From the Guidelines

Hypocalcemia in children is a common condition, particularly in newborns, and can be prevented or treated with calcium infusion.

Hypocalcemia in newborns occurs due to the interruption of placental transfer at birth and relative immaturity of hormonal control, leading to a delayed parathyroid hormone (PTH) surge 1.
Calcium infusion can prevent or treat early neonatal hypocalcemia, which is generally not associated with obvious clinical problems such as tetany 1.

In children on long-term parenteral nutrition (PN), the risk of metabolic bone disease requires periodic monitoring of calcium, phosphorus, vitamin D, and bone mineral status 1.
The recommended calcium intake for infants and children on long-term PN is 0.35-0.4 mmol/kg/d, with an excess of phosphorus (0.7 mmol/kg/d) and a calcium:phosphorus ratio less than 1 1.

Hypercalciuria and negative calcium balance can be attenuated in the short-term by intravenous phosphate 1.
Adequate phosphate intake is essential for optimal bone mineralization, and a calcium:phosphorus ratio of 0.5 may be beneficial in preventing metabolic bone disease 1.

From the Research

Hypocalcemia is defined as total serum calcium <8 mg/dL (2 mmol/L) or ionized calcium <4.4 mg/dL (1.1 mmol/L) for term infants or preterm infants weighing >1500 g at birth 2
For very low birth weight infants weighing <1500 g, hypocalcemia is defined as total serum calcium <7 mg/dL (1.75 mmol/L) or ionized calcium <4 mg/dL (1 mmol/L) 2
Screening for hypocalcemia at the 24th and 48th hour after birth is warranted for infants with high risk of developing hypocalcemia, such as preterm infants with a gestational age <32 weeks, small for gestational age infants, infants of diabetic mothers, and infants with severe prenatal asphyxia with a 1 min Apgar score of <4 2

Hypocalcemia can be caused by a lack of secretion or function of parathyroid hormone, disorders of vitamin D metabolism, and abnormal function of the calcium-sensing receptor 3, 4
Excessive phosphate intake, hypomagnesemia, hypoparathyroidism, and vitamin D deficiency are common causes of late-onset hypocalcemia 2
Vitamin D deficiency rickets and hypoparathyroidism are also common causes of hypocalcemia in infants and children 5

Calcium replacement is the cornerstone of the treatment of hypocalcemia 2
Elementary calcium replacement of 40 to 80 mg/kg/d is recommended for asymptomatic newborns 2
Elementary calcium of 10 to 20 mg/kg (1-2 mL/kg/dose 10% calcium gluconate) is given as a slow intravenous infusion in the acute treatment of hypocalcemia in patients with symptoms of tetany or hypocalcemic convulsion 2
Treatment of hypocalcemia should be initiated immediately in infants with reduced calcium levels while investigating the etiology 2
The use of 1-hydroxyle derivatives of vitamin D has improved the treatment of hypocalcemia 5