SQL SELECT ~ How to detect parent / children categories?

This code gives me all the categories, but how can I filter out parent / children?

<?php
	$categories = $wpdb->get_results("
    SELECT DISTINCT(terms.term_id) as ID, terms.name, terms.slug, tax.description
    FROM $wpdb->posts as posts
    LEFT JOIN $wpdb->term_relationships as relationships ON posts.ID = relationships.object_ID
    LEFT JOIN $wpdb->term_taxonomy as tax ON relationships.term_taxonomy_id = tax.term_taxonomy_id
    LEFT JOIN $wpdb->terms as terms ON tax.term_id = terms.term_id
    WHERE posts.post_status = 'publish' AND
    	posts.post_author IN ($author) AND
        tax.taxonomy = 'category'
    ORDER BY terms.name ASC
    ");

echo $category->name;

    ?>