Model Specification for MetaAnalysis of Individual Patient Data with TimetoEvent Outcomes Keith Abra

1
Model Specification for Meta-Analysis of
Individual Patient Data with Time-to-Event
OutcomesKeith Abrams, Paul Lambert, Fiona
Warren Alex Sutton

• Centre for Biostatistics Genetic Epidemiology,
• Department of Health Sciences,
• University of Leicester, U.K.
• keith.abrams_at_le.ac.uk
• www.le.ac.uk/hs/kra1

2
Outline

• Why use Individual Patient Data (IPD)?
• Model Specification Implementation
• Toy Simulated Example
• Discussion

3
Why use IPD?

• Considered Gold standard
• TTE Survival data
• Heterogeneity of reporting/analysis (Parmar et
  al,1998), e.g. median/HR/survival
• Heterogeneity in study methodology, e.g. length
  of follow-up
• Heterogeneity of effects
• Covariates and subgroups
• Aggregated summary data has limited power to
  detect effects (Lambert et al,2002)

4
Modelling Strategy (Simmonds et al, 2005)

• 2-stage
• Analyse TTE data separately for each study to
  obtain effect estimate and SE
• Use standard meta-analysis methods
• Main advantage is to standardise effect estimates
  included in meta-analysis
• 1-stage
• Fit single model to raw IPD
• Allow for study-to-study variability within model
  by including study as factor/strata/random effect

5
Model Specification

• Cox model overall
• Cox model study as a factor
• Cox model stratified by study
• Cox model study baseline as frailty
• Cox model stratified by study treatment as
  random effect

6
Implementation

• Cox models
• Relatively straightforward to included
  factor/strata/random effect for baseline
  (frailty)
• Stata/SAS/R (Tudur-Smith et al, 2005)
• Computationally expensive to implement random
  treatment/regression effects (Yamaguchi Ohashi,
  1999)
• However, can re-formulate Cox model as Poisson
  regression model (Whitehead, 1980Lindsey, 1995)
• Expand data using unique event times to create
  patient-intervals of observation
• Relatively easy to specify random
  treatment/regression effects
• Implemented in R using lmer function (2.4.1)

7
Toy Simulated Example

• Simulated 5 trials of size 50 with TTE outcome
  (Bender et al, 2005)
• LHR -0.162 sd 0.5 (HR 0.85)
• Baseline Hazard Exponential with Median 3
  years 95 CI 2 to 4 years
• Censored _at_ 1.5 years
• Study-specific summary results
• Study LHR SE HR 95 CI
  
• 1, 0.540 0.398 1.72 0.79 3.75
• 2, 0.694 0.559 2.00 0.67 5.98
• 3, -0.509 0.493 0.60 0.23 1.58
• 4, -0.360 0.465 0.70 0.28 1.74
• 5, -0.196 0.557 0.82 0.28 2.45

8
Example Study-specific Survival Curves
HR 1.72 (0.79, 3.75)
HR 2.00 (0.67, 5.98)
HR 0.60 (0.23, 1.58)
____ Control ---- Intervention
HR 0.70 (0.28, 1.74)
HR 0.82 (0.28, 2.45)
9
Example 2-stage Meta-Analysis
HR 1.06 (0.69 to 1.62) HR 1.05 (0.65 to 1.70)
Log Hazard Ratio (LHR)
?2 0.07 I2 21.5, Q 5.1, P0.2
10
Example 1-stage Cox Model Overall
HR 1.04 (0.68 to 1.57)
____ Control ---- Intervention
11
Example Results 1
12
Example Results 2
Using 18,495 patient-intervals
13
Approximating a Cox Model

• Using unique event times to create
  patient-intervals of observation can be
  computationally intensive!
• Alternative approach is to specify a set (small)
  number of intervals and consider patients being
  at-risk/experiencing events within these

14
Using 1,015 patient-intervals
15
Discussion

• Poisson models can be used to implement Cox PH
  models especially when wanting to include REs,
  but are still computationally expensive (though
  this needs to be considered in relative terms).
• Such models may be advantageous when there are
  rare (adverse) events less intervals! and when
  differential follow-up is an issue.
• However, Poisson regression models allow other
  (flexible) baseline functions to be specified
  (e.g. piecewise constant or splines) which can
  either approximate PH model or provide more
  plausible alternatives and which are
  computationally less intensive.
• More broadly, obtaining IPD is usually lt 100
  successful, and so combination of summary and IPD
  is a methodological issue (Riley et al, 2007).

16
References
Bender R et al. Generating survival times to
simulate Cox proportional hazards models.
Statistics in Medicine 2005241713-1723. Lambert
PC et al. A comparison of summary patient-level
covariates in meta-regression with individual
patient data meta-analysis. JCE 2002
558694. Lindsey JK. Fitting Parametric
Counting Processes by Using Log-Linear Models.
Applied Statistics 199544(2)201-212. Parmar
MKB et al. Extracting summary statistics to
perform meta-analysis of the published literature
for survival end-points. Statistics in Medicine
19981728152834. Riley RD et al. Evidence
synthesis combining individual patient data and
aggregate data a systematic review identified
current practice and possible methods. JCE
200760431-439. Simmonds MC et al.
Meta-analysis of individual patient data from
randomized trials a review of methods used in
practice. Clinical Trials 20052209-217. Tudur-S
mith C et al. Investigating heterogeneity in an
individual patient data meta-analysis of time to
event outcomes. Statistics in Medicine 2005
2413071319. Whitehead J. Fitting Cox's
Regression Model to Survival Data using GLIM.
Applied Statistics 198029(3)268-275. Yamaguchi
T, Ohashi Y. Investigating centre effects in a
multi-centre clinical trial of superficial
bladder cancer. Statistics in Medicine
19991819611971.