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the motivation the past the goal the example the family the surprise the future merlin : Mixed effects regression for linear, non-linear and user-defined models Stata Nordic and Baltic Meeting Oslo, 12th September 2018 Michael J. Crowther

  1. the motivation the past the goal the example the family the surprise the future merlin : Mixed effects regression for linear, non-linear and user-defined models Stata Nordic and Baltic Meeting Oslo, 12th September 2018 Michael J. Crowther Biostatistics Research Group, Department of Health Sciences, University of Leicester, UK, michael.crowther@le.ac.uk @Crowther MJ Funding: MRC (MR/P015433/1) Michael J. Crowther 12th September 2018 1 / 43 merlin

  2. the motivation the past the goal the example the family the surprise the future the plan • the motivation • the past • the goal • the example • the family • the surprise (at least it was last week) • the future Michael J. Crowther 12th September 2018 2 / 43 merlin

  3. the motivation the past the goal the example the family the surprise the future the motivation • More data → more questions • need for appropriate statistical modelling techniques, and implementations Michael J. Crowther 12th September 2018 3 / 43 merlin

  4. the motivation the past the goal the example the family the surprise the future the motivation • More data → more questions • need for appropriate statistical modelling techniques, and implementations • Growth in access to EHR • biomarkers < patients < GP practice area < geographical regions... Michael J. Crowther 12th September 2018 3 / 43 merlin

  5. the motivation the past the goal the example the family the surprise the future the motivation • More data → more questions • need for appropriate statistical modelling techniques, and implementations • Growth in access to EHR • biomarkers < patients < GP practice area < geographical regions... • The standard challenges • time-dependent effects, non-linear covariate effects Michael J. Crowther 12th September 2018 3 / 43 merlin

  6. the motivation the past the goal the example the family the surprise the future the motivation • More data → more questions • need for appropriate statistical modelling techniques, and implementations • Growth in access to EHR • biomarkers < patients < GP practice area < geographical regions... • The standard challenges • time-dependent effects, non-linear covariate effects • The neglected challenges • Within-patient variability • Informative observations times Michael J. Crowther 12th September 2018 3 / 43 merlin

  7. the motivation the past the goal the example the family the surprise the future the motivation • More data → more questions • need for appropriate statistical modelling techniques, and implementations • Growth in access to EHR • biomarkers < patients < GP practice area < geographical regions... • The standard challenges • time-dependent effects, non-linear covariate effects • The neglected challenges • Within-patient variability • Informative observations times We need modelling frameworks that can accommodate a lot of different things Michael J. Crowther 12th September 2018 3 / 43 merlin

  8. the motivation the past the goal the example the family the surprise the future Joint longitudinal-survival models Patient 98 Patient 253 200 1.0 200 1.0 0.8 0.8 150 150 Survival probability Survival probability 0.6 0.6 Biomarker Biomarker 100 100 0.4 0.4 50 50 0.2 0.2 0 0.0 0 0.0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 Follow-up time Follow-up time Longitudinal response Longitudinal fitted values Predicted conditional survival 95% Confidence interval Linking via - current value, gradient, AUC, random effects... Michael J. Crowther 12th September 2018 4 / 43 merlin

  9. the motivation the past the goal the example the family the surprise the future Joint longitudinal-survival models - extensions • Competing risks • Different types of outcomes • Multiple continuous outcomes • Delayed entry • Recurrent events and a terminal event • Prediction • Many others... Michael J. Crowther 12th September 2018 5 / 43 merlin

  10. the motivation the past the goal the example the family the surprise the future Joint longitudinal-survival models - software • stjm in Stata • gsem in Stata • frailtypack in R • joineR in R • JM and JMBayes in R • Many others... Michael J. Crowther 12th September 2018 6 / 43 merlin

  11. the motivation the past the goal the example the family the surprise the future (My) Methods development - software • stjm - joint longitudinal-survival models • stmixed - multilevel survival models • stgenreg - general parametric survival models • ... Michael J. Crowther 12th September 2018 7 / 43 merlin

