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\newcommand{\Title}{Prevalence, incidence and mortality of\\
  type 1 and type 2 diabetes\\ in Denmark 1996--2016}
\newcommand{\Tit}{DMepi}
\newcommand{\Version}{Version 12 (xx words)}
\newcommand{\Dates}{August 2019}
\newcommand{\Where}{SDCC}
\newcommand{\Homepage}{\url{http://bendixcarstensen.com/} }
\newcommand{\Faculty}{\begin{tabular}{rl}
Bendix Carstensen
  & Steno Diabetes Center Copenhagen, Gentofte, Denmark\\
Senior Statistician
  & Clinical Epidemiology \\
  & {\small \& Department of Biostatistics,
               University of Copenhagen} \\
  & \mailto{bcar0029@regionh.dk} \quad \mailto{b@bxc.dk} \\
  & \url{http://BendixCarstensen.com} \\[1em]
Pernille Falberg R\o nn
  & Steno Diabetes Center Copenhagen, Gentofte, Denmark\\
Post Doc 
  & Clinical Epidemiology \\
  &  \mailto{pernille.falberg.roenn@regionh.dk} \\[1em]
Marit Eika J\o rgensen 
  & Steno Diabetes Center Copenhagen, Gentofte, Denmark\\
Head 
  & Clinical Epidemiology \\
  &  \mailto{marit.eika.joergensen@regionh.dk}
                      \end{tabular}}

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\section*{Abstract} 

\paragraph{Objective} was to give an overview of prevalence, incidence
and mortality of type 1 and type 2 diabetes in Denmark, and their
temporal trends.

\paragraph{Research Design and Methods} We constructed a diabetes
register from existing population-based health care registers,
including a classification of patients as type 1 or type 2 diabetes,
with coverage from 1996 to 2016. Using complete population records for
Denmark, we derived prevalence, incidence, mortality and SMR.

\paragraph{Results} The overall prevalence of diabetes at 2016 was
0.5\% for type 1 and 4.4\% for type 2 diabetes, with annual increases
since 1996 of 0.5\% for type 1 and and 5.5\% for type 2 diabetes.

Incidence rates of type 1 diabetes decreased by 3.5\% per year.,
with increase for persons under 25 years of age and a decrease for
older persons. Type 2 diabetes incidence increased 2.5\% per year
until 2011, decreased till 2014 and increased after that, similar in
all ages.

The annual decrease in mortality was 0.3\% for type 1 and 2.9\% for
type 2 diabetes. The mortality rate ratio between type 1 and type 2
diabetes was 1.9 for men and 1.6 for women. SMR decreased annually 2\%
for type 1 and 0.5\% for type 2 diabetes.

\paragraph{Conclusions} Incidence and prevalence of diabetes is
increasing but mortality among diabetes patients in Denmark is
decreasing faster than the mortality among persons without
diabetes. Type 1 diabetes carries a 70\% higher mortality than type 2
diabetes.
 
\newpage
%\input{intro}
\section{Introduction}

Surveillance of disease occurrence and mortality among diseased
persons is a prerequisite of quality control of the health care system
as a whole, and for planning of future resourcing of health care and
prevention.

Recently there have been indications in the literature that incidence
rates of diabetes have been declining in recent years
\cite{Geiss.2014,Read.2016a,Read.2016b,Norhammar.2016,Ruiz.2018}. While
surveillance of type 1 diabetes incidence in childhood and adolescence is well
established, few studies have been able to monitor type 1 diabetes incidence in
adulthood. Consequently, there have only been very few reports
\cite{Xu.2018,Bullard.2018} comparing the occurrence of type 1 diabetes and type 2 diabetes
diabetes and how patients with the two diseases fare relative to each
other with respect to mortality.

In population surveillance the most effective tools are
population-wide disease registers, that is recording of all new cases
of disease as they occur. In Denmark (as in the other Nordic
countries) there is a long tradition for population
registration. Denmark has one of the longest standing comprehensive
medicines registers going back to the beginning of 1995. This means
that it is possible to construct an accurate diabetes register based
on the medicines register and other health care registers. Moreover,
recent administrative developments in Denmark has made it possible to
make a good discrimination between type 1 diabetes and type 2 diabetes at the population
level, enabling a more detailed reporting of trends in diabetes in
Denmark separately for type 1 diabetes and type 2 diabetes.

The aim of this study was to describe the trends in prevalence,
incidence and mortality of type 1 diabetes and type 2 diabetes over the period 1996--2016 as
well as how these vary by age and (for mortality) duration of
diabetes.

%\input{methods}
\section{Material and methods}

\subsection{Register data} 

Denmark has population-wide registers covering virtually all aspects
of life, including heath care; and all registers are linkable by a
unique person id \cite{Pedersen.2011}. The Danish national health
care system (NHS) is run by the state (through 5 health care regions)
and covers all Danish citizens free of charge.

