In randomized cancer screening trials where asymptomatic individuals are assigned to undergo a regimen of screening examinations or standard care, the primary objective typically is to estimate the effect of screening assignment on cancer-specific mortality by carrying out an ’intention-to-screen’ analysis. However, most of the participants in the trial will be cancer-free; only those developing a genuine cancer that is screening-detectable can potentially benefit from screening induced early treatments. Here we consider measuring the effect of early treatments in this partially latent subpopulation in terms of reduction in case fatality. To formalize the estimands and identifying assumptions in a causal modeling framework, we first define two measures, namely proportional and absolute case-fatality reduction, using potential outcomes notation. We re-derive an earlier proposed estimator for the former, and propose a new estimator for the latter motivated by the instrumental variable approach. The methods are illustrated using data from the US National Lung Screening Trial, with specific attention to estimation in the presence of censoring and competing risks.