data bone_marrow;
input g t1 t2 dind rind dfree ta aind tc cind tp pind age dage sex dsex cmv dcmv wait fab
hosp mtx;
label g = "Disease Group"
t1 = "Time To Death Or On Study Time"
T2 = "Disease Free Survial Time"
dind = "Death indicator"
rind = "Relapse indicator"
dfree = "Disease Free Survial"
ta = "Time to Acute GVHD"
aind = "Acute GVHD indicator"
tc = "Time to chronic GVHD"
cind = "Chronic GVHD indicator"
tp = "Time to normal Platelets"
pind = "Platelet Recovery Indicator"
age = "Patient Age"
dage = "Donor Age"
sex = "Patient sex"
dsex = "Donor Sex"
cmv = "Patient CMV Status"
dcmv = "Donor CMV"
wait = "Waiting time: days"
fab = "FAB"
hosp = "Hospital"
mtx = "MTX";
datalines;
1 2081 2081 0 0 0 67 1 121 1 13 1 26 33 1 0 1 1 98 0 1 0
1 1602 1602 0 0 0 1602 0 139 1 18 1 21 37 1 1 0 0 1720 0 1 0
1 1496 1496 0 0 0 1496 0 307 1 12 1 26 35 1 1 1 0 127 0 1 0
1 1462 1462 0 0 0 70 1 95 1 13 1 17 21 0 1 0 0 168 0 1 0
1 1433 1433 0 0 0 1433 0 236 1 12 1 32 36 1 1 1 1 93 0 1 0
1 1377 1377 0 0 0 1377 0 123 1 12 1 22 31 1 1 1 1 2187 0 1 0
1 1330 1330 0 0 0 1330 0 96 1 17 1 20 17 1 0 1 1 1006 0 1 0
1 996 996 0 0 0 72 1 121 1 12 1 22 24 1 0 0 0 1319 0 1 0
1 226 226 0 0 0 226 0 226 0 10 1 18 21 0 1 0 0 208 0 1 0
1 1199 1199 0 0 0 1199 0 91 1 29 1 24 40 1 1 0 1 174 0 3 1
1 1111 1111 0 0 0 1111 0 1111 0 22 1 19 28 1 1 0 1 236 0 3 1
1 530 530 0 0 0 38 1 84 1 34 1 17 28 1 1 0 0 151 0 3 1
1 1182 1182 0 0 0 1182 0 112 1 22 1 24 23 0 0 0 1 203 0 2 1
1 1167 1167 0 0 0 39 1 487 1 1167 0 27 22 0 1 1 1 191 0 2 1
1 418 418 1 0 1 418 0 220 1 21 1 18 14 1 1 0 0 110 0 1 0
1 417 383 1 1 1 417 0 417 0 16 1 15 20 1 1 0 0 824 0 1 0
1 276 276 1 0 1 276 0 81 1 21 1 18 5 0 0 0 0 146 0 1 0
1 156 104 1 1 1 28 1 156 0 20 1 20 33 1 1 0 1 85 0 1 0
1 781 609 1 1 1 781 0 781 0 26 1 27 27 1 0 1 1 187 0 1 0
1 172 172 1 0 1 22 1 172 0 37 1 40 37 0 0 0 1 129 0 1 0
1 487 487 1 0 1 487 0 76 1 22 1 22 20 1 1 0 0 128 0 1 0
1 716 662 1 1 1 716 0 716 0 17 1 28 32 1 1 0 0 84 0 1 0
1 194 194 1 0 1 194 0 94 1 25 1 26 32 0 1 0 0 329 0 1 0
1 371 230 1 1 1 371 0 184 1 9 1 39 31 0 1 0 1 147 0 1 0
1 526 526 1 0 1 526 0 121 1 11 1 15 20 1 1 0 0 943 0 1 0
1 122 122 1 0 1 88 1 122 0 13 1 20 26 1 0 0 1 2616 0 1 0
1 1279 129 1 1 1 1279 0 1279 0 22 1 17 20 0 0 0 0 937 0 3 1
1 110 74 1 1 1 110 0 110 0 49 1 28 25 1 0 1 0 303 0 3 1
1 243 122 1 1 1 243 0 243 0 23 1 37 38 0 1 1 1 170 0 3 1
1 86 86 1 0 1 86 0 86 0 86 0 17 26 1 0 1 0 239 0 3 1
1 466 466 1 0 1 466 0 119 1 100 1 15 18 1 1 0 0 508 0 3 1
1 262 192 1 1 1 10 1 84 1 59 1 29 32 1 1 1 0 74 0 3 1
1 162 109 1 1 1 162 0 162 0 40 1 36 43 1 1 1 0 393 0 2 1
1 262 55 1 1 1 262 0 262 0 24 1 23 16 0 1 1 1 331 0 2 1
1 1 1 1 0 1 1 0 1 0 1 0 42 48 1 1 0 0 196 0 2 1
1 107 107 1 0 1 107 0 107 0 107 0 30 19 1 1 1 1 178 0 2 1
1 269 110 1 1 1 269 0 120 1 27 1 29 20 0 1 1 1 361 0 2 1
1 350 332 1 0 1 350 0 350 0 33 1 22 20 1 0 0 0 834 0 2 1
2 2569 2569 0 0 0 2569 0 2569 0 21 1 19 13 1 1 1 0 270 1 1 0
