MySQL 8.0

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CREATE TABLE mytable (
doctor VARCHAR(255),
patient VARCHAR(255),
bought_x_days_ago INT);

INSERT INTO mytable VALUES
('Aaron','Jeff',10),
('Aaron','Jeff',20),
('Jess','Jason',50),
('Jess','Jason',20),
('Jess','Jason',30),
('Aaron','Stu',90),
('Aaron','Stu',70),
('Aaron','Stu',110),
('Aaron','Stu',105);
SELECT doctor,
       patient,
       AVG(bxd-prev_data)
 FROM
(SELECT doctor,
       patient,
       bought_x_days_ago AS bxd,
       LEAD(bought_x_days_ago) /*using LEAD*/
             OVER (PARTITION BY doctor, patient 
                    ORDER BY bought_x_days_ago DESC) AS prev_data
  FROM                        /*with ORDER BY in descending*/
    mytable) v
 WHERE prev_data IS NOT NULL
 GROUP BY doctor,
          patient


doctor
patient
AVG(bxd-prev_data)


Aaron
Jeff
10.0000

Aaron
Stu
13.3333

Jess
Jason
15.0000


SELECT doctor,
       patient,
       AVG(bxd-prev_data)
 FROM
(SELECT doctor,
       patient,
       bought_x_days_ago AS bxd,
       LAG(bought_x_days_ago) /*using LAG*/
             OVER (PARTITION BY doctor, patient 
                    ORDER BY bought_x_days_ago) AS prev_data
  FROM                     /*with ORDER BY in ascending (default)*/
    mytable) v
 WHERE prev_data IS NOT NULL
 GROUP BY doctor,
          patient


doctor
patient
AVG(bxd-prev_data)


Aaron
Jeff
10.0000

Aaron
Stu
13.3333

Jess
Jason
15.0000