5/29/2014

1

An illustration of the usefulness of the multi-state model survival analysis approach for health economic evaluation modelling

Claire Williams, Jim Lewsey

(correspondence: jim.lewsey@glasgow.ac.uk)

Health Economics and Health Technology Assessment

University of Glasgow, UK

http://www.gla.ac.uk/researchinstitutes/healthwellbeing/research/hehta/

• Rationale

• Examples from the literature

• Comparing multi-state model survival analysis

approach to usual Markov model cohort analysis

• Future research

1

Outline

5/29/2014

2

• Multi-state model survival analysis is an extension

of competing risks survival analysis

• This work is based on Putter’s Statistics in Medicine

tutorial in biostatistics [1]

• Exploring the potential for the approach to be used

in economic evaluation

2

Rationale

• We haven’t found any work that is directly

comparable

• Not common for multi-state survival analysis models

to be fitted to data for use in cost-effectiveness

analysis

• Some papers have appeared in Statistics in

Medicine [2-3]

3

Examples from the literature

5/29/2014

3

4

Data used for illustration [4-5]

• Rituximab in combination with fludarabine

and cyclophosphamide (R-FC) compared

to fludarabine and cyclophosphamide

alone (FC)

• Outcomes:

Progression-free survival (PFS)

Overall survival (OS)

• Observed follow-up approximately 4 years

• Manufacturer’s economic evaluation used

a Markov decision model

5

Partitioned survival modelling

OS

5/29/2014

4

6

Partitioned survival modelling

OS

7

Partitioned survival modelling

OS

5/29/2014

5

8

Partitioned survival modelling

OS + PFS

9

Markov decision modelling

5/29/2014

6

10

Markov decision modelling

11

Markov decision modelling

Log-rank test p = 0.4

Manufacturer's assumptions

PFS -> progression

1 – [P(staying in PFS state) + P(PFS to death)] with P(staying in PFS state) time dependent based upon Weibull extrapolation of PFS trial curves

PFS -> death

Maximum value of either age-specific background mortality or monthly rate at which patients died (all cause) while in PFS. Monthly probability of death whilst in PFS: R-FC = 0.00119627 FC = 0.00138823.

progression -> death

Constant hazard of dying obtained from modelling the CLL-8 post-progression population survival as a single population due to the non-significant difference in survival between the treatment arms.

The inverse of the mean from the Kaplan-Meier is a suitable estimate of the rate of death (constant) assuming that the underlying distribution is exponential. The mean time in progression was 24.1791(se=0.9019) months. The rate of death obtained from modelling the progression to death population converted to a monthly probability, P(death|progression) is 0.0405144 IN EACH ARM.

5/29/2014

7

• Fits the same model as the Markov decision model

in that the same transitions are modelled

• Uses the data to directly model each of the

transitions using regression

• Used increasingly in medical applications

• We follow the approach outlined by Putter et al. [1]

