• adaptive treatment strategies;
  • asymptotic bias;
  • dynamic treatment regimes;
  • g-estimation;
  • optimal structural nested mean models;
  • pretest estimators

Abstract.  A dynamic regime provides a sequence of treatments that are tailored to patient-specific characteristics and outcomes. In 2004, James Robins proposed g–estimation using structural nested mean models (SNMMs) for making inference about the optimal dynamic regime in a multi-interval trial. The method provides clear advantages over traditional parametric approaches. Robins’g–estimation method always yields consistent estimators, but these can be asymptotically biased under a given SNMM for certain longitudinal distributions of the treatments and covariates, termed exceptional laws. In fact, under the null hypothesis of no treatment effect, every distribution constitutes an exceptional law under SNMMs which allow for interaction of current treatment with past treatments or covariates. This paper provides an explanation of exceptional laws and describes a new approach to g–estimation which we call Zeroing Instead of Plugging In (ZIPI). ZIPI provides nearly identical estimators to recursive g-estimators at non-exceptional laws while providing substantial reduction in the bias at an exceptional law when decision rule parameters are not shared across intervals.