\subsubsection{Diabetes data}

We constructed a Danish diabetes register from existing Danish health
care registers, using all available sources to obtain maximal
sensitivity.  Diabetes patients were defined using the earliest of the
following as inclusion date (date of diagnosis):
\begin{itemize}
\item first diagnosis of diabetes (ICD-8: 249, 250; ICD-10: E10, E11;
  these \emph{ex}clude gestational diabetes) in the National Patient
  Register \cite{Lynge.2011} (NPR; 1977--).
\item first use of ``podiatry for diabetes patients'' in the National
  Health Services Register \cite{AndersenJS.2011} (NHSR, 1990--).
\item first date of purchase of any anti-diabetic medication (ATC
  A10xxx) in the Medicines Products Register \cite{Kildemoes.2011}
  (``Prescription register'') (MPR, 1995--).
\item earliest mentioned date of diagnosis in the Danish Adult
  Diabetes Database \cite{Jorgensen.2016} (DADD, 2005--, a clinical
  quality data base, with annual status of patients reported from
  outpatient clinics and GPs).
\item earliest date of eye examination recorded in the diaBase
  \cite{Andersen.2016} (diaB, 2009--, a clinical quality data base
  for eye screening of diabetes patients).
\end{itemize}

\paragraph{Type of diabetes}
Persons were classified as type 1 diabetes in the diabetes register if any of
the following criteria were met (and otherwise as T2D):
\begin{itemize}
\item Purchase of oral antidibatic drugs (OAD) before age 15
\item Purchase of insulin before age 30
\item DADD: classified as type 1 diabetes in the majority of the person's DADD
  records classify the person as type 1 diabetes (and similarly for T2D)
\item Not classified as either type 1 diabetes or T2D in DADD, but the majority of
  the patient's records from NPR classify the person as type 1 diabetes.
\end{itemize}
Finally, a person cannot be classified as type 1 diabetes if there is no recorded
date of insulin purchase. Persons not classifiable as type 1 diabetes were
classified as T2D.

% The main source of type 1 diabetes status was the DADD, which however only
% comprise persons alive at 2005 or later, so the sensitivity of
% the type 1 diabetes classification is declining backwards in time prior to 2005,
% particularly for persons who died before 2005.

Persons with an inclusion date in the register after 1996-01-01 were considered
incident cases of diabetes, whereas those included before were only
considered prevalent cases as of 1996-01-01 with uncertain date of
diagnosis.

Further details of the databases and the algorithm used are given in the ESM.

\subsubsection{Population data} 

Complete individual level register information on the entire Danish
population, including dates of birth, emigration, immigration and
death was available.

\subsection{Tabulation of data} 

We tabulated prevalent cases and total population as of 1 January
1996--2017 by type of diabetes (DM cases only), sex and 1-year age
class.

Follow-up time and new cases of type 1 diabetes, T2D and deaths were tabulated by
diabetes status (no DM, type 1 diabetes, T2D), sex, age and date of diagnosis and
date of birth in 1-year classes (Lexis triangles,
\cite{Carstensen.2007a}). For DM persons diagnosed after 1996 we
further tabulated by duration of disease in 1-year intervals (the
first year 3-month intervals)

A detailed account of data tabulation is given in the ESM.

\subsection{Statistical methods} 

All statistical models were fitted separately for men and women and
for no DM (where relevant), type 1 diabetes and T2D. For each tabulation unit we
devised the mean of current age, current date and duration of diabetes
and date of birth, using these as \emph{quantitative} explanatory
variables.

Prevalence was modeled separately for each of the dates 1 January
1996--2017 using restricted cubic splines by age. We also fitted
models jointly for all dates in order to devise an overall annual
relative change in prevalence.

Incidence and mortality rates were modeled using Poisson models with log
person time as offset and natural cubic spline effects of age and date
of follow-up and date of birth (age-period-cohort (APC) models
\cite{Carstensen.2007a}), using 2015-01-01 as reference point for
calendar time.

Mortality in type 1 diabetes and T2D rates were additionally modeled by duration
of diabetes.  Since the constant and linear effects of current age,
age at diagnosis and duration of diabetes cannot be separated (because
current age = age at diagnosis + duration), we reported the estimated
mortality as a function of current age, using separate curves for
persons diagnosed at ages 30, 45 etc. The mortality curves are thus
showing the \emph{joint} effect of current age, age at diagnosis and
duration of disease (see \textit{e.g.}  \cite{Huo.2018}, and the
detailed account of this in the ESM section on statistical methods).

Since only persons included after 1996-01-01 have a reliable date of
diagnosis, the mortality analyses using age at diagnosis and duration
were restricted to persons included after this date. For comparability
with other studies, age-specific mortality rates ignoring both age at
diagnosis and duration were reported both for the restricted group of
patients diagnosed after 1996-01-01 and for all patients (that is,
also including the prevalent cases as of 1996-01-01).

We computed M/W mortality rate-ratios for each type of diabetes, and
type 1 diabetes/T2D mortality rate-ratios for men and women separately.

The standardized mortality ratio (SMR) was modeled as the mortality,
but using the log of the expected number of deaths as offset, deriving
the SMR as the mortality rate-ratio between type 1 diabetes, resp. type 2 diabetes and no DM.

A complete and detailed description of the models and procedures is
given in the ESM section on Statistical methods.

\subsection{Software and documentation}

All registers mentioned were put at our disposal in deidentified,
linkable form by the research service of Statistics Denmark. 
% Only graphical and tabular information that holds no possibility for
% person identification can be taken out from Statistics Denmark's
% servers; all tables and graphs in this paper were generated there.
Approval for the project was granted by the Danish Data Protection
board. For register processing we used SAS version 12.4, including the
\verb|%Lexis| macro \cite{Lexis-macro}; for statistical
analyses and graphics we used \R\, version 3.5.0 \cite{R-man}, using
the \texttt{Epi} package, version 2.30 \cite{Epi.R}.

Documentation of the construction of the register and the analysis
files of prevalence and follow-up can be found in
\url{http://BendixCarstensen.com/DMreg/NewReg.pdf}, and a complete
account of all statistical analyses based on these is available in
\url{http://BendixCarstensen.com/DMreg/NewAna.pdf}.

