tesi di dottorato di ricerca malvezzi

8/7/2019 Tesi di Dottorato di Ricerca Malvezzi

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UNIVERSIT DEGLI STUDI DI MILANOFacolt di Medicina e Chirurgia

Istituto di Statistica e Biometria GA Maccacaro

Dottorato in Statistica Biomedica Ciclo XXII

TESI DI DOTTORATO DI RICERCAAnalisi dei Tassi di Mortalit Con Modelli Et Periodo Coorte

MED/01

Matteo Charles Malvezzi

Prof. Adriano Decarli

Prof. Silvano Milani

Anno Accademico 2008-2009

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Index

Introduction..........................................................................................................................................3

Materials and Methods.........................................................................................................................4

Age-Standardised-Rates...................................................................................................................4

Instantaneous Incidence Rates....................................................................................................4

Mortality Rates............................................................................................................................5

Standard Rates ............................................................................................................................6

Rate Estimate Accuracy..............................................................................................................8

Age-Period-Cohort Analysis............................................................................................................9

Introduction.................................................................................................................................9

Presenting Data: Tabular View..................................................................................................10

Presenting Data: Graphical Methods........................................................................................12Classical Modelling Approach..................................................................................................16

The Age Model..........................................................................................................................17

The Age-Period Model..............................................................................................................18

The Age-Cohort Model.............................................................................................................19

The Age-Drift Model................................................................................................................21

The Age-Period-Cohort Model ................................................................................................22

Added Constraints................................................................................................................22

Successive Iteration Modelling............................................................................................23

Penalised likelihood Age-Period-Cohort Method.....................................................................27

Confidence Intervals for APC models......................................................................................29

Gastric Cancer Data..................................................................................................................30Oral Cancer Data.......................................................................................................................31

Results................................................................................................................................................33

Gastric Cancer Mortality ..............................................................................................................33

Oral Cancer Mortality....................................................................................................................36

Discussion...........................................................................................................................................40

The Penalised Likelihood APC Model..........................................................................................40

Gastric Cancer Mortality...............................................................................................................41

Oral Cancer Mortality....................................................................................................................42

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Age Period Cohort Analysis of Mortality Rates

Introduction

Descriptive epidemiology is seen as a first approach aimed at defining the scope for a research

problem. Its techniques are primarily aimed at exploratory studies, in that its main concern is to

generate hypotheses rather than verifying them.

The basic techniques of descriptive epidemiology were borrowed from demography, with morbidity

and mortality rates being the key descriptive tools and standardisation being the only method used

for comparative purposes, usually ignoring issues of variability, or acknowledging the problem

working around it with simplistic devices, such as the aggregation of data over longer time frames.

The improvement and greater availability of epidemiological data over the years is possibly the

main factor that brought about the development of modern descriptive epidemiology. Mortality and

incidence data (in particular oncological data) has come in leaps and bounds both quantity and

quality wise over the years, this is mainly due to the proliferation of cancer registries and the

concerted effort to standardise procedures of data collection and classification, not to mention the

improvement in demographic data that has become available for an always greater number of

populations and is published on a more regular basis.

As a consequence of this accumulation of time based incidence and mortality data, time series

modelling techniques were developed to analyse the different factors underlying the changes in

rates for both explanatory and predictive purposes.

In this thesis methods and modelling techniques to study mortality rates are described, in particular

age-period-cohort (APC) analysis is presented for its function in contributing to the aetiologic

purpose of descriptive epidemiology to make inference from the group to the individual.

The methods described herein were used to analyse gastric and oral cancer mortality in Europe to

illustrate the benefits and shortcomings of the methods, as well as, for the intrinsic value of these

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analyses for aetiological research and indications for cancer prevention that arise from the results of

these studies.

Materials and Methods

Age-Standardised-Rates

Instantaneous Incidence Rates

The probability of developing a condition between the ages t0 and t1 with (u) being the age specific

rate and S(u) the probability of survival without disease is given by:

=t0

t1

u Sudu .

We are interested in the conditional probability c of developing the disease given that a subject is

still at risk. This probability is not influenced by general survival until the examined age t 0 and very

little between t0 and t1, as long as this interval is small, giving us

c=t0

t1

uSuSt0

du .

If the interval is small enough that (u) and S(u) can be considered constant ((t0) and S(t0)) then

the equation can be rewritten as:

c t0t1t0

If k is the number of cases observed between t0 and t1, and nt0 is the number of subjects at risk at t0

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we have:

c=k

nt0.

Which gives us the estimate of as: t0

k

nt0t1t0.

Which is to say that the estimate of the instantaneous rate at t0 is the number of cases observed

divided by the number m of persons year between t0 and t1, which translates to the more familiar

t0 km .

Of course this approximation is not very good if (u) varies violently between t0 and t1, or if the

ratio

Su

St0

is very different from unity.

Mortality Rates

The annual incidence rate of a given disease, for a group, over a given time period is equal to the

ratio between the new occurrences of the disease over the given time and the number of persons

year accumulated by the members of the group over the same time period.

As seen above, rates are more meaningful when the examined group is homogeneous and there is a

constant risk over the time period. Under these conditions, the observed incidence rate can be

considered an estimate of the underlying instantaneous rate. These conditions are the reasons why

incidence is calculated separately by age and sex to obtain specific incidence rates.

In the case of annual mortality rates, the numerator of the rate is the number of deaths for the

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observed condition during the calendar year. In the case of descriptive statistics, particularly in

mortality studies, the denominator is made of population estimates derived from official censuses.

I.e. the provided population value is considered to be the mid point of the year, or the yearly

average. This gives us:

x=kx

[nx t0nx t1]/2.

With x being the annual incidence estimate for the studied age group, kx being the number of

observed cases in the observed population, nx(t0) and nx(t1) the number of subjects at risk at the

beginning and end of the studied period. The expression at the denominator corresponds to the

value mx provided by the statistical bureaux.

Standard Rates

To compare incidence rates measured on different populations, some form of standardisation is

necessary. The direct method of standardisation consists in calculating the annual rate that would

have been observed in a theoretical standard population, had this been subjected to the same force

of incidence of that being studied. To obtain this result, expected numbers of cases for each age

group are calculated for the standard population based on the corresponding person years and the

estimated rate for the studied population. This number, that corresponds to the number of expected

cases in the theoretical population, is divided by the total person years of this population. If L is the

size of the total standard population, Lx the number of subjects in the xth age group, with kx and mx

respectively the incidence and number of person years in the corresponding age group for the

studied population, the age specific rate for the observed population is t x= kx/mx. Thus, the number

of expected cases in the xth age group of the standard population if it were subject to the same level

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of risk defined by tx, would be Lxtx. The standardised rate, for a total number of age groups g, is

then:

t=1

Lx=1

g

Lx tx .

