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Simple and complex survival analysis: New developments in merlin Michael J. Crowther Associate Professor of Biostatistics Biostatistics Research Group Department of Health Sciences University of Leicester michael.crowther@le.ac.uk @Crowther

  1. Simple and complex survival analysis: New developments in merlin Michael J. Crowther Associate Professor of Biostatistics Biostatistics Research Group Department of Health Sciences University of Leicester michael.crowther@le.ac.uk @Crowther MJ Stata Nordic and Baltic Conference 30th August 2019

  2. Background survsim (Crowther and Lambert, 2012, 2013) Simulation of simple and complex survival data Michael J. Crowther merlin ’s survival skills 30th August 2019 2

  3. Background survsim (Crowther and Lambert, 2012, 2013) Simulation of simple and complex survival data multistate (Crowther and Lambert, 2017) Parametric multi-state survival analysis Michael J. Crowther merlin ’s survival skills 30th August 2019 2

  4. Background survsim (Crowther and Lambert, 2012, 2013) Simulation of simple and complex survival data multistate (Crowther and Lambert, 2017) Parametric multi-state survival analysis merlin (Crowther, 2017, 2019a,b) Extended mixed effects models for linear, non-linear and user-defined outcomes Michael J. Crowther merlin ’s survival skills 30th August 2019 2

  5. survsim Standard parametric distributions . set obs 1000 . gen trt = runiform()>0.5 . survsim stime died, dist(weib) lambda(0.1) gamma(1.2) > maxtime(5) cov(trt -0.5) Michael J. Crowther merlin ’s survival skills 30th August 2019 3

  6. survsim Standard parametric distributions . set obs 1000 . gen trt = runiform()>0.5 . survsim stime died, dist(weib) lambda(0.1) gamma(1.2) > maxtime(5) cov(trt -0.5) Custom (log) hazard functions . set obs 1000 . gen trt = runiform()>0.5 . survsim stime died, loghazard(-3 :+ #t :+ 0.1 :* log(#t) :* #t) > maxtime(5) cov(trt -0.5) Michael J. Crowther merlin ’s survival skills 30th August 2019 3

  7. multistate Transition matrix . mat list tmat tmat[3,3] to: to: to: start rfi osi from:start . 1 2 from:rfi . . 3 from:osi . . . Data pid _from _to _start _stop _status _trans 1 1 2 0 59.104721 0 1 1 1 3 0 59.104721 0 2 1371 1 2 0 16.558521 1 1 1371 1 3 0 16.558521 0 2 1371 2 3 16.558521 24.344969 1 3 Michael J. Crowther merlin ’s survival skills 30th August 2019 4

  8. multistate Stacked model . streg hormon _trans2 _trans3, dist(weib) . predictms , transmat(tmat) at1(hormon 1) Michael J. Crowther merlin ’s survival skills 30th August 2019 5

  9. multistate Stacked model . streg hormon _trans2 _trans3, dist(weib) . predictms , transmat(tmat) at1(hormon 1) Separate models . streg hormon if _trans1==1, dist(weibull) . estimates store m1 . stpm2 hormon if _trans2==1, scale(h) df(5) . estimates store m2 . strcs hormon if _trans3==1, df(3) . estimates store m3 . predictms , transmat(tmat) at1(hormon 1) models(m1 m2 m3) Michael J. Crowther merlin ’s survival skills 30th August 2019 5

  10. multistate 1.0 0.9 0.8 0.7 Probability 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 5 10 15 temptime Prob. state=1 Prob. state=2 Prob. state=3 Michael J. Crowther merlin ’s survival skills 30th August 2019 6

  11. multistate Post-surgery Relapsed Died 10.0 10.0 10.0 8.0 8.0 8.0 6.0 6.0 6.0 4.0 4.0 4.0 2.0 2.0 2.0 0.0 0.0 0.0 0 5 10 15 0 5 10 15 0 5 10 15 Years since surgery Years since surgery Years since surgery Length of stay 95% confidence interval Michael J. Crowther merlin ’s survival skills 30th August 2019 7

  12. merlin A general framework for the analysis of data of all types 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 ... Michael J. Crowther merlin ’s survival skills 30th August 2019 8

  13. merlin Data . list id time logb pro trt stime died if id==1 | id==2, noobs sepby(id) id time logb prothr~n trt stime died 1 0 2.674149 12.2 D-penicil 1.09517 1 1 .525682 3.058707 11.2 D-penicil . . 2 0 .0953102 10.6 D-penicil 14.1523 0 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 11.5 D-penicil . . 2 7.8907 1.280934 11.5 D-penicil . . 2 8.83255 1.526056 11.5 D-penicil . . Michael J. Crowther merlin ’s survival skills 30th August 2019 9

  14. merlin (logb /// log serum bilirubin time /// covariate , /// options family(gaussian) /// distribution ) Michael J. Crowther merlin ’s survival skills 30th August 2019 10

  15. merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction , /// options family(gaussian) /// distribution ) /// Michael J. Crowther merlin ’s survival skills 30th August 2019 11

  16. merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction M1[id]@1 /// random intercept , /// options family(gaussian) /// distribution ) /// Michael J. Crowther merlin ’s survival skills 30th August 2019 12

  17. 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 merlin ’s survival skills 30th August 2019 13

  18. 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 merlin ’s survival skills 30th August 2019 14

  19. 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 merlin ’s survival skills 30th August 2019 15

  20. 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 merlin ’s survival skills 30th August 2019 16

  21. 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 merlin ’s survival skills 30th August 2019 17

  22. 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 merlin ’s survival skills 30th August 2019 18

  23. 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 merlin ’s survival skills 30th August 2019 19

  24. 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 merlin ’s survival skills 30th August 2019 20

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