2 2506 2506 0 0 0 2506 0 2506 0 17 1 31 34 1 1 0 0 60 0 1 0
2 2409 2409 0 0 0 2409 0 2409 0 16 1 35 31 1 1 1 1 120 0 1 0
2 2218 2218 0 0 0 2218 0 2218 0 11 1 16 16 1 1 1 0 60 1 1 0
2 1857 1857 0 0 0 1857 0 260 1 15 1 29 35 0 0 1 0 90 0 1 0
2 1829 1829 0 0 0 1829 0 1829 0 19 1 19 18 1 1 1 0 210 0 1 0
2 1562 1562 0 0 0 1562 0 1562 0 18 1 26 30 1 1 1 1 90 0 1 0
2 1470 1470 0 0 0 1470 0 180 1 14 1 27 34 1 1 0 1 240 0 1 0
2 1363 1363 0 0 0 1363 0 200 1 12 1 13 24 1 1 1 0 90 0 1 0
2 1030 1030 0 0 0 1030 0 210 1 14 1 25 29 0 0 0 0 210 0 1 0
2 860 860 0 0 0 860 0 860 0 15 1 25 31 0 1 0 1 180 0 1 0
2 1258 1258 0 0 0 1258 0 120 1 66 1 30 16 0 1 1 0 180 0 2 1
2 2246 2246 0 0 0 52 1 380 1 15 1 45 39 0 0 0 0 105 0 4 0
2 1870 1870 0 0 0 1870 0 230 1 16 1 33 30 0 0 1 1 225 0 4 0
2 1799 1799 0 0 0 1799 0 140 1 12 1 32 23 1 0 0 0 120 0 4 0
2 1709 1709 0 0 0 20 1 348 1 19 1 23 28 0 1 1 0 90 1 4 0
2 1674 1674 0 0 0 1674 0 1674 0 24 1 37 34 1 1 0 0 60 1 4 0
2 1568 1568 0 0 0 1568 0 1568 0 14 1 15 19 1 0 0 0 90 0 4 0
2 1527 1527 0 0 0 1527 0 1527 0 13 1 22 12 0 1 0 1 450 1 4 0
2 1324 1324 0 0 0 25 1 1324 0 15 1 46 31 1 1 1 1 75 0 4 0
2 957 957 0 0 0 957 0 957 0 69 1 18 17 1 1 0 0 90 0 4 0
2 932 932 0 0 0 29 1 932 0 7 1 27 30 0 0 0 0 60 1 4 0
2 847 847 0 0 0 847 0 847 0 16 1 28 29 1 1 0 0 75 0 4 0
2 848 848 0 0 0 848 0 155 1 16 1 23 26 1 1 0 0 180 0 4 0
2 1850 1850 0 0 0 1850 0 1850 0 9 1 37 36 0 0 0 1 180 0 3 1
2 1843 1843 0 0 0 1843 0 1843 0 19 1 34 32 0 0 1 1 270 0 3 1
2 1535 1535 0 0 0 1535 0 1535 0 21 1 35 32 0 1 0 0 180 1 3 1
2 1447 1447 0 0 0 1447 0 220 1 24 1 33 28 0 1 1 1 150 0 3 1
2 1384 1384 0 0 0 1384 0 200 1 19 1 21 18 0 0 0 0 120 0 3 1
2 414 414 1 0 1 414 0 414 0 27 1 21 15 1 1 0 1 120 1 1 0
2 2204 2204 1 0 1 2204 0 2204 0 12 1 25 19 0 0 0 1 60 0 1 0
2 1063 1063 1 0 1 1063 0 240 1 16 1 50 38 1 0 1 0 270 1 1 0
2 481 481 1 0 1 30 1 120 1 24 1 35 36 1 0 1 1 90 1 1 0
2 105 105 1 0 1 21 1 105 0 15 1 37 34 1 0 1 1 120 0 1 0
2 641 641 1 0 1 641 0 641 0 11 1 26 24 1 1 0 0 90 0 1 0
2 390 390 1 0 1 390 0 390 0 11 1 50 48 1 1 0 0 120 0 1 0
2 288 288 1 0 1 18 1 100 1 288 0 45 43 1 1 1 1 90 0 1 0
2 522 421 1 1 1 25 1 140 1 20 1 28 30 1 1 0 1 90 1 1 0
2 79 79 1 0 1 16 1 79 0 79 0 43 43 0 0 0 0 90 0 1 0
2 1156 748 1 1 1 1156 0 180 1 18 1 14 19 1 0 0 0 60 0 1 0
2 583 486 1 1 1 583 0 583 0 11 1 17 14 0 1 0 0 120 0 1 0
2 48 48 1 0 1 48 0 48 0 14 1 32 33 0 1 1 0 150 1 1 0
2 431 272 1 1 1 431 0 431 0 12 1 30 23 0 1 1 0 120 1 1 0
2 1074 1074 1 0 1 1074 0 120 1 19 1 30 32 1 1 1 0 150 1 1 0
2 393 381 1 1 1 393 0 100 1 16 1 33 28 0 0 0 0 120 1 1 0
2 10 10 1 0 1 10 0 10 0 10 0 34 54 1 0 1 1 240 0 2 1
2 53 53 1 0 1 53 0 53 0 53 0 33 41 0 1 1 1 180 0 2 1
2 80 80 1 0 1 10 1 80 0 80 0 30 35 0 0 0 1 150 0 2 1
2 35 35 1 0 1 35 0 35 0 35 0 23 25 0 1 1 1 150 0 2 1
2 1499 248 0 1 1 1499 0 1499 0 9 1 35 18 1 1 0 1 30 0 4 0
2 704 704 1 0 1 36 1 155 1 18 1 29 21 0 1 1 0 105 0 4 0
2 653 211 1 1 1 653 0 653 0 23 1 23 16 1 0 0 0 90 1 4 0
