title: Targeted maximum likelihood estimation in safety analysis.
abstract: OBJECTIVE
  To compare the performance of a targeted maximum likelihood estimator (TMLE) and a collaborative TMLE (CTMLE) to other estimators in a drug safety analysis, including a regression-based estimator, propensity score (PS)-based estimators, and an alternate doubly robust (DR) estimator in a real example and simulations.
  
  
  METHODS
  The real data set is a subset of observational data from Kaiser Permanente Northern California formatted for use in active drug safety surveillance. Both the real and simulated data sets include potential confounders, a treatment variable indicating use of one of two antidiabetic treatments and an outcome variable indicating occurrence of an acute myocardial infarction (AMI).
  
  
  RESULTS
  In the real data example, there is no difference in AMI rates between treatments. In simulations, the double robustness property is demonstrated: DR estimators are consistent if either the initial outcome regression or PS estimator is consistent, whereas other estimators are inconsistent if the initial estimator is not consistent. In simulations with near-positivity violations, CTMLE performs well relative to other estimators by adaptively estimating the PS.
  
  
  CONCLUSIONS
  Each of the DR estimators was consistent, and TMLE and CTMLE had the smallest mean squared error in simulations.
authors.affiliation: Division of Biostatistics, UC Berkeley, 101 Haviland Hall, Berkeley, CA 94720, USA. lendle@stat.berkeley.edu
authors.forename: Samuel D
authors.initials: SD
authors.lastname: Lendle
authors.forename: Bruce
authors.initials: B
authors.lastname: Fireman
authors.forename: Mark J
authors.initials: MJ
authors.lastname: van der Laan
mesh_terms: D000465:Algorithms; D015984:Causality; D003198:Computer Simulation; D015986:Confounding Factors, Epidemiologic; D003627:Data Interpretation, Statistical; D003920:Diabetes Mellitus / Q000188:drug therapy; D006801:Humans; D007004:Hypoglycemic Agents / Q000627:therapeutic use*; D016013:Likelihood Functions; D015233:Models, Statistical; D009203:Myocardial Infarction / Q000453:epidemiology; D011358:Product Surveillance, Postmarketing / Q000706:statistics & numerical data*; D057216:Propensity Score; D012107:Research Design; D016896:Treatment Outcome
chemical_list: D007004:Hypoglycemic Agents
keywords: Causal inference; Collaborative targeted maximum likelihood estimation; Doubly robust; Safety analysis; Super learning; Targeted maximum likelihood estimation