Which may also be written as:

t=x=1

g

wx tx

where wx = Lx/L is the proportion of subjects in the xth age group for the standard population

giving:

x=1

g

wx=1

Lx=1

g

Lx=1 .

Therefore t is a weighted average of age specific rates, with the weights being the proportion of

individuals per age group in the standard population. The standard populations used in this thesis

are the World Standard Population and the World Standard Truncated (35-64) Population [1].

Table 1. Age group weights for the world standard and truncated (35-64) populations.

Age Group World Standard Population World Truncated Population

0-4 12

5-9 10

10-14 9

15-19 9

20-24 8

25-29 8

30-34 6

35-39 6 19.35

40-44 6 19.35

45-49 6 19.35

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Age Group World Standard Population World Truncated Population

50-54 5 16.13

55-59 4 12.91

60-64 4 12.91

65-69 370-74 2

75-79 1

80 1

Total 100 100

Rate Estimate Accuracy

The accuracy of rates depends on the accuracy of the number of observed cases K. K follows a

Poisson distribution whose expectation and variance are equal to the theoretical rate multiplied by

the number of person years m accumulated, so E(K)= m and Var(K)= m. Therefore the variance

of the rate estimator K/m is:

Var Km =Var K

m2

=m

.

Its estimate is obtained by replacing with k/m:

Var Km =k

m2

=2

k.

From here we see that the variance for the specific rate tx is:

Vartx =Var Kx

mx2

=xm x

.

For the standardised rate this becomes:

Vart=x=1

g

w x2Vart=

x=1

g

wx2

xmx

x being unknown the variance must be estimated with:

Vart=x=1

g

wx2

mx2 kx .

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Therefore, if the theoretical standard rate is:

=x

w x x

and s is its standard error, (t-)/s approximates to a standard normal variable for which we can write

a 1 confidence interval in the usual form:

[ tZ /2 Vart ; tZ /2 Vart]

For practical purposes rates are usually given as t per 100 000 person years (105 t), consequently the

variance needs to be presented as 1010 Var(t).

Age-Period-Cohort Analysis

Introduction

Standardized rates are a useful descriptive tool when comparing different populations, but offer no

analytical insight, on the other hand, inferential analytic methods, applied to mortality rate time

trends such as joinpoint analysis, offer analytical insight on trends and their change in time, but

completely ignore information on the age and cohort structure of the analysed data [2]. APC

analysis performs a simultaneous study of the effects of age, period and cohort. The age effects

correspond to the variability explained by physiological differences that characterise the different

age groups, period effects are brought about by the change in variability in time that influence all

age groups in the same way, finally cohort effects explain changes that affect groups of subjects

belonging to the same birth cohort. Period effects usually portray the consequences of the

introduction of new therapies or screening interventions, they are also affected by exposures that

manifest their consequences on the studied event over short periods of time. Cohort effects are

usually determined by gestational exposures, or those exposures that influence event frequencies

over long time periods.

However useful, the APC model suffers from an intrinsic structural issue; the age, period and cohort

variables have an exact linear dependence that can be expressed as age = period cohort (A=P-C).

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This causes the infamous identifiability problem that makes this model complicated to treat. In the

recent decades many efforts have been spent in an attempt to overcome this issue, a few examples

are the use of estimable functions, adding extra constraints to the model or performing sequential

fittings of a two variable model and then regressing over residuals with the remaining variable [3]

[4][5][6][7][8]. More recently, solutions using modern techniques such as smoothers and Bayesian

methods have also been proposed [3][8][9][10][11]. All these solutions have their merits and set

backs; estimable functions are epidemiologically hard to interpret, adding constraints requires

biologic and statistical a priori knowledge and is not always justifiable, while cascade regression

results don't always agree with each other, and also require biological justifiability. In the following

paragraphs some of these techniques will be illustrated and the penalised likelihood method, that

offers a good balance between trade-offs and functionality, will be illustrated in detail [12][13].

Presenting Data: Tabular View

Incidence and mortality data are often shown in a two way table in tabular form, where rows

represent age groups (i=1,...,I) and columns the time periods (j=1,..,J). Usually the groupings of age

and periods are of the same size, but this is not necessarily the case. Cells can portray the following

information: the number of events (Oij), which is either the number of deaths for mortality or new

occurrences of a disease in the case of incidence, the number of man years at risk (N ij), or the age

specific rate (rij=Oij/Nij), which synthesises the afore mentioned information. In table 2 Italian male

gastric mortality rates are shown, age groups and time periods are both grouped in quinquennia, the

cells contain the corresponding age specific rates per 100 000 inhabitants. Observing the table, it

can be seen that moving down the rows we study the variation along the age groups (I=12), while

moving horizontally along the columns we can observe the temporal variation through the 5-year

periods (J=11). Moving diagonally down the table changes through the cohorts (K=I+J-1, k=I-i+j)

can be observed, the cohort with the central year of birth in 1930 (C=P-A) is highlighted.

In the example it is easy to see how the rates get bigger at older ages and earlier periods of death,

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the intrinsic dependence of cohort effects from the age and period variables also appears clearly in

this example.

Table 2. Tabulated age specific mortality rates for gastric cancer in Italian men.

Central Year of the Quinquennium of Death

1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 2002

CentralYearoftheA

geQuinquennium

22 0.27 0.33 0.45 0.14 0.22 0.25 0.23 0.16 0.12 0.12 0.04

27 0.82 0.85 0.93 0.73 0.7 0.63 0.51 0.33 0.38 0.24 0.38

32 2.21 2.03 2.35 2.18 1.81 1.65 1.27 1 0.92 0.89 0.57

37 5.86 5.18 5.17 4.92 4.61 4.09 3.32 2.83 2.28 1.82 1.44

42 15.02 13.83 11.5 10.49 9.3 7.73 7.94 5.69 5.15 4.11 3.34

47 32.04 27.65 25.5 20.57 19.18 17.12 13.98 12.23 9.87 8.32 6.58

52 58.09 56.65 48.8 43.05 34.97 31.39 26.81 21.9 18.12 14.53 11.55

57 100.97 95.88 89.69 80.01 68.43 53.3 47.74 41.05 33.43 26.27 21.23

62 159.17 151.69 148.13 136.19 114.49 95.31 77.77 66.89 55.28 45.77 37.11

67 235.55 223.04 220.72 205.64 182.18 145.83 131.09 105.86 88.14 72.06 61.06

72 317.74 313.15 301.82 296.15 259.8 208.33 191.36 171.75 138.05 108.03 92.54

77 366.57 367.31 393.92 367.7 355.83 281.51 267.09 237.9 196.14 158.47 133.61

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Presenting Data: Graphical Methods

To explore the data structure further, a series of two-dimensional logarithmic scale representations

are used. Figure 1 shows death rates per 100 000 inhabitants plotted against period of death with

data stratified by age at death. In the shown case (Italian male gastric cancer mortality) parallelism

between age groups is very strong, underlining the coherence of mortality variation over time. This

parallelism is also seen in figure 2 where the grouping and x axis variables are inverted, i.e. with

data grouped by period of death and death rates plotted against age at death, underlining the

coherence in variation death rates have over the age groups.