% \input{results}
\section{Results}

In the period 1996--2016, 448,445 persons were recorded in our
register as diabetes patients in Denmark (table ESM 1), about 9\% as
type 1 diabetes and the rest as type 2 diabetes, and 83,441 (19\%)
were prevalent cases as of 1996-01-01. The median age at diagnosis for
type 1 diabetes patients was around 30 years, slightly older for men
than women, whereas it was around 63 for type 2 diabetes, a bit older
for women than for men (table 1).

\subsection{Prevalence} 

The age-specific prevalences at 1996, 2003, 2010 and 2017 are shown in
figure \ref{fig:prev-p} separately for type 1 diabetes and type 2
diabetes, the detailed numbers by sex and calendar time are shown in
the Electronic Supplementary Material (ESM), tables ESM 2 \& 3, and
illustrated in figure ESM 1.

The crude prevalence of type 1 diabetes (0--99 years of age) was quite
stable at 0.5\% for men and 0.4\% for women over the study period,
whereas the crude prevalence of type 2 diabetes tripled over the study
period--- from 1.2 to some 4.5\%, slightly more for men than women
(table ESM 3) --- an annual increase of 5.5\% per year (table 1).
 
The fraction of type 1 diabetes among all diabetes patients has
consequently dropped from about 25\% in 1996-01-01 to 10\% at
2017-01-01 (table ESM 1).

For type 1 diabetes the age-specific prevalence increased till about
age 40 for men and about 30 for women (figure \ref{fig:prev-p}, panels
a and b).  type 2 diabetes showed a peak age-specific prevalence at
2017-01-01 at age 80 at 19\% for men and 16\% for women (figure
\ref{fig:prev-p}, panels c and d).

\subsection{Incidence} 

Over the study period 1996--2016 there was a total of 363,664 new
cases of diabetes of which 19,712 (5.4\%) were type 1 diabetes (table
ESM 3). Persons over 100 and persons not resident at diagnosis were
excluded.

For type 1 diabetes we found that incidence rates in younger ages were
slightly increasing, whereas rates in older ages showed a decrease,
more among older persons; the overall average a decrease of 3.5\% per
year (figure \ref{fig:inc-p}, panels a \& b, figure ESM 2). For type 2
diabetes the patterns were almost identical in different ages, with an
increase till 2011, a down-turn until 2014 and an increase during the
last 2 years of the study period (figure \ref{fig:inc-p}, panels c \&
d).

The APC models (figure ESM 3) showed that men had higher incidence
rates than women, and also somewhat different age-patterns for type 1
diabetes incidence rates in men and women. For men there was an
increase to about age 18, a plateau and a slight increase to age 40,
whereas women showed an increase till about age 15 and a decrease
after that.

The absolute sizes of the incidence rates of type 1 diabetes and type
2 diabetes are hard to compare because of the differences in ages at
diagnosis, but broadly speaking type 2 diabetes occur at 20--30 times
the rates of type 1 diabetes (figure ESM 2).

\subsection{Mortality and Standardized Mortality Ratio} 

\subsubsection{Mortality}

Figure \ref{fig:mortSMR} shows the mortality for type 1 diabetes and type
2 diabetes patients by current age and duration of diabetes for select
ages at diagnosis of diabetes. Each curve shows the \emph{joint}
effects of increasing age and increasing diabetes duration.

Both for type 1 diabetes and type 2 diabetes we saw an initial peak in
mortality during the first 1--2 years after diagnosis, most pronounced
for type 1 diabetes, see figure \ref{fig:mortSMR}a. For type 1 diabetes
the mortality was smaller (at a given age) the earlier a person was
diagnosed (that is for longer diabetes durations), but this was not
the case if follow-up was restricted to after 2005 (ESM figures 4 \&
5). For type 2 diabetes men there was a higher mortality for longer
duration (earlier age at diagnosis) at any given age, whereas
mortality in type 2 diabetes women was independent of duration of
diabetes beyond 5 years see figure \ref{fig:mortSMR}b; restricting
follow-up to after 2005 resulted in a more pronounced effect of
duration (ESM figures 4 \& 5).

We found that the M/W mortality RR (black curves in figure ESM 4) were
close to 1.5 both for type 1 diabetes and type 2 diabetes in all ages.

Finally for type 1 diabetes we saw an increase in mortality by
calendar time till about 2005, but after this a consistent decrease
(figure ESM 4), the latter 4.9\% per year, whereas the mortality in
type 2 diabetes patients showed a consistent decrease over the entire
study period of 2.9\% per year (M: 3.3\%/y, W:2.5\%/y, table
\ref{tab:two}).

\paragraph{Type 1 diabetes vs. type 2 diabetes mortality rate ratio}

We found a higher mortality among type 1 diabetes patients relative to
type 2 diabetes (figure ESM 6); the first few years after diagnosis
more than 2-fold, but at 10 years of duration the type 1 diabetes/type
2 diabetes mortality RR was about 1.7, and decreasing by duration (and
hence by current age too). Overall the type 1 diabetes vs. type 2
diabetes mortality RR was 1.86 (1.79;1.93) for men and 1.55
(1.48;1.63) for women.

\subsubsection{Standardized Mortality Ratio}

The lower panels in figure \ref{fig:mortSMR} shows the Standardized
Mortality Ratio (SMR) --- the mortality in diabetes patients relative
to the mortality among persons without diabetes.
% Not surprisingly the peak in mortality for short duration of
% diabetes was also seen for the SMR.

For type 1 diabetes we found decreasing SMR by age/duration for a
given age at diagnosis, and an overall SMR at 2015 of about 4 for men
and 6 for women in younger ages, remaining at about 5 for both sexes
til age 60 and declining to 2 for both sexes in age 80. We also found
that the SMR on average was declining by some 2\%/year (table
\ref{tab:two}) over the period after 2005.

