metarate: Meta-analysis of single incidence rates

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/metarate.R

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

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metarate(
  event,
  time,
  studlab,
  data = NULL,
  subset = NULL,
  exclude = NULL,
  method = "Inverse",
  sm = gs("smrate"),
  incr = gs("incr"),
  allincr = gs("allincr"),
  addincr = gs("addincr"),
  level = gs("level"),
  level.comb = gs("level.comb"),
  comb.fixed = gs("comb.fixed"),
  comb.random = gs("comb.random"),
  overall = comb.fixed | comb.random,
  overall.hetstat = comb.fixed | comb.random,
  hakn = gs("hakn"),
  adhoc.hakn = gs("adhoc.hakn"),
  method.tau,
  method.tau.ci = gs("method.tau.ci"),
  tau.preset = NULL,
  TE.tau = NULL,
  tau.common = gs("tau.common"),
  prediction = gs("prediction"),
  level.predict = gs("level.predict"),
  null.effect = NA,
  method.bias = gs("method.bias"),
  backtransf = gs("backtransf"),
  irscale = 1,
  irunit = "person-years",
  text.fixed = gs("text.fixed"),
  text.random = gs("text.random"),
  text.predict = gs("text.predict"),
  text.w.fixed = gs("text.w.fixed"),
  text.w.random = gs("text.w.random"),
  title = gs("title"),
  complab = gs("complab"),
  outclab = "",
  byvar,
  bylab,
  print.byvar = gs("print.byvar"),
  byseparator = gs("byseparator"),
  test.subgroup = gs("test.subgroup"),
  keepdata = gs("keepdata"),
  warn = gs("warn"),
  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.

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.

allincr

A logical indicating if incr is considered for all studies if at least one study has zero events. If FALSE (default), incr is considered only in studies with zero events.

addincr

A logical indicating if incr is used for all studies irrespective of number of events.

level

The level used to calculate confidence intervals for individual studies.

level.comb

The level used to calculate confidence intervals for pooled estimates.

comb.fixed

A logical indicating whether a fixed effect meta-analysis should be conducted.

comb.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.

hakn

A logical indicating whether the method by Hartung and Knapp should be used to adjust test statistics and confidence intervals.

adhoc.hakn

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 Details.

method.tau

A character string indicating which method is used to estimate the between-study variance τ^2 and its square root τ. Either "DL", "PM", "REML", "ML", "HS", "SJ", "HE", or "EB", can be abbreviated.

method.tau.ci

A character string indicating which method is used to estimate the confidence interval of τ^2 and τ. Either "QP", "BJ", or "J", or "", can be abbreviated.

tau.preset

Prespecified value for the square root of the between-study variance τ^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.

prediction

A logical indicating whether a prediction interval should be printed.

level.predict

The level used to calculate prediction interval for a new study.

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.fixed

A character string used in printouts and forest plot to label the pooled fixed 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.fixed

A character string used to label weights of fixed 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.

byvar

An optional vector containing grouping information (must be of same length as event).

bylab

A character string with a label for the grouping variable.

print.byvar

A logical indicating whether the name of the grouping variable should be printed in front of the group labels.

byseparator

A character string defining the separator between label and levels of grouping variable.

test.subgroup

A logical value indicating whether to print results of test for subgroup differences.

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.

control

An optional list to control the iterative process to estimate the between-study variance τ^2. This argument is passed on to rma.uni or rma.glmm, respectively.

...

Additional arguments passed on to rma.glmm function.

Details

This function provides methods for fixed 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:

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.

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

If the summary measure (argument sm) is equal to "IR" or "IRLN", a continuity correction is applied if any 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.

Estimation of between-study variance

The following methods to estimate the between-study variance τ^2 are available for the inverse variance method:

See metagen for more information on these estimators. Note, the maximum-likelihood method is utilized for GLMMs.

Confidence interval for the between-study variance

The following methods to calculate a confidence interval for τ^2 and τ are available.

Argument Method
method.tau.ci = "J" Method by Jackson
method.tau.ci = "BJ" Method by Biggerstaff and Jackson
method.tau.ci = "QP" Q-Profile method

See metagen for more information on these methods. For GLMMs, no confidence intervals for τ^2 and τ are calculated. Likewise, no confidence intervals for τ^2 and τ are calculated if method.tau.ci = "".

Hartung-Knapp method

Hartung and Knapp (2001a,b) proposed an alternative method for random effects meta-analysis based on a refined variance estimator for the treatment estimate. Simulation studies (Hartung and Knapp, 2001a,b; IntHout et al., 2014; Langan et al., 2019) show improved coverage probabilities compared to the classic random effects method.

In rare settings with very homogeneous treatment estimates, the Hartung-Knapp variance estimate can be arbitrarily small resulting in a very narrow confidence interval (Knapp and Hartung, 2003; Wiksten et al., 2016). In such cases, an ad hoc variance correction has been proposed by utilising the variance estimate from the classic random effects model with the HK method (Knapp and Hartung, 2003; IQWiQ, 2020). An alternative approach is to use the wider confidence interval of classic fixed or random effects meta-analysis and the HK method (Wiksten et al., 2016; Jackson et al., 2017).

