Laura Bonnett

Laura Bonnett

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SAM Conference 2017

July 04, 2017
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  1. 10.
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    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
  3. 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
  4. 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)
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    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
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    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
  7. 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
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    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
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    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
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    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
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    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)
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    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
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    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.
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    Discussion Model validation required Investigate in alternative data Compare to

    count-based models Better understanding of treatment effects Improved statistical power
  21. 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
  22. 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
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    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