For type 2 diabetes we found that beyond 5 years of duration, the
slope in SMR by age/duration was somewhat smaller than the overall
slope by age, with a smaller SMR the older the age at diagnosis. Thus
the decline in overall SMR by age for type 2 diabetes is largely
attributable to an effect of age at diagnosis, and to a lesser extent
an effect of current age. As for type 1 diabetes we also saw that the
SMR for women is larger than for men, but we saw only a moderate
decline of 0.6\%/year (table \ref{tab:two}).

% \input{disc}
\section{Conclusions}

\subsection{Summary of findings}

Based on nationwide registers in Denmark we described the prevalence,
incidence and mortality of type 1 diabetes and T2D. Our main findings are
five fold.

First we found that the prevalence of type 1 diabetes hardly changed over the last
20 years, while type 2 diabetes increased from 1 to 4.5\%, so that type 2 diabetes now
constitute 90\% of all diabetes patients.  Second, the incidence of
type 1 diabetes increased slightly in the younger age groups (approx. 2 \%/year)
and declined in the older age groups (approx. 5\%/year) over the study
period.  Third, the type 2 diabetes incidence increased till 2011, declined till
2014, but seems to increase again after 2015. Fourth, the mortality
of type 1 diabetes patients is more than 50\% higher than that of type 2 diabetes patients.
Finally, we found an excess mortality for type 1 diabetes and type 2 diabetes compared to the
general population, highest for type 1 diabetes.

\subsection{Comparison with other studies}

\subsubsection{Prevalence and incidence}

The overall prevalence estimates by 2017-01-01 found in this study of
0.5\% for type 1 diabetes and 4.5\% for type 2 diabetes, are in the range of findings from
countries like Sweden, Norway and the US
\cite{Dabelea.2014x,Norhammar.2016,Ruiz.2018}. %[1-3].

Most studies in type 1 diabetes have reported the prevalence and incidence in
children and youth
\cite{Dabelea.2014x,Harjutsalo.2013,Dahlquist.2011}, % [1, 4, 5]
and only few \cite{Dahlquist.2011,Thunander.2008} %[5, 6]
have included older age groups as done in our study. The peak type 1 diabetes
incidence rates of 0.35 in men and 0.25 in women per 1,000 PY up to
late adolescence correspond to the rates found in countries like
Sweden, Finland, Norway and UK with an incidence over 0.20 per 1000 PY
\cite{Dahlquist.2011,Thunander.2008,Maahs.2010,Berhan.2011}. %[5-8].

In our study the incidence of type 1 diabetes increased up to 20 years of age and
after that declined for women, while it remained high for men until
age 40 and then decreased. The excess incidence of type 1 diabetes in men compared
to women is consistent with findings from other studies in high-risk
countries \cite{Wandell.2013,Gale.2001}. %[9, 10].
Similar to our findings of differential calendar time trends in type 1 diabetes
incidence at different ages, a nationwide Swedish study also reported
differential effects with increases in ages $<15$ years and decreases in
the older age groups (25--34 years) from 1983--2007, which would imply
a shift to younger age at diagnosis \cite{Berhan.2011}.%[8]

In the older age groups, the type 1 diabetes prevalence declined over the study
period. This was unexpected and may be an artifact, since improvements
in health care should have kept the prevalence more stable. This could
be due to changes in diagnostic criteria with a higher tendency to
diagnose insulin dependent individuals as type 1 diabetes in the past with a shift
to recognizing more of these as type 2 diabetes in the later part of the study
period. Since the type 1 diabetes classification before 2005 primarily relies on
the NPR records, miscoding of insulin using type 2 diabetes patients as type 1 diabetes
patients may be partly responsible for this. This also results in an
implausible increase in type 1 diabetes mortality up to around 2005, so
interpretation of type 1 diabetes mortality trends prior to 2005 should be
cautious.

For type 2 diabetes incidence, we saw an increase up to 2011 followed by a
downturn. The total number with type 2 diabetes in Denmark was 265,728 by
2017-01-01, far from the 386,700 estimated by the International
Diabetes Federation (IDF)
\cite{DiabetesAtlas.2017}. IDF’s assumption was based on the former
Danish Diabetes Register from 2012, and the huge overestimation by IDF
underlines the importance of regularly updated criteria for disease
monitoring. A decline in type 2 diabetes incidence or plateauing have been
reported in studies from Scotland\cite{Read.2016a,Read.2016b}, %[11]
USA\cite{Geiss.2014,Weng.2016} %[12, 13]
and Sweden \cite{Norhammar.2016}, %[2],
but in contrast to our study the decline / plateauing happened
earlier. 
% Analyses from the Scottish Diabetes registry by Read
% \textit{et al.}\cite{Read.2016a,Read.2016b}, %[11]
% found that the incidence of type 2 diabetes remained stable from 2004 to 2013 and
% was overall 4.88 (95\% CI 4.84, 4.90) and 3.33 (3.28, 3.32) per 1000
% PY in men and women, respectively. This is somewhat higher than what
% we observed in our study when comparing the age-specific incidence
% rates. However, while the rates were similar across birth cohorts in
% our study, in the Scottish study the incidence increased among young
% men, remained stable in young women and declined in older men and
% women.

