What is the most appropriate investigation for a 75-year-old man with prostate cancer, confusion, and a shortened QT interval on ECG?

In a 75-year-old man with prostate cancer who presents with confusion and a shortened QT interval on an ECG, assessing the serum calcium level is particularly important. In the context of prostate cancer, confusion can be a sign of hypercalcemia, which is often related to metastatic disease, especially if it has spread to the bones.

The shortened QT interval observed on the ECG is also indicative of hypercalcemia, as high levels of calcium can lead to changes in cardiac repolarization. Therefore, measuring serum calcium is essential to determine if hypercalcemia is the underlying cause of the symptoms and the abnormal ECG findings.

This investigation directly addresses the potential cause of the patient’s confusion and cardiac changes, making it the most appropriate choice in this scenario. Other investigations, such as an MRI of the spine or a DEXA scan, may provide valuable information about bone health and metastatic spread but are not directly relevant to the immediate concerns raised by the patient's symptoms. Serum alkaline phosphatase levels could aid in assessing bone disease but would not specifically evaluate the possibility of hypercalcemia in this case.