Designing studies with recurrent events | Model choices, pitfalls and group sequential design
•Download as PPTX, PDF•
0 likes•299 views
In this free webinar, we will examine the important design considerations for analyzing recurring events and counts. Watch the webinar at: https://www.statsols.com/en/webinar/designing-studies-with-recurrent-events Designing studies with recurrent events (Model choices, pitfalls and group sequential design)
Recommended
More Related Content
What's hot
What's hot (20)
Similar to Designing studies with recurrent events | Model choices, pitfalls and group sequential design
Similar to Designing studies with recurrent events | Model choices, pitfalls and group sequential design (20)
More from nQuery
More from nQuery (12)
Recently uploaded
Recently uploaded (20)
Designing studies with recurrent events | Model choices, pitfalls and group sequential design
- 1. DESIGNING STUDIES WITH RECURRENT EVENTS Model choices, pitfalls and group sequential design DEMONSTRATED ON
- 2. Head of Statistics nQuery Lead Researcher FDA Guest Speaker Guest Lecturer Webinar Host HOSTED BY: Ronan Fitzpatrick
- 3. AGENDA 1. Recurrent Event Data and Models Introduction 2. Sample Size for Recurrent Event Models 3. Group Sequential Design for Recurrent Events 4. Conclusions and Discussion
- 4. The complete trial design platform to make clinical trials faster, less costly and more successful The solution for optimizing clinical trials
- 5. In 2019, 90% of organizations with clinical trials approved by the FDA used nQuery
- 7. Recurrent Events Overview Recurrent event processes are endpoints where subject can have >1 informative event in time period Common endpoint in clinical trials esp. chronic diseases COPD/asthma exacerbations, MS relapses, migraines, seizures Similar considerations and methods also relevant in case of count data e.g. imaging, epidemiology Should use events/counts “as-is” for better estimation but historically often “simplified” to other endpoints
- 8. Recurrent Event Analysis Approaches Event Rate Models: Estimate # of events per time unit Parametric models for (constant over time) event rate ratio e.g. Poisson (incl. quasi-P), negative binomial (both ZI, ZT) Time-to-Events Models: Time(s) between/til next event Semi-parametric models for hazard from each event e.g. Andersen-Gill, Wei-Lin-Weissfeld, Prentice-Williams- Peterson Mean Cumulative Event Function: E(Events) at time t Non-parametric method for cumulative E’s e.g. Nelson-Aalen
- 9. Issues in Recurrent Event Analysis What is the question/target of interest in study? Use event rate, time between events, # of events? Compare groups via rate ratio, # events, intensity/HR? Interested in first K events, later events, more intense events? What assumptions are reasonable for data? Independent events, non-informative censoring, Event process differs per subject, process changes over time Some events more important, effect of terminal events
- 10. Count Model Examples 1 Poisson Model Event Rates, rate ratio, constant rate 2 Negative Binomial Event Rates, RR, event rate/subject 3 Andersen-Gill Time-to-Events, intensity/hazard of all E 4 Wei-Lin-Weissfeld Time-to-Events, time til 1st K events, HR 5 Prentice-Williams-Peterson Time-to-Events, gap between 1st K E’s, HR 6 MCF Non-parametric, # events at time t 7 Approximate Models Survival models (1st E), t-test, event “rates”
- 11. Sample Size for Recurrent Event Models Part 2