A register-based study from Norway recently conducted by Ruiz
\textit{et al.} \cite{Ruiz.2018} found a decline in type 2 diabetes incidence in
the period 2009--2014 which after 2012 seemed to level off. %[3]
Both in Norway and Denmark the recommendation of \hb\ as diagnostic
test for diabetes was introduced in 2012 and is therefore likely to
contribute to changes in incidence rates around this time; however,
while the incidence in Norway seemed to level off we saw a
decline. Whether the decline in type 2 diabetes incidence observed after 2011 (in
ours and other studies) is due to changes in diagnostic criteria, a
true decline in incidence or because less undiagnosed cases is found,
is unknown.

\subsubsection{Mortality and SMR}

A decline in mortality among patients with diabetes have been reported
in several countries
\cite{Read.2016a,Read.2016b,Gregg.2012,Harding.2014,Lind.2013}. %[11, 14-16]
We also found a decline in absolute mortality among both type 1 diabetes and type 2 diabetes
over the period but with differential trends for type 1 diabetes and type 2 diabetes depending
on age at diagnosis and duration.

We found that mortality rates of type 1 diabetes are higher than those of type 2 diabetes for
patients of similar age, but with RR dissimilar between men (RR 1.84)
and women (RR 1.55). The higher mortality in type 1 diabetes corresponds to what
is seen in other studies
\cite{Harding.2014,Morgan.2018,Secrest.2010a}. %[15, 17, 18]

An Australian study found the all-cause mortality to decrease from
1997--2010 for both type 1 diabetes and type 2 diabetes patients with a larger decrease than
found in the general population \cite{Harding.2014}. %[15].
Similar trends have been observed in USA \cite{Gregg.2012} 
and Scotland \cite{Read.2016a,Read.2016b}, %[11]
which is consistent with our finding of an SMR decline for type 2 diabetes of
0.6\% per year.

% An Australian study found the all-cause mortality to decrease from
% 1997--2010 for both type 1 diabetes and type 2 diabetes patients with a larger decrease than
% found in the general population \cite{Harding.2014}. %[15].
% They found an excess risk of all-cause mortality of 3 and 1.2 times
% the mortality in the general population, comparable to the SMRs we
% found.

% In the USA\cite{Gregg.2012} %
% a substantial decline in CVD-mortality and all-cause mortality was
% observed among type 2 diabetes patients in the period 1997--2006 exceeding the
% improvement in the non-diabetic population. Read \textit{et
%   al.}\cite{Read.2016a,Read.2016b} %[11]
% found that the SMRs associated with type 2 diabetes in Scotland remained constant
% from 2004 to 2013, with the highest SMRs observed among younger
% people, consistent with the findings in our study.

Early age at diagnosis (and hence longer duration of diabetes) was
associated with a smaller mortality among type 1 diabetes patients in our study
but a larger mortality among type 2 diabetes patients, although the latter effect
was small and mostly confined to men. This means that duration of type 2 diabetes
has limited effect beyond the first 2 years after diagnosis. In
contrast with our results in type 1 diabetes, a study by Rawshani \ea conduced
in Sweden reported a higher mortality with younger age at diagnosis of
type 1 diabetes \cite{Rawshani.2018}, % [19].
but it was not clear how this study included duration and current
age, which may have affected the reported effect of age at diagnosis.

\subsection{Strengths and weaknesses}

The major strengths of our study is that it covers the entire Danish
population, the long coverage period (21 years) and our ability to
distinguish type 1 diabetes and type 2 diabetes. Moreover, we have made full use of the
register data by modeling the effects of age, calendar time and for
mortality also the \emph{duration} of diabetes, using the quantitative
nature of the time variables age, duration and calendar time.

The weakness of our data base is that inclusion date (which is used as
proxy for date of diagnosis) is based solely on administrative
records. 
% This lead us to only use persons included after 1996-01-01 in
% analyses where duration of diabetes was needed.

% While the total population coverage is a strength it is also a
% weakness, because we are only able to use variables that are recorded
% for the entire population; in this study sex, and dates of birth,
% diagnosis and death and type of diabetes. Including clinical and
% lifestyle variables in the study of diabetes occurrence and -mortality
% would be desirable, but this type of information is not likely to be
% available at the population level anytime soon.

While the classification of patients as type 1 diabetes or type 2 diabetes is a strength, the
limited coverage of the DADD (2005 ff.) most likely
\emph{underestimates} the number of type 1 diabetes patients prior to 2005, and in
particular among those who died before 2005, which possibly means that
our mortality estimates for type 1 diabetes prior to 2005 are downward
biased. Analyses of mortality restricted to
the period after 2005 indicated that our conclusions about duration
effects may be biased downwards, and that mortality at a given is
increasing with increasing duration.

Furthermore, type 2 diabetes incidence among women under 40 may be underestimated
due to the classification as possible PCOS patients if metformin only
is used in the age range 18--40.

\subsection{Conclusion and implications} 

During a 21-year period we observed increasing prevalence and
incidence rates but with a decreasing incidence of type 2 diabetes from 2012,
while the incidence for type 1 diabetes remained more stable over the period. The
decline in mortality were found both among type 1 diabetes and type 2 diabetes, but mostly for
type 1 diabetes in the most recent period, which may be due to improved
treatment. Despite a reduction in mortality, diabetes patients still
experience an excess mortality relative to persons without diabetes,
highest for type 1 diabetes patients, which can only partially be attributed to
differences in disease duration. The excess mortality underlines the
need for continuous improvements in prevention and treatment of
complications especially among type 1 diabetes patients.