2 222 219 1 1 1 222 0 123 1 52 1 28 30 1 1 1 1 120 1 3 1
2 1356 606 0 1 1 1356 0 1356 0 14 1 33 22 1 1 1 0 210 1 3 1
3 2640 2640 0 0 0 2640 0 2640 0 22 1 18 23 1 1 0 0 750 0 1 0
3 2430 2430 0 0 0 2430 0 2430 0 14 1 29 26 1 1 0 1 24 0 1 0
3 2252 2252 0 0 0 2252 0 150 1 17 1 35 31 1 0 0 0 120 0 1 0
3 2140 2140 0 0 0 2140 0 220 1 18 1 27 17 1 1 1 1 210 0 1 0
3 2133 2133 0 0 0 2133 0 250 1 17 1 36 39 0 1 0 0 240 0 1 0
3 1238 1238 0 0 0 1238 0 250 1 18 1 24 28 1 0 1 1 240 0 1 0
3 1631 1631 0 0 0 1631 0 150 1 40 1 27 21 1 0 1 0 690 1 2 1
3 2024 2024 0 0 0 2024 0 180 1 16 1 35 41 0 1 0 0 105 1 4 0
3 1345 1345 0 0 0 32 1 360 1 14 1 50 36 1 1 1 1 120 0 4 0
3 1136 1136 0 0 0 1136 0 140 1 15 1 47 27 1 0 1 0 900 0 3 1
3 845 845 0 0 0 845 0 845 0 20 1 40 39 0 0 1 1 210 1 3 1
3 491 422 1 1 1 491 0 180 1 491 0 22 21 0 0 0 0 210 1 1 0
3 162 162 1 0 1 162 0 162 0 13 1 22 23 1 0 0 1 300 0 1 0
3 1298 84 1 1 1 1298 0 1298 0 1298 0 8 2 0 0 1 0 105 1 1 0
3 121 100 1 1 1 28 1 121 0 65 1 39 48 1 1 1 1 210 1 1 0
3 2 2 1 0 1 2 0 2 0 2 0 20 19 1 1 0 0 75 1 1 0
3 62 47 1 1 1 62 0 62 0 11 1 27 25 1 1 0 0 90 1 1 0
3 265 242 1 1 1 265 0 210 1 14 1 32 32 1 0 0 0 180 1 1 0
3 547 456 1 1 1 547 0 130 1 24 1 31 28 1 0 1 1 630 1 1 0
3 341 268 1 1 1 21 1 100 1 17 1 20 23 0 1 1 1 180 1 1 0
3 318 318 1 0 1 318 0 140 1 12 1 35 40 0 1 1 1 300 0 1 0
3 195 32 1 1 1 195 0 195 0 16 1 36 39 1 1 0 0 90 1 1 0
3 469 467 1 1 1 469 0 90 1 20 1 35 33 0 0 1 0 120 0 1 0
3 93 47 1 1 1 93 0 93 0 28 1 7 2 1 1 0 0 135 1 1 0
3 515 390 1 1 1 515 0 515 0 31 1 23 25 1 1 1 0 210 1 1 0
3 183 183 1 0 1 183 0 130 1 21 1 11 7 0 1 0 0 120 1 1 0
3 105 105 1 0 1 105 0 105 0 105 0 14 18 1 0 0 0 150 1 1 0
3 128 115 1 1 1 128 0 128 0 12 1 37 35 0 0 1 1 270 0 1 0
3 164 164 1 0 1 164 0 164 0 164 0 19 32 0 0 0 1 285 1 1 0
3 129 93 1 1 1 129 0 129 0 51 1 37 34 0 1 1 0 240 1 1 0
3 122 120 1 1 1 122 0 122 0 12 1 25 29 0 1 1 1 510 1 1 0
3 80 80 1 0 1 21 1 80 0 0 1 35 28 1 0 0 0 780 1 1 0
3 677 677 1 0 1 677 0 150 1 8 1 15 14 1 1 1 0 150 1 1 0
3 73 64 1 1 1 73 0 73 0 38 1 45 42 0 1 1 0 180 1 2 1
3 168 168 1 0 1 168 0 200 1 48 1 32 43 0 1 1 1 150 1 2 1
3 74 74 1 0 1 29 1 74 0 24 1 41 29 0 1 1 1 750 0 2 1
3 16 16 1 0 1 16 0 16 0 16 0 27 36 0 0 1 0 180 0 4 0
3 248 157 1 1 1 248 0 100 1 52 1 33 39 0 0 1 1 180 1 4 0
3 732 625 1 1 1 732 0 732 0 18 1 39 43 0 1 1 1 150 1 4 0
3 105 48 1 1 1 105 0 105 0 30 1 17 14 0 1 0 0 210 1 4 0
3 392 273 1 1 1 392 0 122 1 24 1 43 50 1 1 1 0 240 0 3 1
3 63 63 1 0 1 38 1 63 0 16 1 44 37 1 1 0 0 360 1 3 1
3 97 76 1 1 1 97 0 97 0 97 0 48 56 1 1 1 1 330 0 3 1
3 153 113 1 1 1 153 0 153 0 59 1 31 25 0 1 1 1 240 0 3 1
3 363 363 1 0 1 363 0 363 0 19 1 52 48 1 1 1 0 180 0 3 1
;
run;
proc format;
VALUE g 1 = "ALL"
2 = "AML Low Risk"
3 = "AML High Risk" ;
value dind 0 = "Alive"
1 = "Dead";
value rind 0 = "Disease Free"
1 = "Relapsed";
value dfree 0 = "Alive Disease Free"
1 = "Dead or Relapsed";
value aind 0 = "Never Developed Acute GVHD"
1 = "Developed Acute GVHD";