- 12. Example Models for SSD 1) Poisson: Signorini (1991), Lehr (1992), Gu et .al. (2008) Parametric model for rate ratio, assumes constant rate ratio Rate constant over time, same rate per subject unless quasi-P 2) Negative Binomial: Zhu & Lakkis (2014), Tang (2015,18) Parametric model for rate ratio, assumes constant rate ratio Rate constant over T, Poisson rate/subject from gamma dist. 3) Andersen-Gill: Bernardo & Harrington (2001), Tang & Fitzpatrick (2019) Semi-Parametric for intensity/hazard, assume constant RR here Arbitrary rate over T (e.g. Weibull), need proportional hazards
- 13. Sample Size for Recurrent Events SSD initially focussed on simple approx. assuming Poisson (e.g. √) More work done for Poisson regression (& Quasi-Poisson Recent work on Neg. Binomial and extend it & Poisson for unequal follow-up, dropout & NI/equiv SSD also derived for Andersen-Gill incl. flexible approach for design and hazard function assumptions Source: R. Lehr (1992) Source: H. Zhu & H. Lakkis (2014) Source: Y. Tang (2015) Source: D. Signorini (1991) Source: Y. Tang & R. Fitzpatrick (2019)
- 14. Worked Example 1 “On the basis of previous studies of fluticasone propionate–salmeterol combinations we assumed a yearly exacerbation rate with vilanterol of 1·4 and a dispersion parameter of 0·7. Thus, we calculated that a sample size of 390 assessable patients per group in each study would provide each study with 90% power to detect a 25% reduction in exacerbations in the fluticasone furoate and vilanterol groups versus the vilanterol only group at a two-sided 5% significance level” Source: Lancet Respiratory Medicine (2013) Parameter Value Significance Level (Two-Sided) 0.05 Control Incidence Rate (per year) 1.4 Rate Ratio 0.75 Exposure Time (Years) 1 Dispersion Parameter 0.7 Power (%) 90% Negative Binomial/ Recurrent Events Example
- 15. Group Sequential Design for Recurrent Events Part 3
- 16. Group Sequential Designs (GSD) “Group sequential trials can provide ethical and efficiency advantages by reducing the expected sample size and calendar time of clinical trials and by accelerating the approval of effective new treatments. For example, a group sequential design with a single interim analysis and can reduce the expected sample size of the trial by roughly 15 percent relative to a comparable non-adaptive trial.” GSD allows interim analyses to stop early Interim: look while trial is on-going Looks occur at pre-specified times E.g. After 50% subjects measured Can stop for benefit and/or futility Neither? Continue until end/next look However, need to account for effect of multiple analyses Do by “spending” error at each look
- 17. GSD Details 2 early stopping criteria (work similar) 1. Efficacy (α-spending) 2. Futility (β-spending) Use “spending function” to account for multiple analyses/”chances” Spend proportion of total error at each look More conservative N vs. fixed term analysis Multiple SF available (incl. custom) O’Brien-Fleming (conservative), Pocock (liberal), Power, Hwang-Shih-DeCani (flexible) Different heuristics for efficacy/futility Conservative SF expected for efficacy More flexibility for futility (less problematic) 𝛼 𝜏 = 2 1 − Φ 𝑧 𝛼/2 𝜏 O’Brien-Fleming Spending Function
- 18. Recurrent Events GSD Issues Appropriate MLE and test for GST Normal approx. if t same per subject? For NB, no closed form if t differs How turn info. time into “real” time Info. time related to follow-up times, n, rates and dispersion parameter Equal t ~ Means, Unequal ~ TTE Type I Error ↑ if low N/high κ No Exact, some proposed altered stats t-distribution GSD better for low N Source: Mütze, T., Glimm, E., Schmidli, H., & Friede, T. (2019).
