On the application of statistical learning approaches to construct inverse probability weights in marginal structural Cox models: Hedging against weight-model misspecification

ABSTRACT

The marginal structural Cox model (MSCM) estimates can be highly sensitive to weight-model misspecification. We assess the performance of various popular statistical learners, such as LASSO, support vector machines, CART, bagged CART, and boosted CART, in estimating MSCM weights. When weight-models are misspecified, we find that the weights computed from boosted CART generally lead to less MSE and better coverage for the MSCM estimates. This study is motivated by the investigation of the impact of beta-interferon treatment on disability progression in subjects with multiple sclerosis from British Columbia, Canada (1995–2008).

KEYWORDS:

• Causal inference
• Inverse probability weighting
• Machine learning
• Marginal structural models
• Model misspecification
• Multiple sclerosis

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 97K80 Applied statistics
• Secondary 92D30 Epidemiology

Funding Information

This work was supported by a studentship from the Multiple sclerosis (MS) Society of Canada (M.E.K.) and by a grant from the National Multiple Sclerosis Society (RG 4202-A-2, PI: H.T.) and the Canadian Institutes of Health Research (MOP-93646, PI: H.T.). J.P. holds research grants from the National MS Society, and the Natural Sciences and Engineering Research Council of Canada. P.G. is supported by the Natural Sciences and Engineering Research Council of Canada. H.T. is supported by the Canada Research Chair Program, an MS Society of Canada Don Paty Career Development award and is a Michael Smith Foundation for Health Research Scholar. She has also received: research support from the National MS Society, Canadian Institutes of Health Research, and the UK MS Trust. Y.Z. receives research funding from the Canadian Institutes of Health Research, the MS Society of Canada and the National MS Society. A.S. was funded through a Postdoctoral Fellowship from the MS Society of Canada, and grants from the Canadian Institutes of Health Research (MOP-93646; PI = H.T.) and the National MS Society (RG 4202-A-2; PI = H.T.). E.K. was supported by Postdoctoral Fellowships from the Michael Smith Foundation for Health Research and the MS Society of Canada. C.E. was funded through grants from the Canadian Institutes of Health Research (MOP-93646; PI = H.T.) and the National MS Society (RG 4202-A-2; PI = H.T.), and the Michael Smith Foundation for Health Research. M.L.v.d.K. is supported by a Canadian Institutes of Health Research Doctoral Award—Doctoral Foreign Study Award (October 2012), offered in partnership with the Canadian Institutes of Health Research (CIHR) Strategy for Patient-Oriented Research and the CIHR HIV/AIDS Research Initiative. J.O. receives support from the Christopher Foundation and the University of British Columbia (UBC). Over the past five years Dr. Oger has received speaker honoraria, consulting fees, travel grants and/or research grants and/or educational grants of less than < ent > dollar; </ent > 5, 000 each from Bayer, Biogen-Idec, BioMS, Glaxo-Smith-Klein, Novartis, Merck-Serono, Talecris and Teva-neurosciences. Dr. Oger has received fees for services from Bayer and from Biogen Idec to serve on advisory committees.

Thank you’s

We gratefully acknowledge the British Columbia Multiple sclerosis Clinic neurologists who contributed to the study through patient examination and data collection (current members listed here by primary clinic): UBC MS Clinic: Dr. A. Traboulsee, MD, FRCPC (UBC Hospital MS Clinic Director and Head of the UBC MS Programs); Dr. A-L. Sayao, MD, FRCPC; Dr. V. Devonshire, MD, FRCPC; Dr. S. Hashimoto, MD, FRCPC (UBC and Victoria MS Clinics); Dr. J. Hooge, MD, FRCPC (UBC and Prince George MS Clinics); Dr. L. Kastrukoff, MD, FRCPC (UBC and Prince George MS Clinics); Dr. J. Oger, MD, FRCPC. Kelowna MS Clinic: Dr. D. Adams, MD, FRCPC; D. Craig, MD, FRCPC; Dr. S. Meckling, MD, FRCPC. Prince George MS Clinic: Dr. L. Daly, MD, FRCPC. Victoria MS Clinic: Dr. O. Hrebicek, MD, FRCPC; Dr. D. Parton, MD, FRCPC; Dr. K Pope, MD, FRCPC. The views expressed in this article do not necessarily reflect the views of each individual acknowledged. None have received compensation for their role in the study.

Conflict of Interest

M.E.K. is supported by a CNODES post-doctoral award and has had travel and accommodation costs covered from the endMS Research and Training Network (2011, 2012), Statistical Society of Canada (2016) to present at conferences, and from Pacific Institute for the Mathematical Sciences (2013), The Canadian Statistical Sciences Institute (2016) to attend a workshop. Over the past three years, J.P. has received consulting fees and/or fees for service on Data Safety Monitoring Boards from EMD Serono, Myelin Research Foundation and Novartis. P.G. has received consulting fees from Biogen to serve on an advisory board. H.T has received speaker honoraria and/or travel expenses to attend conferences from the Consortium of MS Centres (2013), the MS Society of Canada (2013), the National MS Society (2012, 2014, 2016), Bayer Pharmaceutical (speaker, 2010, honoraria declined), Teva Pharmaceuticals (speaker 2011), ECTRIMS (2011, 2012, 2013, 2014, 2015, 2016), UK MS Trust (2011), the Chesapeake Health Education Program, US Veterans Affairs (2012, honorarium declined), Novartis Canada (2012), Biogen Idec (2014, honorarium declined), and the American Academy of Neurology (2013, 2014, 2015, 2016). All speaker honoraria were either declined or donated to an MS charity or to an unrestricted grant for use by her research group. Y.Z. declares no conflicts of interest. A.S. has received travel grants to present at and attend conferences from the endMS Research and Training Network (2010, 2011), ECTRIMS (2010, 2011), and the Consortium of MS Centres (2012). E.K. has had travel and accommodation costs covered to present at and attend conferences from the endMS Research and Training Network (2008, 2011), the International Society for Pharmacoepidemiology (2010, 2013) and Bayer Schering Pharma (2010). C.E. has received travel grants to present and attend conferences from the endMS Research and Training Network (2011), and the European Committee for Treatment and Research in MS (2011). M.L.v.d.K. declares no conflicts of interest. Over the past five years, J.O. has received speaker honoraria, consulting fees, travel grants and/or research grants and/or educational grants from Aventis, Bayer, Biogen-Idec, BioMS, Corixa, Genentech, Novartis, Serono, Shering, Talecris and Teva-neurosciences. J.O. receives fees for services from Bayer, from Novartis and from Biogen Idec to serve on advisory committees.