value cind 0 = "Never Developed Chronic GVHD"
1 = "Developed Chronic GVHD";
value pind 0 = "Platelet Never Returned to Normal"
1 = "Returned to Normal";
value sex 0 = "Female"
1 = "Male";
value dsex 0 = "Female"
1 = "Male";
value cmv 0 = "CMV Negative"
1 = "CMV Positive";
value dcmv 0 = "CMV Negative"
1 = "CMV Positive";
value fab 0 = "Otherwise"
1 = "FAB Grade 4 or 5 and AML";
value hosp 1 = "Ohio State Univ"
2 = "Alferd"
3 = "St. Vincent"
4 = "Hahnemann";
value mtx 0 = "No"
1 = "Yes";
/********************************************************************************/
/* 4.2a */
/* Estimate the survival functions and their standard errors */
proc sql;
create table raw_data as
select t1, t2, sum(dfree) as num_event, count(t2) as sub_total
from bone_marrow
where g = 2
group by t2;
quit;
data table4_2a;
set raw_data nobs=all;
total1 = lag(sub_total);
retain num_left 54; /*We have 54 obs in AML low group*/
if _n_ > 1 then do;
num_left = - total1 + num_left; end;
retain surv 1 delta 0;
/*Product-Limit Estimator of Survival Function*/
surv = surv*(1-(num_event/num_left));
/*Variance of Product-Limit Estimator (Greenwoods Formula)*/
delta= delta + num_event/(num_left*(num_left-num_event));
var =(surv**2)*delta;
stderr = var**.5;
keep t1 t2 num_left num_event surv stderr ;
if num_event~=0 or _n_ = all;
run;
proc print data=table4_2a noobs;
var t2 num_left num_event surv stderr;
title1 '4.2 A';
title2 'Estimated Survival Functions and their Standard Errors for AML low risk';
run;
/********************************************************************************/
/* 4.2b */
/* Estimated cumulative hazard rates and their standard errors for AML low risk */
data table4_2b;
set raw_data nobs=all;
total1 = lag(sub_total);
retain num_left 54;
if _n_ > 1 then do;
num_left = - total1 + num_left; end;
retain surv 1 delta h sigma2 0;
surv = surv*(1-num_event/num_left);
delta= delta + num_event/(num_left*(num_left-num_event));
var =(surv**2)*delta;
stderr = var**.5;
/*Nelson-Aalen estimator of cumulative hazard*/
H = H + num_event / num_left;
/*Estimated variance of the Nelson-Aalen Estimator*/
sigma2 = sigma2 + num_event /(num_left)**2;
stderrh = sigma2**.5;
keep t1 num_left num_event h stderrh;
if num_event~=0 or _n_ = all;
run;
proc print data=table4_2b noobs;
var t1 num_left num_event H stderrh ;
title1 '4.2 B';
title2 'Estimated Cumulative Hazard Rates and their Standard Errors for AML Low Risk';
run;
/********************************************************************************/
/* 4.2 C */
/* Provide a crude estimate fof the hazard rates for AML Low Risk based on the estimates obtained in b */
data table4_2c;
set raw_data nobs=all;
total1 = lag(sub_total);
retain num_left 54;
if _n_ > 1 then do;
num_left = - total1 + num_left; end;
retain surv 1 delta h sigma2 0;
surv = surv*(1-num_event/num_left);
delta= delta + num_event/(num_left*(num_left-num_event));
var =(surv**2)*delta;
stderr = var**.5;
