Missing Data in Survival Analysis and Results from the MESS Trial

Missing Data in Survival Analysis and Results

from the MESS Trial

J. K. Rogers

J. L. Hutton

K. Hemming

Department of Statistics

University of Warwick

Outline

Background

Survival Analysis

Missing Data

MESS Trial

Background

MRC Multicentre Trial for Early Epilepsy and Single

Seizures

Initial Analysis

Outline

Background

Survival Analysis

Missing Data

MESS Trial

Background

MRC Multicentre Trial for Early Epilepsy and Single

Seizures

Initial Analysis

Suitable Models

Survival Analysis

Modelling Survival Data

I

Time to event

I

Censoring: actual survival time not observed for an

individual

I

_{Right Censoring: observed, censored survival time is less}

than actual, but unknown survival time

I

Two functions are of central interest:

I

_{Survivor function -}

_S

(

t

) =

_P

(

T

≥

t

)

I

_{Hazard function -}

_h

(

t

) =

lim

δt

→0

n

P

(

t

≤

T

≤

t

+

δt

|

T

≥

t

)

δt

Survival Analysis

Modelling Survival Data

I

Time to event

I

Censoring: actual survival time not observed for an

individual

I

_{Right Censoring: observed, censored survival time is less}

than actual, but unknown survival time

I

Two functions are of central interest:

_{Survivor function -}

_S

(

t

) =

_P

(

T

≥

t

)

I

_{Hazard function -}

_h

(

t

) =

limδt→0

n

P

(t≤T

≤t+δt|T

≥t)

δt

Missing Data

Missing Data

Let

Y

=

{y

_ij

}

denote an

(

n

×

k

)

complete-data rectangular data

set, with

n

cases over

k

variables and

Y

= (

Y

obs

,

Y

mis

)

.

I

MCAR - missingness independent of

Y

I

MAR - missingness depends only on

Y

obs

I

MNAR - neither MCAR or MAR

Missing data methods include complete case analysis,

imputation techniques and model based approaches.

Missing Data

Missing Data

Let

Y

=

{y

_ij

}

denote an

(

n

×

k

)

complete-data rectangular data

set, with

n

cases over

k

variables and

Y

= (

Y

obs

,

Y

mis

)

.

I

MCAR - missingness independent of

Y

I

MAR - missingness depends only on

Y

obs

I

MNAR - neither MCAR or MAR

Missing data methods include complete case analysis,

imputation techniques and model based approaches.

Missing Data

Missing Data

Let

Y

=

{y

_ij

}

denote an

(

n

×

k

)

complete-data rectangular data

set, with

n

cases over

k

variables and

Y

= (

Y

obs

,

Y

mis

)

.

I

MCAR - missingness independent of

Y

I

MAR - missingness depends only on

Y

obs

I

MNAR - neither MCAR or MAR

Missing data methods include complete case analysis,

imputation techniques and model based approaches.

Outline

Background

Survival Analysis

Missing Data

MESS Trial

Background

MRC Multicentre Trial for Early Epilepsy and Single

Seizures

Initial Analysis

Suitable Models

Background

Early Epilepsy and Single Seizures

I

On average 50

%

of people do not experience a recurrence

after a single seizure

I

Around 20

−

30

%

of people will never achieve long-term

remission

I

Risk of future seizures increases with the number of

previous seizures

MRC Multicentre Trial for Early Epilepsy and Single Seizures

Aim of Trial

I

When should treatment with antiepileptic drugs commence

I

Antiepileptic drugs come with unpleasant side effects

I

Comparison of policies: immediate versus deferred

treatment in those patients where uncertainty about

starting treatment remained

MRC Multicentre Trial for Early Epilepsy and Single Seizures

Aim of Trial

I

When should treatment with antiepileptic drugs commence

I

Antiepileptic drugs come with unpleasant side effects

I

Comparison of policies: immediate versus deferred

treatment in those patients where uncertainty about

starting treatment remained

MRC Multicentre Trial for Early Epilepsy and Single Seizures

Outcomes Measured

I

Assessed the effects of the two policies on short term

recurrence and long-term remission

I

Time to first seizure

Time to second seizure

Time to fifth seizure

_{Time to one year remission}

_{Time to second year remission}

Outline

Background

Survival Analysis

Missing Data

MESS Trial

Background

MRC Multicentre Trial for Early Epilepsy and Single

Seizures

Initial Analysis

Suitable Models

Kaplan-Meier Plots

Time to first seizure

t S(t) 0 5001000 1500 2000 2500 3000 0.0 0.2 0.4 0.6 0.8 1.0

Time to second seizure

t S(t) 0 5001000 2000 3000 0.0 0.2 0.4 0.6 0.8 1.0

Time to fifth seizure

t S(t) 0.0 0.2 0.4 0.6 0.8 1.0

Time to one year remission

S(t) 0.0 0.2 0.4 0.6 0.8 1.0

Time to two year remission

S(t)

Allocated to START Allocated to DELAY

Suitable Models 0.0 0.2 0.4 0.6 0.8 1.0

Time to one year remission

S(t) 0.0 0.2 0.4 0.6 0.8 1.0

Time to two year remission

The Missing Data Problem

Randomisation Issues

I

Two randomisation forms used during the trial

1.

Randomisation

→

Drug (approx 1

/

3)

2.

Drug

→

Randomisation (approx 2

/

3)

I

Second randomisation strategy allows comparisons

between specific drugs

I

Adopt missing data methods to overcome problem of

missing covariates

The Missing Data Problem

Randomisation Issues

I

Two randomisation forms used during the trial

1.

Randomisation

→

Drug (approx 1

/

3)

2.

Drug

→

Randomisation (approx 2

/

3)

I

Second randomisation strategy allows comparisons

between specific drugs

I

Adopt missing data methods to overcome problem of

missing covariates

The Missing Data Problem

Randomisation Issues

I

Two randomisation forms used during the trial

1.

Randomisation

→

Drug (approx 1

/

3)

2.

Drug

→

Randomisation (approx 2

/

3)

I

Second randomisation strategy allows comparisons

between specific drugs

I

Adopt missing data methods to overcome problem of

missing covariates

Summary

I

Jointly model times to first, second and fifth seizure

I

Concentrate on first and second years after randomisation

I

Overcome missing data problem to allow for comparisons

between drugs

Summary

I

Jointly model times to first, second and fifth seizure

I

Concentrate on first and second years after randomisation

I

Overcome missing data problem to allow for comparisons

between drugs

Summary

I

Jointly model times to first, second and fifth seizure

I

Concentrate on first and second years after randomisation

I

Overcome missing data problem to allow for comparisons

between drugs

Summary

I

Jointly model times to first, second and fifth seizure

I

Concentrate on first and second years after randomisation

I

Overcome missing data problem to allow for comparisons

between drugs

For Further Reading I

D. Collett.

Modelling Survival Data in Medical Research, 2nd Edition

.

Chapman and Hall/CRC, 2003.

R. J. A. Little, D. B. Rubin.

Statistical Analysis with Missing Data, 2nd Edition

For Further Reading II

A. Marson, A. Jacoby, A. Johnson, L. Kim, C. Gamble,

D. Chadwick, on behalf of the Medical Research Council

MESS Study Group.

Immediate versus deferred antiepileptic drug treatment for

early epilepsy and single seizures: a randomised controlled

trial.

The Lancet, 365(9476):2007–2013, June 11 2005.

B. J. Cowling, J. L. Hutton, J. E. H. Shaw.

Joint modelling of event counts and survival times.