Argument adhoc.hakn can be used to choose the ad hoc method:

Argument Ad hoc method
adhoc.hakn = "" not used
adhoc.hakn = "se" use variance correction if HK standard error is smaller
than standard error from classic random effects
meta-analysis (Knapp and Hartung, 2003)
adhoc.hakn = "iqwig6" use variance correction if HK confidence interval
is narrower than CI from classic random effects model
with DerSimonian-Laird estimator (IQWiG, 2020)
adhoc.hakn = "ci" use wider confidence interval of classic random effects
and HK meta-analysis
(Hybrid method 2 in Jackson et al., 2017)

For GLMMs, a method similar to Knapp and Hartung (2003) is implemented, see description of argument tdist in rma.glmm, and the ad hoc variance correction is not available.

Prediction interval

A prediction interval for the proportion in a new study (Higgins et al., 2009) is calculated if arguments prediction and comb.random are TRUE. Note, the definition of prediction intervals varies in the literature. This function implements equation (12) of Higgins et al., (2009) which proposed a t distribution with K-2 degrees of freedom where K corresponds to the number of studies in the meta-analysis.

Subgroup analysis

Argument byvar 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 fixed effect and random effects models are calculated regardless of values choosen for arguments comb.fixed and comb.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 comb.random = FALSE. However, all functions in R package meta will adequately consider the values for comb.fixed and comb.random. E.g. function print.meta will not print results for the random effects model if comb.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.

Value

An object of class c("metarate", "meta") with corresponding print, summary, and forest functions. The object is a list containing the following components:

event, n, studlab, exclude,

As defined above.

sm, incr, allincr, addincr, method.ci,

As defined above.

level, level.comb,

As defined above.

comb.fixed, comb.random,

As defined above.

overall, overall.hetstat,

As defined above.

hakn, adhoc.hakn, method.tau, method.tau.ci,

As defined above.

tau.preset, TE.tau, null.hypothesis,

As defined above.

method.bias, tau.common, title, complab, outclab,

As defined above.

byvar, bylab, print.byvar, byseparator, warn

As defined above.

TE, seTE

Estimated (un)transformed incidence rate and its standard error for individual studies.

lower, upper

Lower and upper confidence interval limits for individual studies.

zval, pval

z-value and p-value for test of treatment effect for individual studies.

w.fixed, w.random

Weight of individual studies (in fixed and random effects model).

TE.fixed, seTE.fixed

Estimated overall (un)transformed incidence rate and standard error (fixed effect model).

lower.fixed, upper.fixed

Lower and upper confidence interval limits (fixed effect model).

statistic.fixed, pval.fixed

z-value and p-value for test of overall effect (fixed effect model).

TE.random, seTE.random

Estimated overall (un)transformed incidence rate and standard error (random effects model).

lower.random, upper.random

Lower and upper confidence interval limits (random effects model).

statistic.random, pval.random

z-value or t-value and corresponding p-value for test of overall effect (random effects model).

prediction, level.predict

As defined above.

seTE.predict

Standard error utilised for prediction interval.

lower.predict, upper.predict

Lower and upper limits of prediction interval.

k

Number of studies combined in meta-analysis.

Q

Heterogeneity statistic Q.

df.Q

Degrees of freedom for heterogeneity statistic.

pval.Q

P-value of heterogeneity test.

Q.LRT

Heterogeneity statistic for likelihood-ratio test (only if method = "GLMM").

df.Q.LRT

Degrees of freedom for likelihood-ratio test

pval.Q.LRT

P-value of likelihood-ratio test.

tau2

Between-study variance τ^2.

se.tau2

Standard error of τ^2.

lower.tau2, upper.tau2

Lower and upper limit of confidence interval for τ^2.

tau

Square-root of between-study variance τ.

lower.tau, upper.tau

Lower and upper limit of confidence interval for τ.

H

Heterogeneity statistic H.

lower.H, upper.H

Lower and upper confidence limit for heterogeneity statistic H.

I2

Heterogeneity statistic I^2.

lower.I2, upper.I2

Lower and upper confidence limit for heterogeneity statistic I^2.

Rb

Heterogeneity statistic R_b.

lower.Rb, upper.Rb

Lower and upper confidence limit for heterogeneity statistic R_b.

method

A character string indicating method used for pooling: "Inverse"

df.hakn

Degrees of freedom for test of treatment effect for Hartung-Knapp method (only if hakn = TRUE).

bylevs

Levels of grouping variable - if byvar is not missing.

TE.fixed.w, seTE.fixed.w

Estimated treatment effect and standard error in subgroups (fixed effect model) - if byvar is not missing.

lower.fixed.w, upper.fixed.w

Lower and upper confidence interval limits in subgroups (fixed effect model) - if byvar is not missing.

statistic.fixed.w, pval.fixed.w

z-value and p-value for test of treatment effect in subgroups (fixed effect model) - if byvar is not missing.

