Missing Data in Survival Analysis and Results from the MESS Trial
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1 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 Research Students Conference, 2008
2 Outline Background Survival Analysis Missing Data MESS Trial Background MRC Multicentre Trial for Early Epilepsy and Single Seizures Initial Analysis Suitable Models The Missing Data Problem
3 Outline Background Survival Analysis Missing Data MESS Trial Background MRC Multicentre Trial for Early Epilepsy and Single Seizures Initial Analysis Suitable Models The Missing Data Problem
4 Survival Analysis Modelling Survival Data Time to event Censoring: actual survival time not observed for an individual Right Censoring: observed, censored survival time is less than actual, but unknown survival time Two functions are of central interest: Survivor function - S(t) = P(T { t) } Hazard function - h(t) = P(t T t+δt T t) limδt 0 δt
5 Survival Analysis Modelling Survival Data Time to event Censoring: actual survival time not observed for an individual Right Censoring: observed, censored survival time is less than actual, but unknown survival time Two functions are of central interest: Survivor function - S(t) = P(T { t) } Hazard function - h(t) = P(t T t+δt T t) limδt 0 δt
6 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 ). MCAR - missingness independent of Y MAR - missingness depends only on Y obs MNAR - neither MCAR or MAR Missing data methods include complete case analysis, imputation techniques and model based approaches.
7 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 ). MCAR - missingness independent of Y MAR - missingness depends only on Y obs MNAR - neither MCAR or MAR Missing data methods include complete case analysis, imputation techniques and model based approaches.
8 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 ). MCAR - missingness independent of Y MAR - missingness depends only on Y obs MNAR - neither MCAR or MAR Missing data methods include complete case analysis, imputation techniques and model based approaches.
9 Outline Background Survival Analysis Missing Data MESS Trial Background MRC Multicentre Trial for Early Epilepsy and Single Seizures Initial Analysis Suitable Models The Missing Data Problem
10 Background Early Epilepsy and Single Seizures On average 50% of people do not experience a recurrence after a single seizure Around 20 30% of people will never achieve long-term remission Risk of future seizures increases with the number of previous seizures One-year remission is of particular interest
11 MRC Multicentre Trial for Early Epilepsy and Single Seizures Aim of Trial When should treatment with antiepileptic drugs commence Antiepileptic drugs come with unpleasant side effects Comparison of policies: immediate versus deferred treatment in those patients where uncertainty about starting treatment remained
12 MRC Multicentre Trial for Early Epilepsy and Single Seizures Aim of Trial When should treatment with antiepileptic drugs commence Antiepileptic drugs come with unpleasant side effects Comparison of policies: immediate versus deferred treatment in those patients where uncertainty about starting treatment remained
13 MRC Multicentre Trial for Early Epilepsy and Single Seizures Outcomes Measured Assessed the effects of the two policies on short term recurrence and long-term remission Time to first seizure Time to second seizure Time to fifth seizure Time to one year remission Time to second year remission
14 Outline Background Survival Analysis Missing Data MESS Trial Background MRC Multicentre Trial for Early Epilepsy and Single Seizures Initial Analysis Suitable Models The Missing Data Problem
15 Suitable Models Kaplan-Meier Plots Time to first seizure Time to second seizure Time to fifth seizure S(t) S(t) S(t) t t t Time to one year remission Time to two year remission S(t) S(t) Allocated to START Allocated to DELAY t t
16 Suitable Models Time to one year remission Time to two year remission S(t) S(t) t t
17 The Missing Data Problem Randomisation Issues Two randomisation forms used during the trial 1. Randomisation Drug (approx 1/3) 2. Drug Randomisation (approx 2/3) Second randomisation strategy allows comparisons between specific drugs Adopt missing data methods to overcome problem of missing covariates
18 The Missing Data Problem Randomisation Issues Two randomisation forms used during the trial 1. Randomisation Drug (approx 1/3) 2. Drug Randomisation (approx 2/3) Second randomisation strategy allows comparisons between specific drugs Adopt missing data methods to overcome problem of missing covariates
19 The Missing Data Problem Randomisation Issues Two randomisation forms used during the trial 1. Randomisation Drug (approx 1/3) 2. Drug Randomisation (approx 2/3) Second randomisation strategy allows comparisons between specific drugs Adopt missing data methods to overcome problem of missing covariates
20 Summary Jointly model times to first, second and fifth seizure Concentrate on first and second years after randomisation Overcome missing data problem to allow for comparisons between drugs
21 Summary Jointly model times to first, second and fifth seizure Concentrate on first and second years after randomisation Overcome missing data problem to allow for comparisons between drugs
22 Summary Jointly model times to first, second and fifth seizure Concentrate on first and second years after randomisation Overcome missing data problem to allow for comparisons between drugs
23 Summary Jointly model times to first, second and fifth seizure Concentrate on first and second years after randomisation Overcome missing data problem to allow for comparisons between drugs
24 Appendix For Further Reading I D. Collett. Modelling Survival Data in Medical Research, 2nd Edition. Chapman and Hall/CRC, R. J. A. Little, D. B. Rubin. Statistical Analysis with Missing Data, 2nd Edition John Wiley and Sons, Inc, 2002.
25 Appendix 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): , June B. J. Cowling, J. L. Hutton, J. E. H. Shaw. Joint modelling of event counts and survival times. JRSSC Appl. Statist., 55(1):31 39, 2006.
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