session 3 analysis of mediation and moderation using instrumental variables richard emsley methods...

Session 3Analysis of mediation and moderation using

instrumental variablesRichard Emsley

Methods of explanatory analysis for psychological treatment

trials workshop

Methodology Research Group

Funded by:MRC Methodology Grant G0600555

MHRN Methodology Research Group

http://www.mrc.ac.uk/

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Plan for session 3

• Quick review of instrumental variables from Ian’s talk.

• Why do we use instrumental variables?

• Where do we find instrumental variables?

• Examples:– PROSPECT mediator example– SoCRATES S+A*S model.

• Designing trials with instruments in mind.

3

Quick review of IVs from Ian’s 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…

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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.

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Some notation

• Ri – treatment group: the outcome of randomisation (Ri=1 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).

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Instrumental variables (IV) (from session 1)

• Popular in econometrics• Simplest idea is:

– Outcome: Yi = + Di + ei

– Treatment: Di = + Ri + fi

– Allow error ei to be correlated with Di but assume it’s independent of Ri

» randomisation Ri only affects outcome through its effect on compliance Di

• Estimation by “two-stage least squares”:

– E[Yi | Ri] = + E[Di | Ri]

– so first regress Di on Ri to get E[Di | Ri]

– then regress Yi on E[Di | Ri]

– NB standard errors not quite correct by this method: general IV uses different standard errors

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Simple Mediation Idea (from session 2)

Treatment

Mediator

Outcomes

dX

dY

αβ

γ

The total effect is the sum of the direct effect (γ) and the indirect effect (α*β)

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Confounded Mediation Diagram

Treatment

Mediator

Outcomes

dX

dY

U

U – the unmeasured confounders

If treatment is randomised then assumption of no confounding of treatment and other variables (outcomes) is justified.

αβ

γ

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Treatment

Mediator

Outcomes

dX

dY

U

If treatment is not randomised then there is likely to be even more unmeasured confounding.

U

U

αβ

γ

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Randomisation

Mediator

Outcomes

dX

dY

U

Thankfully we’re talking about randomised trials!

αβ

γ

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Linking the two previous sessions: Compliance as a mediator

Randomisation

Treatment Received

Outcomes

dX

dY

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Linking the two previous sessions: Randomisation as an IV

Randomisation

Treatment Received

Outcomes

dX

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.

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Plan for session 3






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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

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• 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…

Why do we use instrumental variables?

Randomisation

Mediator

Outcomes

dX

dY

U

αβ

γ

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Definition of an instrumental variable

A variable is an instrumental variable Z if:i. Z has a causal effect on the mediator D;

This can be tested in the data.

ii. Z affects the outcome Y only through Di.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 Yi.e. there is no confounding for the effect of Z on Y.This is another assumption which randomisation satisfies but other IVs may not.

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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).

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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.

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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.

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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/mediators…yet.

See Hernán and Robins (2006), Epidemiology for further details

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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 tohold in our mediation analysis.

• An IV analysis will also increase the precision of our estimates because of allowing for the unmeasured confounding.

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Also…

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

Randomisation

Mediator

Outcomes

dX

dY

U

αβ

γ

Clearly we can’t use randomisation as an instrument here…we need another instrument.

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Plan for session 3






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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.

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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.

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Mediator

Outcomes

dX

dY

U


If treatment is randomised then assumption of no confounding of treatment and other variables (outcomes) is justified.

αβ

γRandomisation

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Mediation Diagram with instruments

Mediator

Outcomes

dX

dY

U


αβ

γ

Covariates

Randomisation*Covariates

Randomisation

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Multiple Instruments

• Here, treatment by covariates interactions represent instrumental variables.

• Assumptions:1. The interactions are significant in the first stage

regression (individually and joint F-test).2. The only effect of the interactions on outcome is

through the mediator, and not a direct effect. This is a very strong assumption

3. No other unmeasured confounders between the interactions and outcome.

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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…

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Plan for session 3






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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.

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Example: PROSPECT - question of interest

Randomisation

Antidepressant Use

DepressionScore

Covariates

Randomisation*Covariates

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Example: PROSPECT - summary stats

Site 1 Site 2 Site 3

Control N=53

Intervention N=53

Control N=57

Intervention N=54

Control N=42

Intervention N=38

Baseline characteristics: number (%)

Antidepressant Use

22 (41.5) 18 (34.0) 25 (43.9) 25 (46.3) 25 (59.5) 21 (55.3)

Previous medication

27 (50.9) 24 (45.3) 25 (43.9) 28 (51.9) 29 (69.1) 20 (52.6)

Suicidal ideation 9 (17.0) 13 (24.5) 12 (21.1) 18 (33.3) 13 (31.0) 16 (42.1)

Post-randomisation adherence to antidepressant medication: number (%)

Adherence 20 (37.7) 44 (83.0) 19 (33.3) 45 (83.3) 30 (71.4) 34 (89.5)

Hamilton Depression Rating Scores (HRDS): mean (SD)

Baseline HDRS 16.5 (5.3) 18.1 (6.2) 17.3 (5.3) 19.9 (6.4) 18.6 (6.3) 18.7 (5.9)

