Exercise $3.$ The following data sets contain BMI measurements for the baseline, $3$ months, and $9$ months, for the intervention and control group patients.

data int;

input ID$ GROUP$ BMI$\_$base BMI$\_3$mos BMI$\_9$mos;

cards;

$101$ int $34\mathrm{.}533\mathrm{.}831\mathrm{.}1$

$102$ int $30\mathrm{.}729\mathrm{.}627\mathrm{.}3$

$103$ int $32\mathrm{.}030\mathrm{.}727\mathrm{.}5$

$105$ int $34\mathrm{.}633\mathrm{.}533\mathrm{.}3$

$106$ int $37\mathrm{.}634\mathrm{.}930\mathrm{.}1$

$107$ int $30\mathrm{.}229\mathrm{.}228\mathrm{.}7$

$108$ int $37\mathrm{.}236\mathrm{.}035\mathrm{.}1$

$109$ int $35\mathrm{.}233\mathrm{.}333\mathrm{.}7$

$111$ int $32\mathrm{.}331\mathrm{.}429\mathrm{.}4$

;

data cnt;

input ID$ GROUP$ BMI$\_$base BMI$\_3$mos BMI$\_9$mos;

cards;

$401$ cnt $33\mathrm{.}733\mathrm{.}433\mathrm{.}2$

$402$ cnt $31\mathrm{.}230\mathrm{.}129\mathrm{.}8$

$404$ cnt $30\mathrm{.}831\mathrm{.}131\mathrm{.}8$

$406$ cnt $29\mathrm{.}229\mathrm{.}028\mathrm{.}9$

$408$ cnt $27\mathrm{.}727\mathrm{.}327\mathrm{.}9$

$409$ cnt $33\mathrm{.}832\mathrm{.}931\mathrm{.}4$

;

$($a$)$ Concatenate the data sets and compute the change in BMI between the baseline and $9$ months. Your output should look like this:

Obs ID GROUP BMI$\_$base BMI$\_3$mos BMI$\_9$mos BMI$\_$change

$1101$ int $34\mathrm{.}533\mathrm{.}831\mathrm{.}1-3\mathrm{.}4$

$2102$ int $30\mathrm{.}729\mathrm{.}627\mathrm{.}3-3\mathrm{.}4$

$3103$ int $32\mathrm{.}030\mathrm{.}727\mathrm{.}5-4\mathrm{.}5$

$4105$ int $34\mathrm{.}633\mathrm{.}533\mathrm{.}3-1\mathrm{.}3$

$5106$ int $37\mathrm{.}634\mathrm{.}930\mathrm{.}1-7\mathrm{.}5$

$6107$ int $30\mathrm{.}229\mathrm{.}228\mathrm{.}7-1\mathrm{.}5$

$7108$ int $37\mathrm{.}236\mathrm{.}035\mathrm{.}1-2\mathrm{.}1$

$8109$ int $35\mathrm{.}233\mathrm{.}333\mathrm{.}7-1\mathrm{.}5$

$9111$ int $32\mathrm{.}331\mathrm{.}429\mathrm{.}4-2\mathrm{.}9$

$10401$ cnt $33\mathrm{.}733\mathrm{.}433\mathrm{.}2-0\mathrm{.}5$

$11402$ cnt $31\mathrm{.}230\mathrm{.}129\mathrm{.}8-1\mathrm{.}4$

$12404$ cnt $30\mathrm{.}831\mathrm{.}131\mathrm{.}81\mathrm{.}0$

$13406$ cnt $29\mathrm{.}229\mathrm{.}028\mathrm{.}9-0\mathrm{.}3$

$14408$ cnt $27\mathrm{.}727\mathrm{.}327\mathrm{.}90\mathrm{.}2$

$15409$ cnt $33\mathrm{.}832\mathrm{.}931\mathrm{.}4-2\mathrm{.}4$

$($b$)$ Remove the intervention group patients whose BMI decreased by less than $3$ points and also the control group patients whose BMI increased over time. Your output should look like this:

Obs ID GROUP BMI$\_$base BMI$\_3$mos BMI$\_9$mos

$1101$ int $34\mathrm{.}533\mathrm{.}831\mathrm{.}1$

$2102$ int $30\mathrm{.}729\mathrm{.}627\mathrm{.}3$

$3103$ int $32\mathrm{.}030\mathrm{.}727\mathrm{.}5$

$4106$ int $37\mathrm{.}634\mathrm{.}930\mathrm{.}1$

$5401$ cnt $33\mathrm{.}733\mathrm{.}433\mathrm{.}2$

$6402$ cnt $31\mathrm{.}230\mathrm{.}129\mathrm{.}8$

$7406$ cnt $29\mathrm{.}229\mathrm{.}028\mathrm{.}9$

$8409$ cnt $33\mathrm{.}832\mathrm{.}931\mathrm{.}4$