This homogeneity can also be seen when plotting involves the cohort of birth factor. In figure 3

death rates are plotted against cohort-of-birth, but divided in age groups. The parallelism seen is

very similar to that seen in figure 1, which is expected since the strata are identical in the two

figures, the difference lies in the fact that in figure 3 they are plotted against the cohort of birth

instead of the period (figure 1).

In figure 4 we see death rates per 100 000 grouped by birth cohorts and plotted against age at death,

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Figure 1: Death rates per 100 000 inhabitants plotted against period of deathwith data stratified by age at death


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the graph has the same shape as that in figure 2 because it plots the same data points, but these are

joined according to different strata. It is immediately noticeable that the broken lines don't all share

the same length, that is because older and younger cohorts are based on fewer cells, compared to the

central ones, since they only exist at the extremes of the studied age spectrum. Nonetheless, good

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Figure 3: Death rates per 100 000 inhabitants plotted against age at birth

with data stratified by age at death

Figure 2: Death rates per 100 000 inhabitants plotted against age at deathwith data stratified by period of death


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parallelism between the lines is evident showing that, with respect to cohorts, data variation over

age is homogeneous. From the four figures representing Italian male gastric cancer mortality, age

appears to be the most important factor, as would be expected with mortality from this cancer. The

parallelism seen in the graphs makes discerning whether there is a stronger age period effect (shown

in figures 1 and 2) or whether the data is influenced by a stronger age cohort effect (as shown in

figures 3 and 4) complicated.

There are more data representation techniques than it is healthy to discuss, the more explanatory

ones tend to be combinations of those shown so far: in the example (figure 5) cohort strata are

added to the graph in figure 1, the effect of this procedure is to create a surface with a varying

topology from which information regarding the roles of age, period and cohort can be gained, in the

example parallelism and linearity on a logarithmic scale dominate the data.

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Figure 4: Death rates per 100 000 inhabitants plotted against age at death

with data divided by age at birth


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The more spectacular representations are undoubtedly three-dimensional plots, of which we give an

example (figure 6), portraying the same data with the logarithm of the death rate per 100 000

inhabitants on the z axis and age and period on the x and y axes respectively.

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Figure 5: Death rates per 100 000 inhabitants plotted against period

of death with data stratified by age at death (black) and age at birth(red)

Figure 6: Death rate per 100 000 inhabitants on the z axis, ageat death on the y axes and period oh death on the y axes


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The strength of the age effect can also be seen on this graph, but it suffers from the limit of being a

three dimensional representation stuck on a two-dimensional surface, this makes the choice of view

point an important and tricky issue.

Classical Modelling Approach

To explain the methods and issues that arise from the application of APC models it's best to start

from the classical illustration of the problem that Clayton and Schifflers make in their double paper

titled Models for Temporal Variation in Cancer Rates [14][5]. In their work, the authors tackle the

problem performing variance analyses of successively more complex models. They start with a

simple age model, moving on to a linear drift model that adds either a cohort or period drift term to

the age model, to then apply the age-period (AP) and age-cohort models (AC) and only in a final

instance, if justified by the variance analysis, apply one of the possible APC solutions. The flow

chart they present in their paper (figure 7), is a synthesis of their proposed method.

This schematic highlights the fact that the AP and AC models are not directly comparable, this is

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Figure 7: Anova procedure schematic for age period cohort analysis

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Age-Period ModelDoF: (I-1)(J-1)

1Age ModelDoF: I(J-1)

2Age-Drift Model

DoF: I(J-1)-1

3

Age-Cohort ModelDoF: (I-1)(J-2)

4Age-Period-Cohort Model

DoF: (I-2)(J-2)

-1

-(J-2)-(I+J-3)

-(I+J-3)-(J-2)

Degrees of Freedom in APC Models.


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due to the AC model using more degrees of freedom than the AP model. The resulting ANOVA is

consequently complicated to interpret. Applying this ANOVA method to the afore-mentioned

models, which will be explained in greater detail in the following section, to the Italian male gastric

mortality rates from the previous examples we obtain:

Examining figure 8, it can be seen that, the age drift model explains the most variance using the

least degrees of freedom, therefore it gives the most economical representation of the data. This

result is also obvious upon close inspection of the graphs presented in the Graphical Methods

section (figures 1-6) where the plots are dominated by strong parallelism and linearity on a

logarithmic scale.

The Age Model

The model that analyses the rate trends using age as a factor can be expressed with the following

function:

Y=log E[ri]=i

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Figure 8: Anova schematic applied to Italian male gastric cancer mortality

3Age-Period ModelDoF:90 Dev:1713

1Age Model

DoF:100 Dev:70183

2Age-Drift Model

DoF:99 Dev:4714

3Age-Cohort ModelDoF:81 Dev:927

4Age-Period-Cohort Model

DoF:72 Dev:306

-1

-9-18

-18-9

Degrees of Freedom in APC Models of Italian male gastric cancer mortality .

Null model DoF: 110 Total Deviance:1479717519


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where is the intercept and the i is the additive effect of the ith age group on the base rate, which

can be expressed as EXP()*100 000 inhabitants, i.e. i is the relative risk as compared to that of a

reference age group 0.

For our purposes the model without the intercept where the i are the log-estimates of the age-

specific rates ri is more useful:

Y=log E[ri ]=i

Applying the model to the example data (figure 9), the slightly wider confidence intervals in the

younger age groups are an indication of the greater variability present in these estimates, this is due

to the very small numbers of deaths recorded in these age groups in the studied pathologies.

The Age-Period Model

This model assumes that the age specific rates maintain the same structure during all the studied

periods, but vary in dimension according to the time period and can be written as:

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Figure 9: Age model for Italian male gastric cancer mortality


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Y=logE[rij]=i j

where i is the log-estimate of the ith age-specific rate in the reference period 0, j is the additive

effect of the jth period on the logarithm of the age-specific rates with rij being the estimate of the

rate of the ith age group in the jth period.

This model is over-parametrised as it has a parameter for each age group and one for each period,

but this is easily solved by constraining one of the period effects to be equal to 0 and set it as the

reference 0 compared to which the other period effects j are to be considered as measures of risk.

In our example (Italian male gastric mortality rates) the fifth period corresponding to the 1970-74

quinquennium was chosen as the reference, therefore the i are the logarithms of age-specific

mortality rates in the reference period 0 (1970-74) and j is the relative risk to be applied to the

age-specific log-rates in the jth period.

