Renal function is estimated using various equations that approximate actual GFR. Inulin and Iothalmate are considered gold standard substances to measure that approximate actual GFR (as they are freely filtered at the glomerulus and not reabsorbed/secreted), but they are difficult to come by and expensive so they are not often used.
Creatnine works ok, it is freely filtered and not reabsorbed, but is secreted in the distal tubule (increasingly so in advancing CKD). The two creatnine based formulas for estimating GFR most commonly used are MDRD and Cockroft-Gualt. MDRD is probably the best estimate of GFR we have as it standardizes GFR to age, race, body surface area, and gender. Cockroft-Gualt standardizes to age, gender, and weight. Both of these formulas were not studied in patients with AKI, so it is truly impossible to estimate with any degree of certainty the actual GFR in that situation.
Cockroft-Gualt: gives you a creat clearance ~ GFR, reported as ml/min, tends to not work as well with advancing CKD 2/2 increased tubular secretion of creatnine, also though it is based on weight, it was validated using actual lean body weight of a patient and that is a very tough and not often done thing in clinical practice.
MDRD: performs better with advancing CKD probably, but tends to underestimate patients true GFR if actual GFR is > 60, it is reported as ml/min/1.73m2- supposedly standardized to a "normal body surface area," but in really big patients or really skinny ones it will have similar problems with estimating true lean body weight, as not all americans have the BSA of 1.73m2.
Dose adjustments are typically made based on stages of CKD, with GFR > 90, 60-89, 30-59, 15-29, <15 or dialysis, many drugs were studied using various doses based on GFR in those different ranges (Zosyn typically 4.5g IV q6h with normal renal function, but if GFR < 15 = 2.25g IV q8h)
But the point is that both these equations were validated in patients with STABLE renal function. Thus if a patient has a Scr of 1.0 on day 1, and Scr of 2.0 day 2, using one of these equations might indicate that they have a eGFR of 80 on day 1 and perhaps 40-50 on day 2 when in actuality the patient is anuric and has an actual GFR of 0. And there are a variety of drugs that interact with creatnine assays in the lab and interfere with tubular secretion of creatnine that can falsely elevate serum creatnine.