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Simple and complex survival analysis: New developments in merlin - - PowerPoint PPT Presentation

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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

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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 MJ

Stata Nordic and Baltic Conference 30th August 2019

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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

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Background

survsim (Crowther and Lambert, 2012, 2013)

Simulation of simple and complex survival data

multistate (Crowther and Lambert, 2017)

Parametric multi-state survival analysis

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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

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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)

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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)

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multistate

Transition matrix

. mat list tmat tmat[3,3] to: to: to: start rfi

  • si

from:start . 1 2 from:rfi . . 3 from:osi . . .

Data

pid _from _to _start _stop _status _trans 1 1 2 59.104721 1 1 1 3 59.104721 2 1371 1 2 16.558521 1 1 1371 1 3 16.558521 2 1371 2 3 16.558521 24.344969 1 3

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multistate

Stacked model

. streg hormon _trans2 _trans3, dist(weib) . predictms , transmat(tmat) at1(hormon 1)

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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)

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multistate

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Probability 5 10 15 temptime

  • Prob. state=1
  • Prob. state=2
  • Prob. state=3

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multistate

0.0 2.0 4.0 6.0 8.0 10.0 5 10 15 Years since surgery

Post-surgery

0.0 2.0 4.0 6.0 8.0 10.0 5 10 15 Years since surgery

Relapsed

0.0 2.0 4.0 6.0 8.0 10.0 5 10 15 Years since surgery

Died Length of stay 95% confidence interval

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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 ...

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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 2.674149 12.2 D-penicil 1.09517 1 1 .525682 3.058707 11.2 D-penicil . . 2 .0953102 10.6 D-penicil 14.1523 2 .498302

  • .2231435

11 D-penicil . . 2 .999343 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 . .

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merlin (logb /// log serum bilirubin time /// covariate , /// options family(gaussian) /// distribution )

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merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction , /// options family(gaussian) /// distribution ) ///

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merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction M1[id]@1 /// random intercept , /// options family(gaussian) /// distribution ) ///

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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 )

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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 ) ///

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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 ) ///

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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

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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.

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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.

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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.

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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.

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merlin (logb time time#trt M1[id]@1 /// model 1 time#M2[id]@1 , /// family(gaussian) /// ) /// (pro rcs(time, df(3)) M3[id]@1 /// model 2 , family(gamma) /// ) /// (stime trt /// trt#fp(stime, power(0)) /// model 3 - cause 1 dEV[logb] EV[pro] /// tde , family(rp, df(3) /// distribution failure(other)) /// event indicator ) /// (stime trt /// model 4 - cause 2 trt#rcs(stime, df(3) log) /// tde EV[logb] iEV[pro] /// associations , family(weibull, /// distribution failure(cancer)) /// event indicator ) /// , /// covariance(unstructured)

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merlin & friends

Model

. merlin (stime hormon , family(rp, df(3) failure(died))) . estimates store m1

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merlin & friends

Model

. merlin (stime hormon , family(rp, df(3) failure(died))) . estimates store m1

Simulate

. survsim stime died, model(m1) maxtime(5)

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merlin & friends

Model

. merlin (stime hormon , family(rp, df(3) failure(died))) . estimates store m1

Simulate

. survsim stime died, model(m1) maxtime(5)

Predict

. predictms, model(m1) at1(hormon 1)

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merlin + survsim

Model

. merlin (stime hormon , family(weibull, failure(died))) Mixed effects regression model Number of obs = 1,000 Log likelihood = -1370.8379

  • |

Coef.

  • Std. Err.

z P>|z| [95% Conf. Interval]

  • ------------+----------------------------------------------------------------

stime: | hormon |

  • .544245

.0967967

  • 5.62

0.000

  • .7339631
  • .3545269

_cons |

  • 2.083643

.0958374

  • 21.74

0.000

  • 2.271481
  • 1.895806

log(gamma) | .110706 .0446086 2.48 0.013 .0232747 .1981372

  • . estimates store m1

Simulate

. survsim stime2 died2, model(m1) maxtime(5)

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merlin + survsim

Model

. merlin (stime hormon , family(weibull, failure(died))) Mixed effects regression model Number of obs = 1,000 Log likelihood = -1370.8379

  • |

Coef.

