How can I, in T-SQL, examine date intervals to remove overlapping intervals before adding totals together - date

Question

I am running an analysis on medication prescribing practices. We want to identify whether someone has been on a class of medications for 60 days out of a 90 day quarter. We have a start and end date for each prescription, and the bounds of the quarter (e.g., 4/1/2022 – 6/30/2022). For each prescription I’ve calculated the number of days between the start and end date (only including days that fall within the bounds of the quarter). There are many instances in which multiple drugs within the same class are prescribed someone might try one antidepressant but not like it, so be given another in the same class.
My original strategy was just to total up number of days for each class of medication and see if it’s 60 or over. The days don’t have to be consecutive, but if they overlap, days during an overlap period shouldn’t count twice (which they would in a simple sum).
For instance in the data table below, patient 1 in row 1 should be included as they are over 60 days. Patient 2 should also get in (rows 2 and 3) because the non-overlapping total (57+8) within the same med class gets them to over 60 days. However, patient 3 should NOT get in, even though the total of 32 + 32 is over 60 because the intervals overlap. This means that they were really on the medication class for only 32 days – this is an instance where someone might be on two different antidepressants simultaneously.
It’s not sufficient to just sum the days in the interval, but I also have to include some way to examine whether the intervals are overlapping and only add days if an interval for a given medication class falls outside another interval for that same class.
Row num Patid Med class Start date End date Interval
1 1 A 2022-04-28 2022-09-12 63
2 2 B 2022-05-03 2022-06-29 57
3 2 B 2022-04-21 2022-04-29 8
4 3 A 2022-01-19 2022-05-03 32
5 3 A 2022-01-19 2022-05-03 32
I’m having a hard time figuring out how to do this. Note, I'm limited to just using SQL for this.
Code that produced the above data. I would embed this in another query to generate a total interval but need to deal with the overlap issue.
DECLARE #startdt DATE;
DECLARE #enddt DATE;
SET #startdt='4/1/2022'
SET #enddt='6/30/2022'
--for q4 fy2022-23 (4/1/2022-6/30/2022)`
SELECT DISTINCT
rx.patid, d.medication_category as medcat, start_date, end_date,
-- case statement to capture days within quarter only
CASE WHEN start_date<#startdt and end_date>#enddt then 90
WHEN start_date<#startdt and end_date>=#startdt then datediff(d,#startdt,end_date)
WHEN start_date>=#startdt and end_date>#enddt then datediff(d,start_date,#enddt)
ELSE datediff(d,start_date,end_date)
END as interval
FROM rx
INNER JOIN Drug_names_categories d
ON rx.drugname=d.drugname
WHERE start_date<'7/1/2022' and end_date>'3/30/2022'
AND rx.patid IS NOT NULL
AND d.medication_category IS NOT NULL
AND d.medication_category <>''

Answer 1

You can accomplish what you want by generating a calendar table (using a Common Table Expression) of individual days within the test range, joining those days with the prescriptions with overlapping days, and then counting distinct days for each patient and medication category combination.
Something like:
DECLARE #startdt DATE = '2022-04-01';
DECLARE #enddt DATE = '2022-06-30';
DECLARE #threshold INT = 60;
WITH Days AS (
SELECT #startdt AS Day
UNION ALL
SELECT DATEADD(day, 1, Day)
FROM Days
WHERE Day < #enddt
)
SELECT
rx.patid, d.medication_category as medcat,
COUNT(DISTINCT DD.Day) AS days_medicated,
MIN(DD.Day) AS start_date,
MAX(DD.Day) AS end_date
FROM rx
INNER JOIN Drug_names_categories d
ON rx.drugname = d.drugname
INNER JOIN Days DD
ON DD.Day BETWEEN rx.start_date AND rx.end_date
WHERE rx.start_date <= #enddt AND #startdt <= rx.end_date
GROUP BY rx.patid, d.medication_category
HAVING COUNT(DISTINCT DD.Day) >= #threshold
ORDER BY rx.patid, start_date;
If using SQL Server 2022 or later, the Days generator can be simplified by using the new GENERATE_SERIES() function:
WITH Days AS (
SELECT DATEADD(day, S.value, #startdt) AS Day
FROM GENERATE_SERIES(0, DATEDIFF(day, #Startdt, #enddt)) S
)
See this db<>fiddle for an example with some sample data.

Answer 2

I would do this using a date/calendar table, then it's pretty easy.
If you don't already have a date table, this link is one of many that describe how to create one easily ( https://www.mssqltips.com/sqlservertip/4054/creating-a-date-dimension-or-calendar-table-in-sql-server/ )
Here's the script from this link (in case the link dies)
DECLARE #StartDate date = '20100101';
DECLARE #CutoffDate date = DATEADD(DAY, -1, DATEADD(YEAR, 30, #StartDate));
;WITH seq(n) AS
(
SELECT 0 UNION ALL SELECT n + 1 FROM seq
WHERE n < DATEDIFF(DAY, #StartDate, #CutoffDate)
),
d(d) AS
(
SELECT DATEADD(DAY, n, #StartDate) FROM seq
),
src AS
(
SELECT
TheDate = CONVERT(date, d),
TheDay = DATEPART(DAY, d),
TheDayName = DATENAME(WEEKDAY, d),
TheWeek = DATEPART(WEEK, d),
TheISOWeek = DATEPART(ISO_WEEK, d),
TheDayOfWeek = DATEPART(WEEKDAY, d),
TheMonth = DATEPART(MONTH, d),
TheMonthName = DATENAME(MONTH, d),
TheQuarter = DATEPART(Quarter, d),
TheYear = DATEPART(YEAR, d),
TheFirstOfMonth = DATEFROMPARTS(YEAR(d), MONTH(d), 1),
TheLastOfYear = DATEFROMPARTS(YEAR(d), 12, 31),
TheDayOfYear = DATEPART(DAYOFYEAR, d)
FROM d
)
SELECT *
INTO MyDateTable
FROM src
ORDER BY TheDate
OPTION (MAXRECURSION 0);
No that you have your new date table you can join to it to get the list of dates that are within the start and end date, something like
SELECT DISTINCT COUNT(TheDate)
FROM rx
INNER JOIN MyDateTable dt on dt BETWEEN rx.start_date AND rx.end_date
INNER JOIN Drug_names_categories d ON rx.drugname=d.drugname
WHERE start_date<'7/1/2022' and end_date>'3/30/2022'
AND rx.patid IS NOT NULL
AND d.medication_category IS NOT NULL
AND d.medication_category <>''
Obviously this is simple example but you could extend this easily to include all the details you need, the point is that you now have a list of dates or distinct list of dates which you can work with easily.
You could also simply the date range applied by referencing the TheQuarter and TheYear columns. If this is a common task consider extending the date table to contain a comound YearQurater columns (e.g. 2023Q1/202301 etc)