The Age-Cohort Model

This model is structurally similar to the AP model replacing the period factor with the cohort one:

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Figure 10: Age period model for Italian male gastric cancer mortality


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Y=log E[rik]=ik

where i is the log-estimate of the ith age-specific rate in the reference cohort 0, k is the additive

effect of the kth cohort on the logarithm of the age-specific rates, similarly to the previous model rij

is the estimate of the rate of the ith age group, but in the kth cohort instead of the jth period. The

over parametrisation problem is solved, similarly to the previous model, taking a reference cohort 0

where the age-specific log-rates take on the values given by EXP( i)*100 000, referred to which k

is the relative risk for the kth cohort. In our example (Italian male gastric mortality rates) the central

reference cohort is the 11th that has its central year of birth in 1930.

The confidence intervals for the cohorts, resulting from the application of the AC model to the

example data (figure 9), show greater variability in the oldest and youngest cohorts. This is due to

these cohorts being built on fewer observations, as can be seen in figure 4. Furthermore, the most

recent cohorts include the youngest age groups, which have the smallest numbers of recorded

deaths, consequently they are affected by the greatest variability.

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Figure 11: Age cohort model for Italian male gastric cancer mortality


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The Age-Drift Model

Observing the previous two models with the period and cohort effects expressed as relative risks,

the question arises as to what would happen if these parameter estimates were substituted with a

log-linear trend. This is called the linear drift and can be expressed either as a function of period or

as a function of cohort, as can be seen respectively in the following formulae:

Y=log E[rij ]=i j j 0

Y=logE[rik]=ikk0

The resulting effects are age-specific rates calculated in the reference period or cohort (j0 and k0

respectively) and a linear trend component representing the relative risk as a linear drift on the

logarithmic scale.

The main feature of these two models is that, as far as the expected value estimates are concerned,

the residual deviance is identical in both models. The only real difference between the two models

is the reference temporal scale, this changes the model interpretation according to whether it is

period or cohort centred, consequently the estimated age-specific rates in the reference

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Figure 12: Age drift models for Italian male gastric cancer mortality


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parameter have a different structure to reflect this.

This model is interpreted as an age-specific rate structure that is influenced by a constant linear

cohort or period effect. In the example (Italian male gastric mortality rates), we see the two models

superimposed in figure 12 to illustrate the previously mentioned features of these models, with the

references j0 and k0.being the same as in the previous AP and AC examples (figures 10 and 11).

The Age-Period-Cohort Model

As mentioned in the introduction, the full APC model suffers from a non-identifiability problem

given by the linear relation A=P-C. Numerous techniques have been used to solve or circumvent

this issue over the years, from simple added constraint solutions to more exotic methods. In the

following paragraphs some of these methods will be illustrated in order to underline their strengths

and weaknesses, before moving on to the chosen method for APC analysis.

Added Constraints

This method solves the non identifiability problem by adding additional constraints to the model. As

well as choosing a cohort 0 and a period 0 as references to solve the ordinary over-parametrisation

problem, an additional constraint is added to the model, usually forcing the effects of 2 parameters

to be the same.

This method has some drawbacks, the most obvious of which is that by changing the constraints the

resulting model is heavily and visibly affected, therefore a priory biological and statistical

knowledge is needed to justify such an intervention.

In the two examples we apply different constraints on the model, the resulting differences are plain

to see. The first model (figure 13) constrains the effects of the to two earliest cohorts (central years

1875 and 1880) so that c1=c2, while the second model (figure 14) constrains the last two age groups

(70-74 and 75-79 years of age) so that a9=a10. As anticipated, the estimates of the two models are

incompatible even though the chosen constraints are closely related: the earliest cohorts and oldest

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age groups overlap greatly. This underlines the fact that this kind of solution should be avoided

unless very strong a priori knowledge is held.

Successive Iteration Modelling

In the case where age is the most important scale (as is the case in most cancer mortality studies)

and cohort or period can be prioritised according to a priori biological or statistical information, a

full APC model can be approximated by regressing an AP or AC model first, then obtaining the

effect of the remaining factor by regressing it over the residuals of the first model.

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Figure 13: Age period cohort model constraining the first two cohorts

Figure 14: Age period cohort model constraining the oldest two age groups


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In the case of an AC model followed by a period model, what is being obtained is the residual

period effect conditional to the age and cohort estimates from the preceding model:

logE[rijk]= i k j

which for the expected cases becomes:

log E[O ijk]= i klog Nijk j .

Now this is similar to the general expression of a Poisson model, with the difference that the offset

now includes the log of the fitted values from the AC model.

This procedure does not provide maximum likelihood estimates for parameters, instead it estimates

marginal age and cohort effects and conditional estimates of the period effects. This technique

allows for the calculation of confidence intervals, which consequently are not maximum likelihood

estimated intervals, but marginal estimates for the age and cohort effect intervals and conditional

estimates for the period effect ones.

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Figure 15: Period model regressed over the residuals of an age cohort model


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To use this procedure starting with an AP model to then regress the cohort factor the following

applies:

log E[rijk]= i j k

and the expected cases become:

log E[O ijk]= i jlog Nijkk .

The same holds for effect and standard error estimates, now age and period are the marginal

estimates while the cohort ones are conditional to the AP model.

From figures 15 and 16 we can see that the two models are similar but not equivalent. Obviously

the effects of the parameters of the starting models are those of the AP and AC models, since the

data examined in this case is strongly driven by drift, the cohort and period parameters for these

first models are very similar to the corresponding age-drift models. Therefore, choosing whether to

start with an AC or AP model depends on where we choose to assign the drift term, and which

factor we want to study without the effects of linear drift.

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Figure 16: Cohort model regressed over the residuals of an age period model


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This method can also be used by fitting one of the possible age-drift models and then regressing

over the residuals with either the period or cohort parameters. For an age-drift-period model, first

the age-drift model using a cohort linear drift is used, successively the model for the period effects

is regressed using the fitted estimates of the first model as the offset. The results of this procedure

are period estimates conditional to age and cohort drift estimates of the drift model, this gives us a

set of period effect estimates unaffected by linear drift as this has already been absorbed by the first

model. This translates to:

log E[rijk]= i kk0 j

and for the expected cases:

logE[O ijk]= i kk0log Nijk j .

Analogously to the previous examples, this results in marginal estimates for the effects and errors of

age and cohort drift and conditional estimates for the period ones. The same thing can be done to

obtain an age-drift-cohort model where the cohort estimates are drift free.

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Figure 17: Period model regressed over the residuals of an age cohort driftmodel


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The period and cohort effects resulting from these two models appear to be virtually identical to the

ones obtained from regressing AP or AC models first (figure 17 and 18). This is because the linear

drift is absorbed completely by the first model fitted. The usefulness of these models is that they

enable us to study the shape of the last factor once the linear-drift effect has been subtracted.

Penalised likelihood Age-Period-Cohort Method

As previously illustrated, the issues with fitting a full APC model are solving the identification

problem and dealing with the linear drift term.