4 month HDRS 13.4 (8.1) 12.0 (7.8) 14.1 (8.6) 12.1 (7.3) 13.0 (8.5) 10.0 (6.9)

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PROSPECT data – Stata describe

. describe

Contains data from P:\SMinMR paper\Prospect.dta obs: 297 vars: 8 11 Sep 2009 16:01 size: 20,196 (99.9% of memory free)-------------------------------------------------------------------------------------------- storage display valuevariable name type format label variable label--------------------------------------------------------------------------------------------cad1 double %10.0g Anti-depressant use at baseline visithdrs0 double %10.0g Hamilton depression score at baseline visitssix01 double %10.0g Suicide ideation at baseline visitscr01 double %10.0g Past medication use at baseline visithdrs4 double %10.0g Hamilton depression score at 4 month visitsite double %10.0g Location of practicesinterven double %10.0g Randomized assignment to interventionAmedx double %10.0g Adherence to prescribed anti-depressant

medication--------------------------------------------------------------------------------------------

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PROSPECT data – Stata ivregress

. xi: ivregress 2sls hdrs4 hdrs0 cad1 ssix01 scr01 i.site i.interven (amedx = i.interven*hdrs0 i.interven*cad1 i.interven*ssix01 i.interven*scr01 i.interven*i.site), first

First-stage regressions

-------------------- Number of obs = 296 F( 13, 282) = 21.71 Prob > F = 0.0000 R-squared = 0.5002 Adj R-squared = 0.4772 Root MSE = 0.3465------------------------------------------------------------------------------ amedx | Coef. Std. Err. t P>|t| [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_IintXhdrs~1 | -.003633 .0071484 -0.51 0.612 -.0177041 .010438_IintXcad1_1 | -.118277 .0341169 -3.47 0.001 -.1854331 -.0511209_IintXssix~1 | .0504564 .0967541 0.52 0.602 -.1399956 .2409083_IintXscr0~1 | -.2627584 .1029091 -2.55 0.011 -.4653259 -.0601909_IintXsit_~2 | -.0099335 .095321 -0.10 0.917 -.1975645 .1776975_IintXsit_~3 | -.1681695 .1054282 -1.60 0.112 -.3756956 .0393566 _cons | -.0465641 .0996531 -0.47 0.641 -.2427223 .1495942------------------------------------------------------------------------------

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PROSPECT data – Stata ivregress

Instrumental variables (2SLS) regression Number of obs = 296 Wald chi2(8) = 102.68 Prob > chi2 = 0.0000 R-squared = 0.2582 Root MSE = 6.8425------------------------------------------------------------------------------ hdrs4 | Coef. Std. Err. z P>|z| [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: amedxInstruments: hdrs0 cad1 ssix01 scr01 _Isite_2 _Isite_3 _Iinterven_1 _IintXhdrs0_1 _IintXcad1_1 _IintXssix0_1 _IintXscr01_1 _IintXsit_1_2 _IintXsit_1_3

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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 γ (s.e.) β (s.e.)

Analytical method Standard regression -2.66 (0.93) -1.24 (1.09)(Baron & Kenny)

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Example: PROSPECT - results

Direct effect Indirect effect γ (s.e.) β (s.e.)

Analytical methodIV (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)

ConclusionAllowing for hidden confounding appears to have had little

effect, except to increase the SE of the estimate.

*From Ten Have et al, Biometrics (2007)

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PROSPECT data – ivregress postestimation

. estat firststageFirst-stage regressions-------------------- Number of obs = 296 F( 13, 282) = 21.71 Prob > F = 0.0000 R-squared = 0.5002 Adj R-squared = 0.4772 Root MSE = 0.3465------------------------------------------------------------------------------ amedx | Coef. Std. Err. t P>|t| [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_IintXhdrs~1 | -.003633 .0071484 -0.51 0.612 -.0177041 .010438_IintXcad1_1 | -.118277 .0341169 -3.47 0.001 -.1854331 -.0511209_IintXssix~1 | .0504564 .0967541 0.52 0.602 -.1399956 .2409083_IintXscr0~1 | -.2627584 .1029091 -2.55 0.011 -.4653259 -.0601909_IintXsit_~2 | -.0099335 .095321 -0.10 0.917 -.1975645 .1776975_IintXsit_~3 | -.1681695 .1054282 -1.60 0.112 -.3756956 .0393566 _cons | -.0465641 .0996531 -0.47 0.641 -.2427223 .1495942------------------------------------------------------------------------------

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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 > F = 0.0000

First-stage regression summary statistics -------------------------------------------------------------------------- | Adjusted Partial Variable | R-sq. R-sq. R-sq. F(6,282) Prob > F -------------+------------------------------------------------------------ amedx | 0.5002 0.4772 0.1622 9.10057 0.0000 --------------------------------------------------------------------------

Minimum eigenvalue statistic = 9.10057

Critical Values # of endogenous regressors: 1 Ho: Instruments are weak # of excluded instruments: 6 --------------------------------------------------------------------- | 5% 10% 20% 30% 2SLS relative bias | 19.28 11.12 6.76 5.15 -----------------------------------+--------------------------------- | 10% 15% 20% 25% 2SLS Size of nominal 5% Wald test | 29.18 16.23 11.72 9.38 LIML Size of nominal 5% Wald test | 4.45 3.34 2.87 2.61 ---------------------------------------------------------------------

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Instrumental Variables in SPSS

Generate interactions as additional variables

using compute

Analyse – Regression –

2-stage Least Squares

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Instrumental Variables in SPSS

Outcome

Covariates and endogenous variable

(mediator)

Covariates and instruments

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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

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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).

