Analysis of mediation and moderation using instrumental variables

1
Methods of explanatory analysis for psychological
treatment trials workshop

• Session 3
• Analysis of mediation and moderation using
  instrumental variables
• Richard Emsley

Funded by MRC Methodology Grant G0600555 MHRN
Methodology Research Group
2
Plan for session 3

• Quick review of instrumental variables from Ians
  talk.
• Why do we use instrumental variables?
• Where do we find instrumental variables?
• Examples
• PROSPECT mediator example
• SoCRATES SAS model.
• Designing trials with instruments in mind.

3
Quick review of IVs from Ians talk

• Ian has demonstrated how we can use instrumental
  variable methods to infer a causal effect of
  treatment in the presence of departures from
  randomised intervention.
• This utilises randomisation as the instrumental
  variable. As we will see, randomisation meets
  the assumptions required for an IV
• But we will also need to consider the situation
  where we cannot use randomisation as an
  instrument

4
Instrumental Variables (IVs)

• In a standard regression model, if an explanatory
  variable is correlated with the error term (known
  as endogeneity) its coefficient cannot be
  unbiasedly estimated.
• An instrumental variable (IV) is a variable that
  does not appear in the model, is uncorrelated
  with the error term and is correlated with the
  endogenous explanatory variable randomisation,
  where available, often satisfies this criteria.
• A two stage least squares (2SLS) procedure can
  then be applied to estimate the coefficient. At
  its simplest, the first stage involves using a
  simple linear regression of the endogenous
  variable on the instrument and saving the
  predicted values. In the second stage the
  outcome is then regressed on the predicted
  values, with the latter regression coefficient
  being the required estimate of the coefficient.

5
Some notation

• Ri treatment group the outcome of
  randomisation (Ri1 for treatment, 0 for
  controls).
• Xi' X1i, X2i Xpi baseline covariates.
• Yi observed outcome.
• Di actual treatment received. This is an
  intermediate outcome that is a putative mediator
  of the effects of treatment on outcome (either a
  quantitative measure or binary).

6
Instrumental variables (IV) (from session 1)

• Popular in econometrics
• Simplest idea is
• Outcome Yi a b Di ei
• Treatment Di g d Ri fi
• Allow error ei to be correlated with Di but
  assume its independent of Ri
• randomisation Ri only affects outcome through its
  effect on compliance Di
• Estimation by two-stage least squares
• EYi Ri a b EDi Ri
• so first regress Di on Ri to get EDi Ri
• then regress Yi on EDi Ri
• NB standard errors not quite correct by this
  method general IV uses different standard errors

7
Simple Mediation Idea (from session 2)
dX
Mediator
ß
a
Treatment
Outcomes
dY
?
The total effect is the sum of the direct effect
(?) and the indirect effect (aß)
8
Confounded Mediation Diagram
U the unmeasured confounders
dX
U
Mediator
ß
a
Treatment
Outcomes
dY
?
If treatment is randomised then assumption of no
confounding of treatment and other variables
(outcomes) is justified.
9
Confounded Mediation Diagram
dX
U
U
Mediator
ß
a
Treatment
Outcomes
dY
?
U
If treatment is not randomised then there is
likely to be even more unmeasured confounding.
10
Confounded Mediation Diagram
dX
U
Mediator
ß
a
Randomisation
Outcomes
dY
?
Thankfully were talking about randomised trials!
11
Linking the two previous sessions Compliance as
a mediator
dX
Treatment Received
Randomisation
Outcomes
dY
12
Linking the two previous sessions Randomisation
as an IV
dX
Treatment Received
Randomisation
Outcomes
dY
By assuming the absence of a direct path from
randomisation to outcome, we assume the entire
effect of randomisation acts through receipt of
treatment. ? randomisation is an instrumental
variable.
13
Plan for session 3

• Quick review of instrumental variables from Ians
  talk.
• Why do we use instrumental variables?
• Where do we find instrumental variables?
• Examples
• PROSPECT mediator example
• SoCRATES SAS model.
• Designing trials with instruments in mind.

