Decide which test best answers a whole-skeleton question. To find spread of tumour to bone anywhere in the body, you want one study that covers head to toe and flags lesions before they are obvious on x-ray.
The radionuclide bone scan fits this requirement. After injecting Tc-99m labelled diphosphonate, the tracer concentrates wherever osteoblasts are busy laying down bone. Because metastatic deposits provoke a reactive increase in bone turnover, they light up as focal hot spots, and the gamma camera sweeps the entire skeleton in a single sitting. It also picks up disease earlier than plain films, which only show a lesion once a large fraction of the bone matrix has been lost.
The alternatives are less suited. MRI and CT resolve a single region in fine detail but are not the routine choice for surveying the whole body for distant deposits. A venogram simply opacifies veins and contributes nothing to detecting skeletal metastasis.
Hence the screening investigation of choice is the radionuclide bone scan.
\[\boxed{\text{Bone scan}}\]