continuous enrollment with gap

[lillymaginta]

data test;
input id$2. start  end ;
attrib start format =date9. informat=date9.;
attrib end format =date9. informat=date9.;
datalines;
1 01JAN2015 14FEB2015
1 18FEB2015 30APR2015
1 05MAY2015 30AUG2015
2 01jan2015 28feb2015
2 01apr2015 30apr2015
3 01JAN2015 14FEB2015
3 15FEB2015 15MAR2015
3 20MAR2015 30APR2015
4 01JAN2015 31JAN2015
4 01JAN2015 15APR2015
;
run;

I want to create a database with continuous enrollment allowing a gap of 7 days between the end of one period and the start of the next one. I want to keep one period per id reflecting only the first period 

Output 

1 01JAN2015  30AUG2015
2 01jan2015 28feb2015
3 15FEB2015 30APR2015
4 01JAN2015 15APR2015

[MarkWik]

You want to keep one period per id reflecting only the first period 

Then what is this?

3 01JAN2015 14FEB2015

3 15FEB2015 30APR2015

[lillymaginta]

Sorry the error was corrected

[Tom]

Does you data ever include overlapping periods? Or nested periods?  If so that makes the problem a little harder.

[lillymaginta]

Yes, I do have overlapping or nested periods. 

[Ksharp · Accepted solution]

data test;
input id$2. start  end ;
attrib start format =date9. informat=date9.;
attrib end format =date9. informat=date9.;
datalines;
1 01JAN2015 14FEB2015
1 18FEB2015 30APR2015
1 05MAY2015 30AUG2015
2 01jan2015 28feb2015
2 01apr2015 30apr2015
3 01JAN2015 14FEB2015
3 15FEB2015 15MAR2015
3 20MAR2015 30APR2015
4 01JAN2015 31JAN2015
4 01JAN2015 15APR2015
;
run;
data temp;
 set test;
 by id;
 if start-lag(end)>7 or first.id then group+1;
run;
data temp;
 do until(last.group);
  set temp(rename=(start=_start));
  by id group;
  if first.group then start=_start;
 end;
 format start date9.;
drop _start group;
run;
data want;
 set temp;
 by id;
 if first.id;
run;

[lillymaginta]

Thank you @Ksharp, you are the best!