but model the hazards using parametric survival

models rather than Cox regression

12

Multi-state modelling

13

Comparison of results

R-FC FC Incremental R-FC FC Incremental R-FC FC Incremental

Mean Life Years 5.78 5.11 0.67 5.73 4.65 1.07 5.89 5.52 0.37

Mean Life Years in PFS 4.09 2.91 1.18 4.11 2.93 1.18 3.88 2.81 1.07

Mean Life Years in Progression 1.69 2.20 -0.51 1.62 1.73 -0.11 2.01 2.71 -0.69

Mean QALYs 4.28 3.65 0.64 4.26 3.38 0.88 4.31 3.87 0.44

Mean QALYs in PFS 3.27 2.33 0.95 3.29 2.34 0.94 3.10 2.25 0.85

Mean QALYs in Progression 1.01 1.32 -0.31 0.97 1.04 -0.07 1.21 1.63 -0.42

Partitioned Survival Roche's Markov model Multi-state modelling

5/29/2014

8

R-FC FC Incremental R-FC FC Incremental R-FC FC Incremental

Mean Life Years 5.78 5.11 0.67 5.73 4.65 1.07 5.89 5.52 0.37

Mean Life Years in PFS 4.09 2.91 1.18 4.11 2.93 1.18 3.88 2.81 1.07

Mean Life Years in Progression 1.69 2.20 -0.51 1.62 1.73 -0.11 2.01 2.71 -0.69

Mean QALYs 4.28 3.65 0.64 4.26 3.38 0.88 4.31 3.87 0.44

Mean QALYs in PFS 3.27 2.33 0.95 3.29 2.34 0.94 3.10 2.25 0.85

Mean QALYs in Progression 1.01 1.32 -0.31 0.97 1.04 -0.07 1.21 1.63 -0.42

Partitioned Survival Roche's Markov model Multi-state modelling

14

Comparison of results

R-FC FC Incremental R-FC FC Incremental R-FC FC Incremental

Mean Life Years 5.78 5.11 0.67 5.73 4.65 1.07 5.89 5.52 0.37

Mean Life Years in PFS 4.09 2.91 1.18 4.11 2.93 1.18 3.88 2.81 1.07

Mean Life Years in Progression 1.69 2.20 -0.51 1.62 1.73 -0.11 2.01 2.71 -0.69

Mean QALYs 4.28 3.65 0.64 4.26 3.38 0.88 4.31 3.87 0.44

Mean QALYs in PFS 3.27 2.33 0.95 3.29 2.34 0.94 3.10 2.25 0.85

Mean QALYs in Progression 1.01 1.32 -0.31 0.97 1.04 -0.07 1.21 1.63 -0.42

Partitioned Survival Roche's Markov model Multi-state modelling

15

Comparison of results

5/29/2014

9

R-FC FC Incremental R-FC FC Incremental R-FC FC Incremental

Mean Life Years 5.78 5.11 0.67 5.73 4.65 1.07 5.89 5.52 0.37

Mean Life Years in PFS 4.09 2.91 1.18 4.11 2.93 1.18 3.88 2.81 1.07

Mean Life Years in Progression 1.69 2.20 -0.51 1.62 1.73 -0.11 2.01 2.71 -0.69

Mean QALYs 4.28 3.65 0.64 4.26 3.38 0.88 4.31 3.87 0.44

Mean QALYs in PFS 3.27 2.33 0.95 3.29 2.34 0.94 3.10 2.25 0.85

Mean QALYs in Progression 1.01 1.32 -0.31 0.97 1.04 -0.07 1.21 1.63 -0.42

Partitioned Survival Roche's Markov model Multi-state modelling

16

Comparison of results

17

Visual assessment of fit: Progression-free survival

5/29/2014

10

18

Visual assessment of fit: Overall survival

19

Visual assessment of fit: Time in progression

5/29/2014

11

• The partitioned survival approach appeared to

provide the better fit

• The censoring was high in this illustration and

therefore there was more reliance on extrapolation

• Adapting the fit of one survival outcome was more

practical than doing it for every transition

• Further investigation is required to decide on the

most appropriate approach

20

Discussion

21

Future research: Cardiovascular Disease Policy Model [6]

5/29/2014

12

22

Future research: Cardiovascular Disease Policy Model [6]

23

Future research: Cardiovascular Disease Policy Model [6]

5/29/2014

13

24

Future research: continuous rather than discrete time

• The predictions from the adjustments made to

‘mstate’ treat time as discrete

• Using shorter cycle lengths has led to long

computation times

Advantages of multi-state model survival analysis

compared to usual Markov model cohort analysis:

1) More efficient to run economic models in

statistics package rather than spreadsheets and

using syntax means you have audit trail

2) Not constrained by Markov property - can

statistically test the Markov assumption (include

covariate that represents history)

3) Predictions can be made using Markov

probability formulae or through simulation 25

Summary

5/29/2014

14

[1] H Putter, M Fiocco, RB Geskus. Tutorial in biostatistics: Competing risks and

multi-state models. Statistics in Medicine 2007; 26:2389-2430.

[2] JC Gardiner, Z Luo, CJ Bradley, et al. A dynamic model for estimating changes in

health status and costs. Statistics in Medicine 2006; 25:3648-3667.

[3] C Castelli, C Combescure, Y Foucher, et al. Cost-effectiveness analysis in

colorectal cancer using a semi-Markov model. Statistics in Medicine 2007;

26:5557-5571.

[4] National Institute for Health and Clinical Excellence. Rituximab for the first line

treatment of chronic lymphocytic leukaemia.

http://guidance.nice.org.uk/TA174

[5] Roche Products Limited. Rituximab for the 1st line treatment of Chronic

Lymphocytic Leukaemia. National Institute for Health and Clinical Excellence

2008.

http://www.nice.org.uk/nicemedia/live/12039/43581/43581.pdf

[6] JD Lewsey, KD Lawson, I Ford, et al. An alternative Cardiovascular Disease

Policy Model: predicting life expectancy accounting for socio-economic

deprivation. Revised paper under consideration at Heart

26

References