Chronic renal failure is a progressive condition that, typically, is asymptomatic for many years. Early detection of incipient kidney failure enables ameliorative treatment that can slow the rate of progression to end-stage renal failure, at which point expensive and invasive renal replacement therapy (dialysis or transplantation) is required. We use routinely collected clinical data from a large sample of primary care patients to develop a system for real-time monitoring of the progression of undiagnosed incipient renal failure. Progression is characterized as the rate of change in a person's kidney function as measured by the estimated glomerular filtration rate, an adjusted version of serum creatinine level in a blood sample. Clinical guidelines in the UK suggest that a person who is losing kidney function at a relative rate of at least 5% per year should be referred to specialist secondary care. We model the time-course of a person's underlying kidney function through a combination of explanatory variables, a random intercept and a continuous-time, non-stationary stochastic process. We then use the model to calculate for each person the predictive probability that they meet the clinical guideline for referral to secondary care. We suggest that probabilistic predictive inference linked to clinical criteria can be a useful component of a real-time surveillance system to guide, but not dictate, clinical decision-making.