limitmeta: Limit meta-analysis

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

View source: R/limitmeta.R

Description

Implementation of the limit meta-analysis method by Rücker et al. (2011) to adjust for bias in meta-analysis.

Usage

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limitmeta(
  x,
  method.adjust = "beta0",
  level = x$level,
  level.comb = x$level.comb,
  backtransf = x$backtransf,
  title = x$title,
  complab = x$complab,
  outclab = x$outclab
)

Arguments

x

An object of class meta.

method.adjust

A character string indicating which adjustment method is to be used. One of "beta0", "betalim", or "mulim", can be abbreviated.

level

The level used to calculate confidence intervals for individual studies.

level.comb

The level used to calculate confidence intervals for pooled estimates.

backtransf

A logical indicating whether results should be back transformed in printouts and plots. If backtransf=FALSE, results for the odds ratio are printed as log odds ratios rather than odds ratio, for example.

title

Title of meta-analysis / systematic review.

complab

Comparison label.

outclab

Outcome label.

Details

This function provides the method by Rücker et al. (2011) to estimate an effect estimate adjusted for bias in meta-analysis. The underlying model is an extended random effects model that takes account of possible small study effects by allowing the treatment effect to depend on the standard error:

theta(i) = beta + sqrt(SE(i)^2 + tau^2)(epsilon(i) + alpha),

where epsilon(i) follows a standard normal distribution. Here theta(i) is the observed effect in study i, beta the global mean, SE(i) the within-study standard error, and tau^2 the between-study variance. The parameter alpha represents the bias introduced by small-study effects. On the one hand, alpha can be interpreted as the expected shift in the standardized treatment effect if precision is very small. On the other hand, theta(adj) = beta + tau*alpha is interpreted as the limit treatment effect for a study with infinite precision (corresponding to SE(i) = 0).

Note that as alpha is included in the model equation, beta has a different interpretation as in the usual random effects model. The two models agree only if alpha=0. If there are genuine small-study effects, the model includes a component making the treatment effect depend on the standard error. The expected treatment effect of a study of infinite precision, beta + tau*alpha, is used as an adjusted treatment effect estimate.

The maximum likelihood estimates for alpha and beta can be interpreted as intercept and slope in linear regression on a so-called generalised radial plot, where the x-axis represents the inverse of sqrt(SE(i)^2 + tau^2) and the y-axis represents the treatment effect estimates, divided by sqrt(SE(i)^2 + tau^2).

Two further adjustments are available that use a shrinkage procedure. Based on the extended random effects model, a limit meta-analysis is defined by inflating the precision of each study with a common factor. The limit meta-analysis yields shrunken estimates of the study-specific effects, comparable to empirical Bayes estimates. Based on the extended random effects model, we obtain three different treatment effect estimates that are adjusted for small-study effects:

See Rücker, Schwarzer et al. (2011), Section 7, for the definition of G^2 and the three heterogeneity statisticics Q, Q.small, and Q.resid.

For comparison, the original random effects meta-analysis is always printed in the sensitivity analysis.

Value

An object of class "limitmeta" with corresponding print, summary and funnel function. The object is a list containing the following components:

x, level, level.comb,method.adjust,title, complab, outclab

As defined above.

TE, seTE

Estimated treatment effect and standard error of individual studies.

TE.limit, seTE.limit

Shrunken estimates and standard error of individual studies.

studlab

Study labels.

TE.random, seTE.random

Unadjusted 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

Statistic and corresponding p-value for test of overall treatment effect (random effects model).

w.random

Weight of individual studies (in random effects model).

tau

Square-root of between-study variance.

TE.adjust, seTE.adjust

Adjusted overall effect and standard error (random effects model).

lower.adjust, upper.adjust

Lower and upper confidence interval limits for adjusted effect estimate (random effects model).

statistic.adjust, pval.adjust

Statistic and corresponding p-value for test of overall treatment effect for adjusted estimate (random effects model).

alpha.r

Intercept of the linear regression line on the generalised radial plot, here interpreted as bias parameter in an extended random effects model. Represents the expected shift in the standardized treatment effect if precision is very small.

beta.r

Slope of the linear regression line on the generalised radial plot.

Q

Heterogeneity statistic.

Q.small

Heterogeneity statistic for small study effects.

Q.resid

Heterogeneity statistic for residual heterogeneity beyond small study effects.

G.squared

Heterogeneity statistic G^2 (ranges from 0 to 100%).

k

Number of studies combined in meta-analysis.

call

Function call.

version

Version of R package metasens used to create object.

Author(s)

Gerta Rücker ruecker@imbi.uni-freiburg.de, Guido Schwarzer sc@imbi.uni-freiburg.de

References

Rücker G, Carpenter JR, Schwarzer G (2011): Detecting and adjusting for small-study effects in meta-analysis. Biometrical Journal, 53, 351–68

Rücker G, Schwarzer G, Carpenter JR, Binder H, Schumacher M (2011): Treatment-effect estimates adjusted for small-study effects via a limit meta-analysis. Biostatistics, 12, 122–42

See Also

funnel.limitmeta, print.limitmeta

Examples

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data(Moore1998)
m1 <- metabin(succ.e, nobs.e, succ.c, nobs.c,
              data = Moore1998, sm = "OR", method = "Inverse")

print(summary(limitmeta(m1)), digits = 2)

Example output

Loading required package: meta
Loading 'meta' package (version 4.15-1).
Type 'help(meta)' for a brief overview.
Loading 'metasens' package (version 0.5-0).
Result of limit meta-analysis:

 Random effects model   OR       95%-CI    z     pval
    Adjusted estimate 1.84 [1.26; 2.68] 3.16   0.0016
  Unadjusted estimate 3.73 [2.80; 4.97] 9.02 < 0.0001

Quantifying heterogeneity:
tau^2 = 0.4660; I^2 = 68.2% [55.4%; 77.4%]; G^2 = 91.5%

Test of heterogeneity:
      Q d.f.  p-value
 113.35   36 < 0.0001

Test of small-study effects:
   Q-Q' d.f.  p-value
  44.03    1 < 0.0001

Test of residual heterogeneity beyond small-study effects:
     Q' d.f.  p-value
  69.32   35   0.0005

Details on adjustment method:
- expectation (beta0)

metasens documentation built on Jan. 16, 2021, 5:38 p.m.