14
Why do we use instrumental variables?

• All available statistical methods we usually use
  (for any standard analysis), including
• Stratification
• Regression
• Matching
• Standardization
• require the one unverifiable condition we
  identified previously
• NO UNMEASURED CONFOUNDING

15
Why do we use instrumental variables?

• Unlike all other methods, IV methods can be used
  to consistently estimate causal effects in the
  presence of unmeasured confounding AND
  measurement error.
• SO WE CAN SOLVE THE PROBLEM OF

dX
U
Mediator
ß
a
Randomisation
Outcomes
dY
?
16
Definition of an instrumental variable

• A variable is an instrumental variable Z if
• Z has a causal effect on the mediator D
• This can be tested in the data.
• ii. Z affects the outcome Y only through D
• i.e. there is no direct effect of Z on Y
• This is an assumption (sometimes a strong
  assumption).
• iii. Z does not share common causes with the
  outcome Y
• i.e. there is no confounding for the effect of Z
  on Y.
• This is another assumption which randomisation
  satisfies but other IVs may not.

17
Assumptions for instrumental variables

• IV methods require FOUR assumptions
• The first 3 assumptions are from the definition
• The association between instrument and mediator.
• no direct effect of the instrument on outcome.
• no unmeasured confounding for the instrument and
  outcome.
• There are a wide variety of fourth assumptions
  and different assumptions result in the
  estimation of different causal effects
• E.g. no interactions, monotonicity (no defiers).

18
Testing assumptions

• There are a number of tests we can use for some
  of these assumptions.
• Stata has three postestimation commands following
  ivregress
• estat overid
• estat endogenous
• estat firststage
• This final option is perhaps the most useful. It
  gives an indication of whether the set of
  instruments strongly predict the mediator see
  PROSPECT example later on.

19
Advantages of IVs

• Can allow for unmeasured confounding
• Can allow for measurement error
• Randomisation meets the definition so is an ideal
  instrument
• When available.
• Obviously not in observational studies.

20
Disadvantages of IVs

• 1. It is impossible to verify that Z is an
  instrument and using a non instrument introduces
  additional bias.
• 2. A weak instrument Z increases the bias over
  that of ordinary regression.
• 3. Instruments by themselves are actually
  insufficient to estimate causal effects and we
  require additional unverifiable assumptions such
  as the no defiers assumption.
• 4. Standard IV methods do not cope well with
  time-varying exposures/mediatorsyet.

See Hernán and Robins (2006), Epidemiology for
further details
21
Assumption trade-off

• IV methods replace one unverifiable assumption of
  no unmeasured confounding between the mediator
  and the outcome by other unverifiable assumptions
• no unmeasured confounding for the instruments, or
• no direct effect of the instruments.
• We need to decide which assumptions are more
  likely to
• hold in our mediation analysis.
• An IV analysis will also increase the precision
  of our estimates because of allowing for the
  unmeasured confounding.

22
Also

• What about if we want to estimate the direct
  effect of randomisation in the presence of a
  potential mediator?

dX
U
Mediator
ß
a
Randomisation
Outcomes
dY
?
Clearly we cant use randomisation as an
instrument herewe need another instrument.
23
Plan for session 3

• Quick review of instrumental variables from Ians
  talk.
• Why do we use instrumental variables?
• Where do we find instrumental variables?
• Examples
• PROSPECT mediator example
• SoCRATES SAS model.
• Designing trials with instruments in mind.

24
Multiple instruments

• When we are trying to estimate the direct effect
  of randomisation we need alternative instruments.
• Likewise, if we have more than one endogenous
  variable (multiple mediators), then we need
  multiple instruments.
• For IV model identification, we always need to
  have as many instruments as we have endogenous
  variables.
• i.e. if considering two mediators in the model
  (therapeutic alliance and number of sessions of
  therapy attended), then we need at least two
  instrumental variables.

25
Where do we find instruments?

• Possibilities for IVs
• Randomisation-by-baseline variable interactions.
• Randomisation involving more than one active
  treatment i.e. to interventions specifically
  targeted at particular intermediate
  variables/mediators.
• Randomisation-by-trial (multiple trials).
• Genetic markers (Mendelian Randomisation) used
  together with randomisation.