An APC model can be considered as a parameter estimate problem in a log-linear Poisson model,

such as those illustrated up till now:

logOijk=log Nijkloga ilog p jlog ck

where ai, pj and ckare the multiplicative parameters for age, period and cohort respectively. These

can be estimated by minimising the following expression using the weighted least squares method:

fa , p , c = Oijk logOijklog Nijkloga ilog p jlog ck2

Seeing as there is a linear relation between A, P and C the solution set X(a,p,c) is infinite, but can be

27

Figure 18: Cohort model regressed over the residuals of an age period driftmodel


28/45

parametrised in in the following manner:

log a 'i=log ai Ii

log p 'i=log p i j

log c 'i=log c i k .

This parametrisation makes it possible to calculate a goodness of fit statistic (G2) that is independent

from .

The solutions estimated by the three two factor models are:

Xc= ac , pc , c0 ; X p= a p , p0 , c p ; Xa=a0 , pa , ca;

where c0 and p0 are unit vectors of length k and j respectively and a0 takes the form:

a0i=exp [j

Oij log Oijlog Nij /j

Oij ] .

The natural logarithms of these solutions are then placed in the real space Ri +j + k, where their

euclidean distances from the parametrised saturated model solutions X()=(a, p, c, ) are defined

as:

dc =XcX

dp =XpX

da=Xa X .

The sum of these distances, weighed by the inverse of the degrees of freedom scaled goodness of

fit:

g X=dc

Gc2 / I1 J1

dp

G p2 / I1 J2

da

Ga2/ I2 J1

can be minimised in . This results in a solution X'() that minimises the distance of the saturated

model from the three two factor models, constructing a geometrical weighted average of the three

28


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two factor models. This way the identification problem is solved and the drift is distributed

according to the goodness of fit statistics.

Confidence Intervals for APC models.

Many APC methods don't allow for the straightforward production of confidence intervals. Such is

the case for the penalised likelihood method. To gain some insight on the variability of the

estimated parameters we resorted to a parametric bootstrap simulation method[15]. Published

Mortality data is usually stratified by age-groups and time-periods. Being count data every cell,

specified by age group and calendar time-period, contains values that are Poisson distributed. With

this in mind, for each cell, 1 000 values were randomly extracted from a Poisson distribution

characterised by the measured value of that cell. The simulated datasets were then fed through the

penalised likelihood APC model, 1 000 sets of estimates for the age, period and cohort parameters

were obtained.

For each parameter the 2.5th and 97.5th percentiles were taken from the one-thousandfold estimate

set as an estimate for the 95% confidence interval for that parameter.

29

Figure 19: Age period cohort model fitted using the penalised likelihood

method


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Gastric Cancer Data

Official death certification data for the period 1950-2004 was derived for gastric cancer, whenever

available, from the World Health Organization (WHO) database [16], for 35 countries of the

European Region (according to the WHO definition), of which 23 were EU countries (Belgium,

Cyprus, Luxembourg and Slovakia were excluded), the other 12 being Albania, Armenia,

Azerbaijan, Belarus, Croatia, Georgia, Kazakhstan, Norway, Moldova, Russia, Switzerland and

Ukraine, and the EU as a whole (27 member states as defined in January 2007). Mortality data was

coded according to the Seventh Revision of the International Classification of Diseases (ICD-7)

from the 1950's to the end of the 1960's, the eighth revision (ICD-8) was used throughout the

1970's, while the ninth ICD-9 was used up to the mid 1990's (with the exception of Switzerland and

Denmark that skipped this revision and moved to the tenth in 1995 and 1994 respectively), the

Tenth Revision of the International statistical Classification of Diseases and Health Related

Problems (ICD-10) was adopted between the late 1990's and early 2000s by most countries [17],

with the exceptions of Albania, Armenia, Bulgaria, Greece and Ireland that still have not adopted it.

30

Figure 20: Age period cohort model fitted using the penalised likelihoodmethod with confidence intervals from the bootstrap procedure


31/45

Encoding for stomach mortality is straightforward and its transition between revisions did not

present particular issues, it was coded as 151 for ICD 7, 8 and 9 and C16 in ICD-10.

Estimates of the resident populations for the corresponding calendar periods, based on official

censuses, were extracted from the same WHO database.

From the matrices of certified deaths and resident population we computed the age-specific

mortality rates per 100 000 inhabitants for 5-year age groups (from 30-34 to 75-79 years), for the 11

5-year periods considered (from 1950-54 to 2000-04) where data was available. No extrapolations

were made for missing data.

From the same matrices, we computed age-specific rates for each 5-year age group (from 0, 1-4 to

85+ years), in order to construct age-standardized mortality rates per 100 000 men and women

using the direct method on the basis of the world standard population at all ages, and the

corresponding percent change in rates over the 1994-2004 decade [1].

Cohorts were defined according to their central year of birth. Thus, the earliest possible cohort (the

1875 one) relates to individuals aged 75 to 79 who died in the quinquennium 1950-54; they could

have been born in any of the 10 years from 1870 to 1879.

Oral Cancer Data

Official death certification data from oral and pharyngeal cancer for 38 European countries and for

the EU in the period 1950-2007 was derived from the World Health Organization (WHO) database

available on electronic support [16].

The EU was defined as the 27 member states as of January 2007, i.e., Austria, Belgium, Bulgaria,

the Czech Republic, Cyprus, Denmark, Estonia, Finland, France, Germany, Greece, Hungary,

Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Poland, Portugal, Romania,

Slovakia, Slovenia, Spain, Sweden, United Kingdom. Data for Cyprus was not available and for

Belgium it was only available up to 1997, and was therefore excluded.

During the calendar period considered (1950-2004), four different Revisions of the International

31


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Classification of Diseases (ICD) were used. Since differences in classifications between various

Revisions were minor, oral and pharyngeal cancer deaths were re-coded for all countries according

to the Tenth Revision of the ICD (ICD-10: C00-C14) [17].

Estimates of the resident population, based on official censuses, were obtained from the same WHO

database. From the matrices of certified deaths and resident populations, we computed age-specific

rates for each 5-year age group (from 0, 14 to 85+ years) and calendar period. Age-standardized

rates per 100 000 men and women, at all ages and truncated 35-64 years, were computed using the

direct method, on the basis of the world standard population [1]. In a few countries, mortality data

was missing for one or more calendar years. No extrapolation was made for missing data.

From these same matrices, we computed the age-specific mortality rates per 100,000 inhabitants for

5-year age groups ( from 30-34 to 80-84 years), for the 12 5-year periods considered (from 1950-54

32

Figure 21: Age period cohort models of male gastric cancer mortality in countries representative of

the European region and the EU as a whole.


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to 2000-04 plus 2007), where data was available. No extrapolations were made for missing data.

