merlin: Mixed effects regression for linear, non-linear and user-defined models
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1 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, MJ Funding: MRC (MR/P015433/1) Michael J. Crowther merlin 7th September / 39
2 the plan the past the goal the example the family the surprise the future Michael J. Crowther merlin 7th September / 39
3 the past last year I introduced megenreg megenreg fitted mixed effects generalised regression models megenreg was awesome...but Michael J. Crowther merlin 7th September / 39
4 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 7th September / 39
5 Michael J. Crowther merlin 7th September / 39
6 Some people were not so keen... Michael J. Crowther merlin 7th September / 39
7 Mixed Effects Regression for LInear, Non-linear and user-defined models merlin Michael J. Crowther merlin 7th September / 39
8 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 7th September / 39
9 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 7th September / 39
10 data from 312 patients with PBC collected at the Mayo Clinic (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 merlin 7th September / 39
11 the data id time logb prothr ~ n trt stime cancer other D-penicil D-penicil D-penicil D-penicil D-penicil D-penicil D-penicil D-penicil D-penicil D-penicil D-penicil... Michael J. Crowther merlin 7th September / 39
12 a model merlin (logb ) /// log serum bilirubin time, /// covariate /// options family(gaussian) /// distribution Michael J. Crowther merlin 7th September / 39
13 a model merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction, /// options family(gaussian) /// distribution ) /// Michael J. Crowther merlin 7th September / 39
14 a model merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction /// random intercept, /// options family(gaussian) /// distribution ) /// Michael J. Crowther merlin 7th September / 39
15 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 7th September / 39
16 a model merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction /// random intercept /// random slope, /// options family(gaussian) /// distribution ) (pro /// /// prothrombin index rcs(time, df(3)), family(gamma) /// covariate /// distribution ) /// Michael J. Crowther merlin 7th September / 39
17 a model merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction /// random intercept /// 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 7th September / 39
18 a model merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction /// random intercept /// 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 7th September / 39
19 a model merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction /// random intercept /// 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) redistribution(t) df(5) /// vcv // re dist. Michael J. Crowther merlin 7th September / 39
20 a model merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction /// random intercept /// 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) redistribution(t) df(5) /// vcv // re dist. Michael J. Crowther merlin 7th September / 39
21 a model merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction /// random intercept /// 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) redistribution(t) df(5) /// vcv // re dist. Michael J. Crowther merlin 7th September / 39
22 a model merlin (logb /// log serum bilirubin time /// covariate time#trt /// interaction /// random intercept /// 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) redistribution(t) df(5) /// vcv // re dist. Michael J. Crowther merlin 7th September / 39
23 a model merlin (logb time time#trt /// 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 ) (stime failure(other)) /// event indicator /// 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 7th September / 39
24 predictions predict cif1, cif marginal outcome(3) at(trt 0) predict cif1, cif marginal outcome(4) at(trt 0) Michael J. Crowther merlin 7th September / 39
25 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 7th September / 39
26 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 7th September / 39
27 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) } end b1 b2 b3 = merlin_util_xzb(gml) = merlin_util_xzb_mod(gml,2) = merlin_util_xzb_mod(gml,3) sdre = exp(merlin_util_ap(gml,1)) xb = b1 :/ (1 :+ exp(-b2 :/ b3)) return(lnnormalden(y,xb,sdre)) merlin (circumf M1[tree]@1, family(user, llf(logl) nap(1))) ( age@1, family(null)) (, family(null)) Michael J. Crowther merlin 7th September / 39
28 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 7th September / 39
29 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 7th September / 39
30 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 a mind of his own... Michael J. Crowther merlin 7th September / 39
31 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 7th September / 39
32 the surprise I ve accidentally written a general implementation for artificial neural networks Michael J. Crowther merlin 7th September / 39
33 the surprise I ve accidentally written a general implementation for artificial neural networks Yes, I do mean accidentally Michael J. Crowther merlin 7th September / 39
34 Michael J. Crowther merlin 7th September / 39
35 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 7th September / 39
36 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(ridge) lambda(1e-07) Michael J. Crowther merlin 7th September / 39
37 . nnplot, inputs(10) outputs(5) hlayers(3) hnodes(8 3 4) Artificial neural network b0 x1 y1 x2 x3 y2 x4 x5 y3 x6 x7 y4 x8 x9 y5 x10 Inputs Hidden layer 1 Hidden layer 2 Hidden layer 3 Outputs Michael J. Crowther merlin 7th September / 39
38 From my website - I m now a data scientist! Michael J. Crowther merlin 7th September / 39
39 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 Michael J. Crowther merlin 7th September / 39
40 the papers Extended multivariate generalised linear and non-linear mixed effects models. merlin - a unified framework for data analysis and methods development in Stata. Multilevel mixed effects parametric survival analysis. Deep learning neural networks and regression modelling: A general penalised likelihood framework for estimation, prediction and quantifying uncertainty. (In Prep.) Michael J. Crowther merlin 7th September / 39
41 the reversal Michael J. Crowther merlin 7th September / 39
42 the reversal Tim is now merlin s Director of Marketing Michael J. Crowther merlin 7th September / 39
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