The Epidemiology of Diabetes and Cancer Detailed...

The Epidemiology ofDiabetes and Cancer

Detailed report

SDCMay 2014

http://BendixCarstensen.com/DMCa/EpiDMCa

Version 1.3

Compiled Thursday 31st July, 2014, 15:10from:

C:/Bendix/Steno/DM-register/NDR/projects/Cancer/papers/EpiDMCa/Report.tex

Bendix Carstensen Steno Diabetes Center, Gentofte, Denmark& Department of Biostatistics, University of Copenhagen

[email protected]

http://BendixCarstensen.com

Marit Eika Jørgensen Steno Diabetes Center, Gentofte, [email protected]

Søren Friis Danish Cancer Society, Copenhagen, [email protected]

http://BendixCarstensen.com/DMCa/EpiDMCahttp://BendixCarstensen.com

Contents

1 Article 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Incidence of cancer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.2 Mortality after cancer diagnosis . . . . . . . . . . . . . . . . . . . . . 31.1.3 The broader picture . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Background calculations 152.1 Comparing cancer RRs from published studies . . . . . . . . . . . . . . . . . 152.2 Overview of rate computation . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2.2 Total population follow-up . . . . . . . . . . . . . . . . . . . . . . . . 252.2.3 The follow-up after DM and Ca . . . . . . . . . . . . . . . . . . . . . 272.2.4 Setting up the analysis data frame . . . . . . . . . . . . . . . . . . . 32

2.3 Modelling of rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.3.1 Prerequisites for the natural splines . . . . . . . . . . . . . . . . . . . 362.3.2 Computing the state probabilities . . . . . . . . . . . . . . . . . . . . 382.3.3 Average change in cancer incidence rates . . . . . . . . . . . . . . . . 392.3.4 Secular trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.3.5 Transition rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.3.6 Transition probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 42

ii

Chapter 1

Article

1

Abstract

The literature on cancer occurrence in persons with diabetes has almost invariably beenconcerned with relative measures. In this paper we briefly review this, but the aim is toquantify the absolute occurrence of diabetes and cancer in the population in order to give afuller picture, which also includes the competing mortality risk. Overall we find that some35% of the population will have a diagnosis of diabetes in their lifetime, 40% a diagnosis ofcancer, and about 15% will have both diagnoses. The impact of differing mortality betweenpersons with and without diabetes is illustrated by the fact that a person without diabetesat age 50 have a smaller lifetime risk of cancer than a person aged 50 with diabetes. Thus,the differences in cancer occurrence between persons with and without diabetes are ofquantitatively smaller importance than the differences in mortality.

2 Article Diabetes & Cancer

Keywords: Diabetes and cancer, epidemiology, demography, lifetime risk of diabetes andcancer, absolute risk of diabetes.

1.1 Introduction

The link between diabetes and cancer occurrence is well established, and comprehensivepopulation-based studies have demonstrated that the association relates to both cancerincidence and mortality [1, 2, 3].

Recently, an increasing number of studies have examined cancer incidence amongpatients with diabetes, particularly following the report in 2009 of a potential associationbetween the insulin analog glargine and cancer risk [4, 5, 6, 7]. The majority of the studieshave focused on comparisons of cancer incidence among diabetes patients using differentantidiabetic regimes. However, these studies are prone to bias due to confounding byindication, as illustrated convincingly Andersson et al. [8] who reported that the use of anytype of antidiabetic drug, whether insulins or various forms of oral antidiabetics (OADs),was associated with a markedly elevated rate ratio (RR) for cancer shortly after initiationof the drug, which subsequently declined to a value close to 1.

To our knowledge, the study by Andersson et al. is the only study published so far thatfollowed the entire population of diabetes patients, avoiding selection of subgroups ofpatients, and thus appear to be the most credible study because of minimized selectionbias. We have previously reported that newly diagnosed diabetes patients experience astrongly elevated excess cancer incidence shortly after the diagnosis which levels off 2–3years following the diagnosis [9], and a similar pattern has also been observed in otherstudies [1, 10, 8]. Hence, based on the the available studies, any potential long-term effectsof antidiabetic drugs are likely to be small and difficult to ascribe to a particularcause-effect relationship, if any.

As any potential long-term effects of diabetes drugs are likely to be small in terms ofmodification of cancer occurrence, we have chosen to ignore these in the present broaderdiscussion of the relationship between diabetes and cancer occurrence.

In this paper we have chosen to focus on the general population impact of diabetes andcancer rather than any comprehensive discussion of the potential relationship betweendiabetes and cancer occurrence. Specifically, we will evaluate the high mortality amongcancer patients with pre-existing diabetes, as demonstrated in a few previous studies[11, 12], and quantify the effects of this at the population level.

1.1.1 Incidence of cancer

Cancer incidence studies have shown cancer incidence rate ratios of similar magnitude incomparisons of diabetes patients and persons without diabetes; Figure 1.1 compares theRR of different types of cancer between people with and without diabetes from the majorpopulation based studies of diabetes occurrence, that is studies with more than 1000 cancercases among persons with diabetes. Key characteristics of these studies are presented inTable 1.1.

The general picture from the major cancer incidence studies are strongly elevatedincidence rates of liver and pancreatic cancer, and somewhat elevated rates of cancer of theendometrium, kidney and to a smaller extent of cancers of the digestive system (Figure

Article 1.1 Introduction 3

Table 1.1: Population based studies of incidence of several major cancer sites in diabetespatients compared to non-diabetics, with more than 1000 cancers among DM patients.

No. cancersStudy Country No. sites in DM ptt.

