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Using pattern mixture modelling to reduce bias due to informative attrition in the Whitehall II study: a simulation study Catherine Welch 1 Martin Shipley 1 everine Sabia 2 S Eric Brunner 1 aki 1 Mika Kivim 1 Research Department of

  1. Using pattern mixture modelling to reduce bias due to informative attrition in the Whitehall II study: a simulation study Catherine Welch 1 Martin Shipley 1 everine Sabia 2 S´ Eric Brunner 1 aki 1 Mika Kivim¨ 1 Research Department of Epidemiology and Public Health, University College London 2 INSERM U1018, Centre for Research in Epidemiology and Population Health, Villejuif, France September 7, 2016 C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 1 / 23 September 7, 2016

  2. Outline 1 Background Methods 2 Results 3 4 Conclusions C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 2 / 23 September 7, 2016

  3. Introduction Informative attrition can bias longitudinal studies reason for attrition associated with missing outcome values Multiple imputation (MI) assumes missing at random - not appropriate Clinical trials use pattern mixture modelling (PMM), monotone data simplifies analysis Observational studies non-monotone, more complex C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 3 / 23 September 7, 2016

  4. Whitehall II cohort study 10,308 London civil servants, began 1985 Health and lifestyle questionnaire completed every 2-3 years (phase), clinic at odd phases Epidemiological investigation: Smoking status at baseline (Phase 5) is associated with 10-year cognitive decline Attrition maybe informative, participants with reduced cognitive function withdraw Replaced missing values with last observed value C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 4 / 23 September 7, 2016

  5. Objectives Simulation study to investigate using pattern mixture modelling to reduce bias caused by informative attrition in longitudinal observational data Using Stata, create 1,000 datasets (10,000 participants) replicating the smoking-cognitive function analysis Make values missing using missing not at random (MNAR) missingness mechanisms Compare bias in intercept and slope Simulated data (no missing values) Complete case analysis Analyse data imputed using MI PMM sensitivity analysis C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 5 / 23 September 7, 2016

  6. Outline 1 Background Methods 2 Results 3 4 Conclusions C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 6 / 23 September 7, 2016

  7. Substantive model Memory score ( y ij ) for participant j at time i [1] Standardised using mean and standard deviation from baseline Stratified by sex - this analysis includes just men Mixed effects model with random intercept and slope with interactions between coefficients and time = β 0 + β 1 smoke 5 j + β 1 smoke 5 j time ij + U 0 j + U 1 j time ij + ε i y ij Model also included participant characteristics at baseline (age, occupation grade and education) and their interactions with time C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 7 / 23 September 7, 2016

  8. Generating missing values Participation status Responder - participated at a given phase, may have item non-response Non-responder - unit non-response Confirmed death MAR - conditional on age, education and occupational grade at baseline If responders with item non-response, non-responder or died, replace y ij with missing value C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 8 / 23 September 7, 2016

  9. Withdrawn Informed Whitehall II they no longer wish to participate Participants withdraw at Phases 7, 9 and 11 Informative (missing not at random) Participants j and phase i assign withdrawal probability p ij conditional on memory score at the same phase Y ij logit ( p ij ) = λ 0 + λ 1 Y ij Selected λ 0 and λ 1 to achieve similar percentage withdrawn as Whitehall II study Lower memory scores more likely to withdraw C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 9 / 23 September 7, 2016

  10. Summary of multiple imputation Specify imputation model, which generates plausible values to replace missing values Generate M imputations for each missing value, creating M completed datasets Analyse each imputed dataset separately Pool estimates and standard errors - Rubins rules [2] Validity relies on plausible assumptions [3] MAR missingness mechanism Substantive model and imputation model are congenial C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 10 / 23 September 7, 2016

  11. Stata command twofold The two-fold fully conditional specification algorithm [4] Suitable for longitudinal data [5] Imputes each time point in turn conditional on observations at adjacent time points (time window) Within-time iteration - imputes missing values in time window Among-time iteration - time window imputes at each time point No interactions with time because phases imputed separately Available from SSC repository [6] C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 11 / 23 September 7, 2016

