Join two tables by MRN and date1 >= MAX(date2) - sql-server

Question

I need to combine the data from two hospital activity reports. What happens is this: Patients get admitted to a spinal department. Some of whom then get referred to put on ventilation. After a while patient is discharged. Later, the same patient may or may not get re-referred back to the spinal department and may or may not be re-referred for ventilation. I am sent activity data in two reports:
Monthly Activity Report:
[MRN] [NHS Number] [Admission Date] [DoB] [Blah] [Blah]
Ventilation Report
[MRN] [Admission Date] [Ventilation Days] [Ventilation Type] [blah] [blah]
N.B. The Admission Date on the Ventilation Report is the date they are referred for ventilation. This may be the same day, or some date after they are referred into spinal dept.
What I need to achieve is this: join each row to the most immediate entry prior to the patient being referred to ventilation. I need to avoid duplicating rows, but I cannot join it to the most recent row in the Monthly Activity Report as this could easily be a subsequent referral and the other information will not be applicable.
By following the answer to a similar question on Stackoverflow, I came up with this code:
SELECT [Year], [Month], MRN, [NHS Number], [Admission Date] AS [VD
Admission Date],
[Admit date] AS [MAR Admit Date], Days,
[Ventilation Type], [Ventilation Route], [Ventilation Time], [Package of
care class],
[Para/Tetra/No deficit], [Social charge date commenced ] AS [Social charge
date], [Discharge date]
FROM Spinal_Costing.Vented_Days VD
LEFT JOIN (SELECT *, ROW_NUMBER() OVER(PARTITION BY [Patient MRN] ORDER BY
[Admit Date] DESC) AS row
FROM Spinal_Costing.MAR
) MAR ON VD.MRN = MAR.[Patient MRN]
WHERE MAR.row = 1;
But this returns the most recent entry in MAR for each patient.

Answer 1

This can also be achieved with an apply that references the values in Vented_Days and simply returns a top 1 for each row. cross apply won't return null values whereas outer apply will:
declare #vd table(MRN int,AdmissionDate date);
declare #mar table(MRN int,AdmissionDate date);
insert into #vd values
(1,'20190102')
,(1,'20190106')
,(2,'20190104')
,(3,'20190101');
insert into #mar values
(1,'20190101')
,(1,'20190105')
,(2,'20190102');
select v.MRN
,v.AdmissionDate
,m.AdmissionDate
from #vd as v
outer apply (select top 1 m.AdmissionDate
from #mar as m
where v.MRN = m.MRN
and v.AdmissionDate >= m.AdmissionDate
order by m.AdmissionDate desc
) as m
order by v.MRN
,v.AdmissionDate;
Output
+-----+---------------+---------------+
| MRN | AdmissionDate | AdmissionDate |
+-----+---------------+---------------+
| 1 | 2019-01-02 | 2019-01-01 |
| 1 | 2019-01-06 | 2019-01-05 |
| 2 | 2019-01-04 | 2019-01-02 |
| 3 | 2019-01-01 | NULL |
+-----+---------------+---------------+

Answer 2

You were on the right track, you just need to add a JOIN to that derived table to limit the rows in the Spinal_Costing.MAR table to those that came at, or before discharge.
SELECT
[Year],
[Month],
MRN,
[NHS Number],
[Admission Date] AS [VD Admission Date],
[Admit date] AS [MAR Admit Date],
Days,
[Ventilation Type],
[Ventilation Route],
[Ventilation Time],
[Package of care class],
[Para/Tetra/No deficit],
[Social charge date commenced ] AS [Social charge date],
[Discharge date]
FROM
Spinal_Costing.Vented_Days VD
LEFT JOIN
(SELECT
*,
ROW_NUMBER() OVER(PARTITION BY [Patient MRN] ORDER BY [Admit Date] DESC) AS row
FROM Spinal_Costing.MAR
--added the JOIN and WHERE clause here
INNER JOIN Spinal_Costing.Vented_Days
ON Spinal_Costing.Vented_Days.MRN = Spinal_Costing.MAR.[Patient MRN]
WHERE Spinal_Costing.MAR.[Admit Date] <= Spinal_Costing.Vented_Days.[Discharge date]
) MAR ON VD.MRN = MAR.[Patient MRN]
WHERE MAR.row = 1;