The intensity-score approach to adjusting for confounding.

*(English)*Zbl 1210.62146Summary: In a recent article on the efficacy of antihypertensive therapy, Berlowitz et al. [New England J. Med. 339, 1957–1963 (1998)] introduced an ad hoc method of adjusting for serial confounding assessed via an intensity score, which records cumulative differences over time between therapy actually received and therapy predicted by prior medical history. Outcomes are subsequently regressed on the intensity score and baseline covariates to determine whether intense treatment or exposure predicts a favorable response. We use a structural nested mean model to derive conditions sufficient for interpreting the Berlowitz results causally. We also consider a modified approach that scales the intensity at each time by the inverse expected treatment given prior medical history. This leads to a simple, two-step implementation of G-estimation if we assume a nonstandard but useful structural nested mean model in which subjects less likely to receive treatment are more likely to benefit from it. These modeling assumptions apply, for example, to health services research contexts in which differential access to care is a primary concern. They are also plausible in our analysis of the causal effect of potent antiretroviral therapy on change in CD4 cell count, because men in the sample who are less likely to initiate treatment when baseline CD4 counts are high are more likely to experience large positive changes. We further extend the methods to accomodate repeated outcomes and time-varying effects of time-varying exposures.

##### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62N02 | Estimation in survival analysis and censored data |

##### Keywords:

causal inference; confounding; differential access-to-care; E-estimation; G-estimation; instrumental variables; longitudinal data; marginal structural model; observational data; propensity score; structural nested mean model
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\textit{B. Brumback} et al., Biometrics 59, No. 2, 274--285 (2003; Zbl 1210.62146)

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