Two-stage individual participant data meta-analysis
and flexible forest plotsDavid Fisher
MRC Clinical Trials Unit Hub for Trials Methodology Research
at UCL
2013 UK Stata Users Group Meeting Cass Business School, London
Outline of presentation• Introduction to individual patient data (IPD) meta-analysis (MA)
• IPD vs aggregate-data (AD) MA• “One-stage” vs “two-stage” IPD MA
• The ipdmetan command• Basic use; comparison with metan• Covariate interactions• Combining AD with IPD• Advanced syntax
• The forestplot command • Interface with ipdmetan• Stand-alone use and “stacking”
• Summary and Conclusion
Introduction to IPD meta-analysis
• Meta-analysis (MA):• Use statistical methods to combine results of “similar”
trials to give a single estimate of effect• Increase power & precision• Assess whether treatment effects are similar in across
trials (heterogeneity)
• Aggregate data (AD) vs IPD:• “Traditional” MAs gather results from publications
• Aggregated across all patients in the trial; nothing is known of individual patients
• IPD MAs gather raw data from trial investigators• Ensures all relevant patients are included• Ensures similar analysis across all trials• Allows more complex analysis, e.g. patient-level
interactions
“One-stage” IPD MA
• Consider a linear regression (extension to GLMs or time-to-event regressions is straightforward)
• For a one-stage IPD MA (i = trial, j = patient):𝑦 𝑖𝑗=𝛼𝑖+ (𝛽+𝑢𝑖 ) 𝑥 𝑖𝑗
• Examples in Stata:• Fixed effects: regress y x i.trial• Random effects:
xtmixed y x i.trial || trial: x, nocons
where αi = trial identifiersβ = overall treatment effect estimated across all trials i(with optional random effect ui)
“Two-stage” IPD MA
• For a two-stage IPD MA:
𝑦 (𝑖 ) 𝑗=𝛼(𝑖)+𝛽(𝑖) 𝑥 (𝑖 ) 𝑗
𝑦 (1 ) 𝑗=𝛼(1 )+𝛽(1) 𝑥( 1) 𝑗…
for trial 1
for trial i…
• Then: �̂�=∑𝑖𝑤 𝑖 𝛽(𝑖)
∑𝑖𝑤𝑖
and
𝑤𝑖=1
𝑠𝑒 ( 𝛽(𝑖))2
• Weights wi may be altered to give random effects• e.g. DerSimonian & Laird,
• Straightforward, but currently messy in Stata
where
𝑠𝑒 ( �̂�)= 1∑𝑖𝑤 𝑖
Treatment-covariate interactions
• Assessment of patient-level covariate interactions is a great advantage of IPD
• Arguably best done with “one-stage”• Main effects & interactions (& correlations) estimated
simultaneously• But basic analysis also possible with “two-stage”
• Relative effect (interaction coefficient) only• Same approach (inverse-variance) as for main effects• Ensures no estimation bias from between-trial effects• Can be presented in a forest plot, with assessment of
heterogeneity etc.• Discussed in a published paper (Fisher 2011)
𝑦 𝑖𝑗=𝛼𝑖+𝛽 𝑥𝑖𝑗+𝛾 𝑧𝑖𝑗+𝛿𝑥𝑖𝑗 𝑧 𝑖𝑗
“One-stage” vs “two-stage”
One-stage Two-stagePros - All coeffs & correls
estimated simultaneously
- Flexible & extendable model structure
- Natural extension of AD MA- Easily presentable in forest plots- Applicable to any set of effect
estimates and SEs(incl. interactions)
- Negligible difference to 1S in most common scenarios
Cons - Requires more statistical expertise
- Challenging in certain situations, e.g. random-effects with time-to-event data
- Not a natural fit with forest plots
- Only a single estimate can be pooled, which limits complexity(e.g. interactions)
- Theoretically inferior in (at least) some scenarios
Example data
• IPD MA of randomised trials of post-operative radiotherapy (PORT) in non-small cell lung cancer• Trial ID (k=11)• Patient ID (n=2343)• Treatment arm
• Outcome is censored time to overall survival (death from any cause)• Time to event (from randomisation)• Event type (death or censorship)
• Certain covariate measurements also available, not necessarily for all trials or patients• Disease stage (factor, but treat as continuous)• (+ others)
ipdmetan syntax
ipdmetan,study(trialid) eform
: stcox arm, strata(sex)
ipdmetan options after comma, before colon
estimation_command and options after colon
Uses “prefix” command syntax:
ipdmetan [exp_list], study(study_ID) [ ipd_options ad(aggregate_data_options) forestplot(forest_plot_options)]
: estimation_command ...