  • Std. Err.

z P>|z| [95% Conf. Interval]

  • ------------+----------------------------------------------------------------

stime: | hormon |

  • .544245

.0967967

  • 5.62

0.000

  • .7339631
  • .3545269

_cons |

  • 2.083643

.0958374

  • 21.74

0.000

  • 2.271481
  • 1.895806

log(gamma) | .110706 .0446086 2.48 0.013 .0232747 .1981372

  • . estimates store m1

Simulate

. survsim stime2 died2, model(m1) maxtime(5)

Modify

. mat b2 = -0.5,-2,0.1 . erepost b = b2 . estimates store m1 . survsim stime3 died3, model(m1) maxtime(5)

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merlin - multiple timescales

Age as the timescale

. merlin (eventage hormon , family(rp, df(3) failure(died) ltruncated(diagage))) . estimates store m1

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merlin - multiple timescales

Age as the timescale

. merlin (eventage hormon , family(rp, df(3) failure(died) ltruncated(diagage))) . estimates store m1

Age and time since diagnosis as timescales

. merlin (eventage hormon rcs(eventage, df(2) log moffset(diagage)) , family(rp, df(3) failure(died) ltruncated(diagage))) . estimates store m1

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merlin - multiple timescales

Age as the timescale

. merlin (eventage hormon , family(rp, df(3) failure(died) ltruncated(diagage))) . estimates store m1

Age and time since diagnosis as timescales

. merlin (eventage hormon rcs(eventage, df(2) log moffset(diagage)) , family(rp, df(3) failure(died) ltruncated(diagage))) . estimates store m1

Predict

. predictms, model(m1) at1(hormon 1)

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merlin - interval censoring

Data

+-----------------------------------------+ | id left time event status trt | |-----------------------------------------| | 1 . 72 Censor 0 | | 2 1 2 Cancer 0 | | 3 . 40 1 CVD 1 | | 4 19 20 2 CVD 0 | | 5 . 65 Censor 0 | +-----------------------------------------+

Model

. merlin (time trt , family(rp, df(3) failure(event) linterval(left))) . estimates store m1

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merlin - interval censoring & competing risks

Data

+---------------------------------------------------------+ | id left time event status cause1 cause2 cause3 | |---------------------------------------------------------| | 1 . 72 Censor 1 1 1 | | 2 1 2 Cancer 1 0 | | 3 . 40 1 CVD 1 0 | | 4 19 20 2 Other 1 | | 5 . 65 Censor 1 1 1 | +---------------------------------------------------------+

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merlin - interval censoring & competing risks

Data

+---------------------------------------------------------+ | id left time event status cause1 cause2 cause3 | |---------------------------------------------------------| | 1 . 72 Censor 1 1 1 | | 2 1 2 Cancer 1 0 | | 3 . 40 1 CVD 1 0 | | 4 19 20 2 Other 1 | | 5 . 65 Censor 1 1 1 | +---------------------------------------------------------+

Model

. merlin (time trt if cause1==1, family(weibull, fail(event) linterval(left))) > (time trt if cause2==1, family(rp, df(3) fail(event) linterval(left))) > (time trt if cause3==1, family(gompertz, fail(event) linterval(left))) > , transmatrix(tmat)

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merlin - interval censoring & competing risks

Data

+---------------------------------------------------------+ | id left time event status cause1 cause2 cause3 | |---------------------------------------------------------| | 1 . 72 Censor 1 1 1 | | 2 1 2 Cancer 1 0 | | 3 . 40 1 CVD 1 0 | | 4 19 20 2 Other 1 | | 5 . 65 Censor 1 1 1 | +---------------------------------------------------------+

Model

. merlin (time trt if cause1==1, family(weibull, fail(event) linterval(left))) > (time trt if cause2==1, family(rp, df(3) fail(event) linterval(left))) > (time trt if cause3==1, family(gompertz, fail(event) linterval(left))) > , transmatrix(tmat)