Cohorts were defined according to their central year of birth. Thus the earliest possible cohort (the

1865 one) relates to individuals aged 80 to 84 who died in the quinquennium 1950-54; they could

have been born in any of the 10 years from 1860 to 1869.

Results

Gastric Cancer Mortality

Table 3 shows age-standardized rates for men and women in 1994, 1999 and 2004 with percentage

differences between periods. We see that for the EU taken as a whole in 2004 we have an age-

standardized mortality rate of 9.09/100 000 inhabitants for men and 4.17/100 000 for women, but

this total rate is the result of many differing contributions; central and northern European countries

33

Figure 22: Age period cohort models of female gastric cancer mortality in countries representative

of the European region and the EU as a whole.


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like France, Finland and Sweden showing low rates around 5/100 000 in men and between 2 and

4/100 000 in women in 2004, while southern and Mediterranean countries like Italy and Portugal

have mortality rates of 10.43 and 16.36/100 000 in men and 5.04 and 7.30 /100 000 in women

respectively. Eastern countries belonging to the EU show even higher mortality rates with Latvia

and Lithuania peaking slightly above 20/100 000 in men and nearly 8 /100 000 in women, with

Estonia showing the highest values for women in the EU with 9.66/100 000.

Table 3. Age standardised mortality rates for gastric cancer in men and women in countries from

the European geographical region.

MEN WOMEN

Calendar

Yearsa1994 1999 2004

% Change

1999/94

% Change

2004/991994 1999 2004

% Change

1999/94

% Change

2004/99

EUROPE

. 16.29 13.92 . -14.59 . 7.54 7.73 . 2.55Albania 1987-2004

Armenia (2003) 1981-2003 15.91 13.35 16.79 -16.08 25.76 6.98 5.82 7.09 -16.61 21.81

Austria 1980-2005 14.10 9.89 8.07 -29.83 -18.38 7.65 5.35 4.63 -30.12 -13.42

Azerbaijan

(2002)1981-2002 24.32 25.24 21.64 3.81 -14.28 10.27

10.0

6

11.0

6-2.03 9.90

Belarus (2003) 1981-2003 35.51 32.97 27.44 -7.17 -16.76 15.0713.0

2

10.5

1-13.63 -19.22

Bulgaria 1980-2004 18.55 14.91 13.25 -19.62 -11.15 8.75 7.49 6.25 -14.43 -16.50

Croatia 1985-2005 21.15 22.79 16.38 7.77 -28.12 8.27 7.49 6.21 -9.50 -17.09

Czech Republic 1986-2005 16.57 11.73 10.15 -29.20 -13.53 7.34 5.88 4.78 -19.79 -18.82

Denmark (2001) 1980-2001 6.40 5.19 5.13 -18.81 -1.20 3.02 2.83 2.75 -6.25 -2.85

Estonia 1981-2005 25.92 23.45 18.94 -9.52 -19.24 13.4012.0

99.66 -9.75 -20.10

Finland 1980-2005 10.81 7.89 6.31 -27.06 -20.02 4.64 3.64 3.86 -21.65 6.06

France 1980-2005 7.30 6.53 5.63 -10.46 -13.85 2.81 2.46 2.08 -12.45 -15.16

Georgia (2001) 1981-2001 11.20 12.02 8.51 7.36 -29.20 5.25 5.10 4.99 -2.74 -2.26

Germany 1980-2004 12.88 9.94 7.95 -22.81 -20.08 6.72 5.19 4.23 -22.75 -18.44

Greece 1980-2005 . 8.70 7.25 . -16.68 . 3.73 3.65 . -2.18

Hungary 1980-2005 21.64 17.79 13.49 -17.79 -24.16 9.45 7.50 6.49 -20.63 -13.51

Iceland 1980-2005 10.29 7.68 6.88 -25.35 -10.42 4.04 3.30 3.06 -18.20 -7.48

Ireland 1980-2005 10.26 8.32 6.90 -18.87 -17.04 5.51 4.29 2.64 -22.17 -38.55

Italy (2003) 1980-2003 15.06 11.95 10.43 -20.64 -12.73 7.23 5.46 5.04 -24.46 -7.68

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MEN WOMEN

Calendar

Yearsa1994 1999 2004

% Change

1999/94

% Change

2004/991994 1999 2004

% Change

1999/94

% Change

2004/99

Israel (2003) 1980-2003 8.87 7.49 7.81 -15.59 4.34 5.07 4.33 3.41 -14.50 -21.42

Kazakhstan 1981-2005 33.92 30.57 25.71 -9.88 -15.92 13.9412.6

5

10.7

7-9.25 -14.87

Kyrgyzstan 1981-2005 30.58 24.49 23.24 -19.92 -5.13 10.6810.8

48.30 1.44 -23.37

Latvia 1980-2005 26.38 22.49 20.55 -14.74 -8.62 11.48 9.83 7.85 -14.40 -20.18

Lithuania 1981-2005 25.67 22.86 21.09 -10.92 -7.77 9.70 9.36 7.98 -3.51 -14.76

Luxembourg 1980-2005 9.04 7.52 7.03 -16.83 -6.55 4.40 3.55 2.86 -19.33 -19.54

Macedonia

TFYR (2003)1991-2003 22.01 17.17 17.77 -22.00 3.50 10.52 7.80 7.98 -25.88 2.28

Malta 1980-2005 9.99 12.25 8.03 22.66 -34.42 5.77 3.70 3.65 -35.78 -1.55

Netherlands 1980-2004 10.75 8.47 6.53 -21.17 -22.99 4.43 3.55 3.37 -19.79 -5.04

Norway 1980-2005 9.61 8.55 5.57 -10.96 -34.90 4.68 4.28 2.94 -8.41 -31.47

Poland 1980-2005 19.68 16.52 14.28 -16.05 -13.57 6.97 5.70 5.00 -18.27 -12.23

Portugal (2003) 1980-2003 21.02 18.69 16.36 -11.09 -12.46 9.66 8.93 7.30 -7.57 -18.24

Republic of

Moldova1981-2005 19.74 16.51 16.89 -16.35 2.33 9.51 6.69 7.52 -29.63 12.41

Romania 1980-2004 17.79 16.67 16.00 -6.33 -4.02 6.83 6.08 6.29 -10.95 3.43

RussianFederation

1980-2005 37.46 31.70 27.16 -15.40 -14.32 15.5813.0

211.1

8-16.43 -14.14

Slovakia 1992-2005 . 16.69 13.63 . -18.34 . 5.84 5.78 . -0.92

Slovenia 1985-2005 21.18 17.82 14.84 -15.86 -16.75 7.82 7.67 5.42 -1.86 -29.44

Spain 1980-2005 13.16 10.90 9.02 -17.14 -17.26 5.69 4.67 3.79 -17.99 -18.74

Sweden 1980-2004 7.05 6.13 4.94 -13.12 -19.32 3.75 3.05 2.73 -18.78 -10.29

Switzerland 1980-2005 7.98 5.53 4.50 -30.75 -18.55 3.58 2.71 2.10 -24.48 -22.35

Tajikistan 1981-2004 19.25 17.99 14.88 -6.53 -17.28 10.6310.8

29.26 1.80 -14.38

Ukraine 1981-2005 28.85 24.86 21.23 -13.84 -14.61 11.24 9.58 8.28 -14.76 -13.65

United Kingdom 1980-2005 10.41 8.08 6.09 -22.36 -24.68 4.22 3.26 2.75 -22.80 -15.65

