Producing an adjusted Kaplan Meier with a risk table and confidence intervals, and log-rank

[Ashar Asif]

I'm struggling with producing a KM curve with its corresponding 95% CIs and risk table when I'm adjusting for a variable. Here is my data:

* Example generated by -dataex-. For more info, type help dataex
clear
input byte(No Genderm1 Age) int _intervention_date byte Calcification int length_calc byte lengthgrade int circ_calc byte(calcgrade interaction RIP) int(Timetodeath M)
 1 0 77 20598 1   0 1 150 2 3 0 2871 23469
 2 1 56 20517 1  10 1  60 1 1 1   22     .
 3 1 84 20033 1  45 1 220 3 5 1 3140     .
 4 0 70 20144 1   2 1  10 1 1 1  652     .
 6 1 73 20977 1  30 1 130 2 3 1  403     .
 7 1 74 21125 1   1 1 285 4 7 1 1677     .
 8 0 66 20116 0   0 0   0 0 0 1  107     .
 9 0 67 20518 0   0 0   0 0 0 1  107     .
10 0 73 21321 1   5 1  60 1 1 1  957     .
11 0 78 18738 1  40 1  40 1 1 1  556     .
12 1 58 20142 0   0 0   0 0 0 1 1453     .
13 0 76 22308 1   5 1  35 1 1 0 1161 23469
14 0 82 20957 1  10 1 360 4 7 1 1682     .
15 0 68 22650 1  80 2 290 4 8 0  819 23469
16 0 58 21210 0   0 0   0 0 0 1 1174     .
17 0 60 21676 0   0 0   0 0 0 1 1162     .
18 0 74 22242 1  10 1  70 1 1 0 1227 23469
19 1 76 20986 1  10 1  50 1 1 1  501     .
20 1 73 20430 1   5 1  45 1 1 1  668     .
21 0 58 19186 1  50 2 120 2 4 1  375     .
22 1 81 19775 1 120 2 360 4 8 1  105     .
23 1 46 18472 0   0 0   0 0 0 1 2494     .
24 0 70 18993 1   1 1 210 3 5 1 1062     .
25 0 70 18993 1   1 1 230 3 5 1 1062     .
26 1 65 21628 0   0 0   0 0 0 1  755     .
27 1 66 22133 0   0 0   0 0 0 1  250     .
28 0 69 21474 0   0 0   0 0 0 0 1995 23469
29 1 49 20161 0   0 0   0 0 0 0 3308 23469
30 0 82 22791 1   1 1 290 4 7 1  142     .
31 1 72 21663 1  40 1  65 1 1 0 1806 23469
32 0 69 20908 1  30 1 320 4 7 1  643     .
33 1 62 19073 0   0 0   0 0 0 0 4089 23469
34 0 52 20611 0   0 0   0 0 0 0 2858 23469
35 0 51 20966 0   0 0   0 0 0 0 2503 23469
36 0 67 21055 0   0 0   0 0 0 0 1798 23469
37 0 54 21151 0   0 0   0 0 0 0 2318 23469
38 0 54 19977 0   0 0   0 0 0 1  262     .
39 0 76 21805 1   1 1  60 1 1 1 1411     .
40 0 55 20341 0   0 0   0 0 0 0 1766 23469
41 1 67 21487 0   0 0   0 0 0 1   11     .
42 1 78 20866 1  10 1 190 3 5 1 1232     .
43 1 51 21759 0   0 0   0 0 0 0 1710 23469
44 1 51 21759 0   0 0   0 0 0 0 1710 23469
45 0 62 20241 0   0 0   0 0 0 0  475 23469
46 0 61 22580 1  15 1  85 1 1 0  889 23469
47 0 70 21375 0   0 0   0 0 0 0 1589 23469
48 0 87 21898 1   4 1 190 3 5 1    2     .
49 0 89 21047 1  56 2 360 4 8 1   36     .
50 0 92 22552 1   7 1  70 1 1 0  917 23469
51 0 62 21578 1   4 1  65 1 1 1 1119     .
52 0 62 21578 0   0 0   0 0 0 1 1119     .
53 0 79 20523 0   0 0   0 0 0 0 2582 23469
54 0 68 22644 0   0 0   0 0 0 0  825 23469
55 1 53 22245 0   0 0   0 0 0 0  805 23469
56 0 50 18961 0   0 0   0 0 0 1 1880     .
57 0 50 18961 0   0 0   0 0 0 1 1880     .
58 0 51 21851 0   0 0   0 0 0 0 1618 23469
59 1 66 21649 1   4 1  60 1 1 0 1820 23469
60 1 66 21655 1   2 1  25 1 1 0 1814 23469
61 1 54 20152 0   0 0   0 0 0 1    6     .
62 1 59 18872 0   0 0   0 0 0 1 2236     .
63 1 74 19625 1  55 2 360 4 8 1 2888     .
64 1 74 19625 1  15 1 250 3 5 1 2888     .
65 0 76 20548 1  17 1 360 4 7 1 2070     .
66 0 50 20242 0   0 0   0 0 0 0 1938 23469
67 0 75 20794 1  17 1 360 4 7 1  374     .
68 0 76 20838 1  25 1 185 3 5 0 2631 23469
69 0 77 20978 1   1 1 135 2 3 0 2491 23469
70 0 48 21875 0   0 0   0 0 0 0  700 23469
72 1 66 20969 1  25 1 320 4 7 0 2500 23469
73 1 67 22257 1  35 1 275 4 7 1  654     .
74 0 65 21187 0   0 0   0 0 0 0  541 23469
75 0 83 22166 1   4 1 240 3 5 1   46     .
76 1 37 22630 1   4 1  60 1 1 1  233     .
77 0 63 19845 0   0 0   0 0 0 0 3624 23469
78 0 74 21641 1  18 1 180 2 3 0 1828 23469
79 1 72 21405 0   0 0   0 0 0 0 2064 23469
94 0 70 22977 1  10 1 360 4 7 0  492 23469
95 1 58 22902 0   0 0   0 0 0 0  567 23469
end
format %tdnn/dd/CCYY _intervention_date
format %tdnn/dd/CCYY M

