bayesmeta (version 3.4)

SchmidliEtAl2017: Historical variance example data

Description

Estimates of endpoint variances from six studies.

Usage

data("SchmidliEtAl2017")

Format

The data frame contains the following columns:

study	character	study label
N	integer	total sample size
stdev	numeric	standard deviation estimate
df	integer	associated degrees of freedom

Details

Schmidli et al. (2017) investigated the use of information on an endpoint's variance from previous (“historical”) studies for the design and analysis of a new clinical trial. As an example application, the problem of designing a trial in wet age-related macular degeneration (AMD) was considered. Trial design, and in particular considerations regarding the required sample size, hinge on the expected amount of variability in the primary endpoint (here: visual acuity, which is measured on a scale ranging from 0 to 100 via an eye test chart).

Historical data from six previous trials are available (Szabo et al.; 2015), each trial providing an estimate \(\hat{s}_i\) of the endpoint's standard deviation along with the associated number of degrees of freedom \(\nu_i\). The standard deviations may then be modelled on the logarithmic scale, where the estimates and their associated standard errors are given by $$y_i=\log(\hat{s}_i) \quad \mbox{and} \quad \sigma_i=\sqrt{\frac{1}{2\,\nu_i}}$$

The unit information standard deviation (UISD) for a logarithmic standard deviation then is at approximately \(\frac{1}{\sqrt{2}}\).

References

S.M. Szabo, M. Hedegaard, K. Chan, K. Thorlund, R. Christensen, H. Vorum, J.P. Jansen. Ranibizumab vs. aflibercept for wet age-related macular degeneration: network meta-analysis to understand the value of reduced frequency dosing. Current Medical Research and Opinion, 31(11):2031-2042, 2015. tools:::Rd_expr_doi("10.1185/03007995.2015.1084909").

See Also

uisd, ess.

Examples

# load data:
data("SchmidliEtAl2017")

# show data:
SchmidliEtAl2017

if (FALSE) {
# derive log-SDs and their standard errors:
dat <- cbind(SchmidliEtAl2017,
             logstdev    = log(SchmidliEtAl2017$stdev),
             logstdev.se = sqrt(0.5/SchmidliEtAl2017$df))
dat

# alternatively, use "metafor::escalc()" function:
es <- escalc(measure="SDLN",
             yi=log(stdev), vi=0.5/df, ni=N,
             slab=study, data=SchmidliEtAl2017)
es

# perform meta-analysis of log-stdevs:
bm <- bayesmeta(y=dat$logstdev,
                sigma=dat$logstdev.se,
                label=dat$study,
                tau.prior=function(t){dhalfnormal(t, scale=sqrt(2)/4)})

# or, alternatively:
bm <- bayesmeta(es,
                tau.prior=function(t){dhalfnormal(t, scale=sqrt(2)/4)})

# draw forest plot (see Fig.1):
forestplot(bm, zero=NA,
           xlab="log standard deviation")

# show heterogeneity posterior:
plot(bm, which=4, prior=TRUE)

# posterior of log-stdevs, heterogeneity,
# and predictive distribution:
bm$summary

# prediction (standard deviations):
exp(bm$summary[c(2,5,6),"theta"])
exp(bm$qposterior(theta=c(0.025, 0.25, 0.50, 0.75, 0.975), predict=TRUE))

# compute required sample size (per arm):
power.t.test(n=NULL, delta=8, sd=10.9, power=0.8)
power.t.test(n=NULL, delta=8, sd=14.0, power=0.8)

# check UISD:
uisd(es, indiv=TRUE)
uisd(es)
1 / sqrt(2)

# compute predictive distribution's ESS:
ess(bm, uisd=1/sqrt(2))
# actual total sample size:
sum(dat$N)

# illustrate predictive distribution
# on standard-deviation-scale (Fig.2):
x <- seq(from=5, to=20, length=200)
plot(x, (1/x) * bm$dposterior(theta=log(x), predict=TRUE), type="l",
     xlab=expression("predicted standard deviation "*sigma[k+1]),
     ylab="predictive density")
abline(h=0, col="grey")
}