|Laubender, Rüdiger P.; Mansmann, Ulrich (24. December 2014): Estimating individual treatment effects from responses and a predictive biomarker in a parallel group RCT. Department of Statistics: Technical Reports, No.176|
When being interested in administering the best of two treatments to an individual patient i, it is necessary to know the individual treatment effects (ITEs) of the considered subjects and the correlation between the possible responses (PRs) for two treatments. When data are generated in a parallel–group design RCT, it is not possible to determine the ITE for a single subject since we only observe two samples from the marginal distributions of these PRs and not the corresponding joint distribution due to the ’Fundamental Problem of Causal Inference’ [Holland, 1986, p. 947]. In this article, we present a counterfactual approach for estimating the joint distribution of two normally distributed responses to two treatments. This joint distribution can be estimated by assuming a normal joint distribution for the PRs and by using a normally distributed baseline biomarker which is defined to be functionally related to the sum of the ITE components. Such a functional relationship is plausible since a biomarker and the sum encode for the same information in a RCT, namely the variation between subjects. As a result of the interpretation of the biomarker as a proxy for the sum of ITE components, the estimation of the joint distribution is subjected to some constraints. These constraints can be framed in the context of linear regressions with regard to the proportions of variances in the responses explained and with regard to the residual variation. As a consequence, a new light is thrown on the presence of treatment–biomarker interactions. We applied our approach to a classical medical data example on exercise and heart rate.
|Item Type:||Paper (Technical Report)|
|Keywords:||Individual treatment effect, parallel group design, missing values, structural model|
|Faculties:||Mathematics, Computer Science and Statistics|
Mathematics, Computer Science and Statistics > Statistics > Technical Reports
|Subjects:||500 Science > 510 Mathematics|
600 Technology > 610 Medicine and health
|Deposited On:||27. Dec 2014 11:22|
|Last Modified:||17. Mar 2015 08:24|
Anderson, T.W. (1957). Maximum likelihood estimates for a multivariate normal distribution when some observations are missing. Journal of the American Statistical Association 52, 200–203. Arens, T., Hettlich, F., Karpfinger, C., Kockelkorn, U., Lichtenegger, K. and Stachel, H. (2012). Mathematik. Heidelberg: Spektrum Akademischer Verlag. Bartko, J.J. (1994). General methodology II measures of agreement: a single procedure. Statistics in Medicine 13, 737–745. Bryc, W. (1995). The Normal Distribution: Characterizations with Applications. Heidelberg: Springer. Buyse, M. (2007). Towards validation of statistically reliable biomarkers. European Journal of Cancer Supplements 5, 89–95. Cheng, J., Small, D.S., Tan, Z. and Ten Have, T.R. (2009). Efficient nonparametric estimation of causal effects in randomized trials with noncompliance. Biometrika 96, 19–36. Cleophas, T.J.M. (1996a). Crossover trials are only useful when there is a positive correlation between the response to different treatment modalities. British Journal of Clinical Pharmacology 41, 235–239. Cleophas, T.J.M. (1996b). Criticism of cardiovascular studies with negative results due to a negative correlation. Angiology 47, 139–147. Cleophas, T.J.M. and de Vogel, E.M. (1998). Crossover studies are a better format for comparing equivalent treatments than parallel–group studies. Pharmacy World and Science 20, 113–117. Cleophas, T.J. (2000). Crossover trials should not be used to test one treatment against another treatment with a totally different chemical class/mode of action. Journal of Clinical Pharmacology 40, 1503–1508. Cleveland, W.S. (1985). The Elements of Graphing Data. Monterey: Wadsworth Advanced Books and Software. Cox, D.R. and Reid, N. (2000). The Theory of the Design of Experiments. Boca Raton: Chapman & Hall/CRC. Davidson, R. and MacKinnon, J.G. (1993). Estimation and Inference in Econometrics. New York: Oxford University Press. Freidlin, B. and Simon, R. (2005). Adaptive signature design: An adaptive clinical trial design for generating and prospectively testing a gene expression signature for sensitive patients. Clinical Cancer Research 11, 7872–7878. Gadbury, G.L. and Iyer, H.K. (2000). Unit–treatment interaction and its practical consequences. Biometrics 56, 882–885. Gadbury, G.L., Iyer, H.K. and Allison, D.B. (2001). Evaluating subject–treatment interaction when comparing two treatments. Journal of Biopharmaceutical Statistics 11, 313–333. Gneiting, T. and Raftery, A.E. (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association 102, 359–378. Greene, W.H. (2003) Econometric Analysis. Upper Saddle River: Prentice Hall. Holland, P. W. (1986). Statistics and causal inference. Journal of the American Statistical Association 81, 945–960. Huang, Y., Gilbert, P.B. and Janes, H. (2012). Assessing treatment–selection markers using a potential outcomes framework. Biometrics 68, 687–696. Janes, H., Pepe, M.S., Bossuyt, P.B. and Barlow, W.E. (2011). Measuring the performance of markers for guiding treatment decisions. Annals of Internal Medicine 154, 253–259. Johnson, R.A. and Wichern, D.W. (1992). Applied Multivariate Statistical Analysis. Prentice–Hall International: London. Laubender, R.P. (2014). Estimation of a joint distribution with two normally distributed treatment responses as marginals generated in a randomized controlled trial based on the parallel–group design by using a normally distributed covariate. Dr. Hut Verlag: Munich. Lord, F.M. (1955). Estimation of parameters from incomplete data. Journal of the American Statistical Association 50, 870–876. Sargent, D.J., Conley B.A., Allegra C. and Collette L. (2005). Clinical trial designs for predictive marker validation in cancer treatment trials. Journal of Clinical Oncology 23, 2020–2027. Schwenke, J.R. (1990). On the equivalence of the Johnson–Neyman technique and Fieller’s Theorem. Biometrical Journal 32, 441–447. Searle, S.R. (1982). Matrix Algebra Useful for Statistics. Hoboken: Wiley. Senn, S. (2001). Individual therapy: new dawn or false dawn? Drug Information Journal 35, 1479–1494. Shumaker, R.C. and Metzler, C.M. (1998). The phenytoin trial is a case study of ’individual bioequivalence’. Drug Information Journal 32, 1063–1072. Simon, R. (2008). The use of genomics in clinical trial design. Clinical Cancer Research 14, 5954–5958. Simon, R.M., Paik, S. and Hayes, D.F. (2009). Use of archived specimens in evaluation of prognostic and predictive biomarkers. Journal of the National Cancer Institute 21, 1446–1452. Veraverbeke, N., Omelka, M. and Gijbels, I. (2011). Estimation of a conditional copula and association measures. Scandinavian Journal of Statistics 38, 766–780.