Laura Bonnett

Transcript

1. Estimating risk of seizure recurrence for people with epilepsy Laura Bonnett, NIHR Post-Doctoral Fellow
2. The Clinical Condition
3. The Clinical Condition
4. The Clinical Condition
5. The Challenge
6. The Challenge
7. The Challenge
8. The Challenge
9. The Challenge Start of observation period X Time X X
10. Outline
11. Statistical Methods
12. Statistical Methods Count Based Models Multiple time-to- event analyses
13. Statistical Methods log = + log( )  Poisson  Negative Binomial  Zero-inflated Poisson  Zero-inflated Negative Binomial Expected number of events for subject i Length of time subject i is at risk Covariate design matrix Parameter estimates
14. Statistical Methods log = + log( )  Poisson  Negative Binomial  Zero-inflated Poisson  Zero-inflated Negative Binomial Expected number of events for subject i Length of time subject i is at risk Covariate design matrix Parameter estimates
15. Statistical Methods  Extended Cox models for multiple events of the same type:  Independent increment – Anderson-Gill (AG)  Marginal – Wei, Lin and Wiessfeld (WLW)  Conditional – Prentice, Williams and Peterson (PWP)
16. Statistical Methods , = Ι ()0 ()() Anderson-Gill Hazard function for ith subject at time t Common baseline hazard for all events over time Vector of covariate processes for ith individual Fixed vector of coefficients Predictable process taking values in {1,0} indicating when the ith individual is under observation Anderson & Gill (1982). Cox’s regression model for counting processes: a large same study. Annals of Statistics 10(4):1100-20
17. Anderson-Gill Statistical Models  Efficient  Accommodates heterogeneity via robust standard errors  Simple to visualise & set up  Strong distributional assumption – event does not change the subject  Lacks the detail & versatility of event-specific models Pros Cons
18. Statistical Methods , = ()0 ()() WLW Hazard function for kth event of the ith subject at time t Common baseline hazard for all events over time Vector of covariate processes for ith individual Fixed vector of coefficients At-risk process is 1 until the kth event, unless censored Wei, Lin & Weissfeld(1989). Regression analysis of multivariate incomplete failure time data by modelling marginal distributions. J. Amer. Statist. Assoc. 84:1065-73
19. WLW Statistical Models  Allows for changes in the model effects over time  Datasets get quite large  Semi-restricted risk set – subjects to be at risk of the event (where = , , …) even if they have only had one event. Pros Cons
20. Statistical Methods , = ()0 ()() PWP Hazard function for kth event of the ith subject at time t Common baseline hazard for all events over time Vector of covariate processes for ith individual Fixed vector of coefficients At-risk process on the interval from the k-1th event to the kth event unless censored Prentice, Williams, Peterson (1981). On the regression analysis of multivariate failure time data. Biometrika 68(2):373-79
21. PWP Statistical Models  Underlying intensity function can vary from event to event  Natural interpretation  Easy to set up  Biased when an important covariate is omitted due to loss of balance in later strata  Risk sets for later event numbers will get small, making estimates of per-stratum risk unstable Pros Cons
22. Statistical Methods  Extended Cox models for multiple events of the same type:  Counting process - Anderson-Gill (AG)  Marginal – Wei, Lin and Wiessfeld (WLW)  Conditional – Prentice, Williams and Peterson (PWP)
23. Statistical Methods PWP-GT Time since previous event PWP-CP Time since randomisation
24. Statistical Methods PWP-GT Time since previous event PWP-CP Time since randomisation
25. Statistical Methods  PWP-CP for risk of seizure recurrence  Comparison with published Cox models  Risk of 1st seizure after randomisation  Chance of 12-month remission  Multivariable model development via forwards and backwards selection according to AIC  Treatment forced into each model
26. Data
27. Data  Standard versus New Antiepileptic Drug (SANAD) Study (n=2437)  Un-blinded RCT  Hospital based outpatient clinics in U.K.  December 1999 → August 2004 → January 2006  Outcomes  Time to treatment failure  Time to 12 month remission Arm Patients Standard Drug Typical Seizure Type Randomised Drugs A 1721 CBZ Focal Onset CBZ, GBP, LTG, TPM, OXC* B 716 VPS Generalised Onset VPS, LTG, TPM Marson, A.G., et al., The SANAD study of effectiveness of carbamazepine, gabapentin, lamotrigine, oxcarbazepine, or topiramate for treatment of partial epilepsy: an unblinded randomised controlled trial. Lancet, 2007. 369(9566): p. 1000-15. Marson, A.G., et al., The SANAD study of effectiveness of valproate, lamotrigine, or topiramate for generalised and unclassifiable epilepsy: an unblinded randomised controlled trial. Lancet, 2007. 369(9566): p. 1016-26.
28. Data
29. Results
30. Results
31. Results
32. Results
33. Discussion
34. Discussion Model validation required Investigate in alternative data Compare to count-based models Better understanding of treatment effects Improved statistical power
35. Discussion
36. Acknowledgements Professor Tony Marson Professor Catrin Tudur Smith Professor Jane Hutton
37. Spare Material
38. Count & Rate Based Models: Poisson Statistical Models  Very simple  Commonly used to compare event rates across different groups  Ignores heterogeneity amongst patients within different groups  Assumes independence of events within individuals  Tends to underestimate the underlying true rate Pros Cons
39. Count & Rate Based Models: Negative Binomial Statistical Models  Simple & straightforward to use  Does not require complicated data files  Offers more valid mean rates than Poisson  Allows different patient risks Pros Cons
40. Count & Rate Based Models: ZIP & ZINB Statistical Models  Handle data with excess 0s, and potential over-dispersion  Simpler models do not allow mixing with respect to the 0s  Mixture effect is require as variance is not just in the number of 0s Pros Cons