26
Confounded Mediation Diagram
U the unmeasured confounders
dX
U
Mediator
ß
a
Randomisation
Outcomes
dY
?
If treatment is randomised then assumption of no
confounding of treatment and other variables
(outcomes) is justified.
27
Mediation Diagram with instruments
U the unmeasured confounders
dX
U
RandomisationCovariates
Mediator
ß
a
Randomisation
Outcomes
dY
?
Covariates
28
Multiple Instruments

• Here, treatment by covariates interactions
  represent instrumental variables.
• Assumptions
• The interactions are significant in the first
  stage regression (individually and joint F-test).
• The only effect of the interactions on outcome is
  through the mediator, and not a direct effect.
  This is a very strong assumption
• No other unmeasured confounders between the
  interactions and outcome.

29
Summary so far

• The analysis of mediation is more complex than it
  first seems because of potential unmeasured
  confounding (mediators are endogenous).
• We use moderators of the relationship between
  randomisation and the mediator (i.e. the baseline
  by randomisation interactions) as instruments.
• The analysis of mediation by instrumental
  variables requires additional assumptions.
  Primarily, that these covariates are not
  moderators of the randomisation on outcome
  relationship (no direct effect).
• We illustrate these points on two examples now

30
Plan for session 3

• Quick review of instrumental variables from Ians
  talk.
• Why do we use instrumental variables?
• Where do we find instrumental variables?
• Examples
• PROSPECT mediator example
• SoCRATES SAS model.
• Designing trials with instruments in mind.

31
Example PROSPECT

• PROSPECT (Prevention of Suicide in Primary Care
  Elderly Collaborative Trial) was a multi-site
  prospective, randomised trial designed to
  evaluate the impact of a primary care-based
  intervention on reducing major risk factors
  (including depression) for suicide in elderly
  depressed primary care patients.
• The two conditions were either
• (a) an intervention based on treatment guidelines
  tailored for the elderly with care management,
• (b) treatment as usual.
• An intermediate outcome in the PROSPECT trial was
  whether the trial participant adhered to
  antidepressant medication during the period
  following allocation of the intervention.
• The question here is whether changes in
  medication adherence following the intervention
  might explain some or all of the observed (ITT)
  effects on clinical outcome.

See Bruce et al, JAMA (2004) Ten Have et al,
Biometrics (2007) Bellamy et al, Clinical
Trials (2007) Lynch et al, Health Services and
Outcome Research Methodology (2008). Thanks to
Tom Ten Have for use of the data.
32
Example PROSPECT - question of interest
RandomisationCovariates
Antidepressant Use
Depression Score
Randomisation
Covariates
33
Example PROSPECT - summary stats
34
PROSPECT data Stata describe

• . describe
• Contains data from P\SMinMR paper\Prospect.dta
• obs 297
• vars 8 11
  Sep 2009 1601
• size 20,196 (99.9 of memory free)
• --------------------------------------------------
  ------------------------------------------
• storage display value
• variable name type format label
  variable label
• --------------------------------------------------
  ------------------------------------------
• cad1 double 10.0g
  Anti-depressant use at baseline visit
• hdrs0 double 10.0g
  Hamilton depression score at baseline visit
• ssix01 double 10.0g
  Suicide ideation at baseline visit
• scr01 double 10.0g
  Past medication use at baseline visit
• hdrs4 double 10.0g
  Hamilton depression score at 4 month visit
• site double 10.0g
  Location of practices
• interven double 10.0g
  Randomized assignment to intervention
• Amedx double 10.0g
  Adherence to prescribed anti-depressant
  medication

35
PROSPECT data Stata ivregress

• . xi ivregress 2sls hdrs4 hdrs0 cad1 ssix01
  scr01 i.site i.interven (amedx i.intervenhdrs0
  i.intervencad1 i.intervenssix01
  i.intervenscr01 i.interveni.site), first
• First-stage regressions
• --------------------
  Number of obs 296
• 
  F( 13, 282) 21.71
• 
  Prob gt F 0.0000
• 
  R-squared 0.5002
• 
  Adj R-squared 0.4772
• 
  Root MSE 0.3465
• --------------------------------------------------
  ----------------------------
• amedx Coef. Std. Err. t
  Pgtt 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• hdrs0 .0065731 .0051473 1.28
  0.203 -.0035588 .0167051
• cad1 .166495 .0254223 6.55
  0.000 .1164533 .2165366
• ssix01 -.0475454 .0721387 -0.66
  0.510 -.1895441 .0944533
• scr01 .2530611 .0746616 3.39
  0.001 .1060962 .4000259
• _Isite_2 -.018463 .0664307 -0.28
  0.781 -.149226 .1123
• _Isite_3 .1969925 .0734302 2.68
  0.008 .0524516 .3415334
• _Iinterven_1 .7825965 .1398924 5.59
  0.000 .5072307 1.057962

