For those using named parameters, here's how to do a % partial match using LIKE in a MySQL database:

WHERE column_name LIKE CONCAT('%', :dangerousstring, '%')

The named parameter is :dangerousstring.

In other words, you use explicit unescaped % symbols in your queries, which are separate from user input.

EDIT: For Oracle Database, the join syntax uses the join operator: ||, so it will simplify to:

WHERE column_name LIKE '%' || :dangerousstring || '%'

I found the answer after posting:

$query = $database->prepare('SELECT * FROM table WHERE column LIKE ?');
$query->execute(array('value%'));

while ($results = $query->fetch())
{
    echo $results['column'];
}