Example: default is to pool coeffs from first dep. var. (excluding baseline factor levels)
Trials included: 11Patients included: 2342 Meta-analysis pooling of main (treatment) effect estimate armusing Fixed-effects --------------------------------------------------------------------trial reference |number | Effect [95% Conf. Interval] % Weight----------------------+---------------------------------------------belgium | 1.456 1.072 1.979 11.09EORTC 08861 | 1.643 0.913 2.956 3.02LILLE | 1.568 1.060 2.319 6.81... ... ... ... ...----------------------+---------------------------------------------Overall effect | 1.178 1.064 1.305 100.00--------------------------------------------------------------------
Test of overall effect = 1: z = 3.153 p = 0.002
Heterogeneity Measures--------------------------------------------------- | value df p-value---------------+-----------------------------------Cochrane Q | 15.88 10 0.103I² (%) | 37.0%Modified H² | 0.588tau² | 0.0180---------------------------------------------------
I² = between-study variance (tau²) as a percentage of total varianceModified H² = ratio of tau² to typical within-study variance
Output style similar to metan
or metaan
Variable label
Basic forest plot
belgium
LCSG 773
CAMS
MRC LU11
EORTC 08861
SLOVENIA
LILLE
GETCB 04CB86
GETCB 05CB86
ITALY
KOREA
Overall (I-squared = 37.0%, p = 0.103)
reference number
trial
1.46 (1.07, 1.98)
1.12 (0.83, 1.53)
1.03 (0.77, 1.38)
0.96 (0.74, 1.24)
1.64 (0.91, 2.96)
0.89 (0.54, 1.49)
1.57 (1.06, 2.32)
1.14 (0.80, 1.62)
1.44 (1.13, 1.83)
0.69 (0.40, 1.20)
1.16 (0.76, 1.76)
1.18 (1.06, 1.31)
Effect (95% CI)
11.09
11.13
12.20
16.00
3.02
3.97
6.81
8.48
17.84
3.49
5.98
100.00
Weight
%
1 2.5 4.25
Forest plot of covariate interactions
belgium
LCSG 773
CAMS
MRC LU11
EORTC 08861
GETCB 04CB86
GETCB 05CB86
KOREA
SLOVENIA
LILLE
ITALY
Overall (I-squared = 2.7%, p = 0.409)
reference number
trial
0.92 (0.61, 1.40)
0.76 (0.40, 1.45)
0.77 (0.43, 1.39)
0.62 (0.36, 1.07)
0.39 (0.14, 1.09)
0.94 (0.50, 1.77)
0.97 (0.72, 1.30)
2.09 (0.70, 6.27)
(Insufficient data)
(Insufficient data)
(Insufficient data)
0.87 (0.72, 1.04)
Effect (95% CI)
18.70
8.11
9.49
11.26
3.16
8.22
38.35
2.73
100.00
Weight
%
1 2.5 4.25 8.125
Trials included: 8Patients included: 1962
Meta-analysis pooling of interaction effect estimate
1.arm#c.stage2
using Fixed-effects
ipdmetan, study(trialid) eform interaction keepall: stcox arm##c.stage
default is to pool coeffs from first interaction term
Inclusion of aggregate data
• I don’t have a separate aggregate dataset, so I will create one artificially from my IPD dataset
. ** Generate artificial trial subgrouping
