Estimates of absolute risks and risk differences are necessary for evaluating the clinical and population impact of biomedical research findings. We have developed a linear-expit regression model (LEXPIT) to incorporate linear and nonlinear risk effects to estimate absolute risk from studies of a binary outcome. The LEXPIT is a generalization of both the binomial linear and logistic regression models. The coefficients of the LEXPIT linear terms estimate adjusted risk differences, whereas the exponentiated nonlinear terms estimate residual odds ratios. The LEXPIT could be particularly useful for epidemiological studies of risk association, where adjustment for multiple confounding variables is common. We present a constrained maximum likelihood estimation algorithm that ensures the feasibility of risk estimates of the LEXPIT model and describe procedures for defining the feasible region of the parameter space, judging convergence, and evaluating boundary cases. Simulations demonstrate that the methodology is computationally robust and yields feasible, consistent estimators. We applied the LEXPIT model to estimate the absolute 5-year risk of cervical precancer or cancer associated with different Pap and human papillomavirus test results in 167,171 women undergoing screening at Kaiser Permanente Northern California. The LEXPIT model found an increased risk due to abnormal Pap test in human papillomavirus-negative that was not detected with logistic regression. Our R package blm provides free and easy-to-use software for fitting the LEXPIT model. Published 2012. This article is a US Government work and is in the public domain in the USA.