Uzbekistan 1981-2005 15.93 11.98 12.34 -24.77 2.93 7.11 5.56 6.22 -21.86 12.04

EU 13.22 10.85 9.09 -17.90 -16.28 5.98 4.81 4.17 -19.42 -13.45

This geographical division of results is also reflected in the curves resulting from the APC analysis

that can be seen in Figures 21 (men) and 22 (women). The age curves for France, Sweden and the

UK are relatively shallow in both men and women as compared to those found in southern and

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eastern countries such as Italy, Portugal and Hungary. The central and northern countries with the

more favourable rates also have distinctive cohort and period effect curves, they have strong

descending period effect trends and cohort effects that fall steeply from the earliest cohorts until

about the 1940s to then stabilize. Southern and Eastern countries, on the other hand, display a later

start in the cohort effect fall with eastern countries not seeing the stabilization found in the younger

cohorts that southern European countries share with central northern states. The difference between

sexes is mainly seen in the age curves that are much shallower than the male ones throughout the

observed countries.

Oral Cancer Mortality

Table 4 gives the overall age-standardized mortality rates from oral and pharyngeal cancer in men

and women from various European countries and the EU as a whole in 1990-1994 and 2000-2004

with the corresponding percent changes.

For EU men, rates declined by 8% between the early 1990s and 2000-2004, to reach an overall

age-standardized rate of 6.1/100 000 in 2000-2004. In 1990-1994, the highest male rates were in

Hungary (17.1/100 000), Slovakia (16.0/100,000), and France (12.4/100 000); the lowest ones in

Greece and Iceland (1.8/100 000), and Finland (2.2/100 000). In 2000-2004, the highest male rates

were in Hungary (21.1/100 000) and other countries from central and eastern Europe, such as

Slovakia (16.9/100 000), the Republic of Moldova, Lithuania, Ukraine and Croatia (around 10-

11/100 000), while the lowest ones were in Nordic countries, such Iceland, Sweden, Finland

(around 2/100 000), the United Kingdom (2.8/100 000) and Greece (1.8/100 000). Oral and

pharyngeal cancer mortality declined over the last decade in several large European countries,

including France (with a rate of 8.6/100 000 in the early 2000s), Spain (6.0/100 000), Germany

(5.7/100 000) and Italy (4.3/100 000). Persisting rises were, however, observed in several central

and eastern European countries, including in particular Hungary, but also Belarus, Lithuania and

Romania. Rates were much lower in women, but increased moderately from 1.08 to 1.14/100 000

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over the last decade in the EU as a whole. In 2000-2004 the highest rates for women were in

Hungary too (3.3/100 000), followed by Denmark (1.6/100 000) and Scotland (1.4/100 000), the

lowest ones were in Bulgaria (0.8/100 000) and Greece (0.7/100 000).

37

Figure 23: Male age-specific mortality rates from oral and pharyngeal cancer from 30-34 to 80-84years plotted against the year of birth


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Table 4. Age standardised mortality rates for oral cancer in men and women in countries from theEuropean geographical region.

CountriesMen Women

1990-94 2000-04

% Change

2000-04/1990-94

1990-94 2000-04

% Change

2000-04/1990-94

Albania (1992-94) 3.81 2.41 -36.77 1.35 1.15 -14.94

Austria 6.07 6.28 3.47 0.96 1.35 40.49

Belarus (2000-03) 8.28 9.70 17.25 0.72 0.72 -0.23

Bulgaria (2000-03) 4.27 4.48 5.07 0.69 0.81 17.54

Croatia 11.88 10.43 -12.15 1.15 1.07 -7.44

Czech Republic 6.53 7.13 9.14 0.97 1.06 9.03

Denmark (2000-01) 4.28 4.93 15.30 1.38 1.64 19.16

Estonia 8.71 8.83 1.31 1.06 1.30 22.56

Finland 2.21 2.31 4.15 0.83 0.83 0.24

France 12.43 8.57 -31.01 1.30 1.27 -2.37Germany 6.63 5.67 -14.47 1.13 1.18 4.97

Greece 1.80 1.84 2.60 0.49 0.66 32.62

Hungary 17.13 21.12 23.25 2.22 3.25 46.34

Iceland 1.81 2.09 15.23 0.66 1.45 117.85

Ireland 4.52 3.51 -22.26 1.09 1.13 3.27

Italy (2000-03) 5.81 4.31 -25.78 1.00 1.01 1.67

Latvia 6.96 8.06 15.80 0.81 0.92 13.85

Lithuania 7.94 10.57 33.03 0.95 0.96 0.16

Luxembourg 8.49 7.70 -9.31 1.40 1.47 4.98

Macedonia (2000-03) 3.22 3.04 -5.41 0.60 0.83 37.50

Malta 3.49 2.86 -18.04 1.40 0.78 -44.30

Netherlands 2.78 2.96 6.29 1.04 1.27 22.16

Norway 3.14 2.76 -11.93 0.93 0.98 5.47

Poland 6.27 5.98 -4.70 1.06 1.12 5.39

Portugal (2000-03) 5.87 6.81 16.10 0.91 0.83 -9.18

Republic of Moldova 10.57 11.21 6.13 1.02 1.10 7.72

Romania 6.45 9.99 55.00 1.02 1.23 20.38

Russian Federation 8.92 8.85 -0.75 1.03 1.08 4.15

Slovakia 16.01 16.85 5.28 1.10 1.19 8.32

Slovenia 11.41 8.35 -26.82 0.95 1.08 14.39

Spain 6.94 5.98 -13.76 0.83 0.85 2.06Sweden 2.54 2.15 -15.39 0.91 0.88 -2.85

Switzerland 6.14 4.60 -25.06 1.17 1.23 5.15

Ukraine 9.73 10.55 8.32 0.94 0.88 -6.36

United Kingdom 2.98 2.75 -7.64 1.15 1.07 -6.72

United Kingdom,

England and Wales 2.83 2.58 -8.96 1.11 1.05 -5.41

United Kingdom,

Northern Ireland 3.16 2.74 -13.30 0.96 1.12 16.43

United Kingdom,

Scotland 4.48 4.19 -6.46 1.52 1.37 -9.69

European Union 6.62 6.09 -7.92 1.08 1.14 6.23

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selection of European countries and the EU. Examining the graph for the EU, age-specific mortality

rate estimates for this cancer rise linearly with age, reaching a value lower than 50/100 000, in the

oldest age group. Period estimates rise steadily up to the late 1980's/ early 1990's, to then invert the

trend and fall until the most recent studied period. Cohort estimates rise sharply from the earliest

cohort up the beginning of the 19th century, then they fall until the 1920's to rise up to the 1960's and

then fall again for the more recent cohorts. With the exception of Portugal, that shows a fall up to

the 1920's and then a continuous rise, cohort effects for the studied countries closely resemble the

ones from the EU, however there are differences in variability, Lithuania and the Republic of