TE.random.w, seTE.random.w

Estimated treatment effect and standard error in subgroups (random effects model) - if byvar is not missing.

lower.random.w, upper.random.w

Lower and upper confidence interval limits in subgroups (random effects model) - if byvar is not missing.

statistic.random.w, pval.random.w

z-value or t-value and corresponding p-value for test of treatment effect in subgroups (random effects model) - if byvar is not missing.

w.fixed.w, w.random.w

Weight of subgroups (in fixed and random effects model) - if byvar is not missing.

df.hakn.w

Degrees of freedom for test of treatment effect for Hartung-Knapp method in subgroups - if byvar is not missing and hakn = TRUE.

n.harmonic.mean.w

Harmonic mean of number of observations in subgroups (for back transformation of Freeman-Tukey Double arcsine transformation) - if byvar is not missing.

event.w

Number of events in subgroups - if byvar is not missing.

n.w

Number of observations in subgroups - if byvar is not missing.

k.w

Number of studies combined within subgroups - if byvar is not missing.

k.all.w

Number of all studies in subgroups - if byvar is not missing.

Q.w.fixed

Overall within subgroups heterogeneity statistic Q (based on fixed effect model) - if byvar is not missing.

Q.w.random

Overall within subgroups heterogeneity statistic Q (based on random effects model) - if byvar is not missing (only calculated if argument tau.common is TRUE).

df.Q.w

Degrees of freedom for test of overall within subgroups heterogeneity - if byvar is not missing.

pval.Q.w.fixed

P-value of within subgroups heterogeneity statistic Q (based on fixed effect model) - if byvar is not missing.

pval.Q.w.random

P-value of within subgroups heterogeneity statistic Q (based on random effects model) - if byvar is not missing.

Q.b.fixed

Overall between subgroups heterogeneity statistic Q (based on fixed effect model) - if byvar is not missing.

Q.b.random

Overall between subgroups heterogeneity statistic Q (based on random effects model) - if byvar is not missing.

df.Q.b

Degrees of freedom for test of overall between subgroups heterogeneity - if byvar is not missing.

pval.Q.b.fixed

P-value of between subgroups heterogeneity statistic Q (based on fixed effect model) - if byvar is not missing.

pval.Q.b.random

P-value of between subgroups heterogeneity statistic Q (based on random effects model) - if byvar is not missing.

tau.w

Square-root of between-study variance within subgroups - if byvar is not missing.

H.w

Heterogeneity statistic H within subgroups - if byvar is not missing.

lower.H.w, upper.H.w

Lower and upper confidence limit for heterogeneity statistic H within subgroups - if byvar is not missing.

I2.w

Heterogeneity statistic I^2 within subgroups - if byvar is not missing.

lower.I2.w, upper.I2.w

Lower and upper confidence limit for heterogeneity statistic I^2 within subgroups - if byvar is not missing.

incr.event

Increment added to number of events.

keepdata

As defined above.

data

Original data (set) used in function call (if keepdata = TRUE).

subset

Information on subset of original data used in meta-analysis (if keepdata = TRUE).

.glmm.fixed

GLMM object generated by call of rma.glmm function (fixed effect model).

.glmm.random

GLMM object generated by call of rma.glmm function (random effects model).

call

Function call.

version

Version of R package meta used to create object.

version.metafor

Version of R package metafor used for GLMMs.

Author(s)

Guido Schwarzer sc@imbi.uni-freiburg.de

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

Higgins JPT, Thompson SG, Spiegelhalter DJ (2009): A re-evaluation of random-effects meta-analysis. Journal of the Royal Statistical Society: Series A, 172, 137–59

Hartung J, Knapp G (2001a): On tests of the overall treatment effect in meta-analysis with normally distributed responses. Statistics in Medicine, 20, 1771–82

Hartung J, Knapp G (2001b): A refined method for the meta-analysis of controlled clinical trials with binary outcome. Statistics in Medicine, 20, 3875–89

IntHout J, Ioannidis JPA, Borm GF (2014): The Hartung-Knapp-Sidik-Jonkman method for random effects meta-analysis is straightforward and considerably outperforms the standard DerSimonian-Laird method. BMC Medical Research Methodology, 14, 25

IQWiG (2020): General Methods: Version 6.0. https://www.iqwig.de/en/about-us/methods/methods-paper/

Jackson D, Law M, Rücker G, Schwarzer G (2017): The Hartung-Knapp modification for random-effects meta-analysis: A useful refinement but are there any residual concerns? Statistics in Medicine, 36, 3923–34

Langan D, Higgins JPT, Jackson D, Bowden J, Veroniki AA, Kontopantelis E, et al. (2019): A comparison of heterogeneity variance estimators in simulated random-effects meta-analyses. Research Synthesis Methods, 10, 83–98

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

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

Wiksten A, Rücker G, Schwarzer G (2016): Hartung-Knapp method is not always conservative compared with fixed-effect meta-analysis. Statistics in Medicine, 35, 2503–15

See Also

update.meta, metacont, metagen, print.meta

Examples

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# 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 Sept. 14, 2021, 5:14 p.m.