. gen subgroup = inlist(trialid, 1, 8, 12, 15)
. label define subgroup_ 0 "Trial group 1" 1 "Trial group 2"
. label values subgroup subgroup_
. ** Run ipdmetan within one of the subgroups; save the dataset
. qui ipdmetan,study(trialid) by(subgroup) nooverall nographsaving(subgroup1.dta)
: stcox arm if subgroup==1, strata(sex)
(Aside: Contents of subgroup1.dta)
_use trialid _labels _ES _seES _lci _uci _wgt _NN1 1belgium 0.376 0.156 0.069 0.682 0.286 2021 8EORTC 08861 0.496 0.300 -0.091 1.084 0.078 1051 12LILLE 0.450 0.200 0.058 0.841 0.176 1631 15GETCB 05CB86 0.362 0.123 0.120 0.603 0.460 539
Inclusion of aggregate data: Syntax
. ipdmetan, study(trialid) eform nooverall
ad(subgroup1.dta, byad)
: stcox arm if subgroup==0, strata(sex)
Do not pool IPD and aggregate
together
Aggregate data syntax
estimation_command
“byad” = treat IPD & aggregate data as
subgroups
Trials included from IPD: 7Patients included: 1333 Trials included from aggregate data: 4Patients included: 1009 Pooling of main (treatment) effect estimate armusing Fixed-effects
-------------------------------------------------------------------trial reference |number | Effect [95% Conf. Interval] % Weight---------------------+---------------------------------------------IPD |LCSG 773 | 1.123 0.827 1.526 11.13CAMS | 1.029 0.768 1.378 12.20... | ...Subgroup effect | 1.021 0.896 1.163 61.25---------------------+---------------------------------------------Aggregate |belgium | 1.456 1.072 1.979 11.09EORTC 08861 | 1.643 0.913 2.956 3.02... | ...Subgroup effect | 1.479 1.256 1.743 38.75-------------------------------------------------------------------
Tests of effect size = 1:IPD z = 0.305 p = 0.760Aggregate z = 4.682 p = 0.000
Inclusion of aggregate data: Screen output
Inclusion of aggregate data: Forest plot
IPD
LCSG 773
CAMS
MRC LU11
SLOVENIA
GETCB 04CB86
ITALY
KOREA
Subtotal (I-squared = 0.0%, p = 0.740)
Aggregate
belgium
EORTC 08861
LILLE
GETCB 05CB86
Subtotal (I-squared = 0.0%, p = 0.964)
reference number
trial
1.12 (0.83, 1.53)
1.03 (0.77, 1.38)
0.96 (0.74, 1.24)
0.89 (0.54, 1.49)
1.14 (0.80, 1.62)
0.69 (0.40, 1.20)
1.16 (0.76, 1.76)
1.02 (0.90, 1.16)
1.46 (1.07, 1.98)
1.64 (0.91, 2.96)
1.57 (1.06, 2.32)
1.44 (1.13, 1.83)
1.48 (1.26, 1.74)
Effect (95% CI)
18.18
19.92
26.12
6.48
13.85
5.69
9.76
100.00
28.61
7.79
17.56
46.03
100.00
Weight
%
1 2.5 4.25
Advanced syntax example:non “e-class” estimation command
ipdmetan (u[1,1]/V[1,1]) (1/sqrt(V[1,1]))
, study(trialid) eformad(subgroup1.dta, byad)
lcols(evrate=_d %3.2f "Event rate")
rcols(u[1,1] %5.2f "o-E(o)" V[1,1] %5.1f "V(o)")
forest(nooverall nostats nowt)
: sts test arm if subgroup==0, mat(u V)
