You say "missing year" but do not show any "missing" values for year. Do you mean a year out of sequence?
This would likely be a lot easier if the year and dates were actually numeric and dates an not character values as then you could use something like Proc Summary with the dates after inserting a grouping variable.
This duplicates your desired output.
data Have;
length ID $3 Year $ 4 Program $ 15 Course $ 5 Start $ 10 End $ 10;
infile datalines delimiter='' missover dsd;
input ID $ Year : $char4. Program : $char15. Course : $char5. Start : $char10. End : $char10.;
datalines;
100 2016 AutoMechanics A 2016-11-03 2017-04-20
100 2018 AutoMechanics B 2018-09-07 2019-04-20
100 2018 AutoMechanics C 2018-10-15 2019-06-25
100 2019 AutoMechanics D 2019-10-17 2020-01-20
100 2020 AutoMechanics E 2020-08-27 2020-09-15
;
run;
data need;
set have;
by id year;
Retain ordergroup;
yeardif = dif(year);
if first.id then ordergroup=1;
if yeardif>1 then ordergroup+1;
drop yeardif;
run;
proc sql;
create table want as
select a.*,b.min_start,b.max_end
from need as a left join
(select id,ordergroup,min(start) as min_start, max(end) as max_end
from need
group by id, ordergroup
) as b
on a.id=b.id
and a.ordergroup=b.ordergroup
;
quit;
Examples with only one set of "groups" such as Id and Program are poor examples as I do not know if ID is unique for Program or not.
Also, bad things come to people who insist on storing dates as character values. None of the SAS functions or formats that work with dates will work with characters meaning that much work may be needed to get actual dates before most types of valid comparisons, intervals or grouping is done.