/*Nelson-Aalen estimator of cumulative hazard*/
H = H + num_event / num_left;
/* Crude estimate of hazard rate is slope of Nelson-Aalen estimate
OR change in cumulative hazard/change in time*/
t1_0 = lag(t1);
H_0 = lag(H);
h_rate= (H-H_0)/(t1-t1_0);
if t1=10 then h_rate=(H/t1);
keep t1 num_left num_event h h_rate;
if num_event~=0 or _n_ = all;
run;
proc print data=table4_2c noobs;
var t1 num_left num_event H h_rate ;
title1 '4.2 C';
title2 'Crude Estimate for the Hazard Rate AML Low Risk';
run;
/********************************************************************************/
/* 4.2 D */
/* Estimate the mean time to death and find 95% confidence intervals for the mean survival time for AML low risk */
/* Calculations for Survival Function & Variance */
data work4_2d;
set raw_data nobs = all;
total1 = lag(sub_total);
retain num_left 54;
if _n_ > 1 then do;
num_left = num_left - total1; end;
retain surv 1 delta H sigma2 0;
surv = surv*(1-num_event/num_left);
delta= delta + num_event/(num_left*(num_left-num_event));
var =(surv**2)*delta;
stderr = sqrt(var);
if num_event~=0 or _n_ = all;
keep t2 surv num_event num_left;
run;
/* Note our greatest obs time is t1=2569 */
proc sort data=work4_2d;
by t2 descending t2;
run;
data table4_2d;
set work4_2d nobs = last;
lagt = lag(t2);
if _n_ = 1 then
med = surv*(2569 - t2);
else med = surv*(lagt- t2); output;
if _n_ =last then do; med = 10; output; end;
run;
data table4_2d;
set table4_2d nobs=last;
retain sumd vmean 0 ;
sumd = sumd + med;
vmean = vmean + ( sumd**2 ) * num_event/(num_left*(num_left-num_event));
if _n_ =last then vmean=sqrt(vmean);
run;
proc print data=table4_2d;
run;
data table4_2d;
set table4_2d nobs=last;
if _n_ =last then do;
se_mean = vmean;
clow = sumd - 1.96*se_mean;
chigh = sumd + 1.96*se_mean;
end;
if _n_ ~= last then delete;
run;
proc print data = table4_2d noobs ;
var sumd se_mean clow chigh;
title1 '4.2 D';
title2 'Estimate of the Mean Time to Death & 95% Confidence Intervals for the Mean Survival Time for AML Low Risk';
run;
/********************************************************************************/
/* 4.2 E */
/* Work out estimates of the median time to death and find 95% confidence intervals for the median survival time */
/* t2=2204 sumd=1263.27 vmean=126132.00 */
data table4_2e;
/*From table 4.2a*/
t2=2240;
sumd_med=1263.27;
se_med=sqrt(126132);
clow = sumd_med - 1.96*se_med;
chigh = sumd_med + 1.96*se_med;
run;
proc print data = table4_2e noobs;
var sumd_med se_med clow chigh;
title1 '4.2 E';
title2 'Estimate of the Median Time to Death & 95% Confidence Intervals for the Median Survival Time for AML Low Risk';
run;
proc print data=table4_2a;
run;
PROC LIFEREG DATA = table4_2a ;
MODEL t2*surv(0)= / DIST=exponential COVB ;
OUTPUT OUT=myq Q=0.75 TO 0.95 BY .10 P=qest STD=se ;
RUN ;
DATA out;
SET myq ;
loci = qest - 1.96 * se ;
hici = qest + 1.96 * se ;
RUN ;
PROC PRINT DATA=out ;
VAR t2 _PROB_ loci hici ;
RUN ;
