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

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14 7 Stratified models 7 Stratified models A stratified Cox-model is a model where the underlying hazard is allowed to differ between strata, i.e. the effect of time varies across the levels of a categorical variable. Thus this is merely an interaction between time and a categorical variable. If a spline basis has been chosen as model for the time variable, a model with separate baseline hazards for each level of a factor F this is easily modelled by saying: # Simple model with splines modeling time-effects, proportional hazards # m1
Practical use of the Lexis diagram 15 Time since diagnosis 30 20 10 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 ● 1970 1980 1990 2000 ● ● Calendar time ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● Time since diagnosis 30 20 10 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 ● 1970 1980 1990 2000 ● ● Calendar time ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Figure 5: Lexis diagrams illustrating follow-up of cancer patients. Period analysis suggest to use only the follow-up in the box on the left panel. A stratified model or interaction model assumes different mortality pattern by time since diagnosis in each of the boxes in the right panel. In this case we would even have time-varying strata! success. In the 1980s it was effectively the only possibility; the use of Poisson models for datasets with 10000+ observations was out of the question in practical analyses due to lack of computing power. An entire generation of statisticians have learnt to think in terms of one time scale and was never exposed to the demographic way of looking at individual-based follow-up studies. The demographic thinking was restricted to tabulated data from cancer registries and the like, and the intimate connection between the two is still not widely recognized, particularly in the epidemiological community. A drawback of the Cox-model is the overly detailed modelling of survival curves that may lead to over-interpretation of little humps and notches on the survival curve. When stratification or time-dependent variables are involved, the facilities in the standard Cox-analysis programs limits the ways in which the desired interactions can be modelled, and moreover distracts the user from realizing that other interactions between covariates may be of interest. Thus it seems that the Cox-model is useful in the following cases: • Clinical follow-up studies with only one relevant timescale and the focus on the effect of other covariates than time. • Studies where a pathologically detailed modelling of one time-scale is desired. • Studies analysed on computing equipment pre-1985. In other settings it seems preferable to split time and use the Poisson approach, because it: • Clarifies the distinction between (risk) time as response variable and time(scales) as covariates. ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●
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