![References
• Scott JM, deCamp A, Juraska M, Fay MP, Gilbert PB. Finite-sample
corrected generalized estimating equation of population average treatment
effects in stepped wedge cluster randomized trials. Stat Methods Med Res.
2014 Sep 29. pii: 0962280214552092. [Epub ahead of print] PubMed PMID:
25267551.
• Ukoumunne OC, Carlin JB, Gulliford MC. A simulation study of odds ratio
estimation for binary outcomes from cluster randomized trials. Stat Med.
2007 Aug 15;26(18):3415-28. PubMed PMID: 17154246.
• Heo M, Leon AC. Comparison of statistical methods for analysis of
clustered binary observations. Stat Med. 2005 Mar 30;24(6):911-23.
PubMed PMID: 15558576](https://image.slidesharecdn.com/session6analysis-160830134618/85/The-stepped-wedge-cluster-randomised-trial-workshop-session-5-34-320.jpg)
The stepped wedge cluster randomised trial workshop: session 5
- 1. Some illustrative examples on the analysis of the SW-CRT 30/08/2016 Karla Hemming
- 2. Calendar time is a confounder
- 3. Why calendar time is a confounder…
- 4. Time effects • When designing a SW-CRT time needs to be allowed for in the sample size calculation. • Time also needs to be allowed for in the analysis
- 5. Analysis
- 6. Analysis • Summarise key characteristics by exposure / unexposed status – Identify selection biases • Analysis either GEE or mixed models – Clustering – Time effects • Imbalance of calendar time between exposed / unexposed: – The majority of the control observations will be before the majority of the intervention observations – Time is a confounder! • Unadjusted effect meaningless
- 7. Treatment effect • After accounting for any secular changes, what is the effect of the intervention, averaged across steps? • The intervention effect is modelled as a change in level, constant across steps (or time)
- 8. 0 0.1 0.2 0.3 0.4 0.5 0.6 0 1 2 3 4 5 6 7 MeanOutcome Year Interpretation of intervention effect in SW design: continuous time Control Intervention Estimated after averaging across all sites / time points in each condition
- 9. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 1 2 3 4 5 6 7 8 Meanoutcome Year Interpretation of intervention effect in SW: categorical time Control Intervention
- 10. Example one
- 11. 11 Example 1: Maternity sweeping • Objective: evaluate a training scheme to improve the rate of membrane sweeping in post term pregnancies – Primary outcome: • Proportion of women having a membrane sweep • Baseline rate 40% • Hope to increase to 50% during 12 weeks post intervention – Cluster design: • 10 teams (clusters); 12 births per cluster per week • Pragmatic design – rolled out when possible • Transition period to allow training
- 12. 12 Example 1: Maternity sweeping (transition period)
- 13. Example 1: Underlying trend0 .2.4.6.8 20005/03/12 23/04/12 18/06/12 13/08/12 week commencing
- 14. Example 1: results Unexposed to intervention n=1417 Exposed to intervention n=1356 Relative Risk P- value Number of women offered and accepting membrane sweeping Number (%) 629 (44.4%) 634 (46.8%) Cluster adjusted 1.06 (0.97, 1.16) 0.21 Time and cluster adjusted Fixed effects time 0.88 (0.69, 1.05) 0.11 Linear time effect 0.90 (0.73, 1.11) 0.34
- 15. Example 1: Impact of secular trend 0 .2.4.6.8 20005/03/12 23/04/12 18/06/12 13/08/12 week commencing Unadjusted RR = 1.06 95% CI (0.97, 1.16) Adjusted (for time) RR = 0.88 95% CI (0.69, 1.05) Rising Tide? Contamination?
- 16. Explanations • Rising tide – General move towards improving care – perhaps due to very initiative that prompted study investigators to do this study • Contamination – Unexposed clusters became exposed before their randomisation date • Lack of precision – Intervention wasn’t ruled out as being effective
- 17. Example 2
- 18. Example 2: Critical care outreach • Intervention: Critical care outreach • Setting: Hospital in Iran • Clusters: Wards • Outcome: Mortality
- 20. Example 2: Underlying trend 0 .05 .1 .15 07/10 04/1111/10 09/11 Study epoch (each epoch represents a four week period)
- 21. Example 2: results Unexposed to intervention Exposed to intervention Treatment effect P-value Number of Patients 7,802 10,880 Mortality Number (%) 370 (4.74) 384 (3.53) OR (95% CI) Unadjusted 0.73 (0.64, 0.85) 0.000 Cluster adjusted 1.02 (0.83, 1.26) 0.817 Fixed effects for time 0.82 (0.56, 1.19) 0.297 Linear effect for time 0.96 (0.76, 1.22) 0.750 Covariate adjusted 0.97 (0.64, 1.47) 0.489
- 22. Example 2: Underlying trend 0 .05 .1 .15 07/10 04/1111/10 09/11 Study epoch (each epoch represents a four week period) Unadjusted OR = 1.02 95% CI (0.83, 1.26) Adjusted OR = 0.82 95% CI (0.56,1.19) Lack of power?
