Many observational studies assessing the effects of treatments or exposures are limited to comparisons between treatment users and nonusers or exposed and unexposed participants at study entry. However, the underlying and etiologically relevant exposure may gradually increase over time before reaching some plateau. This amount of time required for this latent cumulative exposure to reach a maximum hazard will be referred to as the "lag", coming from the concept that the association between exposure and outcome is lagged or delayed. Accounting for the lag is essential when analyzing exposure-response associations adequately. My challenge was to simultaneously estimate the lag-time and the exposure's lagged-association with the outcome at plateau. In this dissertation, I draw an analogy with the pharmacokinetic one-compartment model (OCM). OCM describes the accumulation of a medication in the body based on an exponential cumulative density function whose rate of increase is defined by a half-life parameter. Upon discontinuation, the OCM assumes that a medication will eliminate at the same half-life rate. The decline, for my purposes, can be interpreted as the time to return to a null effect of exposure, which occurs at roughly 4-5 half-lives. My methods model the association of a latent exposure and dichotomous outcome using a half-life of effect, similar to the OCM, in longitudinal analyses of single and repeated exposures. I derive profile likelihood-based algorithms to estimate of the upper limit of association simultaneously with the rate of latent exposure growth towards or away from plateau. Lastly, I extend this approach to allow different half-life parameters for incline and decline. Using simulations, I analyze the performance of my approach by comparing bias and coverage of the estimates for the half-life and effect parameters. With data from the Black Women's Health Study Cohort (a prospective cohort of 59,000 women followed 1995-2015), I show that prolonged cigarette smoking is associated with a maximum hazard of cardiovascular disease (CVD) at 2.5 times the hazard of never smokers. Additionally, I estimate that it takes about 7 years of smoking cessation for an individual's hazard of CVD to decrease by 50%. / 2020-11-13T00:00:00Z

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