Summary. Typical oncology practice often includes not only an initial front-line treatment but also subsequent treatments given if the initial treatment fails. The physician chooses a treatment at each stage based on the patient's baseline covariates and history of previous treatments and outcomes. Such sequentially adaptive medical decision-making processes are known as dynamic treatment regimes, treatment policies or multistage adaptive treatment strategies. Conventional analyses in terms of front-line treatments that ignore subsequent treatments may be misleading, because they actually are an evaluation of more than front-line treatment effects on outcome. We are motivated by data from a randomized trial of four combination chemotherapies given as front-line treatments to patients with acute leukaemia. Most patients in the trial also received a second-line treatment, which was chosen adaptively and subjectively rather than by randomization, either because the initial treatment was ineffective or the patient's cancer later recurred. We evaluate effects on overall survival time of the 16 two-stage strategies that actually were used. Our methods include a likelihood-based regression approach in which the transition times of all possible multistage outcome paths are modelled, and estimating equations with inverse probability of treatment weighting to correct for bias. Although the two approaches give different numerical estimates of mean survival time, they lead to the same substantive conclusions when comparing the two-stage regimes.