MySQL - maximum of sum over different months with ties over multiple years
My attempt to solve this is as follows. I would appreciate any advice on how this query could be improved:

SELECT 
  t3.c_year AS "Year",
  t3.c_month AS "Month", 
  t3.il_mc AS  "Tumour count", 
  t4.ill_nat AS "Type" FROM
(
  SELECT c_year, c_month, il_mc FROM
  (
    SELECT  
    c_year, 
    c_month,
    MAX(month_count) AS il_mc
  FROM
    (
      SELECT nature_of_illness as illness,
        EXTRACT(YEAR  FROM created_at) AS c_year,
        EXTRACT(MONTH FROM created_at) AS c_month,
        COUNT(EXTRACT(MONTH FROM created_at)) AS month_count
      FROM illness
      GROUP BY illness, c_year, c_month
      ORDER BY c_year, c_month
    ) AS t1
  GROUP BY c_year, c_month
  ) AS t2
) AS t3
JOIN
(
SELECT 
  EXTRACT(YEAR FROM created_at) AS t_year, 
  EXTRACT(MONTH FROM created_at) AS t_month,  
  nature_of_illness AS ill_nat, 
  COUNT(nature_of_illness) AS ill_cnt
FROM illness
GROUP BY t_year, t_month, nature_of_illness
ORDER BY t_year, t_month, nature_of_illness
) AS t4
ON t3.c_year = t4.t_year
AND t3.c_month = t4.t_month
AND t3.il_mc = t4.ill_cnt


And it does give the correct result, as can be seen in the fiddle here!