% \subsection{Summary}

% \begin{itemize}
% \item The number of type 1 diabetes patients is about 10\% of all diabetes patients
% \item The overall prevalence of type 1 diabetes by 2017-01-01 was 0.5\%, for type 2 diabetes 4.5\%
% \item Incidence rates of type 1 diabetes decreased overall 3.5\%/year, but
%   increased for young ages (2\%/y at age 15) and decreased for older
%   ages ($-5$\%/y at age 50).
% \item Incidence rates of type 2 diabetes increased on average 2.2\% year, but
%   showed considerable fluctuations after 2011.
% \item Mortality rates of type 1 diabetes are higher than those of type 2 diabetes for patients
%   of similar age; mortality RR is 1.84 for men and 1.55 for women.
% \item Mortality is 2-3 fold elevated during the first 1.5 year after
%   diagnosis both for type 1 diabetes and type 2 diabetes, most pronounced for type 1 diabetes
% \item Early age at diagnosis is associated with smaller mortality for
%   type 1 diabetes patients, but has little impact on type 2 diabetes mortality. The latter
%   means that duration of type 2 diabetes has negligible effect beyond the first
%   2 years after diagnosis 
% \item The men/women mortality rate-ratio was around 1.5 for both type 1 diabetes
%   and type 2 diabetes
% \item The SMR was around 5 for type 1 diabetes, for type 2 diabetes it was 4 at age 40,
%   decining to 1.5 at age 80
% \item The relative mortality (SMR) was decreasing 2\% per year, for
%   type 2 diabetes only 0.5\% per year
% \end{itemize}

% \input{xtra}
\section{Paraphernalia}

\subsubsection{Acknowledgments}

We are grateful to the Danish Clinical Registries (RKKP) for providing
access to the DADD and diaB for the construction of the diabetes
register. We appreciate the meticulous and speedy support of the
Research Service of Statistics Denmark.

\subsubsection{Data availability}

The data for this study are population wide registers, placed at our
disposal on the servers of Statistics Denmark. They are barred from
release to the public on grounds of confidentiality. 

\subsubsection{Funding}

The substudy regarding T1D was funded by Sanofi Aventis. The company
had no influence on study design or analyses. The remainder of the
study was funded through the core research budget of SDCC.

\subsubsection{Duality of interest}

BC and MEJ own shares in NovoNordisk. BC has received lecture and
consultancy fees from NovoNordisk and LeoPharma. MEJ is PI on a trial
sponsored by AstraZeneca, and received research grants from AMGEN AB,
Astra Zeneca and Sanofi Avensis,

\subsubsection{Contribution statement}

BC and MEJ conceived the structure of the underlying register, and
designed the study. PFR provided support for obtaining data access
and contributed to data definition. BC detailed the statistical
methods needed, performed all data analysis, and wrote a first draft
of the manuscript. MEJ and PFR contributed substantially to the
writing of the manuscript. All authors contributed to critical
revision and take responsibility for the content.


}
\newpage
\renewcommand{\refname}{References}
\bibliographystyle{unsrt}
\bibliography{%
/home/bendix/art/bibtex/BxC,%
/home/bendix/art/bibtex/Stat,%
/home/bendix/art/bibtex/DMCa,%
/home/bendix/art/bibtex/Diabetes,%
../DMreg%
}
\addcontentsline{toc}{section}{\refname}

