merlin : Mixed effects regression for linear, non-linear and - - PowerPoint PPT Presentation

▶
merlin mixed effects regression for linear non linear and
SMART_READER_LITE
LIVE PREVIEW

merlin : Mixed effects regression for linear, non-linear and - - PowerPoint PPT Presentation

Jun 11, 2023 5 likes •510 views

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

slide-1
SLIDE 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 merlin 12th September 2018 1 / 43

slide-2
SLIDE 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 merlin 12th September 2018 2 / 43

slide-3
SLIDE 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 merlin 12th September 2018 3 / 43

slide-4
SLIDE 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 merlin 12th September 2018 3 / 43

slide-5
SLIDE 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 merlin 12th September 2018 3 / 43

slide-6
SLIDE 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 merlin 12th September 2018 3 / 43

slide-7
SLIDE 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 merlin 12th September 2018 3 / 43

slide-8
SLIDE 8

the motivation the past the goal the example the family the surprise the future

Joint longitudinal-survival models

0.0 0.2 0.4 0.6 0.8 1.0 Survival probability 50 100 150 200 Biomarker 2 4 6 8 10 12 14

Follow-up time Patient 98

0.0 0.2 0.4 0.6 0.8 1.0 Survival probability 50 100 150 200 Biomarker 2 4 6 8 10 12 14

Follow-up time Patient 253 Longitudinal response Longitudinal fitted values Predicted conditional survival 95% Confidence interval

Linking via - current value, gradient, AUC, random effects...

Michael J. Crowther merlin 12th September 2018 4 / 43

slide-9
SLIDE 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 merlin 12th September 2018 5 / 43

slide-10
SLIDE 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 merlin 12th September 2018 6 / 43

slide-11
SLIDE 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 merlin 12th September 2018 7 / 43

slide-12
SLIDE 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 merlin 12th September 2018 7 / 43

slide-13
SLIDE 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 merlin 12th September 2018 8 / 43

slide-14
SLIDE 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 merlin 12th September 2018 8 / 43

slide-15
SLIDE 15

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

slide-16
SLIDE 16

the motivation the past the goal the example the family the surprise the future

Some people were not so keen...

Michael J. Crowther merlin 12th September 2018 10 / 43

slide-17
SLIDE 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 merlin 12th September 2018 11 / 43

slide-18
SLIDE 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 merlin 12th September 2018 12 / 43

slide-19
SLIDE 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 merlin 12th September 2018 13 / 43

slide-20
SLIDE 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
  • bserved
  • 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 merlin 12th September 2018 14 / 43

slide-21
SLIDE 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 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 1 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 . D-penicil . . . 2 7.8907 1.280934 . D-penicil . . . 2 8.83255 1.526056 . D-penicil . . .

Michael J. Crowther merlin 12th September 2018 15 / 43

slide-22
SLIDE 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 merlin 12th September 2018 16 / 43

slide-23
SLIDE 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 merlin 12th September 2018 17 / 43

slide-24
SLIDE 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 merlin 12th September 2018 18 / 43

slide-25
SLIDE 25

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 time#M2[id]@1 /// random slope , /// options family(gaussian) /// distribution )

Michael J. Crowther merlin 12th September 2018 19 / 43

slide-26
SLIDE 26

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 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 12th September 2018 20 / 43

slide-27
SLIDE 27

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 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 12th September 2018 21 / 43

slide-28
SLIDE 28

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 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 12th September 2018 22 / 43

slide-29
SLIDE 29

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 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 12th September 2018 23 / 43

slide-30
SLIDE 30

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 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 12th September 2018 24 / 43

slide-31
SLIDE 31

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 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 12th September 2018 25 / 43

slide-32
SLIDE 32

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 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 12th September 2018 26 / 43

slide-33
SLIDE 33

the motivation the past the goal the example the family the surprise the future

a model

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)

