title: Dimension reduction and shrinkage methods for high dimensional disease risk scores in historical data.
abstract: BACKGROUND
  Multivariable confounder adjustment in comparative studies of newly marketed drugs can be limited by small numbers of exposed patients and even fewer outcomes. Disease risk scores (DRSs) developed in historical comparator drug users before the new drug entered the market may improve adjustment. However, in a high dimensional data setting, empirical selection of hundreds of potential confounders and modeling of DRS even in the historical cohort can lead to over-fitting and reduced predictive performance in the study cohort. We propose the use of combinations of dimension reduction and shrinkage methods to overcome this problem, and compared the performances of these modeling strategies for implementing high dimensional (hd) DRSs from historical data in two empirical study examples of newly marketed drugs versus comparator drugs after the new drugs' market entry-dabigatran versus warfarin for the outcome of major hemorrhagic events and cyclooxygenase-2 inhibitor (coxibs) versus nonselective non-steroidal anti-inflammatory drugs (nsNSAIDs) for gastrointestinal bleeds.
  
  
  RESULTS
  Historical hdDRSs that included predefined and empirical outcome predictors with dimension reduction (principal component analysis; PCA) and shrinkage (lasso and ridge regression) approaches had higher c-statistics (0.66 for the PCA model, 0.64 for the PCA + ridge and 0.65 for the PCA + lasso models in the warfarin users) than an unreduced model (c-statistic, 0.54) in the dabigatran example. The odds ratio (OR) from PCA + lasso hdDRS-stratification [OR, 0.64; 95 % confidence interval (CI) 0.46-0.90] was closer to the benchmark estimate (0.93) from a randomized trial than the model without empirical predictors (OR, 0.58; 95 % CI 0.41-0.81). In the coxibs example, c-statistics of the hdDRSs in the nsNSAID initiators were 0.66 for the PCA model, 0.67 for the PCA + ridge model, and 0.67 for the PCA + lasso model; these were higher than for the unreduced model (c-statistic, 0.45), and comparable to the demographics + risk score model (c-statistic, 0.67).
  
  
  CONCLUSIONS
  hdDRSs using historical data with dimension reduction and shrinkage was feasible, and improved confounding adjustment in two studies of newly marketed medications.
authors.affiliation: Division of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, 1620 Tremont Street (Suite 3030), Boston, MA 02120 USA ; Department of Healthcare Quality Assessment, Graduate School of Medicine, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8654 Japan.
authors.forename: Hiraku
authors.initials: H
authors.lastname: Kumamaru
authors.affiliation: Division of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, 1620 Tremont Street (Suite 3030), Boston, MA 02120 USA.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Schneeweiss
authors.affiliation: Division of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, 1620 Tremont Street (Suite 3030), Boston, MA 02120 USA.
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Glynn
authors.affiliation: Duke Clinical Research Institute, Duke University, 2400 Pratt Street, Durham, NC 27705 USA.
authors.forename: Soko
authors.initials: S
authors.lastname: Setoguchi
authors.affiliation: Division of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, 1620 Tremont Street (Suite 3030), Boston, MA 02120 USA.
authors.forename: Joshua J
authors.initials: JJ
authors.lastname: Gagne
keywords: Comparative study; Confounding; Disease risk score; High dimensional propensity score; Historical data; Shrinkage