\clearpage
% \input{tables}
% \begin{table}[t]
%   \centering
%   \caption[Persons, follow-up time and ages and dates of entry and
%   follow-up from the Danish Diabetes Register.]{Persons, follow-up
%     time and ages and dates of entry and follow-up from the Danish
%     Diabetes Register. Includes also persons over 100 years of age
%     and time during nonresidency in Denmark. Medians and
%     inter-quartile ranges (IQR, \nth{25} and \nth{75}
%     percentiles). $<\!\!1996$ refer to the prevalent cases as of
%     \nth{1} January 1996; $1996+$ refer to diabetes cases included in
%     the register after this date.}  
%   \label{tab:one}
%   % \begin{tabular}{@{\extracolsep{1ex}}rrr@{\hspace*{1ex}(\hspace*{-1ex}}r@{;\hspace*{-1ex}}r@{)}r%
%   %                                        @{\hspace*{1ex}(\hspace*{-1ex}}r@{;\hspace*{-1ex}}r@{)}r}
% \begin{tabular}{@{\extracolsep{1ex}}rrrrrrrr}
% \toprule
% %\multicolumn{3}{l}{Number of persons} \\
% No. persons & Sex && \multicolumn{1}{c}{T1D} 
%                   && \multicolumn{1}{c}{T2D} 
%                   && \multicolumn{1}{c}{DM} \\
% \cmidrule{1-1}
% \cmidrule{2-2}
% \cmidrule{3-4}
% \cmidrule{5-6}
% \cmidrule{7-8}
% %\midrule
% %            sex         M         W       Sum
% % >1995 DMtp                                  
% % FALSE T1          12,378     9,596    21,974
% %       T2          30,338    31,129    61,467
% %       Sum         42,716    40,725    83,441
% % TRUE  T1          11,646     8,173    19,819
% %       T2         192,418   152,767   345,185
% %       Sum        204,064   160,940   365,004
% % Sum   T1          24,024    17,769    41,793
% %       T2         222,756   183,896   406,652
% %       Sum        246,780   201,665   448,445
% $<1996$ & M & \multicolumn{2}{r}{12,378} & \multicolumn{2}{r}{ 30,338} & \multicolumn{2}{r}{ 42,716} \\ 
%         & W & \multicolumn{2}{r}{ 9,596} & \multicolumn{2}{r}{ 31,129} & \multicolumn{2}{r}{ 40,725} \\[0.1em]
%       & M+W & \multicolumn{2}{r}{21,974} & \multicolumn{2}{r}{ 61,467} & \multicolumn{2}{r}{ 83,441} \\[0.3em]
% $1996+$ & M & \multicolumn{2}{r}{11,646} & \multicolumn{2}{r}{192,418} & \multicolumn{2}{r}{204,064} \\ 
%         & W & \multicolumn{2}{r}{ 8,173} & \multicolumn{2}{r}{152,767} & \multicolumn{2}{r}{160,940} \\[0.1em]
%       & M+W & \multicolumn{2}{r}{19,819} & \multicolumn{2}{r}{345,185} & \multicolumn{2}{r}{365,004} \\[0.4em]
% Total & M+W & \multicolumn{2}{r}{41,793} & \multicolumn{2}{r}{406,652} & \multicolumn{2}{r}{448,445} \\ 
% \bottomrule
% \ \\[0.2ex]
%      & & \multicolumn{3}{c}{T1D} 
%        & \multicolumn{3}{c}{T2D} \\
% \cmidrule{3-5}
% \cmidrule{6-8}
%      & & Median & \multicolumn{2}{c}{IQR} 
%        & Median & \multicolumn{2}{c}{IQR} \\
% \cmidrule{3-3}
% \cmidrule{4-5}
% \cmidrule{6-6}
% \cmidrule{7-8}
% \multicolumn{3}{l}{Date of inclusion$^{1,2}$} \\
% $1996+$ & M &   2005.7 &   2000.5 &   2010.9 &    2008.5 &    2003.1 &    2012.4 \\
%         & W &   2005.6 &   2000.4 &   2011.0 &    2008.3 &    2002.8 &    2012.3 \\
% \midrule
% \multicolumn{3}{l}{Age at inclusion$^1$} \\
% $1996+$ & M &  30.7   &15.7   &47.6   &62.1   &53.0   &70.6 \\
%         & W &  26.8   &12.4   &48.5   &64.6   &54.1   &74.2 \\
% \midrule
% \multicolumn{3}{l}{Person-years} \\
% $<1996$ & M &  21.0 &   9.5 &  21.0 &   8.9 &   3.6 &  18.2 \\
%         & W &  21.0 &   9.3 &  21.0 &   9.1 &   3.8 &  18.9 \\
% $1996+$ & M &   8.9 &   4.3 &  14.5 &   6.0 &   3.0 &  10.5 \\
%         & W &   9.3 &   4.4 &  14.9 &   6.1 &   3.1 &  10.9 \\
% \midrule
% \multicolumn{3}{l}{Date of follow-up$^{2,3}$} \\
% $<1996$ & M & 2006.5 & 2000.7 & 2006.5 & 2000.4 & 1997.8 & 2005.1 \\
%         & W & 2006.5 & 2000.6 & 2006.5 & 2000.6 & 1997.9 & 2005.5 \\
% $1996+$ & M & 2011.0 & 2008.0 & 2013.9 & 2012.5 & 2008.8 & 2014.6 \\
%         & W & 2011.0 & 2008.1 & 2014.0 & 2012.3 & 2008.7 & 2014.6 \\
% \midrule
% \multicolumn{3}{l}{Age at follow-up$^3$} \\
% $<1996$ & M &    53.5 &   41.3 &   65.3 &   70.9 &   62.5 &   78.2\\
%         & W &    55.5 &   41.3 &   71.0 &   76.0 &   66.6 &   82.7\\
% $1996+$ & M &    36.5 &   20.6 &   52.4 &   65.9 &   57.1 &   73.9\\
%         & W &    32.4 &   17.4 &   53.8 &   68.4 &   58.2 &   77.7\\
% \bottomrule
%   \end{tabular}\\[0.2ex]
% \raggedright
% \noindent \small $^1$ Persons included before 1996 do not have a
% reliable date of inclusion, hence neither\\[-0.4ex]\quad date nor age
% at inclusion can be meaningfully computed.\\[0.2em]
% \noindent \small $^2$ Dates are coded so that \nth{1} January 2006 is
% 2006.000 and \nth{31} December 2006 is 2006.997.\\[0.2em]
% \noindent \small $^3$ Median and IQR for the median
% date/age of follow-up for each person.
% \end{table}

\begin{table}[t]
  \centering
  \caption[Time trends in prevalence, incidence, mortality and SMR.]%
    {Average change (\%/year) in prevalence, incidence, mortality
    and SMR of diabetes in Denmark over the period 1996--2016.}     
  \label{tab:two}
  \begin{tabular}{llr@{\ \ (}r@{;}r@{)}c%
                    r@{\ \ (}r@{;}r@{)}}
\toprule
&& \multicolumn{3}{c}{Men} &
 & \multicolumn{3}{c}{Women} \\
\cmidrule{3-5} \cmidrule{7-9}
\multicolumn{2}{l}{\% per year} 
 & \multicolumn{1}{r}{Change} & \multicolumn{2}{c}{95\%CI} &
 & \multicolumn{1}{r}{Change} & \multicolumn{2}{c}{95\%CI}\\
\midrule
  Prevalence & T1D & $ 0.51$ & $ 0.46$ & $ 0.57$ && $ 0.52$ & $ 0.46$ & $ 0.59$ \\
             & T2D & $ 5.64$ & $ 5.61$ & $ 5.67$ && $ 5.22$ & $ 5.19$ & $ 5.24$ \\[1ex]
  Incidence  & T1D & $-3.27$ & $-3.59$ & $-2.94$ && $-3.78$ & $-4.19$ & $-3.37$ \\
             & T2D & $ 3.43$ & $ 3.15$ & $ 3.61$ && $ 3.16$ & $ 2.98$ & $ 3.34$ \\[1ex]
  Mortality  & T1D & $-0.51$ & $-1.34$ & $ 0.33$ && $-0.17$ & $-1.19$ & $ 0.86$ \\
             & T2D & $-3.30$ & $-3.48$ & $-3.13$ && $-2.53$ & $-2.73$ & $-2.33$ \\[1ex]
  SMR        & T1D & $ 2.55$ & $ 1.69$ & $ 3.42$ && $ 2.45$ & $ 1.40$ & $ 3.51$ \\
             & T2D & $-0.46$ & $-0.28$ & $-0.64$ && $-0.23$ & $-0.44$ & $-0.03$ \\
\midrule
\multicolumn{3}{l}{Follow up only $>2005$}\\
  Mortality  & T1D & $-5.10$ & $-3.53$ & $-6.63$ && $-4.98$ & $-2.88$ & $-7.03$ \\     
             & T2D & $-3.64$ & $-3.36$ & $-3.92$ && $-3.06$ & $-2.74$ & $-3.38$ \\[1ex]
  SMR        & T1D & $-1.89$ & $-0.28$ & $-3.48$ && $-2.28$ & $-0.07$ & $-4.36$ \\     
             & T2D & $-0.72$ & $-0.43$ & $-1.01$ && $-0.60$ & $-0.27$ & $-0.92$ \\     
\bottomrule
  \end{tabular}
\end{table}