  12. the motivation the past the goal the example the family the surprise the future (My) Methods development - software • stjm - joint longitudinal-survival models • stmixed - multilevel survival models • stgenreg - general parametric survival models • ... Each new project brings a new code base to maintain...could I make my life easier? Michael J. Crowther 12th September 2018 7 / 43 merlin

  13. the motivation the past the goal the example the family the surprise the future the past • last year I introduced megenreg • megenreg fitted mixed effects generalised regression models • megenreg was awesome...but Michael J. Crowther 12th September 2018 8 / 43 merlin

  14. the motivation the past the goal the example the family the surprise the future the past • last year I introduced megenreg • megenreg fitted mixed effects generalised regression models • megenreg was awesome...but I really hated the name Michael J. Crowther 12th September 2018 8 / 43 merlin

  15. the motivation the past the goal the example the family the surprise the future Michael J. Crowther 12th September 2018 9 / 43 merlin

  16. the motivation the past the goal the example the family the surprise the future Some people were not so keen... Michael J. Crowther 12th September 2018 10 / 43 merlin

  17. the motivation the past the goal the example the family the surprise the future Mixed Effects Regression for LInear, Non-linear and user-defined models merlin Michael J. Crowther 12th September 2018 11 / 43 merlin

  18. the motivation the past the goal the example the family the surprise the future the goal • multiple outcomes of varying types • measurement schedule can vary across outcomes • any number of levels and random effects • sharing and linking random effects between outcomes • sharing functions of the expected value of other outcomes • a reliable estimation engine • easily extendable by the user • ... a unified framework for data analysis and methods development Michael J. Crowther 12th September 2018 12 / 43 merlin

  19. the motivation the past the goal the example the family the surprise the future the example • there’s no equations in this talk • there’s 14 models • each of them is applied to the same dataset • most of them can be considered new models • we can fit all of them with a single line of code Michael J. Crowther 12th September 2018 13 / 43 merlin

  20. the motivation the past the goal the example the family the surprise the future • data from 312 patients with PBC collected at the Mayo Clinic 1974-1984 (Murtaugh et al. (1994)) • 158 randomised to receive D-penicillamine and 154 to placebo • survival outcome is all-cause death, with 140 events observed • we’re going to pretend we have competing causes of death - cancer and other causes • 1945 measurements of serum bilirubin, among other things Michael J. Crowther 12th September 2018 14 / 43 merlin

  21. the motivation the past the goal the example the family the surprise the future the data id time logb prothr~n trt stime cancer other 1 0 2.674149 12.2 D-penicil 1.09517 1 0 1 .525682 3.058707 11.2 D-penicil . . . 2 0 .0953102 10.6 D-penicil 14.1523 0 1 2 .498302 -.2231435 11 D-penicil . . . 2 .999343 0 11.6 D-penicil . . . 2 2.10273 .6418539 10.6 D-penicil . . . 2 4.90089 .9555114 11.3 D-penicil . . . 2 5.88928 1.280934 11.5 D-penicil . . . 2 6.88588 1.435084 . D-penicil . . . 2 7.8907 1.280934 . D-penicil . . . 2 8.83255 1.526056 . D-penicil . . . Michael J. Crowther 12th September 2018 15 / 43 merlin

  22. the motivation the past the goal the example the family the surprise the future a model merlin (logb /// log serum bilirubin time /// covariate , /// options family(gaussian) /// distribution ) Michael J. Crowther 12th September 2018 16 / 43 merlin

  23. the motivation the past the goal the example the family the surprise the future a model merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction , /// options family(gaussian) /// distribution ) /// Michael J. Crowther 12th September 2018 17 / 43 merlin

  24. the motivation the past the goal the example the family the surprise the future a model merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction M1[id]@1 /// random intercept , /// options family(gaussian) /// distribution ) /// Michael J. Crowther 12th September 2018 18 / 43 merlin

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