Thanks to Kit Baum there is a new package -tteir- on the SSC
Description
The command tteir is a wrapper for the use of stset, stsplit, and collapse as described in sections 4.3 to 4.5 in Royston and Lambert (2011) to prepare time-to-event datasets for poisson regressions with piecewise constant incidence rates. A piecewise constant incidence rate for an interval can be interpreted as the average hazard rate for that same interval. The main idea is to get a minimal but sufficient dataset for analysis.
Examples
The command tteir generates
five variables summarizing the original dataset:
The list is a summary of number of events and total follow-up time for each group.
Instead of the Kaplan-Meyer failure curve,
one can use the tteir command and the predicted incidence rates from the post estimation of the poisson regression
to get a piece-wice constant Nelson-Aalen failure curve, i.e., the cummulative incidence rates
The simplest way to compare is to use (if installed) addplot
To reproduce a cox regression like
can be done simple by
To handle non-proportional hazards or time-dependent effects is simple
Visualizing the time-dependent effects by BMI groups on CHD
To secure better estimates, it would often be better to chose that events are evenly distributed into the time intervals. Here 5 intervals are chosen.
Or one can chose intervals with a minimum number of 20 events in each interval.
Description
The command tteir is a wrapper for the use of stset, stsplit, and collapse as described in sections 4.3 to 4.5 in Royston and Lambert (2011) to prepare time-to-event datasets for poisson regressions with piecewise constant incidence rates. A piecewise constant incidence rate for an interval can be interpreted as the average hazard rate for that same interval. The main idea is to get a minimal but sufficient dataset for analysis.
Examples
The command tteir generates
Code:
. webuse diet, clear . tteir dox, failure(fail) origin(time doe) scale(365.25) at(0(2)18)
Code:
. list
+--------------------------------------------+
| _start _stop _total _x _futm |
|--------------------------------------------|
1. | 0 2 337 8 665.775 |
2. | 2 4 329 9 649.929 |
3. | 4 6 319 14 618.721 |
4. | 6 8 302 10 594.716 |
5. | 8 10 292 7 566.991 |
|--------------------------------------------|
6. | 10 12 269 13 491.916 |
7. | 12 14 220 7 414.802 |
8. | 14 16 199 7 361.907 |
9. | 16 18 144 5 177.780 |
10. | 18 20.041068 44 0 61.131 |
+--------------------------------------------+
Instead of the Kaplan-Meyer failure curve,
Code:
. webuse diet, clear . stset dox, failure(fail) origin(time doe) scale(365.25) id(id) . sts graph, by(hienergy) failure name(km, replace)
Code:
. tteir dox, failure(fail) origin(time doe) scale(365.25) at(0(2)18) by(hienergy) . qui poisson _x bn._start#i.hienergy, irr exposure(_futm) nocons vce(robust) . predict ir, it . format ir %6.4f
Code:
. generate dt = _stop - _start . bysort hienergy (_stop): generate cir = 1 - exp(-sum(ir*dt)) . format cir %6.4f
Code:
. addplot km: (line cir _stop if !hienergy,sort) (line cir _stop if hienergy,sort)
To reproduce a cox regression like
Code:
. webuse diet, clear
. stset dox, failure(fail) origin(time doe) scale(365.25) id(id)
. stcox i.hienergy
Failure _d: fail
Analysis time _t: (dox-origin)/365.25
Origin: time doe
ID variable: id
Iteration 0: log likelihood = -442.59555
Iteration 1: log likelihood = -441.65468
Iteration 2: log likelihood = -441.65462
Refining estimates:
Iteration 0: log likelihood = -441.65462
Cox regression with no ties
No. of subjects = 337 Number of obs = 337
No. of failures = 80
Time at risk = 4,603.6687
LR chi2(1) = 1.88
Log likelihood = -441.65462 Prob > chi2 = 0.1701
------------------------------------------------------------------------------
_t | Haz. ratio Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
1.hienergy | 0.736 0.165 -1.37 0.17 0.474 1.141
------------------------------------------------------------------------------
Code:
. tteir dox, failure(fail) origin(time doe) scale(365.25) every(.) by(hienergy)
. qui poisson _x bn._start i.hienergy, irr exposure(_futm) nocons vce(robust)
. lincom _b[1.hienergy], eform
( 1) [_x]1.hienergy = 0
------------------------------------------------------------------------------
_x | exp(b) Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | 0.736 0.117 -1.93 0.05 0.539 1.004
------------------------------------------------------------------------------
Code:
. webuse diet, clear . generate bmi = weight / height / height * 10000 . egen bmi_grp = cut(bmi), at(15 18.5 25 30 200) label . tteir dox, failure(fail) origin(time dob) enter(time doe) scale(365.25) id(id) at(30(10)70) by(bmi_grp) . qui poisson _x i.bmi_grp#bn._start, irr exposure(_futm) nocons vce(robust)
Code:
. quietly margins _start#bmi_grp, predict(ir)
. marginsplot, xtitle(Age (years)) title("") ytitle("Incidence rates and 95% CI")
To secure better estimates, it would often be better to chose that events are evenly distributed into the time intervals. Here 5 intervals are chosen.
Code:
. webuse diet, clear . tteir dox, failure(fail) origin(time doe) scale(365.25) nintervals(5) . list, sep(0) noobs +------------------------------------------------+ | _start _stop _total _x _futm | |------------------------------------------------| | 0 3.5687885 337 16 1178.097 | | 3.5687885 6.2642026 320 16 836.090 | | 6.2642026 9.9794661 301 16 1076.422 | | 9.9794661 12.583162 269 16 622.070 | | 12.583162 20.041068 209 16 890.990 | +------------------------------------------------+
Code:
. webuse diet, clear . tteir dox, failure(fail) origin(time doe) scale(365.25) mininterval(20) . list, sep(0) noobs +------------------------------------------------+ | _start _stop _total _x _futm | |------------------------------------------------| | 0 4.4147844 337 20 1447.696 | | 4.4147844 7.8097194 316 20 1025.819 | | 7.8097194 11.868583 293 20 1085.313 | | 11.868583 20.041068 225 20 1044.841 | +------------------------------------------------+
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