Michael J. Crowther merlin 12th September 2018 27 / 43

slide-34
SLIDE 34

the motivation the past the goal the example the family the surprise the future

predictions predict cif1, cif marginal outcome(3) at(trt 0) predict cif1, cif marginal outcome(4) at(trt 0)

Michael J. Crowther merlin 12th September 2018 28 / 43

slide-35
SLIDE 35

the motivation the past the goal the example the family the surprise the future

a user-defined model

real matrix gauss logl(gml) { y = merlin util depvar(gml) // dep. var. linpred = merlin util xzb(gml) // lin. pred. sdre = exp(merlin util ap(gml,1)) // anc. param. return(lnnormalden(y,linpred,sdre)) // logl } merlin (logb ... , family(user, llfunction(gauss logl) nap(1))) ... ... ...

Michael J. Crowther merlin 12th September 2018 29 / 43

slide-36
SLIDE 36

the motivation the past the goal the example the family the surprise the future

a user-defined model

real matrix gauss logl(gml) { y = merlin util depvar(gml) // dep. var. linpred = merlin util xzb(gml) // lin. pred. sdre = exp(merlin util xzb_mod(gml,2)) // anc. param. return(lnnormalden(y,linpred,sdre)) // logl } merlin (logb ... , family(user, llfunction(gauss logl))) (age M1[id]@1, family(null)) ... ...

Michael J. Crowther merlin 12th September 2018 30 / 43

slide-37
SLIDE 37

the motivation the past the goal the example the family the surprise the future

a user-defined nonlinear model - Yulia’s talk

webuse orange, clear menl circumf = (b1+U1[tree])/(1+exp(-(age-b2)/b3)) mata: real matrix logl(transmorphic gml) { y = merlin_util_depvar(gml) b1 = merlin_util_xzb(gml) b2 = merlin_util_xzb_mod(gml,2) b3 = merlin_util_xzb_mod(gml,3) sdre = exp(merlin_util_ap(gml,1)) xb = b1 :/ (1 :+ exp(-b2 :/ b3)) return(lnnormalden(y,xb,sdre)) } end merlin (circumf M1[tree]@1, family(user, llf(logl) nap(1))) ( age@1 , family(null)) ( , family(null))

Michael J. Crowther merlin 12th September 2018 31 / 43

slide-38
SLIDE 38

the motivation the past the goal the example the family the surprise the future

stuff I didn’t show

  • random effects at arbitrary levels - M4[centre>id]@1
  • B-splines - bs(time, df(3) order(4))
  • d2EV[], ?XB[]
  • linterval(varname) - interval censoring
  • ltruncated(varname) - left-truncation
  • 9 (so far) other inbuilt families, e.g. beta, ologit
  • bhazard(varname) - relative survival
  • mf(func name) - user-defined element function

Michael J. Crowther merlin 12th September 2018 32 / 43

slide-39
SLIDE 39

the motivation the past the goal the example the family the surprise the future

the family

  • merlin’s syntax is not simple
  • we can develop more user-friendly shell files to allow a

simpler syntax for special cases

  • merlin’s minions...
  • excalibur (stmixed) for multilevel survival analysis

(SJ under revision)

  • lancelot - meta-analysis
  • arthur - to be revealed next!
  • galahad - maybe next year
  • ...

Michael J. Crowther merlin 12th September 2018 33 / 43

slide-40
SLIDE 40

the motivation the past the goal the example the family the surprise the future

the surprise Two useful features of merlin are:

  • EV[depvar/#] element type
  • implemented for their use in joint longitudinal-survival

models

  • family(null)
  • implemented for use with user-defined models

their combination gives merlin some new capabilities

Michael J. Crowther merlin 12th September 2018 34 / 43

slide-41
SLIDE 41

the motivation the past the goal the example the family the surprise the future

the surprise

merlin (y x1 x2 EV[2] EV[3], family(bernoulli) link(logit)) (x1 x2, family(null) link(logit)) (x1 x2, family(null) link(logit))

any idea what this is?