Moldova display wider confidence intervals than other countries for their cohort effects. Age effects

reflect the standard rates reported for the countries, Hungary's age curves reaches the highest point

at about 100/100 000, while Germany doesn't reach 40 /100 000 at its highest point. The bigger EU

countries, like France, Germany, Italy and Spain, show period estimate trends that reflect the

patterns already seen in the EU with a rise for the earlier periods, an inversion in the 1990's and

then continue to descend up to the last studied period. Countries that showed rises in standard rate

trends, like Lithuania, Romania and Ukraine, have rising period effect trends for the more recent

periods.

Discussion

The Penalised Likelihood APC Model

Before proceeding to the interpretation of results, a few general considerations on the model are

due. To start with, random variation problems differ in relation to age, period and cohort estimates.

These are minor when related to period of death estimates, since these are based upon relatively

similar total numbers of events over subsequent calendar periods; for age values the issue tends to

manifest with the younger age groups where the absolute numbers of deaths for most oncological

pathologies are low. In cohort effects these problems are potentially greater at both ends of the

curve, the earliest and latest cohorts are based on very few observations, while moving towards the

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central cohorts the number of observations rise. In addition to this, the more recent cohorts are

based on smaller numbers of deaths because they contain the youngest age groups. It follows that

changes in trends in these recent cohorts should be examined with caution, as is reflected by the

wider confidence intervals for their estimates, even though they provide important information

towards future trends.

Another limit of the model is that it has difficulties discerning whether the major underlying trend is

a cohort or a period one when both their estimated effects share the same direction [18]. This model

also has a systematic tendency to favour cohort effects due to the greater weight its larger number of

parameters have in the modelling process.

Gastric Cancer Mortality

The widespread favourable trends in the cohort of birth and period of death effects in gastric cancer

mortality are not clearly understood, but most certainly reflect the effects of a more affluent diet,

that is richer in fresh fruit and vegetables, of better food conservation (including refrigeration), as

well as better hygiene, with a lower level ofHelicobacter pylori infection [19][20]. There is also

consistent proof of a correlation between the consumption of salt and salted foods [21][22][23]. As

well as salt, other methods of food conservation, such as smoking and curing, have been linked to

stomach cancer, but the evidence is less consistent. Tobacco smoking is also an important risk factor

in stomach cancer mortality [24].

In countries with more advanced health infrastructures, improved and newly developed methods of

diagnosis and treatment may also have played a role over the most recent calendar periods, but this

effect remains hard to quantify [25].

These favourable changes, that are essentially the result of a more developed socio-economic

environment and healthier lifestyle, have been slower to occur and are less widespread in some

countries of southern and eastern Europe. In particular the high prevalence ofH. pylori, aspects of

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diet, nutrition and food conservation as well as a higher prevalence of tobacco smoking are more

probably the causes of the differences observed between central-northern Europe and the south-

eastern countries.

The conclusions that can be drawn from this study are that, although in some countries such as

France, Sweden and Switzerland there seems to be an asymptote in gastric cancer mortality due to

the levelling seen in the effects of the most recent cohorts, there appears to be a lot of room for

improvement for the mortality rates of this cancer, particularly in southern and eastern European

countries, where these rates are high and the effects of the more recent cohorts have not shown

signs of slowdown such as in the Czech Republic, Estonia, Latvia and Italy.

Oral Cancer Mortality

The main finding from this analysis of oral and pharyngeal cancer mortality in Europe is the strong

excess mortality in Hungary, where the rate for middle aged men was 55/100,000, comparable to

those of lung cancer in several western countries (i.e., 50 to 60/100,000 in Germany, Italy and the

United Kingdom) [26][27]. In the most recent cohorts (i.e., those born after 1960) there were signs

of a possible near future reversal in trends. Male rates appreciably decreased in southern European

countries, such as France, Italy and Spain, which had the highest rates in the past, but not in several

northern European countries, such as Denmark, the United Kingdom and the Netherlands [28][29].

Oral and pharyngeal cancer mortality is comparatively low in European women, though trends were

upwards over the last decades [30], and rates in some countries (Hungary in particular, but also

Denmark and Romania) have reached relatively high levels, especially in middle aged women,

reflecting female drinking and smoking patterns in those populations. Across European countries,

there was still an over 10-fold variation in male oral and pharyngeal mortality between the highest

rates in Hungary (21.1/100,000) and Slovakia (16.9/100,000), and the lowest ones in Greece

(1.8/100,000) and Sweden (2.2/100,000).

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The diverging trends in the two sexes essentially reflect different patterns in tobacco smoking and

alcohol drinking. The favourable trends in male mortality rates reflect the fall in tobacco

consumption in men from most (western) European countries over the last few decades. A

favourable effect of stopping smoking is in fact evident already within few years after smoking

cessation, while the risk may remain persistently high for several years after stopping drinking [31]

[32]. Conversely, tobacco consumption has increased in women in several countries and this has led

to unfavourable oral and pharyngeal cancer mortality trends [33].

The geographic pattern of oral and pharyngeal cancer mortality trends also appears to be related to

changes in alcohol consumption [34]. The exceedingly high rates in Hungary and in a few other

countries of central and eastern Europe (Slovakia, Moldova, Lithuania, Croatia, Romania) can be

related to the overall quantity of alcohol consumed, but also to the drinking patterns (out of meals,

binge drinking) and to the type of alcohol consumed. In these countries, in fact, a substantial

proportion of alcohol derives from fruit (plums, peaches, apricots) and home-made alcoholic

beverages are widespread [35][36]. These may include high levels of acetaldehyde, which is an

established human carcinogen [37].

Age and cohort-specific analyses appear to reflect available information on the prevalence of

tobacco smoking in subsequent generations of men from major European countries, as well as

possibly the patterns of alcohol drinking, though generation specific data on alcohol consumption is

not available for most countries.

Although oral and pharyngeal mortality in Europe has declined in the last decade in men, there were

still rises in a few central and eastern European countries, reaching exceedingly high rates in

Hungary and Slovakia, which have now the highest rates on a European scale. The control of oral

and pharyngeal cancer, as well as of other alcohol- and tobacco-related cancers, remains therefore a

major public health problem in those areas of the continent.

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