G-estimation for Accelerated Failure Time Models

There is an increasing interest in life-course epidemiology (Ben-Shlomo 2007; Ben-Shlomo and Kuh 2002), with the quantification of the effects of exposures over long periods of time. For example, several papers recently have examined the effects of socioeconomic position at different stages of life, and changes in that exposure between these stages, on outcomes including risk of stroke and respiratory function, and health behaviours including midlife drinking and smoking patterns (Amuzu et al. 2009; Glymour et al. 2008; Tehranifar et al. 2009; Tennant et al. 2008). In longitudinal studies, the effects of risk factors on outcome may be estimated in different ways, with different interpretations. The usual approach is to examine the relationship between baseline exposure and rates of disease or death. For reasonably constant exposures, this estimates the cumulative effects of exposure. For example, in a longitudinal study the association between baseline diabetes and subsequent mortality represents the association of lifetime diabetes with mortality. Alternatively we may estimate time-varying effects of exposure. For example, subjects may take up smoking or quit smoking at various stages during the longitudinal study (usually we assume that the exposure level remains constant from one measurement occasion to the next). Here, the time-varying association between smoking and mortality represents the relationship between smoking at a given visit and mortality after that visit. If follow-up is fairly short this represents the instantaneous association between smoking and mortality and can be investigated using standard regression methods (e.g. survival models, structural