Time trends in the incidence

We limited the study of time trends in the incidence of schizophrenia to persons born between 1954 and 1965 to permit us to reliably identify the age at onset and to allow identical follow-up times for each cohort. Each person was followed from the 16th through 26th birthday. Those born outside Finland or of unknown birthplace were excluded. Patients had to have received the first diagnosis of schizophrenia between their 16th and 26th birthday. However, age at onset was defined as age at the beginning of the first hospitalisation for any psychotic disorder excluding psychotic disorders caused by alcohol or substance abuse, because it is a closer approximation of the time of emergence of first psychotic symptoms than the age at the beginning of first hospitalisation for schizophrenia. In addition, patients for whom disability pension because of schizophrenia had been granted somewhere between their 16th and 26th

birthday and who were hospitalized for any psychotic disorder at that age were also included. Their age at onset was also defined as age at the beginning of the first hospitalisation for any psychotic disorder. Persons who received the first diagnosis of schizophrenia after the 26th or before the 16th birthday were not included in the sample because the available follow-up time was not identical for all cohorts. These patients were identified from the registers and their numbers in each cohort compared to estimate whether their exclusion caused any bias. We also excluded patients with no hospitalizations, because a meaningful age at onset could not be defined. Their numbers allowed us to estimate the proportion of patients treated as outpatients in each cohort.

Age-specific incidences in each cohort and period were first calculated using exact person-years at risk for each cohort. Period refers to the year of onset, and cohort to the year of birth. Age, period, and cohort were each divided into 2-year intervals.

4.5.3.1. Age-period-cohort analysis

Time trends in the incidence of a disease may provide important clues to its aetiology.

The three time factors of interest are age, period (date of diagnosis), and cohort (date of birth), and the analysis method by which the effects of these three factors on incidence is estimated is called age-period-cohort analysis, and is widely used in cancer epidemiology (Holford 1991, McNally et al 1997, Robertson & Boyle 1998). In psychiatric research it has been used to study time trends in the incidence of major depression (Klerman 1988, Wickramaratne 1989) and in suicide rates (Moens et al 1987, Granizo et al 1996), while only one previous study has used the method to assess time trends in the incidence of schizophrenia (Takei et al 1996).

The problem with this method arises because age, period, and cohort are linearly dependent: knowing any two of them, the third can be calculated. For example, if we are currently living in 1999 and we meet a 30-year-old man, we know that he has been born in either 1968 or 1969. This linear dependence means that the linear effects of age, period, and cohort cannot be separated, because there is no unique set of regression parameters. Different methods to overcome this nonidentifiability problem have been

suggested. The only ones that avoid using arbitrary constraints or making strong assumptions about the effects of age or cohort are those that do not attempt to separate the effects of cohort and period on the linear component of the change but only estimate deviations from linearity. We have used one of these methods, that of Clayton and Schifflers. (Clayton & Schifflers 1987, Holford 1991, Robertson & Boyle 1998)

Clayton and Schifflers avoid the nonidentifiability problem by estimating solely the curvature effects of period and cohort, which can be reliably estimated. They introduced the term “drift” to describe the sum of linear cohort and period effects. Drift cannot be partitioned into linear cohort and linear period effects and is therefore not usually reported. After fitting the drift term, the curvature effects of age, cohort and period can be reliably estimated. The underlying model used is the Poisson regression model with standard Poisson assumptions (see 4.5.2.). The effects of age, period, and cohort are assumed to be multiplicative. (Clayton & Schifflers 1987)

Curvature or “non-drift” effects operate in such a way that the relative risks between adjacent cohorts (or periods) are not identical. They are calculated as contrasts between relative risks in adjacent periods or cohorts:

where βi denotes the Poisson regression parameter estimates and i the distinct periods (or cohorts). On the logarithmic scale, these contrasts are second derivatives, βi+1-2 βi+ βi-1. Although there are also other methods to calculate the curvature effects, these second derivatives have the advantage that their value is affected only by neighbouring data. (Clayton & Schifflers 1987)

Besides age, period, and cohort, the Poisson regression model used in this study included as explanatory variables sex and seasonal variation of births. Seasonal variation of monthly number of births was modelled using the method of Jones et al,

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which allows an arbitrary shape for the seasonal effect by representing the data as a short Fourier series (Jones et al 1988). Only the first harmonic was found significant, and was entered into the main model as “seasonality”. The model included all main effects and all two-variable interactions involving sex. The significance of each explanatory variable, after adjusting for the effect of other variables, was assessed by comparing the full age-period model with one including all other variables except that whose significance was tested. The goodness of fit of the models was compared using χ² likelihood ratio tests.