2010 smg training_cardiff_day1_session2a (1 of 1) tudur-smith

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Meta‐analysis of
Time‐to‐event data

Catrin Tudur Smith
cat1@liv.ac.uk

MRC North West Hub for Trials
Met...

Contents
• Introduction to time‐to‐event data
• Meta‐analysis of time‐to‐event data
• Estimating log(HR) and its var...

Time‐to‐event data
● Data arising when we measure the length of time
taken for an event to occur
● The event migh...

Censoring
• Event is often not observed on all subjects
• Reasons for this might be:
– drop‐out
– the study ends befor...

Examples of censoring
• A patient with cancer is still alive at the time of
analysis. Time to death would be censored.
...

Why special methods of analysis?
• Why not analyse the time to event as a
continuous response variable?

• Assuming ce...

Why special methods of analysis?
• Why not analyse the time to event as a binary response variable?

– May be reasonab...

Kaplan‐Meier curves
• A Kaplan‐Meier plot
gives a graphical
display of the survival
...

Plotting the results

Survival Number Survival
...

Interpreting the results
Median survival:
...

Accuracy of the K‐M estimates
• T...

The Logrank test
• The Logrank Test is a simple
...

The logrank test cont’d…
• The logrank test compares the total number of deaths observed with
the number of deaths ...

The hazard ratio
• The hazard is the chance that at any given moment, the event will
occur, given that it hasn’t al...

More on the hazard ratio
• Cox proportional hazards (PH) regression model ‐
most commonly used regression model
• The h...

Interpretation of b1, b2 …
• Find the hazard of death for a person on Treatment (x1 = 1) compared to
Control (x1 = 0), ...

Meta‐analysis of TTE data
• Suppose that there are K trials, and for each trial,
i=1,2.. K, an estimate of the log haza...

Meta‐analysis of TTE data

SMG course Cardiff 2010

Meta‐analysis of TTE data

SMG course Cardiff 2010

Direct
(1)

(2)

SMG course Cardiff 2010

Cox model coefficient and SE

Report may present results from the Cox regression
model

Direct estimate of logHR and its ...

HR with confidence interval

Where UPPCIi and LOWCIi are the upper and
lower confidence limits for log(HRi)
is the ...

P‐value

SMG course Cardiff 2010

p‐value (balanced randomisation)

(3)

pi is the reported (two si...

p‐value (balanced randomisation)

(4)

SMG course Cardiff 2010

p‐value (unequal randomisation)

(5)

Number of patients in...

(2)

SMG course Cardiff 2010

Choice of Vri
• Approximation (3) and (4) are identical when number of
events are equal in both arms
• Approximation (3...

Published survival curves

Chemotherapy in pancreatic cancer: results of a
controlled prospective randomised multicentr...

Published survival curves

1. Estimating numbers at risk
Parmar et al Statistics in Medicine 1998, 17:2815‐34.

2. Incorpo...

Survival curves – Parmar et al
Step 1 ‐ For each trial split the time‐axis into T non‐
overlapping time intervals – chosen...

Survival curves – Parmar et al

0.65

0.42

0.39

0.24

SMG course Cardiff 2010

Survival curves – Parmar et al
Step 3

From reading the manuscript, estimate the minimum ( )
and maximum ( ...

Survival curves – Parmar et al

Time point t s ...

Survival curves – Parmar et al

Time point t s t e
NAR at star...

Survival curves – Parmar et al

Time point t s t e
NAR at s...

Survival curves – Parmar et al

Time point t s t e
NAR at s...

Survival curves – Parmar et al

Time point t s t e
NAR at s...

Survival curves – Parmar et al
Step 9

Calculate log(HR) and its variance for the first interval

...

Survival curves – Parmar et al
Step 10

Repeat steps 4‐9 for all intervals

SMG course C...

Survival curves – Parmar et al
Step 11

Calculate pooled log(HR) and its variance for the trial by combining
es...

Zero deaths
• Difficulties with calculating logHR and its variance
will arise whenever estimated number of deaths
wi...

Survival curves – Williamson et al

SMG course Cardiff 2010

Practical
• For the trial of Gemcitabine in combination with Oxaliplatin
for pancreatic cancer (Louvet et al 20...

SMG course Cardiff 2010

Data Extraction

Tierney et al 2007
SMG course Cardiff 2010

HR calculations spreadsheet
• Spreadsheet to facilitate the estimation of
hazard ratios from published summary
stati...

Empirical comparison
• Parmar et al studied 209 randomized controlled trials comparing the
survival of women treate...

Empirical comparison
• Tudur C, Williamson PR, Khan S, Best L: The value of the aggregate data
approach in meta‐ana...

SMG course Cardiff 2010

SMG course Cardiff 2010

Empirical comparison
• Conclusions of Tudur et al 2001
– Good agreement between non‐survival curve indirect
metho...

Empirical comparison
• D'Amico et al (2000) assessed the performance of the indirect estimate of
HR when estimat...

Median survival or survival rate at
time point
• The median survival and survival rates at specific time po...

Individual patient data
• Meta‐analysis of TTE outcomes often use individual
patient data (IPD)
• Many advantages inclu...

Conclusions
• Aggregate Data meta‐analysis of time‐to‐event
data is possible
• Estimates based on survival curve may no...

References
1. Parmar MKB, Torri V, Stewart L: Extracting summary statistics to perform meta‐analyses
of the published ...

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