Typically, case-control studies only include incident cases to estimate odds-ratios for the association of risk factors with outcome from logistic regression models. Incorporating prevalent cases requires adjustment of the logistic model for the time between disease diagnosis and sampling, the backward time, to ensure unbiased odds-ratio estimates. To accommodate this survival bias in prevalent cases via backward time adjustment, one needs to estimate the distribution of time from disease onset to death. To relax parametric assumptions on this distribution, needed when only backward times are available, we propose a computationally simple two-step procedure to incorporate additionally observed prospective survival time from all cases into the analysis of case-control studies with prevalent cases. First, we estimate the survival distribution based on a semiparametric Cox model using standard partial likelihood or an expectation-maximization algorithm that yields fully efficient estimates. Then, we use the estimated survival distribution in an extension of the logistic model to three groups (controls, incident and prevalent cases), to accommodate survival bias in the prevalent cases.