36
PROSPECT data Stata ivregress

• Instrumental variables (2SLS) regression
  Number of obs 296
• 
  Wald chi2(8) 102.68
• 
  Prob gt chi2 0.0000
• 
  R-squared 0.2582
• 
  Root MSE 6.8425
• --------------------------------------------------
  ----------------------------
• hdrs4 Coef. Std. Err. z
  Pgtz 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• amedx -1.95302 2.672201 -0.73
  0.465 -7.190438 3.284397
• hdrs0 .6226062 .070337 8.85
  0.000 .4847482 .7604642
• cad1 -.0654087 .4304821 -0.15
  0.879 -.9091381 .7783208
• ssix01 1.251204 .9399736 1.33
  0.183 -.5911102 3.093518
• scr01 1.585044 1.074312 1.48
  0.140 -.5205695 3.690658
• _Isite_2 -.4971475 .9469522 -0.52
  0.600 -2.35314 1.358845
• _Isite_3 -2.046048 1.08319 -1.89
  0.059 -4.169062 .0769655
• _Iinterven_1 -2.375598 1.328982 -1.79
  0.074 -4.980353 .2291584
• _cons 3.344043 1.467043 2.28
  0.023 .4686928 6.219394
• --------------------------------------------------
  ----------------------------
• Instrumented amedx

37
Example PROSPECT - results

• Using all baseline variables as covariates in an
  ANCOVA.
• ITT effect -3.15 (0.82)
• Small but statistically significant effect
• Direct effect Indirect effect
• ? (s.e.) ß (s.e.)
• Analytical method
• Standard regression -2.66 (0.93) -1.24 (1.09)
• (Baron Kenny)

38
Example PROSPECT - results

• Direct effect Indirect effect
• ? (s.e.) ß (s.e.)
• Analytical method
• IV (ivreg) -2.38 (1.35) -1.95 (2.71)
• IV (treatreg - ml) -2.34 (1.27) -2.05 (2.49)
• G-estimation -2.58 (1.27) -1.43 (2.34)
• Conclusion
• Allowing for hidden confounding appears to have
  had little effect, except to increase the SE of
  the estimate.

From Ten Have et al, Biometrics (2007)
39
PROSPECT data ivregress postestimation

• . estat firststage
• First-stage regressions
• --------------------
  Number of obs 296
• 
  F( 13, 282) 21.71
• 
  Prob gt F 0.0000
• 
  R-squared 0.5002
• 
  Adj R-squared 0.4772
• 
  Root MSE 0.3465
• --------------------------------------------------
  ----------------------------
• amedx Coef. Std. Err. t
  Pgtt 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• hdrs0 .0065731 .0051473 1.28
  0.203 -.0035588 .0167051
• cad1 .166495 .0254223 6.55
  0.000 .1164533 .2165366
• ssix01 -.0475454 .0721387 -0.66
  0.510 -.1895441 .0944533
• scr01 .2530611 .0746616 3.39
  0.001 .1060962 .4000259
• _Isite_2 -.018463 .0664307 -0.28
  0.781 -.149226 .1123
• _Isite_3 .1969925 .0734302 2.68
  0.008 .0524516 .3415334
• _Iinterven_1 .7825965 .1398924 5.59
  0.000 .5072307 1.057962
• _IintXhdrs1 -.003633 .0071484 -0.51
  0.612 -.0177041 .010438