Centre 1 - Liv Centre 2 - Man Centre 3 - Nott

Mean (SD)Control N=39

Treated N=29

Control N=35

Treated N=49

Control N=26

Treated N=23

Baseline PANSS

80.0 (12.36)

77.7 (13.93)

97.9 (16.6)

100.5 (16.3)

84.9 (14.91)

83.4 (10.84)

18 month PANSS

69.5 (13.55)

50.2 (13.48)

73.2 (22.4)

74.4 (20.00)

54.5 (10.07)

49.1 (7.25)

CALPAS - 5.73 (0.81)

- 5.07 (0.88)

- 5.15 (1.47)

Sessions 0 18.14 (3.60)

0 16.16 (4.58)

0 13.87 (4.95)

High Alliance: N(%)

- 23 (79.3)

- 30 (61.2)

- 13 (56.5)

# of observed 18m PANSS

23 23 25 39 21 22

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Confounded Dose-Response

Randomisation

SessionsAttended

PsychoticSymptoms

dX

dY

U

αβ

Are the effects of Randomisation on Sessions (α) and, more interestingly, the effects ofSessions on Outcome (β), influenced by the strength of the therapeutic alliance?

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The S + A*S 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:E[Yi(1)-Yi(0)| Xi, Di(1)=s, Di(0)=0 & Ai=a] =

βs*s + βsa*s*(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)

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SoCRATES analysis results

Method βs (se) βsa (se)Instrumental variables -2.40 (0.70) -1.28 (0.48)Standard regression (B&K) -0.95 (0.22) -0.39 (0.11)

Note: A has been rescaled so that maximum=0.

When A=0 (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 + 7*1.28 = +6.56

This suggests that when alliance is very poor attending more sessions makes the outcome worse!

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SoCRATES – S + A*S 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 > 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 P>|t| [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 yearsed | -1.110149 .5318061 -2.09 0.039 -2.161242 -.0590559 _cons | 43.94059 11.21352 3.92 0.000 21.77752 66.10366------------------------------------------------------------------------------

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SoCRATES – S + A*S 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 > F = 0.0000 R-squared = 0.8599 Adj R-squared = 0.8490 Root MSE = 3.3588------------------------------------------------------------------------------ sessions | Coef. Std. Err. t P>|t| [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 c1gp | -1.281224 1.574428 -0.81 0.417 -4.39376 1.831312 c2gp | -3.772746 1.471898 -2.56 0.011 -6.682588 -.8629052 yrgp | .1835663 .2475856 0.74 0.460 -.3058935 .6730261 pgp | -.0104563 .0407688 -0.26 0.798 -.0910534 .0701407 _cons | -3.05e-12 4.115125 -0.00 1.000 -8.135319 8.135319------------------------------------------------------------------------------

Model for sessions

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Number of obs = 153 F( 11, 141) = 16.59 Prob > F = 0.0000 R-squared = 0.5641 Adj R-squared = 0.5301 Root MSE = 12.0225

------------------------------------------------------------------------------ s_a | Coef. Std. Err. t P>|t| [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 c2gp | -4.923988 5.268477 -0.93 0.352 -15.33941 5.49143 yrgp | -.1321276 .8862022 -0.15 0.882 -1.884089 1.619833 pgp | .0765408 .1459268 0.52 0.601 -.2119464 .3650281 _cons | 2.96e-12 14.72958 0.00 1.000 -29.11937 29.11937------------------------------------------------------------------------------

Model for sessions*alliance

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Instrumental variables (2SLS) regression Number of obs = 153 Wald chi2(7) = 83.17 Prob > chi2 = 0.0000 R-squared = 0.1795 Root MSE = 17.401

------------------------------------------------------------------------------ pant18 | Coef. Std. Err. z P>|z| [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------------------------------------------------------------------------------Instrumented: sessions s_aInstruments: pantot logdup c1 c2 yearsed group lgp c1gp c2gp yrgp pgp

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Plan for session 3






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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)– Physician’s 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

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Example: Series of parallel trials

Randomisation 1

Mediator 1

CommonOutcome

Randomisation 2

Mediator 2

CommonOutcome

Randomisation 3

Mediator 3

CommonOutcome

Trial 1

Trial 2

Trial 3

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Example: measuring additional variables

Randomisation

TherapeuticAlliance

Outcomes

Putative mediator is a measure of the therapist/patient

interaction or relationshipe.g. Measure of

patient’s 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

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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”?

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Potential mediators for discussion

What are the participant’s 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?

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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/healthmethodology/

research/biostatistics/

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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.

session 3 analysis of mediation and moderation using instrumental variables richard emsley methods...

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