metainc: Meta-analysis of incidence rates

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

View source: R/metainc.R

Description

Calculation of fixed effect and random effects estimates (incidence rate ratio or incidence rate difference) for meta-analyses with event counts. Mantel-Haenszel, Cochran, 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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metainc(
  event.e,
  time.e,
  event.c,
  time.c,
  studlab,
  data = NULL,
  subset = NULL,
  exclude = NULL,
  method = if (sm == "IRSD") "Inverse" else "MH",
  sm = gs("sminc"),
  incr = gs("incr"),
  allincr = gs("allincr"),
  addincr = gs("addincr"),
  model.glmm = "UM.FS",
  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 = ifelse(!is.na(charmatch(tolower(method), "glmm", nomatch = NA)), "ML",
    gs("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"),
  method.bias = gs("method.bias"),
  n.e = NULL,
  n.c = NULL,
  backtransf = if (sm == "IRSD") FALSE else 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 = "",
  label.e = gs("label.e"),
  label.c = gs("label.c"),
  label.left = gs("label.left"),
  label.right = gs("label.right"),
  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.e

Number of events in experimental group.

time.e

Person time at risk in experimental group.

event.c

Number of events in control group.

time.c

Person time at risk in control group.

studlab

An optional vector with study labels.

data

An optional data frame containing the study information, i.e., event.e, time.e, event.c, and time.c.

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 "MH", "Inverse", "Cochran", or "GLMM" can be abbreviated.

sm

A character string indicating which summary measure ("IRR", "IRD" or "IRSD") is to be used for pooling of studies, see Details.

incr

A numerical value which is added to each cell frequency for studies with a zero cell count, see Details.

allincr

A logical indicating if incr is added to each cell frequency of all studies if at least one study has a zero cell count. If FALSE (default), incr is added only to each cell frequency of studies with a zero cell count.

addincr

A logical indicating if incr is added to each cell frequency of all studies irrespective of zero cell counts.

model.glmm

A character string indicating which GLMM should be used. One of "UM.FS", "UM.RS", and "CM.EL", see Details.

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 τ^2.

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.

method.bias

A character string indicating which test is to be used. Either "Begg", "Egger", or "Thompson", can be abbreviated. See function metabias.

n.e

Number of observations in experimental group (optional).

n.c

Number of observations in control group (optional).

backtransf

A logical indicating whether results for incidence rate ratio (sm = "IRR") should be back transformed in printouts and plots. If TRUE (default), results will be presented as incidence rate ratios; otherwise log incidence rate ratios will be shown.

irscale

A numeric defining a scaling factor for printing of incidence rate differences.

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.

label.e

Label for experimental group.

label.c

Label for control group.

label.left

Graph label on left side of forest plot.

label.right

Graph label on right side of forest plot.

byvar

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

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 warnings should be printed (e.g., if incr is added to studies with zero cell frequencies).

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

Calculation of fixed and random effects estimates for meta-analyses comparing two incidence rates.

The following measures of treatment effect are available:

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.

Meta-analysis method

By default, both fixed effect and random effects models are considered (see arguments comb.fixed and comb.random). If method is "MH" (default), the Mantel-Haenszel method is used to calculate the fixed effect estimate (Greenland & Robbins, 1985); if method is "Inverse", inverse variance weighting is used for pooling; if method is "Cochran", the Cochran method is used for pooling (Bayne-Jones, 1964, Chapter 8).

A distinctive and frequently overlooked advantage of incidence rates is that individual patient data (IPD) can be extracted from count data. Accordingly, statistical methods for IPD, i.e., generalised linear mixed models, can be utilised in a meta-analysis of incidence rate ratios (Stijnen et al., 2010). These methods are available (argument method = "GLMM") by calling the rma.glmm function from R package metafor internally.

Three different GLMMs are available for meta-analysis of incidence rate ratios using argument model.glmm (which corresponds to argument model in the rma.glmm function):

1. Poisson regression model with fixed study effects (default)
(model.glmm = "UM.FS", i.e., Unconditional Model - Fixed Study effects)
2. Mixed-effects Poisson regression model with random study effects
(model.glmm = "UM.RS", i.e., Unconditional Model - Random Study effects)
3. Generalised linear mixed model (conditional Poisson-Normal)
(model.glmm = "CM.EL", i.e., Conditional Model - Exact Likelihood)

Details on these three GLMMs as well as additional arguments which can be provided using argument '...' in metainc are described in rma.glmm where you can also find information on the iterative algorithms used for estimation. Note, regardless of which value is used for argument model.glmm, results for two different GLMMs are calculated: fixed effect model (with fixed treatment effect) and random effects model (with random treatment effects).