40
PROSPECT data ivregress postestimation

• (no endogenous regressors)
• ( 1) _IintXhdrs0_1 0
• ( 2) _IintXcad1_1 0
• ( 3) _IintXssix0_1 0
• ( 4) _IintXscr01_1 0
• ( 5) _IintXsit_1_2 0
• ( 6) _IintXsit_1_3 0
• F( 6, 282) 9.10 Prob gt F
  0.0000
• First-stage regression summary statistics
• ------------------------------------------------
  --------------------------
• Adjusted Partial
• Variable R-sq. R-sq. R-sq.
  F(6,282) Prob gt F
• -----------------------------------------------
  --------------------------
• amedx 0.5002 0.4772 0.1622
  9.10057 0.0000
• ------------------------------------------------
  --------------------------
• Minimum eigenvalue statistic 9.10057

41
Instrumental Variables in SPSS
Generate interactions as additional variables
using compute
Analyse Regression 2-stage Least Squares
42
Instrumental Variables in SPSS
Outcome
Covariates and endogenous variable (mediator)
Covariates and instruments
43
Example the SoCRATES trial

• SoCRATES was a multi-centre RCT designed to
  evaluate the effects of cognitive behaviour
  therapy (CBT) and supportive counselling (SC) on
  the outcomes of an early episode of
  schizophrenia.
• 201 participants were allocated to one of three
  groups
• Control Treatment as Usual (TAU)
• Treatment TAU plus psychological intervention,
  either CBT TAU or SC TAU
• The two treatment groups are combined in our
  analyses
• Outcome psychotic symptoms score (PANSS) at 18
  months

44
Example SoCRATES - summary stats
Lewis et al, BJP (2002) Tarrier et al, BJP
(2004) Dunn Bentall, Stats in Medicine (2007)
Emsley, White and Dunn, Stats Methods in Medical
Research (2009).
45
Confounded Dose-Response
dX
U
Sessions Attended
ß
a
Randomisation
Psychotic Symptoms
dY
Are the effects of Randomisation on Sessions (a)
and, more interestingly, the effects of Sessions
on Outcome (ß), influenced by the strength of the
therapeutic alliance?
46
The S AS model

• We want to estimate the joint effects of the
  strength of the therapeutic alliance as measured
  by CALPAS (A) and number of sessions attended
  (S).
• We postulate a structural model as follows
• EYi(1)-Yi(0) Xi, Di(1)s, Di(0)0 Aia
  
• ßss ßsas(a-7)
• No sessions implies no treatment effect.
• The effect of alliance is multiplicative so we
  only have an interaction effect of alliance no
  sessions no alliance.

Dunn and Bentall, SiM (2007)
47
SoCRATES analysis results

• Method ßs (se) ßsa (se)
• Instrumental variables -2.40 (0.70) -1.28 (0.48)
• Standard regression (BK) -0.95 (0.22) -0.39
  (0.11)
• Note A has been rescaled so that maximum0.
• When A0 (i.e. maximum alliance)
• the slope for effect of Sessions is -2.40
• When A-7 (i.e. minimum alliance)
• the slope is -2.40 71.28 6.56
• This suggests that when alliance is very poor
  attending more sessions makes the outcome worse!

48
SoCRATES S AS using regress

• . regress pant18 sessions s_a pantot logdup c1
  c2 yearsed
• Source SS df MS
  Number of obs 153
• -------------------------------------------
  F( 7, 145) 15.78
• Model 24414.5544 7 3487.79349
  Prob gt F 0.0000
• Residual 32051.4194 145 221.044272
  R-squared 0.4324
• -------------------------------------------
  Adj R-squared 0.4050
• Total 56465.9739 152 371.48667
  Root MSE 14.868
• --------------------------------------------------
  ----------------------------
• pant18 Coef. Std. Err. t
  Pgtt 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• sessions -.9459469 .2209236 -4.28
  0.000 -1.382593 -.5093003
• s_a -.3866447 .1117784 -3.46
  0.001 -.6075702 -.1657192
• pantot .3843765 .087454 4.40
  0.000 .2115272 .5572259
• logdup 2.331363 2.398488 0.97
  0.333 -2.409152 7.071878
• c1 4.322976 3.48805 1.24
  0.217 -2.571014 11.21697
• c2 -11.96141 3.292382 -3.63
  0.000 -18.46867 -5.454147

