Estimating dose-response effects in psychological treatment trials: the role of instrumental variables

We present a relatively non-technical and practically orientated review of statistical methods that can be used to estimate dose—response relationships in randomised controlled psychotherapy trials in which participants fail to attend all of the planned sessions of therapy. Here we are investigating the effects on treatment outcome of the number of sessions attended when the latter is possibly subject to hidden selection effects (hidden confounding). The aim is to estimate the parameters of a structural mean model (SMM) using randomisation, and possibly randomisation by covariate interactions, as instrumental variables. We describe, compare and illustrate the equivalence of the use of a simple G-estimation algorithm and two two-stage least squares procedures that are traditionally used in economics.

[1]  Michael P. Murray,et al.  Instrumental Variables , 2011, International Encyclopedia of Statistical Science.

[2]  X H Zhou,et al.  Multiple Imputation Methods for Treatment Noncompliance and Nonresponse in Randomized Clinical Trials , 2009, Biometrics.

[3]  John M. Abowd,et al.  Multiple Imputation , 2009, Encyclopedia of Database Systems.

[4]  Graham Dunn,et al.  Modelling treatment‐effect heterogeneity in randomized controlled trials of complex interventions (psychological treatments) , 2007, Statistics in medicine.

[5]  Carlos A. Flores Estimation of Dose-Response Functions and Optimal Doses with a Continuous Treatment , 2007 .

[6]  James J Heckman,et al.  Understanding Instrumental Variables in Models with Essential Heterogeneity , 2006, The Review of Economics and Statistics.

[7]  Els Goetghebeur,et al.  Structural mean models for compliance analysis in randomized clinical trials and the impact of errors on measures of exposure , 2005, Statistical methods in medical research.

[8]  Graham Dunn,et al.  Estimating treatment effects from randomized clinical trials with noncompliance and loss to follow-up: the role of instrumental variable methods , 2005, Statistical methods in medical research.

[9]  J. Dekker,et al.  Dose–effect relations in time-limited combined psycho-pharmacological treatment for depression , 2005, Psychological Medicine.

[10]  Alastair R. Hall,et al.  Generalized Method of Moments , 2005 .

[11]  E. Goetghebeur,et al.  Structural Mean Effects of Noncompliance , 2004 .

[12]  Søren Feodor Nielsen,et al.  1. Statistical Analysis with Missing Data (2nd edn). Roderick J. Little and Donald B. Rubin, John Wiley & Sons, New York, 2002. No. of pages: xv+381. ISBN: 0‐471‐18386‐5 , 2004 .

[13]  Petra E. Todd,et al.  Evaluating Preschool Programs When Length of Exposure to the Program Varies: A Nonparametric Approach , 2000, Review of Economics and Statistics.

[14]  S. Vansteelandt,et al.  Using potential outcomes as predictors of treatment activity via strong structural mean models , 2004 .

[15]  F. L. Newman,et al.  Longitudinal Analysis when the Experimenter does not Determine when Treatment Ends: What is Dose-Response? , 2003, Clinical psychology & psychotherapy.

[16]  E. Foster,et al.  Propensity Score Matching: An Illustrative Analysis of Dose Response , 2003, Medical care.

[17]  C. Dowrick,et al.  Estimating psychological treatment effects from a randomised controlled trial with both non-compliance and loss to follow-up , 2003, British Journal of Psychiatry.

[18]  Marshall M Joffe,et al.  The compliance score as a regressor in randomized trials. , 2003, Biostatistics.

[19]  J. Angrist Treatment Effect Heterogeneity in Theory and Practice , 2003 .

[20]  J. Wooldridge Further results on instrumental variables estimation of average treatment effects in the correlated random coefficient model , 2003 .

[21]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[22]  L. Bickman,et al.  Dose Response in Child and Adolescent Mental Health Services , 2002, Mental health services research.

[23]  S. Rabe-Hesketh,et al.  Reliable Estimation of Generalized Linear Mixed Models using Adaptive Quadrature , 2002 .

[24]  J. Palmgren,et al.  Effect modification in a randomized trial under non‐ignorable non‐compliance: an application to the alpha‐tocopherol beta‐carotene study , 2002 .

[25]  Jeffrey M. Woodbridge Econometric Analysis of Cross Section and Panel Data , 2002 .

[26]  H. Kordy,et al.  Therapy Amount and Outcome of Inpatient Psychodynamic Treatment of Eating Disorders in Germany: Data From a Multicenter Study , 2001 .

[27]  Barbara Sianesi,et al.  What is propensity score matching , 2001 .

[28]  C. Dowrick,et al.  Problem solving treatment and group psychoeducation for depression: multicentre randomised controlled trial , 2000, BMJ : British Medical Journal.

[29]  Dean A. Follmann,et al.  On the Effect of Treatment among Would-Be Treatment Compliers: An Analysis of the Multiple Risk Factor Intervention Trial , 2000 .

[30]  Foster Em Is more better than less? An analysis of children's mental health services. , 2000 .

[31]  N. Nagelkerke,et al.  Estimating treatment effects in randomized clinical trials in the presence of non-compliance. , 2000, Statistics in medicine.

[32]  G Dunn,et al.  The problem of measurement error in modelling the effect of compliance in a randomized trial. , 1999, Statistics in medicine.

[33]  G. Imbens The Role of the Propensity Score in Estimating Dose-Response Functions , 1999 .

[34]  E Goetghebeur,et al.  Practical properties of some structural mean analyses of the effect of compliance in randomized trials. , 1997, Controlled clinical trials.

[35]  James J. Heckman,et al.  Instrumental Variables Methods for the Correlated Random Coefficient Model: Estimating the Average Rate of Return to Schooling When the Return is Correlated with Schooling , 1998 .

[36]  J. Wooldridge On two stage least squares estimation of the average treatment effect in a random coefficient model , 1997 .

[37]  Els Goetghebeur,et al.  The Effect of Treatment Compliance in a Placebo‐controlled Trial: Regression with Unpaired Data , 1997 .

[38]  W. Stiles,et al.  Dose-Effect Relations in Time-Limited Psychotherapy for Depression , 1996 .

[39]  W. Stiles,et al.  Outcomes of time-limited psychotherapy in applied settings: replicating the Second Sheffield Psychotherapy Project. , 1996, Journal of consulting and clinical psychology.

[40]  D. Rubin,et al.  Identification of Causal Effects Using Instrumental Variables: Rejoinder , 1996 .

[41]  Kenneth A. Bollen,et al.  An alternative two stage least squares (2SLS) estimator for latent variable equations , 1996 .

[42]  Kenneth A. Bollen,et al.  STRUCTURAL EQUATION MODELS THAT ARE NONLINEAR IN LATENT VARIABLES: A LEAST- SQUARES ESTIMATOR , 1995 .

[43]  M. Barkham,et al.  Effects of treatment duration and severity of depression on the effectiveness of cognitive-behavioral and psychodynamic-interpersonal psychotherapy. , 1994, Journal of consulting and clinical psychology.

[44]  J. Robins Correcting for non-compliance in randomized trials using structural nested mean models , 1994 .

[45]  J. Hausman Specification tests in econometrics , 1978 .

[46]  D. Rubin Estimating causal effects of treatments in randomized and nonrandomized studies. , 1974 .

[47]  A. Beck,et al.  An inventory for measuring depression. , 1961, Archives of general psychiatry.