Determine Days Since Last Visit

Question

I think I may be overthinking this problem.
What I have is a table that consists of membership data including visit dates. For each visit date, I need to determine the number of days since the last visit.
I'm trying a combination of CTEs and partitions, but it is simply not coalescing in my head.
Following is a sample set of data;
KeyID          MemberID          AdmitDate          Last_Admit_Days
1                 2601                 2014-04-17         
2                 2001                 2014-05-04         
3                 1001                 2014-05-15         
4                 8001                 2014-05-28         
5                 2601                 2014-05-23         
6                 2601                 2014-05-28         
7                 9301                 2014-03-21         
8                 9301                 2014-05-15         
9                 9301                 2014-05-21         
10                8601                2014-05-26         
11                3601                2014-04-13         
12                3601                2014-05-05
I tried putting that in as a code block, but it ended up putting everything on one line.
Anyway, Member # 2601 has three admit dates; 2014-04-17, 2014-05-23 and 2014-05-28. So, the number in the Last_Admit_Days column for those records, should be the DATEDIFF in days between the AdmitDate and the AdmitDate of the immediately prior AdmitDate
for #2601, like this;
KeyID          MemberID          AdmitDate          Last_Admit_Days
1                 2601                 2014-04-17         
0
5                 2601                 2014-05-23         
36
6                 2601                 2014-05-28         
5
I am stumped. Maybe the weekend will refresh me to take a better stab at it, but it's confounding me at the moment and I thought I'd ask here to see if anyone had a quick idea off the top of their heads.
I truly appreciate any assistance.
Thanx!

Answer 1

Please post DDL, so that people do not have to guess what the keys, constraints, Declarative Referential Integrity, data types, etc. in your schema are. Learn how to follow ISO-11179 data element naming conventions and formatting rules. Temporal data should
use ISO-8601 formats. Code should be in Standard SQL as much as possible and not local dialect. 
This is minimal polite behavior on SQL forums. There is no such crap as a“key_id” in RDBMS; that night mare is mix of meta-data and attribute proprieties.
CREATE TABLE Visits
(member_id CHAR(4)NOT NULL,
admission_date DATE NOT NULL,
PRIMARY KEY(member_id,admission_date));
INSERT INTO Visits
VALUES
('2601','2014-04-17'),
('2001','2014-05-04'),
('1001','2014-05-15'),
('8001','2014-05-28'),
('2601','2014-05-23'),
('2601','2014-05-28),
('9301','2014-03-21'),
('9301','2014-05-15'),
('9301','2014-05-21'),
('8601','2014-05-26'),
('3601','2014-04-13'),
('3601','2014-05-05');
SELECT member_id, admission_date,
       DATEDIFF(DAY,
            LAG(admission_date)
            OVER(PARTITION BY member_id
                 ORDER BY admission_date),
             admission_date)
       AS visit_delta
  FROM Visits
  ORDER BY member_id, admission_date;
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