Michael J. Crowther merlin 12th September 2018 35 / 43

slide-42
SLIDE 42

the motivation the past the goal the example the family the surprise the future

the surprise

merlin (y x1 x2 EV[2] EV[3], family(bernoulli) link(logit)) (x1 x2, family(null) link(logit)) (x1 x2, family(null) link(logit))

any idea what this is? It’s an artificial neural network!

Michael J. Crowther merlin 12th September 2018 35 / 43

slide-43
SLIDE 43

the motivation the past the goal the example the family the surprise the future Michael J. Crowther merlin 12th September 2018 36 / 43

slide-44
SLIDE 44

the motivation the past the goal the example the family the surprise the future

the surprise

merlin (y x1 x2 EV[2] EV[3], family(bernoulli) link(logit)) (x1 x2, family(null) link(logit)) (x1 x2, family(null) link(logit)) neuralnet x1 x2, output1(y, family(bernoulli) link(logit)) hlayers(1) hlink(logit) hnodes(2) penalty(ridge) lambda(1e-07)

Michael J. Crowther merlin 12th September 2018 37 / 43

slide-45
SLIDE 45

the motivation the past the goal the example the family the surprise the future

the surprise

merlin (y x1_nn x2_nn EV[4] EV[5] EV[6] , family(bernoulli) link(logit)) (x1_nn x2_nn, family(null) link(atanh)) (x1_nn x2_nn, family(null) link(atanh)) (EV[2] EV[3], family(null) link(atanh)) (EV[2] EV[3], family(null) link(atanh)) (EV[2] EV[3], family(null) link(atanh)) neuralnet x1 x2, output1(y, family(bernoulli) link(logit)) hlink(atanh) hlayers(2) hnodes(2 3) penalty(lasso) lambda(1e-07)

Michael J. Crowther merlin 12th September 2018 38 / 43

slide-46
SLIDE 46

the motivation the past the goal the example the family the surprise the future

. nnplot , inputs(10) outputs(5) hlayers(3) hnodes(8 3 4)

x10 x9 x8 x7 x6 x5 x4 x3 x2 x1 b0 y5 y4 y3 y2 y1 Inputs Hidden layer 1 Hidden layer 2 Hidden layer 3 Outputs

Artificial neural network

Michael J. Crowther merlin 12th September 2018 39 / 43

slide-47
SLIDE 47

the motivation the past the goal the example the family the surprise the future

From my website - I’m now a data scientist!

Michael J. Crowther merlin 12th September 2018 40 / 43

slide-48
SLIDE 48

the motivation the past the goal the example the family the surprise the future

the future

  • merlin can do a lot of things, hopefully in a usable way
  • merlin is easily extended
  • I continue to discover more and more things it can do
  • arthur (neuralnet)
  • It’s a rubbish implementation of neural networks
  • Needs analytic gradients to be useful
  • penalisation
  • But - all capabilities of merlin can be used in a neural

network, and vice versa

  • predict newvar, statistic ci

www.mjcrowther.co.uk/software/merlin

Michael J. Crowther merlin 12th September 2018 41 / 43

slide-49
SLIDE 49

the motivation the past the goal the example the family the surprise the future

the papers

  • Extended multivariate generalised linear and non-linear

mixed effects models. https://arxiv.org/abs/1710.02223

  • merlin - a unified framework for data analysis and

methods development in Stata. https://arxiv.org/abs/1806.01615

  • Multilevel mixed effects parametric survival analysis.

https://arxiv.org/abs/1709.06633

  • Deep learning neural networks and regression modelling:

A general penalised likelihood framework for estimation, prediction and quantifying uncertainty. (In Prep.)

Michael J. Crowther merlin 12th September 2018 42 / 43

slide-50
SLIDE 50

the motivation the past the goal the example the family the surprise the future

the reversal

Michael J. Crowther merlin 12th September 2018 43 / 43