years"). This information is printed in summaries and forest plots if argument irscale is not equal to 1.

A prediction interval will only be shown if prediction = TRUE.

Value

An object of class c("metarate", "meta") with corresponding generic functions (see meta-object).

Author(s)

Guido Schwarzer [e-mail]

References

Borenstein M, Hedges LV, Higgins JP, Rothstein HR (2010): A basic introduction to fixed-effect and random-effects models for meta-analysis. Research Synthesis Methods, 1, 97–111

Freeman MF & Tukey JW (1950): Transformations related to the angular and the square root. Annals of Mathematical Statistics, 21, 607–11

Stijnen T, Hamza TH, Ozdemir P (2010): Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Statistics in Medicine, 29, 3046–67

Van den Noortgate W, López-López JA, Marín-Martínez F, Sánchez-Meca J (2013): Three-level meta-analysis of dependent effect sizes. Behavior Research Methods, 45, 576–94

Viechtbauer W (2010): Conducting Meta-Analyses in R with the Metafor Package. Journal of Statistical Software, 36, 1–48

See Also

meta-package, update.meta, metacont, metagen, print.meta

Examples

# Apply various meta-analysis methods to estimate incidence rates
#
m1 <- metarate(4:1, c(10, 20, 30, 40))
m2 <- update(m1, sm = "IR")
m3 <- update(m1, sm = "IRS")
m4 <- update(m1, sm = "IRFT")
#
m1
m2
m3
m4
#
forest(m1)
forest(m1, irscale = 100)
forest(m1, irscale = 100, irunit = "person-days")
forest(m1, backtransf = FALSE)
## Not run: 
forest(m2)
forest(m3)
forest(m4)

## End(Not run)

m5 <- metarate(40:37, c(100, 200, 300, 400), sm = "IRFT")
m5

meta documentation built on Oct. 31, 2024, 5:07 p.m.