## 4.2 A
## Estimated Survival Functions and their Standard Errors for AML low risk
##
## num_
## t2 num_left event surv stderr
##
## 10 54 1 0.98148 0.01835
## 35 53 1 0.96296 0.02570
## 48 52 1 0.94444 0.03117
## 53 51 1 0.92593 0.03564
## 79 50 1 0.90741 0.03945
## 80 49 1 0.88889 0.04277
## 105 48 1 0.87037 0.04571
## 211 47 1 0.85185 0.04834
## 219 46 1 0.83333 0.05072
## 248 45 1 0.81481 0.05286
## 272 44 1 0.79630 0.05481
## 288 43 1 0.77778 0.05658
## 381 42 1 0.75926 0.05818
## 390 41 1 0.74074 0.05964
## 414 40 1 0.72222 0.06095
## 421 39 1 0.70370 0.06214
## 481 38 1 0.68519 0.06320
## 486 37 1 0.66667 0.06415
## 606 36 1 0.64815 0.06499
## 641 35 1 0.62963 0.06571
## 704 34 1 0.61111 0.06634
## 748 33 1 0.59259 0.06686
## 1063 26 1 0.56980 0.06807
## 1074 25 1 0.54701 0.06905
## 2204 6 1 0.45584 0.10118
## 2569 1 0 0.45584 0.10118
##
##
##
## 4.2 B
## Estimated Cumulative Hazard Rates and their Standard Errors for AML Low Risk
##
## num_
## t1 num_left event h stderrh
##
## 10 54 1 0.01852 0.01852
## 35 53 1 0.03739 0.02644
## 48 52 1 0.05662 0.03269
## 53 51 1 0.07623 0.03812
## 79 50 1 0.09623 0.04305
## 80 49 1 0.11663 0.04764
## 105 48 1 0.13747 0.05200
## 653 47 1 0.15874 0.05618
## 222 46 1 0.18048 0.06024
## 1499 45 1 0.20270 0.06421
## 431 44 1 0.22543 0.06811
## 288 43 1 0.24869 0.07197
## 393 42 1 0.27250 0.07581
## 390 41 1 0.29689 0.07964
## 414 40 1 0.32189 0.08347
## 522 39 1 0.34753 0.08732
## 481 38 1 0.37384 0.09120
## 583 37 1 0.40087 0.09512
## 1356 36 1 0.42865 0.09909
## 641 35 1 0.45722 0.10313
## 704 34 1 0.48663 0.10724
## 1156 33 1 0.51694 0.11144
## 1063 26 1 0.55540 0.11789
## 1074 25 1 0.59540 0.12449
## 2204 6 1 0.76206 0.20803
## 2569 1 0 0.76206 0.20803
##
##
##
## 4.2 C
## Crude Estimate for the Hazard Rate AML Low Risk
##
## num_
## t1 num_left event h h_rate
##
## 10 54 1 0.01852 0.001852
## 35 53 1 0.03739 0.000755
## 48 52 1 0.05662 0.001479
## 53 51 1 0.07623 0.003922
## 79 50 1 0.09623 0.000769
## 80 49 1 0.11663 0.020408
## 105 48 1 0.13747 0.000833
## 653 47 1 0.15874 0.000039
## 222 46 1 0.18048 -0.000050
## 1499 45 1 0.20270 0.000017
## 431 44 1 0.22543 -0.000021
## 288 43 1 0.24869 -0.000163
## 393 42 1 0.27250 0.000227
## 390 41 1 0.29689 -0.008130
## 414 40 1 0.32189 0.001042
## 522 39 1 0.34753 0.000237
## 481 38 1 0.37384 -0.000642
## 583 37 1 0.40087 0.000265
## 1356 36 1 0.42865 0.000036
## 641 35 1 0.45722 -0.000040
## 704 34 1 0.48663 0.000467
## 1156 33 1 0.51694 0.000067
## 1063 26 1 0.55540 0.001166
## 1074 25 1 0.59540 0.003636
## 2204 6 1 0.76206 0.000499
## 2569 1 0 0.76206 0.000000
##
##
##
## 4.2 C
## Crude Estimate for the Hazard Rate AML Low Risk
##
## num_
## Obs t2 event num_left surv lagt med sumd vmean
##
## 1 10 1 54 0.98148 . 