An example of multilevel modelling using gllamm: a cluster intervention trial

1
An example of multi-level modelling using gllamm
a cluster intervention trial

• Tansy Edwards
• TEG, IDEU

2
Contents

• Introduction to gllamm
• Data a cluster intervention trial in Ethiopia
• Using gllamm to model the data
• Possible future analysis applying causal
  modelling techniques
• Intend to keep theory to a bare minimum in order
  to demonstrate use of gllamm
• Please share gllamm experiences at the end

3
What is gllamm?

• User-written program for Stata
• Generalized linear, latent and mixed models
• Generalized Linear Mixed Models
• Factor Models
• Item Response Models
• Structural Equation Models
• Latent Class Models
• Multilevel Regression Models
• Installation instructions at www.gllamm.org
• Manual other useful references also available
  from this site

4
Example Modelling data from a cluster
intervention trialImpact of health education on
prevalence of active trachoma in rural Ethiopia
Collaborators J Todd (LSHTM) P Cumberland
(ICH)
5
Study Design

• Health education intervention
• made up of several components
• components combined to give staggered levels of
  intervention
• Education at village level
• Main outcome
• Binary signs of active trachoma in children aged
  3 9

6
Intervention structure allocation

• Components
• Radio broadcasts (received by all)
• NGO activities
• Video Broadcasts
• Control arm (10 communities)
• Standard arm (20 communities)
• NGO activities
• Enhanced arm (10 communities)
• NGO activities video showings

7
Study Area Participants

• 2 large areas identified with
• high prevalence of active trachoma
• NGOs actively working in eye health
• 40 rural villages
• households randomly selected
• all children aged 3 to 9 in HHs eligible

8
Data Structure
Village (3)
Household (2)
Child (1)
9
Data (1)

• Village Level
• intervention arm
• Household Level
• presence of animals animal faeces
• presence of human faeces and household waste
• presence of flies
• access to water (within 15 min walk)
• personal hygiene of children
• knowledge of trachoma transmission prevention

10
Data (2)

• Child Level
• signs of active trachoma (outcome)
• signs of trachomatous scarring
• age
• flies on the eyes
• discharge from the eyes and nose
• Collection
• repeated cross-sectional surveys
• baseline (2002)
• follow up (2003)

11
Baseline data by intervention group
Methods included face-washing, domestic
environmental hygiene, eliminating flies, not
sharing towels
12
Multilevel modelling

• random effects modelling, mixed models
• hierarchical data, repeated measures data
• STATA software xt commands
• Multilevel and Longitudinal Modelling using
  Stata.
• Rabe-Hesketh, S. and Skrondal, A. (2005). Stata
  Press.
• http//statcomp.ats.ucla.edu/mlm/default.htm

13
Modelling the data (1)

• Logistic regression with 1 covariate
• logit(pij) a ßinterventionj
• Random intercept model with 2 levels
• logit(pij) (const Uj) ßinterventionj
• Assume Uj
• normally distributed
• mean 0 and variance su2

14
Modelling the data (2)

• Variance between the level 2 units su2
• Total variance
• sum (variances at each level)
• The ICC at level 2
• proportion of the total variance
• between the level 2 units
• su2 / total variance

15
Modelling the data with Stata (3)

• Fitted 4 random intercept models
• Modelling the follow-up data
• Each included intervention group as a fixed
  effect
• Models 1 2 have a random intercept at village
  level only (a 2-level model)
• Model 1 fitted using xtlogit, model 2 using
  gllamm
• Models 3 4 have random intercepts levels 2 3
• Model 4 also adjusts for logit transformed
  baseline prevalence

16
command syntax model 3

• gen cons1
• eq l2_c cons
• eq l3_c cons
• xi gllamm tr i.grp, i(hh village) nrf(1 1)
  eqs(l2_c l3_c)
• family(binomial) link(logit) nip(4) nolog eform
• mat inite(b)
• xi gllamm tr i.grp, i(hh village) nrf(1 1)
  eqs(l2_c l3_c)
• family(binomial) link(logit) from(init) adapt
  nolog eform

17
gen cons1 eq l2_c cons eq l3_c cons xi gllamm
trachoma i.grp, i(hh village) nrf (1 1) eqs(l2_c
l3_c) family(binomial) link(logit) nolog eform
adapt number of level 1 units 2008 number of
level 2 units 974 number of level 3 units 40
log likelihood -1216.7526 ---------------------
------------------------------------------- tracho
ma exp(b) Std. Err. z Pgtz 95 Conf.
Interval ------ --------------------------------
------------------------ _Igrp_1 .8477485
.3167323 -0.44 0.658 .4076098
1.763151 _Igrp_2 .907824 .3928112 -0.22
0.823 .3887682 2.119886 -----------------------
----------------------------------------- Varianc
es and covariances of random effects -------------
----------------------------------------------
level 2 (hh) var(1) .47227179 (.18614591)
level 3 (village) var(1) .79554109
(.22071555)
18
Results

• Level 1 variance 3.29
• Models 3 4 took 10 mins to run

19
Random slope model

• Random slope term for intervention group
• logit(pij) (a Uj) (b
  Sj)interventionj
• Investigating whether effect of the intervention
  varies within intervention arm
• To model this
• Specify another eq for the random slope term

20
. eq l3_s grp . xi gllamm tr i.grp, i(hh
village) nrf(1 2) eqs(l2_c l3_c l3_s) link(logit)
family(binomial) nolog eform from(init)
adapt --------------------------------------------
--------------------- tf exp(b) Std.
Err. z Pgtz 95 Conf. Interval ---------
-------------------------------------------------
------ _Igrp_1 .8588554 .2624249 -0.50
0.619 .4718825 1.56317 _Igrp_2 .9488757
.4315146 -0.12 0.908 .3891468
2.31369 ------------------------------------------
----------------------- Variances and covariances
of random effects level 2 (hh) var(1)
.47469993 (.18647758) level 3 (village)
var(1) .38048455 (.22026869) cov(2,1)
.05994385 (.16862811) cor(2,1) .21458453
var(2) .20509514 (.21710728)
21
Extensions

• Data from a 2nd follow-up survey are available
• Covariate Adjustment
• Investigate baseline imbalance further
• Adjust for baseline imbalance
• Investigating how the intervention works
• in terms of the F and E components of the SAFE
  strategy

22
Causal Diagram
baseline prevalence
health education
age of child
sanitation facilities access to water
face-washing
sanitation practices
wealth
baseline knowledge
trachoma
animals
flies

• child level
• household level
• village level
• unmeasured

23

• Comments questions ???