MySQL - Optimize JOIN only grouping necessary rows - mysql

Question

My query selects the maximum value of a second table (laboratory values) for a subset of cases. Obviously this method is extremely slow (>25seconds) as I am using a subquery that, not knowing parent's filter, groups all laboratory.CaseID (15k in a 10mil record table) before just using 10 of them. The problem is easy to see in an EXPLAIN.
SELECT cases.CaseID,t.val FROM cases
LEFT JOIN
(SELECT Max(laboratory.LaboratoryValue) as val , CaseID FROM laboratory
WHERE laboratory.LaboratoryID =682
GROUP by laboratory.CaseID) as t
ON t.CaseID = cases.CaseID
WHERE cases.Diagnosis = 16;
I tried to optimize the query using a TEMPORARY TABLE, which speeds up to 0,008s, but this method seems a bit clumsy when doing it to many fields.
CREATE TEMPORARY TABLE tmptest
SELECT cases.CaseID FROM cases WHERE cases.Diagnosis = 16;
SELECT cases.CaseID,t.val FROM cases
LEFT JOIN
(SELECT Max(laboratory.LaboratoryValue) as val , CaseID FROM laboratory
WHERE laboratory.LaboratoryID =682
AND laboratory.CaseID IN (SELECT CaseID FROM tmptest)
GROUP by laboratory.CaseID) as t
ON t.CaseID = cases.CaseID
WHERE cases.Diagnosis = 16;
Is there a simpler solution for query optimization?
As requested the EXPLAIN. It shows the problem, CaseID is (as expected) not used.
The second query does it right (NoDoubles contains both indexes);

Answer 1

These indexes are needed:
laboratory: INDEX(LaboratoryID, CaseID, LaboratoryValue)
cases: INDEX(Diagnosis, CaseID)
Two more formulations to try and time:
SELECT c.CaseID, L.val
FROM
( SELECT CaseID, Max(laboratory.LaboratoryValue) as val
FROM laboratory
WHERE laboratory.LaboratoryID = 682
GROUP by laboratory.CaseID
) AS L
JOIN cases AS c USING(CaseID)
WHERE c.Diagnosis = 16;
SELECT c.CaseID,
( SELECT Max(laboratory.LaboratoryValue)
FROM laboratory
WHERE laboratory.LaboratoryID = 682
AND CaseID = c.CaseID
) AS val
FROM cases AS c
WHERE c.Diagnosis = 16;
They are not identical because of "LEFT". So, verify that you get the "right" answers. The first uses JOIN; the second is equivalent to your LEFT JOIN.
For further discussion, please provide EXPLAIN for whatever formulations you want to discuss. And SHOW CREATE TABLE.