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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 UK Meeting London, 7th September 2018 Michael J. Crowther Biostatistics Research Group,

  1. 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 UK Meeting London, 7th 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 7th September 2018 1 / 39 merlin

  2. the past the goal the example the family the surprise the future the plan • the past • the goal • the example • the family • the surprise • the future Michael J. Crowther 7th September 2018 2 / 39 merlin

  3. 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 7th September 2018 3 / 39 merlin

  4. 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 7th September 2018 3 / 39 merlin

  5. the past the goal the example the family the surprise the future Michael J. Crowther 7th September 2018 4 / 39 merlin

  6. the past the goal the example the family the surprise the future Some people were not so keen... Michael J. Crowther 7th September 2018 5 / 39 merlin

  7. 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 7th September 2018 6 / 39 merlin

  8. 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 7th September 2018 7 / 39 merlin

  9. 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 7th September 2018 8 / 39 merlin

  10. 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 7th September 2018 9 / 39 merlin

  11. 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 7th September 2018 10 / 39 merlin

  12. 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 7th September 2018 11 / 39 merlin

  13. 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 7th September 2018 12 / 39 merlin

  14. 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 7th September 2018 13 / 39 merlin

  15. 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 time#M2[id]@1 /// random slope , /// options family(gaussian) /// distribution ) Michael J. Crowther 7th September 2018 14 / 39 merlin

  16. 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 time#M2[id]@1 /// random slope , /// options family(gaussian) /// distribution ) /// (pro /// prothrombin index rcs(time, df(3)) /// covariate , family(gamma) /// distribution ) /// Michael J. Crowther 7th September 2018 15 / 39 merlin

  17. 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 time#M2[id]@1 /// random slope , /// options family(gaussian) /// distribution ) /// (pro /// prothrombin index rcs(time, df(3)) /// covariate M3[id]@1 /// random effect , family(gamma) /// distribution ) /// Michael J. Crowther 7th September 2018 16 / 39 merlin

  18. 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 time#M2[id]@1 /// random slope , /// options family(gaussian) /// distribution ) /// (pro /// prothrombin index rcs(time, df(3)) /// covariate M3[id]@1 /// random effect , family(gamma) /// distribution ) /// , /// main options covariance(unstructured) // vcv Michael J. Crowther 7th September 2018 17 / 39 merlin

  19. 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 time#M2[id]@1 /// random slope , /// options family(gaussian) /// distribution ) /// (pro /// prothrombin index rcs(time, df(3)) /// covariate M3[id]@1 /// random effect , family(gamma) /// distribution ) /// , /// main options covariance(unstructured) /// vcv redistribution(t) df(5) // re dist. Michael J. Crowther 7th September 2018 18 / 39 merlin

  20. 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 time#M2[id]@1 /// random slope , /// options family(gaussian) /// distribution ) /// (pro /// prothrombin index rcs(time, df(3)) /// covariate M3[id]@1 /// random effect , family(gamma) /// distribution ) /// (stime trt /// response + covariate , family(rp, df(3) /// distribution failure(other)) /// event indicator ) /// , /// main options covariance(unstructured) /// vcv redistribution(t) df(5) // re dist. Michael J. Crowther 7th September 2018 19 / 39 merlin

  21. 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 time#M2[id]@1 /// random slope , /// options family(gaussian) /// distribution ) /// (pro /// prothrombin index rcs(time, df(3)) /// covariate M3[id]@1 /// random effect , family(gamma) /// distribution ) /// (stime trt /// response + covariate dEV[logb] EV[pro] /// associations , family(rp, df(3) /// distribution failure(other)) /// event indicator ) /// , /// main options covariance(unstructured) /// vcv redistribution(t) df(5) // re dist. Michael J. Crowther 7th September 2018 20 / 39 merlin

  22. 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 time#M2[id]@1 /// random slope , /// options family(gaussian) /// distribution ) /// (pro /// prothrombin index rcs(time, df(3)) /// covariate M3[id]@1 /// random effect , family(gamma) /// distribution ) /// (stime trt /// response + covariate trt#fp(stime, power(0)) /// tde dEV[logb] EV[pro] /// associations , family(rp, df(3) /// distribution failure(other)) /// event indicator ) /// , /// main options covariance(unstructured) /// vcv redistribution(t) df(5) // re dist. Michael J. Crowther 7th September 2018 21 / 39 merlin

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