# Untied time data → Tied

(Not completed yet)

The codes used in this tutorial are available below.
rs.surv
stns, stpp, strs, stnet

This example showed how the relative survival estimates change given more and more ties are added into the data.

### Dataset

The dataset (scenario2_1.dta) is a simulated data, containing 1000 subjects. The original survival time is untied data with 651 distinct values in years (min: 0.0027; max: 12). We then added ties into the data by flooring the time into discrete days, weeks, months, quaters, or years. More ties are added (i.e., less distinct values) as the time interval becomes larger (days→years). If any survival time became 0 due to flooring, we then made it 0.5 of the time interval (e.g., 0.5 months).

The following table shows how the time was treated in different units.

Time variable Discrete time in Stata code Distinct values
tt1 Original continuous time 651
tt2 Days (floor(tt1*365.241) + 0.5) /365.241 569
tt3 Weeks (floor(tt1*52.177) + 0.5) /52.177 332
tt4 Months (floor(tt1*12) + 0.5) /12 132
tt5 Quarters (floor(tt1*4) + 0.5) /4 49
tt6 Years (floor(tt1) + 0.5) 13

### Relative survival estimates

The following tables show the estimates of 1-, 5-, and 10-year relative survival (RS) using the Pohar-Perme estimator by rs.surv, stpp, strs, and stnet. To make the tables look tidier, here we dismissed the 95% CI, which however can be found in the outputs of the syntax.

#### rs.surv()

Time
(year)
tt1
original
tt2
days
tt3
weeks
tt4
months
tt5
quarters
tt6
years
1 0.797 0.797 0.797 0.790 0.796 0.788
5 0.618 0.618 0.618 0.618 0.617 0.613
10 0.534 0.534 0.534 0.536 0.535 0.529

#### stns

Time
(year)
tt1
original
tt2
days
tt3
weeks
tt4
months
tt5
quarters
tt6
years
1 0.797 0.797 0.796 0.790 0.777 0.711
5 0.613 0.613 0.613 0.614 0.604 0.600
10 0.512 0.512 0.512 0.514 0.513 0.510

#### stpp

Time
(year)
tt1
original
tt2
days
tt3
weeks
tt4
months
tt5
quarters
tt6
years
1 0.797 0.797 0.796 0.790 0.777 0.709
5 0.613 0.613 0.613 0.613 0.603 0.595
10 0.512 0.512 0.512 0.509 0.502 0.484

#### strs

Time
(year)
tt1
original
tt2
days
tt3
weeks
tt4
months
tt5
quarters
tt6
years
1 0.798 0.797 0.795 0.792 0.778 0.732
5 0.612 0.612 0.612 0.616 0.605 0.617
10 0.513 0.513 0.513 0.512 0.505 0.506

#### stnet

Time
(year)
tt1
original
tt2
days
tt3
weeks
tt4
months
tt5
quarters
tt6
years
1 0.798 0.797 0.795 0.798 0.798 0.799
5 0.612 0.612 0.612 0.612 0.613 0.614
10 0.513 0.513 0.513 0.513 0.513 0.514

### Explanation

• Generally, introducing ties into the data did not change the esitmates of relative survival no matter which package was used for calculation in this case. One exception happened if discrete time was made into years (tt6), which merely 13 distinct values exist, rs.surv() and strs gave slightly lower estimates for 1-year relative survival (0.788 and 0.732 separately); stns and stpp gave much lower survival, particularly in 1-year net survival; surprisingly, the output estimated by stnetalmost did not change given heavy ties were added.
• One thing we should bear in mind is that introducing ties to the data has in fact changed the original data. I tried to add ties in a sensible way and not to change the order of the data as much as possible. However, I am innocent of the lower or higher estimates rs.surv(), stns, stpp, and strs gave.

### Conclusion

• It is common that the data from cancer register has tied time, e.g., due to protection on patients' privacy. As estimating survival, we should pay attention to the potential change on the estimates given the amount of tie is introduced.