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metainc

Meta-analysis of incidence rates

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

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"),
  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.
`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:

Incidence Rate Ratio (sm = "IRR")
Incidence Rate Difference (sm = "IRD")
Square root transformed Incidence Rate Difference (sm = "IRSD")

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:

DerSimonian-Laird estimator (method.tau = "DL")
Paule-Mandel estimator (method.tau = "PM")
Restricted maximum-likelihood estimator (method.tau = "REML")
Maximum-likelihood estimator (method.tau = "ML")
Hunter-Schmidt estimator (method.tau = "HS")
Sidik-Jonkman estimator (method.tau = "SJ")
Hedges estimator (method.tau = "HE")
Empirical Bayes estimator (method.tau = "EB")

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

Examples

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)