2511.61 2511.61 2204.12
## 2 35 1 53 0.96296 10 -24.07 2487.54 4449.34
## 3 48 1 52 0.94444 35 -12.28 2475.26 6759.64
## 4 53 1 51 0.92593 48 -4.63 2470.63 9153.37
## 5 79 1 50 0.90741 53 -23.59 2447.04 11597.45
## 6 80 1 49 0.88889 79 -0.89 2446.15 14141.51
## 7 105 1 48 0.87037 80 -21.76 2424.39 16746.86
## 8 211 1 47 0.85185 105 -90.30 2334.09 19266.74
## 9 219 1 46 0.83333 211 -6.67 2327.43 21883.61
## 10 248 1 45 0.81481 219 -23.63 2303.80 24564.15
## 11 272 1 44 0.79630 248 -19.11 2284.69 27323.03
## 12 288 1 43 0.77778 272 -12.44 2272.24 30181.87
## 13 381 1 42 0.75926 288 -70.61 2201.63 32996.72
## 14 390 1 41 0.74074 381 -6.67 2194.96 35934.45
## 15 414 1 40 0.72222 390 -17.33 2177.63 38974.23
## 16 421 1 39 0.70370 414 -4.93 2172.70 42159.55
## 17 481 1 38 0.68519 421 -41.11 2131.59 45391.19
## 18 486 1 37 0.66667 481 -3.33 2128.26 48791.71
## 19 606 1 36 0.64815 486 -77.78 2050.48 52128.59
## 20 641 1 35 0.62963 606 -22.04 2028.44 55586.23
## 21 704 1 34 0.61111 641 -38.50 1989.94 59115.53
## 22 748 1 33 0.59259 704 -26.07 1963.87 62767.79
## 23 1063 1 26 0.56980 748 -179.49 1784.38 67666.29
## 24 1074 1 25 0.54701 1063 -6.02 1778.37 72937.27
## 25 2204 1 6 0.45584 1074 -515.10 1263.27 126132.00
## 26 2569 0 1 0.45584 2204 -166.38 1096.88 126132.00
## 27 2569 0 1 0.45584 2204 10.00 1106.88 355.15
##
##
##
## 4.2 D
## Estimate of the Mean Time to Death & 95% Confidence Intervals for the Mean Survival Time for AML Lo
##
## sumd se_mean clow chigh
##
## 1106.88 355.151 410.789 1802.98
##
##
##
## 4.2 E
## Estimate of the Median Time to Death & 95% Confidence Intervals for the Median Survival Time for AM
##
## sumd_med se_med clow chigh
##
## 1263.27 355.151 567.175 1959.37
##
##
##
## 4.2 E
## Estimate of the Median Time to Death & 95% Confidence Intervals for the Median Survival Time for AM
##
## num_
## Obs t1 t2 event num_left surv stderr
##
## 1 10 10 1 54 0.98148 0.01835
## 2 35 35 1 53 0.96296 0.02570
## 3 48 48 1 52 0.94444 0.03117
## 4 53 53 1 51 0.92593 0.03564
## 5 79 79 1 50 0.90741 0.03945
## 6 80 80 1 49 0.88889 0.04277
## 7 105 105 1 48 0.87037 0.04571
## 8 653 211 1 47 0.85185 0.04834
## 9 222 219 1 46 0.83333 0.05072
## 10 1499 248 1 45 0.81481 0.05286
## 11 431 272 1 44 0.79630 0.05481
## 12 288 288 1 43 0.77778 0.05658
## 13 393 381 1 42 0.75926 0.05818
## 14 390 390 1 41 0.74074 0.05964
## 15 414 414 1 40 0.72222 0.06095
## 16 522 421 1 39 0.70370 0.06214
## 17 481 481 1 38 0.68519 0.06320
## 18 583 486 1 37 0.66667 0.06415
## 19 1356 606 1 36 0.64815 0.06499
## 20 641 641 1 35 0.62963 0.06571
## 21 704 704 1 34 0.61111 0.06634
## 22 1156 748 1 33 0.59259 0.06686
## 23 1063 1063 1 26 0.56980 0.06807
## 24 1074 1074 1 25 0.54701 0.06905
## 25 2204 2204 1 6 0.45584 0.10118
## 26 2569 2569 0 1 0.45584 0.10118
##
##
##
## 4.2 E
## Estimate of the Median Time to Death & 95% Confidence Intervals for the Median Survival Time for AM
##
## The LIFEREG Procedure
##
## Model Information
##
## Data Set WORK.TABLE4_2A
## Dependent Variable Log(t2) Disease Free Survial Time
## Censoring Variable surv
## Censoring Value(s) 0
## Number of Observations 26
## Noncensored Values 26
## Right Censored Values 0
## Left Censored Values 0
## Interval Censored Values 0
## Number of Parameters 1
## Name of Distribution Exponential
## Log Likelihood -42.68008057
##
##
## Number of Observations Read 26
## Number of Observations Used 26
##
##
## Parameter Information
##
## Parameter Effect
##
## Intercept Intercept
##
##
## Fit Statistics
##
## -2 Log Likelihood 85.360
## AIC (smaller is better) 87.360
## AICC (smaller is better) 87.527
## BIC (smaller is better) 88.618
##
##
## Fit Statistics (Unlogged Response)
##
## -2 Log Likelihood 378.378
## Exponential AIC (smaller is better) 380.378
## Exponential AICC (smaller is better 380.545
## Exponential BIC (smaller is better) 381.636
##
##
## Algorithm converged.
