PHP で複数のパラメータを含む動的検索フォームを構築するにはどうすればよいですか?

<?php

$wheres = array();
$params = array();

if (!empty($_GET['id'])) {
    $wheres[] = 'a.uid = :uid';
    $params[':uid'] = $_GET['id'];
}
if (!empty($_GET['major'])) {
    $wheres[] = 'a.major = :major';
    $params[':major'] = $_GET['major'];
}
if (!empty($_GET['name'])) {
    $wheres[] = 'b.name LIKE :name';
    $params[':name'] = '%'.$_GET['name'].'%';
}

$sql = "SELECT * 
        FROM user_details AS a
        JOIN user AS b ON a.uid = b.id";

if (!empty($wheres)) {
    $sql .= " WHERE " . implode(' AND ', $wheres);
}

$stmt = $db->prepare($sql);
$stmt->execute($params);

while ($student = $stmt->fetch()) {
    echo '
        <tr>
            <td>'.$student['uid'].'</td>
            <td>'.$student['name'].'</td>
            <td>'.$student['major'].'</td>
            <td>'.$student['college'].'</td>
            <td><a href="?m=profile&amp;id='.$student['id'].'">