- 23. Explanations • Rising tide – General move towards improving care – perhaps due to very initiative that prompted study investigators to do this study • Contamination – Unexposed clusters became exposed before their randomisation date • Lack of precision – Intervention wasn’t ruled out as being effective
- 24. Models fitted • Mixed effects model • Random effect for cluster • Fixed effect for time and intervention 𝑌𝑖𝑗𝑙 = 𝜇 + 𝛽𝑗 + θ𝑋𝑖𝑗 + 𝑢𝑖 + 𝑒𝑖𝑗𝑙 𝑢𝑖~𝑁 0, 𝜎 𝑏 ; 𝑒𝑖𝑗𝑙 ~𝑁(0, 𝜎 𝑤) (time j, cluster i, individual l )
- 25. Parameter estimation • Models fitted used Stata 13 – Used meglm function – Uses mean-variance adaptive Gauss-Hermite quadrature – Default number of integration points (7) – Experienced convergence difficulty (LOS example) then used the Laplace approximation – but clear instability • Used random effects – GEE alternative – GEE possibly more robust to model miss-specification – GEE possibly problematic when small number of clusters (there exist adjustments)
- 26. Model assumptions and extensions
- 27. Model assumptions 1 • Underlying secular trend – The underlying secular trend is same across all clusters
- 28. Variation in underlying secular trends S is strata 0 5 10 15 20 25 30 0 2 4 6 8 10 12 Meanoutcome Year Strata 1 Strata 2 Strata 3
- 29. Model assumptions 2 • Time invariant treatment effect – There is no delayed intervention effect – No change in intensity of the effect over the course of time – No time by treatment interaction – Time (since introduction) isn't an effect modifier
- 30. Time variant treatment effect 𝑌𝑖𝑗𝑙 = 𝜇 + 𝛽𝑗 + 𝜃𝑗 𝑋𝑖𝑗 + 𝑢𝑖 + 𝑒𝑖𝑗𝑙 0 5 10 15 20 25 30 1 2 3 4 5 6 7 8 Meanoutcome Year Control Intervention
- 31. Model assumptions 3 • Intra cluster correlation – The correlation between two individuals is independent of time – Two observations in the same cluster / time period have the same degree of correlation as two observations in the same cluster but different time periods Time 𝑌𝑖𝑗𝑙 = 𝜇 + 𝛽𝑗 + θ𝑋𝑖𝑗 + 𝑢𝑖 + 𝑣𝑖𝑗 + 𝑒𝑖𝑗𝑙 𝑢𝑖~𝑁 0, 𝜎𝑏 ; 𝑣𝑖𝑗~𝑁 0, 𝜎𝑣 ; 𝑒𝑖𝑗𝑙 ~𝑁(0, 𝜎 𝑤)
- 32. Model assumptions 4 • Treatment effect heterogeneity – The effect of the intervention is the same across all clusters – Typical assumption in CRTs – In a meta-analysis common to assume between cluster heterogeneity in treatment effect 𝑌𝑖𝑗𝑙 = 𝜇 + 𝛽𝑗 + 𝜃𝑖 𝑋𝑖𝑗 + 𝑢𝑖 + 𝑒𝑖𝑗𝑙 𝜃𝑖 ~𝑁(𝜃, 𝜎 𝜃)
- 33. Summary • Time is a potential partial confounder • Designs which are completely confounded with time shouldn’t be used • Time must be allowed for as a covariate in primary analysis • Model extensions require sufficient power and pre-specification
- 34. References • Scott JM, deCamp A, Juraska M, Fay MP, Gilbert PB. Finite-sample corrected generalized estimating equation of population average treatment effects in stepped wedge cluster randomized trials. Stat Methods Med Res. 2014 Sep 29. pii: 0962280214552092. [Epub ahead of print] PubMed PMID: 25267551. • Ukoumunne OC, Carlin JB, Gulliford MC. A simulation study of odds ratio estimation for binary outcomes from cluster randomized trials. Stat Med. 2007 Aug 15;26(18):3415-28. PubMed PMID: 17154246. • Heo M, Leon AC. Comparison of statistical methods for analysis of clustered binary observations. Stat Med. 2005 Mar 30;24(6):911-23. PubMed PMID: 15558576