Basic Statistics

21 0 INTRODUCTION TO SURVIVAL ANALYSIS

Table 14.1 Patient Data for a Clinical Life Table

Patient Days Status Patient Days Status Patient Days Status

1 2 3 4 5 6 7 8 9

10

11

12

13

14

21 1

39 1

77 1

133 1

141 2

152 1

153 1

161 1

179 1

184 1

197 1

199 1

214 1

228 1

15

16

17

18

19

20

21

22

23

24

25

26

27

28

256

260

26 1

266

269

287

295

308

311

321

326

355

361

374

2 29

1 30

1 31

1 32

1 33

3 34

1 35

1 36

1 37

2 38

1 39

1 40

1

1

398

414

420

468

483

489

505

539

5 65

618

193

794

1 1 1 2 1 1 1 1 3 1 1 1

Table 14.2 Computations for a Clinical Life Table

Interval nent c nexp d ?j 3(t) j(t) L(t)

.O to < .5 40 1 39.5 8 ,203 .797 1.000 .406 451

.5 to <1.0 31 3 29.5 15 .508 ,492 .797 ,810 1.364

1.0to <1.5 13 1 12.5 8 .640 .360 .392 .502 1.882

1.5 to <2.0 1 .5 1 ,286 ,714 .141 .081 667

2.0 to <2.5 0 .O 2 1.000 ,000 .lo1 ,202 4.000

The remaining columns in the clinical life table are obtained by performing cal-
culations on the columns previously filled in. The column labeled nexp gives the
number exposed to risk. It is computed as

If there are no censored patients, the number exposed to risk is the number entering the
interval. If there is censoring, it is assumed that the censoring occurs evenly distributed
throughout the interval. Thus, on average, the censored patients are assumed to be
censored from the study for one-half of the total interval. Hence, the number censored
in each interval is divided by 2 in estimating the number exposed to risk. The number
exposed to risk decreases in a clinical life table with successive intervals as long as at
least one patient dies or is censored. For the first interval, nexp = 40 - 112 = 39.5
since one patient is censored. For the second interval, neXp = 31 - 312 = 29.5, and
so on. Note in the last row or two of Table 14.2 that very few patients are left in the
sample. The estimates obtained from the final row may be quite variable.
In survival analysis, the number of patients exposed to risk decreases as patients
either die or are censored. In Table 4.5, all the percents or proportions are computed