49
SoCRATES S AS using ivregress

• . ivregress 2sls pant18 pantot logdup c1 c2
  yearsed (sessions s_a group lgp c1gp c2gp yrgp
  pgp)
• First-stage regressions
• -----------------------
  Number of obs 153
• 
  F( 11, 141) 78.68
• 
  Prob gt F 0.0000
• 
  R-squared 0.8599
• 
  Adj R-squared 0.8490
• 
  Root MSE 3.3588
• --------------------------------------------------
  ----------------------------
• sessions Coef. Std. Err. t
  Pgtt 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• pantot 1.71e-14 .0310634 0.00
  1.000 -.0614103 .0614103
• logdup 2.46e-13 .858628 0.00
  1.000 -1.697449 1.697449
• c1 -3.59e-13 1.125814 -0.00
  1.000 -2.225657 2.225657
• c2 4.70e-14 1.022741 0.00
  1.000 -2.021889 2.021889
• yearsed 1.17e-13 .1929797 0.00
  1.000 -.3815077 .3815077
• group 16.09465 5.201659 3.09
  0.002 5.811326 26.37798
• lgp .1800265 1.104039 0.16
  0.871 -2.002583 2.362636

Model for sessions
50
SoCRATES S AS using ivregress

• 
  Number of obs 153
• 
  F( 11, 141) 16.59
• 
  Prob gt F 0.0000
• 
  R-squared 0.5641
• 
  Adj R-squared 0.5301
• 
  Root MSE 12.0225
• --------------------------------------------------
  ----------------------------
• s_a Coef. Std. Err. t
  Pgtt 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• pantot -1.89e-14 .1111878 -0.00
  1.000 -.2198106 .2198106
• logdup -1.89e-13 3.073353 -0.00
  1.000 -6.075809 6.075809
• c1 3.31e-13 4.029712 0.00
  1.000 -7.966465 7.966465
• c2 -3.78e-14 3.660775 -0.00
  1.000 -7.237101 7.237101
• yearsed -1.00e-13 .6907472 -0.00
  1.000 -1.36556 1.36556
• group -16.2085 18.6187 -0.87
  0.385 -53.0164 20.59939
• lgp -6.186983 3.951771 -1.57
  0.120 -13.99936 1.625398
• c1gp -11.44637 5.635471 -2.03
  0.044 -22.58731 -.3054279

Model for sessionsalliance
51
SoCRATES S AS using ivregress

• Instrumental variables (2SLS) regression
  Number of obs 153
• 
  Wald chi2(7) 83.17
• 
  Prob gt chi2 0.0000
• 
  R-squared 0.1795
• 
  Root MSE 17.401
• --------------------------------------------------
  ----------------------------
• pant18 Coef. Std. Err. z
  Pgtz 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• sessions -2.401159 .6776074 -3.54
  0.000 -3.729245 -1.073073
• s_a -1.281461 .4380021 -2.93
  0.003 -2.139929 -.4229929
• pantot .3864756 .1024045 3.77
  0.000 .1857664 .5871848
• logdup -.2044085 3.091853 -0.07
  0.947 -6.264329 5.855512
• c1 -1.21612 4.868577 -0.25
  0.803 -10.75836 8.326116
• c2 -16.32291 4.324444 -3.77
  0.000 -24.79866 -7.847155
• yearsed -.9923864 .6258703 -1.59
  0.113 -2.21907 .2342968
• _cons 49.26983 13.27743 3.71
  0.000 23.24655 75.29311
• --------------------------------------------------
  ----------------------------

52
Plan for session 3

• Quick review of instrumental variables from Ians
  talk.
• Why do we use instrumental variables?
• Where do we find instrumental variables?
• Examples
• PROSPECT mediator example
• SoCRATES SAS model.
• Designing trials with instruments in mind.