\clearpage
% \input{figures}
\newcommand{\ff}{/home/bendix/sdc/DMreg/NewReg/nyr/graph}

\begin{figure}
  \centering
  \includegraphics[width=1.0\textwidth]{\ff/prev-2tp2sxci-glm}
  \caption[Age-specific prevalence of T1D and T2D in Denmark as of 1
  January 1996, 2003,\ldots,2017]{Age-specific prevalence of T1D (a,b)
    and T2D (c,d) in Denmark as of 1 January
    1996,2003,\ldots,2017. Note the different $y$-axes in the upper
    and lower panels. Blue curves are men, red curves women; shaded
    areas represent 95\% confidence intervals. a: men, T1D; b: women,
    T1D; c: men, T2D; d: women, T2D.}
  \label{fig:prev-p}
\end{figure}

\begin{figure}
  \centering
  \includegraphics[width=1.0\textwidth]{\ff/inc-per-apc}
  \caption[Incidence rates of T1D at ages 10--60 and T2D at ages
  40,\ldots,90.]{Age-specific incidence rates in different ages as of
    1 January 2015, derived from Age-Period-Cohort models. Note the
    different $y$-axes in the upper and lower panels but that the
    \emph{relative} extent of the axes are the same for T1D and
    T2D. Blue curves are men, red curves women; shaded areas represent
    95\% confidence intervals. a: men, T1D; b: women, T1D; c: men,
    T2D; d: women, T2D}
  \label{fig:inc-p}
\end{figure}

\begin{figure}
  \centering
  \includegraphics[width=1.0\textwidth]{\ff/mort-art-mortsmr}
  \caption[Mortality and SMR among type 1 diabetes and type 2 diabetes
  patients.]{Age-specific mortality rates (a,b) and SMR (c,d) as of
    2015-01-01 for type 1 diabetes (a,c) and type 2 diabetes
    (b,d). Each curve represents the mortality among patients
    diagnosed at ages 15, 25, 35, 45, 55 (type 1 diabetes)
    respectively 30, 40, 50, 60, 70 (type 2 diabetes), indicated by
    gray vertical lines. Each curve thus
    represents the \emph{joint} effect of attained age and duration of
    diabetes for a given age at diagnosis and duration from 0 to 20
    years. \newline Thick dotted curves are from a model ignoring age
    at diagnosis and duration of diabetes; thin full lines
    additionally includes prevalent cases as of 1996-01-01 in the
    modelling.\newline Blue curves are men, red curves women.}
  \label{fig:mortSMR}
\end{figure}

% \begin{figure}
%   \centering
%   \includegraphics[width=1.0\textwidth]{\ff/mort-art-m}
%   \caption[Mortality rates among T1D and T2D patients.]{Age-specific
%   mortality rates as of 2015-01-01 for T1D (upper panel) and T2D
%   (lower panel). Each curve represents the mortality among patients
%   diagnosed in ages 15, 25, 35, 45, 55 (T1D) respectively 30, 40,
%   50, 60, 70 (T2D). Each curve thus represents the \emph{joint}
%   effect of attained age and duration of diabetes for a given age at
%   diagnosis. \newline Thick dotted curves are from a model ignoring
%   age at diagnosis and duration of diabetes; thin full lines
%   includes prevalent cases as of 1996-01-01 in the model.\newline
%   Blue curves are men, red curves women.}
%   \label{fig:mort}
% \end{figure}

% \begin{figure}
%   \centering
%   \includegraphics[width=1.0\textwidth]{\ff/mort-art-smr}
%   \caption[SMR among T1D and T2D patients.]{Age-specific SMR
%     (rate-ratio relative to non-DM population) as of 2015-01-01 for
%     T1D (upper panels) and T2D (lower panels). Each curve represents
%     the SMR among patients diagnosed in ages 15, 25, 35, 45, 55 (T1D) respectively
%     30, 40, 50, 60, 70 (T2D). Each curve thus represents the \emph{joint}
%     effect of attained age and duration of diabetes for a given age at
%     diagnosis. \newline Thick dotted curves are from a model ignoring
%     age at diagnosis and duration of diabetes; thin full curves additionally
%     includes prevalent cases as of 1996-01-01.\newline Blue curves are
%     men, red curves women, and shaded areas represent 95\% confidence
%     intervals.}
%   \label{fig:SMR}
% \end{figure}

\end{document}
