In a patient with muscle cramps and tetany after thyroid surgery, serum calcium is low, phosphate is high, and magnesium is low with decreased urinary calcium and phosphate. The presumptive diagnosis is:

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Loss or damage to the parathyroid glands during thyroid surgery causes a deficiency of parathyroid hormone, which is the main regulator of calcium and phosphate balance. PTH normally raises serum calcium by increasing bone resorption, enhancing renal calcium reabsorption, and boosting intestinal calcium absorption via activation of vitamin D. It also lowers serum phosphate by promoting its excretion in the kidneys. When PTH is deficient, calcium falls while phosphate rises. Magnesium deficiency can worsen this picture by impairing PTH secretion and action.

In this patient, the combination of low serum calcium and high phosphate fits hypoparathyroidism. The finding of low urinary calcium and phosphate can occur because the reduced PTH activity decreases phosphate excretion (phosphate retention) and the overall low calcium reduces the filtered load of calcium, leading to less calcium excretion. Taken with the recent thyroid surgery and the presence of cramps and tetany, this pattern points to hypoparathyroidism as the presumptive diagnosis.