Effect estimate & SE not from e(b)
– must specify manually
Advanced syntax example:columns of data in forestplot
ipdmetan (u[1,1]/V[1,1]) (1/sqrt(V[1,1]))
, study(trialid) eformad(subgroup1.dta, byad)
lcols(evrate=_d %3.2f "Event rate")
rcols(u[1,1] %5.2f "o-E(o)" V[1,1] %5.1f "V(o)")
forest(nooverall nostats nowt)
: sts test arm if subgroup==0, mat(u V)
Mean of var currently in memory (note user-assigned name, to
match with varname in aggregate dataset)
Collect lists of returned stats
Advanced syntax example: Forest plot
IPDLCSG 773CAMSMRC LU11SLOVENIAGETCB 04CB86ITALYKOREASubtotal(I-squared = 0.0%, p = 0.710)
AggregatebelgiumEORTC 08861LILLEGETCB 05CB86Subtotal(I-squared = 0.0%, p = 0.964)
reference numbertrial
0.720.580.780.850.680.510.810.69
0.830.430.640.50
rateEvent
4.771.07-2.48-2.564.95-4.503.063.24
o-E(o)
41.044.959.415.631.613.222.4229.6
V(o)
1 2.5 4.25
Advanced syntax example: Forest plot
IPDLCSG 773CAMSMRC LU11SLOVENIAGETCB 04CB86ITALYKOREASubtotal(I-squared = 0.0%, p = 0.710)
AggregatebelgiumEORTC 08861LILLEGETCB 05CB86Subtotal(I-squared = 0.0%, p = 0.964)
reference numbertrial
0.720.580.780.850.680.510.810.69
0.830.430.640.50
rateEvent
4.771.07-2.48-2.564.95-4.503.063.24
o-E(o)
41.044.959.415.631.613.222.4229.6
V(o)
1 2.5 4.25
These vars do not appear in the
aggregate dataset, so are not plotted
Subtotal cannot be calculated for
aggregate data
The forestplot command
• Does not perform any calculations/estimations; simply plots existing data as a forest plot
• Overall/subgroup estimates, spacings, labels, text columns etc. need to be created/arranged in advance• Ordering & spacing; marking of subgroup/overall
estimates for plotting “diamonds”: _use• Principal left-hand data column (study IDs,
heterogeneity etc. – string fmt): _labels• This setup is done automatically by ipdmetan before
passing to forestplot• (but can also be done manually by user)
• Multiple datasets can be passed to forestplot at once to create a single large “stacked” plot on common x-axis
forestplot syntax
forestplot [varlist] [if] [in][, plot_options graph_options using_option]
• varlist = manually specify varnames to plot• plot_options control the data plotting (within plot region)• graph_options control the surroundings (outside plot region;
graph region)• using_option represents one or more options that allow
suitable datasets (or parts of datasets) to be fed to forestplot, possibly with different plot_options, to form a single large forest plot on a single x-axis.
using_option syntax
using(filenamelist [if] [in] [, plot_options]) [using(filenamelist [if] [in] [, plot_options)] ...]
