cara buat variable di switch case

gimana yah caranya buat variable di switch case jadi nanti variable nya di panggil ke a href buat pemanggilan link menu, soal nya menu nya di ambil dari database....

<li><a href="'.$link.'" ><i class="fa fa-caret-right"></i> '.$menu['name'].'</a></li> ';
// jadi variable switch case tadi di panggil disini

------------------------------------------------------------
$menu["xh"];

switch ($menu)

{
    case "10120110":
        if (!file_exist("page1.php")) die("kosong");
	include = "page1.php";
        break;
    case "10120120":
        if (!file_exist("page2.php")) die("kosong");
	include = "page2.php";
        break;
    case "10120150":
        if (!file_exist("page3.php")) die("kosong");
	include = "page3.php";
        break;
     case "10120160":
        if (!file_exist("page4.php")) die("kosong");
	include = "page4.php";
        break;
}