Simulate

. estimates store m1 . survsim stime died, model(m1) outcome(2) maxtime(5)

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merlin - interval censoring & competing risks

We can predict the cause-specific cumulative incidence functions

range tvar 0 60 500 predict cif1, cif outcome(1) timevar(tvar) at(trt 1) predict cif2, cif outcome(2) timevar(tvar) at(trt 1) predict cif3, cif outcome(3) timevar(tvar) at(trt 1)

And quantify the impact of treatment

. predict cifdiff1, cifdifference outcome(1) timevar(tvar) /// > at1(trt 1) at2(trt 0) ci . predict cifdiff2, cifdifference outcome(2) timevar(tvar) /// > at1(trt 1) at2(trt 0) ci . predict cifdiff3, cifdifference outcome(3) timevar(tvar) /// > at1(trt 1) at2(trt 0) ci

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merlin - interval censoring & competing risks

  • 0.20
  • 0.10

0.00 0.10 0.20 Difference in CIFs 20 40 60 Follow-up (months)

Cancer

  • 0.20
  • 0.10

0.00 0.10 0.20 Difference in CIFs 20 40 60 Follow-up (months)

CVD

  • 0.20
  • 0.10

0.00 0.10 0.20 Difference in CIFs 20 40 60 Follow-up (months)

Other

Difference in CIFs

Difference in CIFs 95% Confidence Interval

Figure 1: Difference in cumulative incidence functions, and associated 95% confidence interval, across treatment groups, for each cause of death.

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merlin - interval censoring & competing risks

We can calculate the loss in (restricted) life expectancy for each cause

predict lile1, timelost outcome(1) timevar(tvar) at(trt 1) ci predict lile2, timelost outcome(2) timevar(tvar) at(trt 1) ci predict lile3, timelost outcome(3) timevar(tvar) at(trt 1) ci

Or directly calculate the total

predict lile0, totaltimelost outcome(1) timevar(tvar) at(trt 0) ci predict lile1, totaltimelost outcome(1) timevar(tvar) at(trt 1) ci

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merlin - interval censoring & competing risks

5 10 15 20 25 Total time lost 20 40 60 Lifetime available (months)

Treated

5 10 15 20 25 Total time lost 20 40 60 Lifetime available (months)

Placebo

Loss in restricted life expectancy

Time lost to cancer Time lost to CVD Time lost to other Total time lost

Figure 2: Loss in restricted life expectancy due to each cause of death.

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Discussion and future work

survsim now talks to merlin predictms now talks to merlin By syncing up the codebases, extensions to merlin will filter down I also showed some extensions for interval censored data We can still derive clinically useful predictions, regardless of the complexity of the underlying models More examples on mjcrowther.co.uk/software/merlin

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Discussion and future work

survsim now talks to merlin predictms now talks to merlin By syncing up the codebases, extensions to merlin will filter down I also showed some extensions for interval censored data We can still derive clinically useful predictions, regardless of the complexity of the underlying models More examples on mjcrowther.co.uk/software/merlin ...most of this talk isn’t released yet

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References

Crowther, M. J. 2017. Extended multivariate generalised linear and non-linear mixed effects

  • models. arXiv . URL https://arxiv.org/abs/1710.02223.

. 2019a. merlin - a unified modelling framework for data analysis and methods development in Stata. Stata Journal . URL https://arxiv.org/abs/1806.01615. . 2019b. Multilevel mixed effects parametric survival analysis: Estimation, prediction and software . URL https://arxiv.org/abs/1709.06633. Crowther, M. J., and P. C. Lambert. 2012. Simulating complex survival data. Stata J 12(4): 674–687. . 2013. Simulating biologically plausible complex survival data. Stat Med 32(23): 4118–4134. URL http://dx.doi.org/10.1002/sim.5823. . 2017. Parametric multistate survival models: Flexible modelling allowing transition-specific distributions with application to estimating clinically useful measures of effect differences. Statistics in medicine 36: 4719–4742.

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