• filenamelist is a list of one or more Stata-format datasets• parts may be specified with [if] [in]• same filename can appear more than once• order of filenames determines placement in graph
• Different plot_options may be specified to each using option
• For same options applied to multiple files, place them in a filenamelist• For different options applied to each file, place each file
in a different using option
plot_options syntax• Based on metan syntax, options refer to different parts
of the forest plot• Most options appropriate to the underlying twoway plot
type are acceptable, with some exceptionsOption Function twoway plot typeboxopt Weighted boxes for
study point estimatesscatter [aweight]
pointopt Points for study point estimates
scatter
ciopt Lines for confidence intervals
rspike, horpcarrow
diamopt Diamond for summary estimate
pcspike (x4)
olineopt Vertical line through summary estimate
rspike
Example forestplot dataset(“resultsset” from last ipdmetan example)
_use _by _study _labels _ES _lci _uci _wgt evrate u_1_1_ V_1_1_ _NN0 1 IPD1 1 3 LCSG 773 0.116 -0.190 0.422 0.111 0.72 4.77 41.01 1 5 CAMS 0.024 -0.269 0.316 0.121 0.58 1.07 44.91 1 6 MRC LU11 -0.042 -0.296 0.213 0.160 0.78 -2.48 59.41 1 9 SLOVENIA -0.164 -0.660 0.332 0.042 0.85 -2.56 15.61 1 14 GETCB 04CB86 0.157 -0.192 0.506 0.085 0.68 4.95 31.61 1 13 ITALY -0.341 -0.881 0.199 0.036 0.51 -4.50 13.21 1 16 KOREA 0.136 -0.278 0.550 0.061 0.81 3.06 22.43 1 Subtotal 0.019 -0.111 0.149 0.615 0.69 3.24 229.64 1 (I-squared = 0.0%, p = 0.710)4 10 2 Aggregate1 2 17 belgium 0.376 0.069 0.682 0.110 0.83 2021 2 18 EORTC 08861 0.496 -0.091 1.084 0.030 0.43 1051 2 19 LILLE 0.450 0.058 0.841 0.068 0.64 1631 2 20 GETCB 05CB86 0.362 0.120 0.603 0.177 0.50 5393 2 Subtotal 0.392 0.228 0.556 0.385 10094 2 (I-squared = 0.0%, p = 0.964)4 2
4Heterogeneity between groups:p = 0.000
5 Overall 0.162 0.061 0.264 1.000 10094 (I-squared = 38.4%, p = 0.093)
Estimates; CIs; weights Extra data columns
“Stacking” of forest plots
• Imagine:• dataset on previous slide is saved as ipdtest.dta• we want IPD boxes to be red, and AD boxes to be green
• We proceed as follows:• Run forestplot with two using(...) options, one for
each part of the plot, with the same filename• (Alternatively: run ipdmetan twice and save under
different filenames)• Specify our desired plot_options as suboptions to using()
forestplot,using(ipdtest.dta if _by==1, boxopt(mcolor(red)))using(ipdtest.dta if _by==2, boxopt(mcolor(green)))lcols(evrate) rcols(u_1_1_ V_1_1_)nooverall nostats nowt
(I-squared = 0.0%, p = 0.964)SubtotalGETCB 05CB86LILLEEORTC 08861belgiumAggregate
(I-squared = 0.0%, p = 0.710)SubtotalKOREAITALYGETCB 04CB86SLOVENIAMRC LU11CAMSLCSG 773IPD
reference numbertrial
0.500.640.430.83
0.690.810.510.680.850.780.580.72
rateEvent
3.243.06-4.504.95-2.56-2.481.074.77
o-E(o)
229.622.413.231.615.659.444.941.0
V(o)
1 2.5 4.25
Summary and conclusion
• IPD is increasingly used, and its advantages widely accepted• Large numbers of MA scientists use two-stage models for
analysing IPD• Currently only AD MA (e.g. metan) and
one-stage IPD (e.g. xtmixed) commands exist in Stata
• ipdmetan is a universal command for two-stage IPD MA• forestplot is a flexible forest plot command
• does not carry out analysis itself, thus not restricted by it• may be useful outside the MA context (e.g. presenting
trial subgroups)
Further information
• Other related programs (all call forestplot by default):• admetan: calls ipdmetan to analyse AD
(direct alternative to metan)• ipdover: fit model within series of subgroups• petometan: perform meta-analysis of time-to-event
data using the Peto (log-rank) method
• SSC and Stata Journal article in near future
Thankyou!
• Questions, requests, bug reports:[email protected]
• Thanks to:• Jayne Tierney, Patrick Royston• Ross Harris (author of metan) for advice & support• Assorted colleagues for testing
• Reference:• Fisher D. J. et al. 2011. Journal of Clinical
Epidemiology 64: 949-67