Update postmeta Parent when post_status child change

From WP 3.7 you have the option to hook to the save_post hook directly for you post_type.

For example:

function update_post_parent_status_on_complete( $post_id ) {
    if(!isset($post))
      $post = get_post($post_id);

    // checking the status you want and also that has a parent
    if ($post->post_status == 'completed' && $post->post_parent !=0 ){
        $parent_id = $post->post_parent;
        update_post_meta($parent_id, 'screening_status', 'screen');
    }
}

add_action('save_post_screening', 'update_post_parent_status_on_complete');