- 19. Group Sequential Design for Negative Binomial Parameter Value Number of Looks 3 Efficacy Bound O’Brien Fleming Futility Bound Non-Binding Beta Spending Function Hwang-Shih-DeCani HSD Parameter -1.25 Extend previous example to group sequential design with 2 interim analyses with O’Brien Fleming efficacy bound and non-binding Hwang-Shih-DeCani futility bound with gamma = -1.25 Worked Example 2 Source: Lancet Respiratory Medicine (2013) Parameter Value Significance Level (Two-Sided) 0.05 Control Incidence Rate (per year) 1.4 Rate Ratio 0.75 Exposure Time (Years) 1 Dispersion Parameter 0.7 Power (%) 90%
- 20. Discussion and Conclusions Recurrent Events/Count data common in clinical trials Move away from approximations to modelling process fully Variety of models depending on scientific question Parametric: event rate; Semi-parametric: t between/to events SSD methods available for most common models Negative Binomial, Poisson, Andersen-Gill; one less barrier GSD methods available for recurrent events growing Approx. work adequately for standard Phase III assumptions
- 21. Further information at Statsols.com Questions? Thank You info@statsols.com
- 23. For video tutorials and worked examples Statsols.com/start
- 24. The solution for optimizing clinical trials PRE-CLINICAL / RESEARCH EARLY PHASE CONFIRMATORY POSTMARKETING Animal Studies ANOVA / ANCOVA 1000+ Scenarios for Fixed Term, Adaptive & Bayesian Methods Survival, Means, Proportions & Count endpoints Sample Size Re-Estimation Group Sequential Trials Bayesian Assurance Cross over & personalized medicine CRM MCP-Mod Simon’s Two Stage Cohort Study Case-control Study
- 25. Cameron, A. C., & Trivedi, P. K. (2013). Regression analysis of count data. Cambridge university press. Cook, R. J., & Lawless, J. (2007). The statistical analysis of recurrent events. Springer Science & Business Media. The Analysis of Recurrent Events: A Summary of Methodology; J Rogers, Oxford: https://www.psiweb.org/docs/default-source/resources/psi-subgroups/scientific/2016/time- to-event-and-recurrent-event-endpoints/jrogers.pdf?sfvrsn=a86d2db_2 Lehr, R. (1992). Sixteen S‐squared over D‐squared: A relation for crude sample size estimates. Statistics in medicine, 11(8), 1099-1102. Signorini, D. F. (1991). Sample size for Poisson regression. Biometrika, 78(2), 446-450. Gu, K., Ng, H. K. T., Tang, M. L., & Schucany, W. R. (2008). Testing the ratio of two poisson rates. Biometrical Journal, 50(2), 283-298. References
- 26. References Zhu, H. (2017). Sample size calculation for comparing two poisson or negative binomial rates in noninferiority or equivalence trials. Statistics in Biopharmaceutical Research, 9(1), 107- 115. Zhu, H., & Lakkis, H. (2015). Sample size calculation for comparing two negative binomial rates. Statistics in medicine, 33(3), 376-387. Tang, Y. (2015). Sample size estimation for negative binomial regression comparing rates of recurrent events with unequal follow-up time. Journal of biopharmaceutical statistics, 25(5), 1100-1113. Tang, Y. (2017). Sample size for comparing negative binomial rates in noninferiority and equivalence trials with unequal follow-up times. Journal of biopharmaceutical statistics, 1-17. Tang, Y., & Fitzpatrick, R. (2019). Sample size calculation for the Andersen‐Gill model comparing rates of recurrent events. Statistics in Medicine, 38(24), 4819-4827.
- 27. References Dransfield, M. T., et. al. (2013). Once-daily inhaled fluticasone furoate and vilanterol versus vilanterol only for prevention of exacerbations of COPD: two replicate double-blind, parallel- group, randomised controlled trials. The lancet Respiratory medicine, 1(3), 210-223. Jennison, C., & Turnbull, B. W. (1999). Group sequential methods with applications to clinical trials. CRC Press. Cook R. & Lawless J. (1996). Interim monitoring of longitudinal comparative studies with recurrent event responses. Biometrics 52: 1311–1323. Mütze, T., Glimm, E., Schmidli, H., & Friede, T. (2019). Group sequential designs for negative binomial outcomes. Statistical methods in medical research, 28(8), 2326-2347. Mutze, T., E. Glimm, H. Schmidli, and T. Friede. (2019). Group sequential designs with robust semiparametric recurrent event models. Statistical Methods in Medical Research