I am investigating the effects of calcification of arteries on outcomes following intervention. The sample are grossly categorised by "Calcification" status- 1= calcified, 0= non calcified. I measured both the length ("length_calc" in mm) and circumference ("circl_calc" in degrees) of the calcification. Given the small sample size, I converted them from continuous to categorical variables- "lengthgrade"- 0= no calcification, 1= <50mm, 2= >=50mm, and "calcgrade" 0= none, 1= 1-90 degrees, 2=91-180 degrees, 181-270 degrees, 271-360 degrees.

On Stata, I define the endpoint with the following:

 stset Timetodeath, failure(RIP==1)

I create the following KM curve:

with this code:

 sts graph, by(Calcification) risktable ci

I created an interaction term with the length and circumference of calcium ("lengthgrade#calcgrade") as they would be linked with the extent of calcification. I try to create a KM curve with a risk table and confidence intervals like above, however I'm returned with the following:

 sts graph, strata(Calcification) adjustfor(lengthgrade#calcgrade) risktable ci

      

options adjustfor() and ci may not be combined
r(198);

The only KM I can produce is like this (i.e. without a risk table or confidence intervals):

I've tried to manually produce an interaction term between length and circumference in then "interaction" column; a scale of 0-8 which is a combination of lengthgrade and calcgrade. Again, I'm unable to create a KM curve with a risk table and confidence interval, only a "plain" KM curve:

with the following code:

sts graph, by(Calcification) adjustfor(interaction)

As you can see, this KM curve is very similar to the first one.

1. Which curve is "correctly" adjusting for an interaction term- 2 or 3? They are very different despite adjusting for, I think (I may be wrong here!), the same variable
2. How can I create an adjusted KM curve that has a risk table and confidence intervals like curve 1?
3. The red lines on the KM curves all drop down to 0, implying that 100% of calcified patients have died at a certain point- which is not true. As you can see, 14 calcified patients did not die- many of which have survived for a long period. Why do the red lines drop to 0- is this something to do with interval-censoring? Is there a way to fix this? If this is something that needs fixing.
   • Subsequently are these KMs "correct"?

Many thanks!

[Ashar Asif]

Similarly, I can easily perform a logrank test for the unadjusted model:

sts test Calcification, logrank

However, if I try to adjust with the following:

sts test Calcification, strata(lengthgrade#calcgrade) logrank

I am returned with

interactions not allowed
(error in option strata())
r(101);

sts test Calcification, strata(interaction) logrank

seems to work, however, given the antics with this "interaction" variable with the KM curve, I'm not convinced that it accurately represents the interaction between length and circumference in degrees (however, I could be wrong!)