53
Instrumental Variables in observational studies

• There are numerous examples of instruments in the
  absence of randomisation
• Access to health care
• Distance to hospital
• Genes (known as Mendelian randomisation)
• Proxy measures of genes (product intolerance)
• Physicians preference (ask, or use proportion of
  patients on treatment)

54
Designing trials with IVs in mind

• Thinking back to some of the possibilities for
  IVs we introduced earlier with design
  considerations
• Randomisation-by-baseline variable
  interactions.Can we measure any extra baseline
  variables?
• Randomisation involving more than one active
  treatment i.e. to interventions specifically
  targeted at particular intermediate
  variables/mediators.
• More complicated designs/parallel trials
• Randomisation-by-trial (multiple trials).
• Meta-regression approaches (new MRC grant)
• Genetic markers (Mendelian Randomisation) used
  together with randomisation.
• Need to measure genotype in patients

55
Example Series of parallel trials
Mediator 1
Randomisation 1
Common Outcome
Trial 1
Mediator 2
Randomisation 2
Common Outcome
Trial 2
Mediator 3
Randomisation 3
Common Outcome
Trial 3
56
Example measuring additional variables
Putative mediator is a measure of the
therapist/patient interaction or relationship
e.g. Measure of patients interaction with other
individuals Care coordinator, family members,
etc. e.g. Patient characteristics which could
influence ability to form alliance personality
disorders, etc.
Similar Baseline measures
Therapeutic Alliance
Randomisation
Outcomes
57
Short small group discussion

• We will work in small groups again.
• We are thinking about designing psychological
  treatment trials in order to answer some of the
  explanatory questions discussed in this session?
• When considering the following potential
  mediators
• How would we accurately measure the mediator?
• What additional baseline variables might we be
  able to collect which would help in the causal/IV
  analysis?
• What problems could you foresee in the collection
  of this information?
• How might you justify the need to collect this
  information to funders of the trials who would
  prefer to keep it large and simple?

58
Potential mediators for discussion

• What are the participants beliefs?
• Does psychotherapy change attributions
  (beliefs), which, in turn, lead to better
  outcome?
• What is the concomitant medication?
• Does psychotherapy improve compliance with
  medication which, in turn, leads to better
  outcome?
• What is the concomitant substance abuse?
• Does psychotherapy reduce substance use, which
  in turn leads to improvements in psychotic
  symptoms?

59
References Mediation Effect Moderation in
Psychological Treatment Trials

• Methodology for IV methods with mediation
• Emsley RA, Dunn G White IR (2009). Mediation
  and moderation of treatment effects in randomised
  trials of complex interventions. Statistical
  Methods in Medical Research. In press (available
  online).
• Maracy M Dunn G (2009). Estimating
  dose-response effects in psychological treatment
  trials the role of instrumental variables.
  Statistical Methods in Medical Research. In
  press (available online).
• Dunn G Bentall R (2007). Modelling
  treatment-effect heterogeneity in randomized
  controlled trials of complex interventions
  (psychological treatments). Statistics in
  Medicine 26, 4719-4745.
• Website with downloads
• http//www.medicine.manchester.ac.uk/healthmethodo
  logy/research/biostatistics/

60
Some Further Reading

• Ten Have TR, Joffe MM, Lynch KG, Brown GK, Maisto
  SA Beck AT (2007). Causal mediation analyses
  with rank preserving models. Biometrics 63,
  926-934.
• Gallop R, Small DS, Lin JY, Elliot MR, Joffe MM
  Ten Have TR (2009). Mediation analysis with
  principal stratification. Statistics in Medicine
  28, 1108-1130.
• Bellamy SL, Lin JY Ten Have TR (2007). An
  introduction to causal modelling in clinical
  trials. Clinical Trials 4, 58-73.
• Lynch K, Cary M, Gallop R, Ten Have TR (2008).
  Causal mediation analyses for randomized trials.
  Health Services Outcomes Research Methodology
  8, 57-76.
• Albert JM (2008). Mediation analysis via
  potential outcomes models. Statistics in Medicine
  27, 1282-1304.
• Jo B (2008). Causal inference in randomized
  experiments with mediational processes.
  Psychological Methods 13, 314-336.
• Gennetian LA, Morris PA, Bos JM Bloom HS
  (2005). Constructing instrumental variables from
  experimental data to explore how treatments
  produce effects. In Bloom HS, editor. Learning
  More From Social Experiments Evolving Analytic
  Approaches. New York Russell Sage Foundation
  pp. 75-114.
• MacKinnon DP (2008). Introduction to Statistical
  Mediation Analysis. New York Taylor Francis
  Group.