Sì, ecco una versione aggiornata della query che guarda indietro di 7 giorni dalla data corrente senza utilizzare parametri. 
Questa versione non include alcun filtro per categorie o sottocategorie.
WITH no_response_total AS (
SELECT *
FROM (
SELECT
t.id,
t.created_at,
MIN(p.post_number) AS first_reply
FROM
topics t
LEFT JOIN
posts p
ON
p.topic_id = t.id
AND p.user_id != t.user_id
AND p.deleted_at IS NULL
AND p.post_type = 1
WHERE
t.archetype <> 'private_message'
AND t.deleted_at IS NULL
AND (
t.category_id = :category_id
OR t.category_id IN (
SELECT id FROM categories WHERE parent_category_id = :category_id
)
)
GROUP BY
t.id
) tt
WHERE
tt.first_reply IS NULL
OR tt.first_reply < 2
)
SELECT
DATE(nrt.created_at) AS date,
COUNT(nrt.id) AS topics_without_response
FROM
no_response_total nrt
WHERE
nrt.created_at::date BETWEEN CURRENT_DATE - INTERVAL '7 days' AND CURRENT_DATE
GROUP BY
date
ORDER BY
date ASC
Se volessi regolare quanto indietro guarda la query, dovresti solo cambiare questa riga nella query:
nrt.created_at::date BETWEEN CURRENT_DATE - INTERVAL '7 days' AND