  12. twofold syntax (data in wide form) . gen start = 3 gen end = 11 (or phase participant died) gen base = 5 . twofold, timein(start) timeout(end) base(base) depmis(mem exsmoke) indobs(agec5 grade academ nonsmoke) conditionon(nonsmoke) condval(0) condvar(exsmoke) indmis(smkstop5) clear cat(nonsmoke exsmoke grade academ) m(20) ba(20) bw(5) seed(100) . mi reshape long ... . mi estimate: mixed mem b4.smokebase##c.time c.agec5##c.time i.grade##c.time i.academ##c.time || stno: time C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 12 / 23 September 7, 2016

  13. Pattern mixture modelling Specify separate distributions for the observed and missing data [7] Distribution of observed outcomes - substantive model y ij = β 0 + β 1 smoke 5 j + β 1 smoke 5 j time ij + U 0 j + U 1 j time ij + ε i Withdrawn indicator R ij Distribution of missing outcomes - for withdrawn, use substantive model and change by k in the imputed outcome y ij = β 0 + β 1 smoke 5 j + β 1 smoke 5 j time ij + U 0 j + U 1 j time ij + ε i + kR ij For withdrawn participants, change already imputed y ij values by k Sensitivity analysis: k=-0.2, -0.4, -0.6, -0.8 and -1.0 C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 13 / 23 September 7, 2016

  14. Outline 1 Background Methods 2 Results 3 4 Conclusions C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 14 / 23 September 7, 2016

  15. Simulated participation status 6,210 male participants from Whitehall II study Whitehall II study Participation Status 5 7 9 11 Participated,% 88.1 78.8 76.6 71.8 Died, % N/A 2.6 5.9 10.1 Non-response, % 11.9 14.6 12.2 11.8 Withdraw, % N/A 4.0 5.3 6.3 Simulated data Participation Status 5 7 9 11 Participated,% 89.6 80.3 78.1 73.3 Died, % N/A 2.4 5.5 9.0 Non-response, % 10.4 13.6 11.2 11.0 Withdraw, % N/A 3.8 5.3 6.6 C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 15 / 23 September 7, 2016

  16. Analysing simulated data, mean Simulated data, complete case and imputed data estimates averaged over 1,000 datasets Smoking status WII Simulated Complete Multiple at baseline study data Case imputation Intercept Current smoker -0.080 -0.079 -0.140 -0.051 Recent ex-smoker -0.081 -0.079 -0.138 -0.016 Long-term ex-smoker 0.071 0.073 0.004 0.098 Never smoker 0.026 0.027 -0.039 0.057 Slope Current smoker -0.412 -0.414 -0.354 -0.338 (per 10 years) Recent ex-smoker -0.313 -0.316 -0.264 -0.282 Long-term ex-smoker -0.409 -0.410 -0.366 -0.368 Never smoker -0.354 -0.355 -0.311 -0.311 Also adjusted for age, education and employment grade and interactions with time C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 16 / 23 September 7, 2016

  17. Pattern mixture modelling results, mean Simulated data, imputed and pattern mixture modelling estimates averaged over 1,000 datasets Smoking status WII Imputed Pattern mixture modelling ( k ) at baseline study data -0.2 -0.4 -0.6 -0.8 -1.0 Intercept Current -0.079 -0.051 -0.051 -0.054 -0.056 -0.057 -0.059 Recent ex -0.079 -0.016 -0.016 -0.019 -0.021 -0.022 -0.024 Long-term ex 0.073 0.098 0.096 0.094 0.093 0.091 0.090 Never 0.027 0.057 0.056 0.055 0.054 0.053 0.051 Slope Current -0.414 -0.338 -0.360 -0.383 -0.406 -0.429 -0.452 (per 10 Recent ex -0.316 -0.282 -0.304 -0.324 -0.346 -0.367 -0.388 years) Long-term ex -0.410 -0.368 -0.388 -0.407 -0.427 -0.448 -0.468 Never -0.355 -0.311 -0.328 -0.345 -0.362 -0.378 -0.395 Also adjusted for age, education and employment grade and interactions with time C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 17 / 23 September 7, 2016

  18. Outline 1 Background Methods 2 Results 3 4 Conclusions C Welch, M Shipley, S Sabia, E Brunner, M Kivim¨ aki (UCL, INSERM) Pattern mixture modelling 18 / 23 September 7, 2016

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