##
##
## Analysis of Maximum Likelihood Parameter Estimates
##
## Standard 95% Confidence Chi-
## Parameter DF Estimate Error Limits Square Pr > ChiSq
##
## Intercept 1 6.2765 0.1961 5.8921 6.6609 1024.26 <.0001
## Scale 0 1.0000 0.0000 1.0000 1.0000
## Weibull Scale 1 531.9231 104.3187 362.1717 781.2377
## Weibull Shape 0 1.0000 0.0000 1.0000 1.0000
##
##
## Lagrange Multiplier Statistics
##
## Parameter Chi-Square Pr > ChiSq
##
## Scale 0.2681 0.6046
##
##
##
## 4.2 E
## Estimate of the Median Time to Death & 95% Confidence Intervals for the Median Survival Time for AM
##
## Obs t2 _PROB_ loci hici
##
## 1 10 0.75 453.954 1020.85
## 2 10 0.85 621.228 1397.02
## 3 10 0.95 980.978 2206.02
## 4 35 0.75 453.954 1020.85
## 5 35 0.85 621.228 1397.02
## 6 35 0.95 980.978 2206.02
## 7 48 0.75 453.954 1020.85
## 8 48 0.85 621.228 1397.02
## 9 48 0.95 980.978 2206.02
## 10 53 0.75 453.954 1020.85
## 11 53 0.85 621.228 1397.02
## 12 53 0.95 980.978 2206.02
## 13 79 0.75 453.954 1020.85
## 14 79 0.85 621.228 1397.02
## 15 79 0.95 980.978 2206.02
## 16 80 0.75 453.954 1020.85
## 17 80 0.85 621.228 1397.02
## 18 80 0.95 980.978 2206.02
## 19 105 0.75 453.954 1020.85
## 20 105 0.85 621.228 1397.02
## 21 105 0.95 980.978 2206.02
## 22 211 0.75 453.954 1020.85
## 23 211 0.85 621.228 1397.02
## 24 211 0.95 980.978 2206.02
## 25 219 0.75 453.954 1020.85
## 26 219 0.85 621.228 1397.02
## 27 219 0.95 980.978 2206.02
## 28 248 0.75 453.954 1020.85
## 29 248 0.85 621.228 1397.02
## 30 248 0.95 980.978 2206.02
## 31 272 0.75 453.954 1020.85
## 32 272 0.85 621.228 1397.02
## 33 272 0.95 980.978 2206.02
## 34 288 0.75 453.954 1020.85
## 35 288 0.85 621.228 1397.02
## 36 288 0.95 980.978 2206.02
## 37 381 0.75 453.954 1020.85
## 38 381 0.85 621.228 1397.02
## 39 381 0.95 980.978 2206.02
## 40 390 0.75 453.954 1020.85
## 41 390 0.85 621.228 1397.02
## 42 390 0.95 980.978 2206.02
## 43 414 0.75 453.954 1020.85
## 44 414 0.85 621.228 1397.02
## 45 414 0.95 980.978 2206.02
## 46 421 0.75 453.954 1020.85
## 47 421 0.85 621.228 1397.02
## 48 421 0.95 980.978 2206.02
## 49 481 0.75 453.954 1020.85
## 50 481 0.85 621.228 1397.02
## 51 481 0.95 980.978 2206.02
## 52 486 0.75 453.954 1020.85
## 53 486 0.85 621.228 1397.02
## 54 486 0.95 980.978 2206.02
## 55 606 0.75 453.954 1020.85
## 56 606 0.85 621.228 1397.02
## 57 606 0.95 980.978 2206.02
## 58 641 0.75 453.954 1020.85
## 59 641 0.85 621.228 1397.02
## 60 641 0.95 980.978 2206.02
## 61 704 0.75 453.954 1020.85
## 62 704 0.85 621.228 1397.02
## 63 704 0.95 980.978 2206.02
## 64 748 0.75 453.954 1020.85
## 65 748 0.85 621.228 1397.02
## 66 748 0.95 980.978 2206.02
## 67 1063 0.75 453.954 1020.85
## 68 1063 0.85 621.228 1397.02
## 69 1063 0.95 980.978 2206.02
## 70 1074 0.75 453.954 1020.85
## 71 1074 0.85 621.228 1397.02
## 72 1074 0.95 980.978 2206.02
## 73 2204 0.75 453.954 1020.85
## 74 2204 0.85 621.228 1397.02
## 75 2204 0.95 980.978 2206.02
## 76 2569 0.75 453.954 1020.85
## 77 2569 0.85 621.228 1397.02
## 78 2569 0.95 980.978 2206.02