Continuity correction

For studies with a zero cell count, by default, 0.5 is added to all cell frequencies of these studies (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 Mantel-Haenszel method, Cochran method, and GLMMs, nothing is added to zero cell counts. Accordingly, estimates for these methods are not defined if the number of events is zero in all studies either in the experimental or control group.

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.

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.

Value

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

event.e, time.e, event.c, time.c, studlab, exclude,

As defined above.

sm, method, incr, allincr, addincr, model.glmm, warn,

As defined above.

level, level.comb, 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, method.bias,

As defined above.

tau.common, title, complab, outclab,

As defined above.

label.e, label.c, label.left, label.right,

As defined above.

byvar, bylab, print.byvar, byseparator

As defined above.

TE, seTE

Estimated treatment effect and standard error of 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 treatment effect 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 treatment effect (fixed effect model).

TE.random, seTE.random

Estimated overall treatment effect 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 treatment 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.

sparse

Logical flag indicating if any study included in meta-analysis has any zero cell frequencies.

incr.event

Increment added to number of events.

df.hakn

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

k.MH

Number of studies combined in meta-analysis using Mantel-Haenszel method.

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.

event.e.w

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

time.e.w

Total person time in subgroups (experimental group) - if byvar is not missing.

n.e.w

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

event.c.w

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

time.c.w

Total person time in subgroups (control group) - if byvar is not missing.

n.c.w

Number of observations in control group 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.

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

Bayne-Jones S et al. (1964): Smoking and Health: Report of the Advisory Committee to the Surgeon General of the United States. U-23 Department of Health, Education, and Welfare. Public Health Service Publication No. 1103.

DerSimonian R & Laird N (1986): Meta-analysis in clinical trials. Controlled Clinical Trials, 7, 177–88

Greenland S & Robins JM (1985): Estimation of a common effect parameter from sparse follow-up data. Biometrics, 41, 55–68

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

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

Knapp G & Hartung J (2003): Improved tests for a random effects meta-regression with a single covariate. Statistics in Medicine, 22, 2693–710

Paule RC & Mandel J (1982): Consensus values and weighting factors. Journal of Research of the National Bureau of Standards, 87, 377–85

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

metabin, update.meta, print.meta

Examples

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data(smoking)
m1 <- metainc(d.smokers, py.smokers, d.nonsmokers, py.nonsmokers,
              data = smoking, studlab = study)
print(m1, digits = 2)

m2 <- update(m1, method = "Cochran")
print(m2, digits = 2)

data(lungcancer)
m3 <- metainc(d.smokers, py.smokers,
              d.nonsmokers, py.nonsmokers,
              data = lungcancer, studlab = study)
print(m3, digits = 2)

# Redo Cochran meta-analysis with inflated standard errors
#
# All cause mortality
#
TEa <- log((smoking$d.smokers/smoking$py.smokers) /
           (smoking$d.nonsmokers/smoking$py.nonsmokers))
seTEa <- sqrt(1 / smoking$d.smokers + 1 / smoking$d.nonsmokers +
              2.5 / smoking$d.nonsmokers)
metagen(TEa, seTEa, sm = "IRR", studlab = smoking$study)

# Lung cancer mortality
#
TEl <- log((lungcancer$d.smokers/lungcancer$py.smokers) /
           (lungcancer$d.nonsmokers/lungcancer$py.nonsmokers))
seTEl <- sqrt(1 / lungcancer$d.smokers + 1 / lungcancer$d.nonsmokers +
              2.25 / lungcancer$d.nonsmokers)
metagen(TEl, seTEl, sm = "IRR", studlab = lungcancer$study)

## Not run: 
# Meta-analysis using generalised linear mixed models
# (only if R packages 'metafor' and 'lme4' are available)

# Poisson regression model (fixed study effects)
#
m4 <- metainc(d.smokers, py.smokers, d.nonsmokers, py.nonsmokers,
              data = smoking, studlab = study, method = "GLMM")
m4

# Mixed-effects Poisson regression model (random study effects)
#
update(m4, model.glmm = "UM.RS", nAGQ = 1)
#
# Generalised linear mixed model (conditional Poisson-Normal)
#
update(m4, model.glmm = "CM.EL")

## End(Not run)

meta documentation built on Sept. 14, 2021, 5:14 p.m.