Demography and epidemiology: Practical use of the Lexis diagram ...

10 Example: Renal failure data.
Th phrase “age (at entry) is controlled for” in a Cox model often means that the
(log)linear effect of age (at entry or current) is included along with an arbitrary effect of
time since entry. No consideration neither qualitatively nor quantitatively has been given
to wheather a non-linear effect of age at entry and/or current age would be reasonable.
If “controlling for age at entry” is done by entering age at entry as a categorized
covariate or parametric function of some sort, the effect of current age is still assumed
only linear on the log-rate scale. Introducing a non-linear effect for the last time-scale
will open the well known can of worms: The age-period-cohort parametrization
problems, as mentioned above.
Example: Renal failure data.
As an example we shall consider an extension of the analysis of time to death among
diabetic patients with nephrotic range albuminuria (NRA), i.e. a U-albumin excretion
exceeding 300 mg/24h, as reported in [3].
The data base for this analysis is illustrated in the Lexis diagrams in figure 3. The
results from the paper’s table 3 are shown here in table 1.
There is clearly a linear effect of age at entry (or current age), but the analysis
presented does not address the question of whether there are non-linear effects of the
two time-scales.
Table 1: Results from a traditional Cox-analysis with remission as time-dependent covariate,
as reported in Hovind et al. (2004), table 4.
Remission
Total Yes No
No. patients 125 32 93
No. events 77 8 69
Follow-up time (years) 1084.7 259.9 824.8
Cox-model:
time-scale: Time since nephrotic range albuminuria (NRA)
Entry: 2.5 years of GFR-measurements after NRA
Outcome: ESRD or Death
Estimates: RR 95% c.i. p
Fixed covariates:
Sex (F vs. M): 0.92 (0.53,1.57) 0.740
Age at NRA (per 10 years): 1.42 (1.08,1.87) 0.011
Time-dependent covariate:
Obtained remission: 0.28 (0.13,0.59) 0.001