Adami et al. [1] Sweden 21 2,417Wideroffa et al. [2] Denmark 29 8,831Coughlinb et al. [3] USA 16 2,183Johnson et al. [10] Canada 10 12,438Carstensena et al. [9] Denmark 24 22,826Sasazuki et al. [13] Japan 16 2,388Kajüter et al. [14] Germany 8 3,664

aThese two Danish studies are non-overlapping.bCancer mortality study.

1.1). Single-site studies have generally reported colon cancer as a cancer type occurring inclear excess among people with diabetes. However, this is likely because colon cancer is afairly frequent disease and hence exhibits clearly detectable rate elevations as opposed torarer cancers which could have similarly elevated rates without formally significantelevation due to limited number of events in the study populations.

However, little attention has been paid to differences between people with and withoutdiabetes in relation to the actual size and shape of age-specific cancer incidence rates.Using Danish data we found that the average increase in cancer incidence rates from age 40to age 70 years was 10.6% per year for men and 7.2% per year for women, corresponding toincreases of 35% and 23%, respectively, over 3 years of age. This means that the observedelevation of cancer risk in persons with diabetes by a factor of 1.1–1.2 is of a magnitudethat is smaller than that conveyed by an aging of 3 years.

1.1.2 Mortality after cancer diagnosis

It is also well known that cancer patients with pre-existing diabetes have a higher mortalitythan cancer patients without diabetes at diagnosis, however, it is difficult to discernwhether this is due solely to the impaired survival associated with the two diseases or ifthere is interaction between diabetes and cancer which worsen the cancer prognosis. In asystematic review, Barone et al. [15] estimated that the overall mortality rate-ratiobetween cancer patients with and without cancer was 1.41. In a recent nationwide study inDenmark [11], we observed a similar excess mortality among cancer patients with diabetesat diagnosis, and with increasing mortality rates by increasing severity of diabetes.

1.1.3 The broader picture

The above mentioned studies are all aimed at describing differences in patterns of cancerincidence rates or mortality rates of cancer patients between persons with and withoutdiabetes.

These types of comparisons are illustrated in context in Figure 1.2 in which cancerincidence rates are shown in red and mortality rates among cancer patients in black.


Studies of diabetes and cancer incidence and mortality have traditionally focused only onpairwise comparison of the thick and thin transition rates in Figure 1.2. It is commendableto describe variations between these rates that may give clues to mechanisms underlyingthe different (typically higher) rates among persons with diabetes compared with thosewithout diabetes. For most of the rates in Figure 1.2, however, the major determinant isage, so by only comparing the rates (controlling for age), the impact of the aging in thepopulation is lost.

As an example of how to incorporate the impact of the age-dependence of the incidenceof cancer and mortality in the general population, we will use nationwide Danish data toestimate all 9 sets of rates shown in Figure 1.2 by sex, age and calendar time. This willeventually enable us to illustrate what fraction of persons in a given age who willeventually contract cancer, depending on whether they suffer from diabetes at the giventime. It will also provide the possibility to quantify the fraction of persons in a birth cohortwho will end in each of the 5 “death” states.

1.1.3.1 Duration dependence

While it is known that both mortality and cancer incidence depends strongly on diabetesduration, in that it is elevated during the initial period after diagnosis (surveillance bias),the period is for most types of events quite short, so ignoring the duration effects will haveonly minor influence on the summary measures.

1.2 Methods

We merged the Danish National Diabetes Register [16, 17] with the Danish CancerRegister [18], and classified all follow up time after 1995 and after any of the two diagnosesby sex, age, calendar time and date of birth in 1-year classes (Lexis triangles). We classifieddeaths and diagnoses of diabetes and cancer similarly. We also extracted the totalpopulation size and number of deaths from the Human Mortality Data Base [19]. Bysubtracting the total number of person-years and deaths in the diabetes and/or cancerpopulation, we obtained the risk time and person-years in the part of the population notdiagnosed with any of the two diseases (the ”Well” state in Figure 1.2).

We then modelled all 9 transition rates shown in Figure 1.2 using age-period models withnatural splines [20]. We assumed that the mortality rates for cancer patients with andwithout diabetes were proportional, that is differed only by a multiplicative constant forany combination of age and calendar time.

We used the estimated age-specific rates from these models to calculate the burden ofdisease in a hypothetical population under the scenario of age-specific rates equal to theestimated cross-sectional age-specific rates as of 1 January 2005. The practical calculationswere done by multiplying a vector of initial state-distribution (with all persons starting atage 0 in state “Well”) successively by the age-specific transition matrices derived from thethe rates for every 1/10 of a year of age.

A complete account of the data acquisition, rate-estimation and state-probabilitycalculations and graphical displays are available ashttp://BendixCarstensen.com/DMCa/EpiDMCa/Report.pdf.

We computed the following quantities:

http://BendixCarstensen.com/DMCa/EpiDMCa/Report.pdf

Article 1.3 Results 5

• The fraction of a population in each of the 9 different states at any age.

• The fraction of a 50/60/70 year old non-diseased population that are in each of thestates at any subsequent age.

• The fraction of a 50/60/70 year old population with diabetes but not cancer that arein each of the states at any subsequent age.

This approach yields insight into what fraction of the population that is likely to beaffected by the two diseases, and in particular how the relationship of cancer incidencerates between people with and without diabetes translate into population experience whenthe mortality rates are taken into account.

1.3 Results

Figure 1.3 shows the estimated rates by age and calendar time. It is seen that both thecancer incidence and, notably, diabetes rates are increasing, whereas the mortality rates aredecreasing by calendar time, and more rapidly among people with diabetes.

Moreover, it is seen that mortality rates for persons with diabetes and/or cancer areconverging by age, so that there are only minor differences between the three groups ofpersons after age 80. This is presumably reflecting the fact that persons without bothdiabetes and cancer in high ages most likely suffer from other severe diseases.

When using these rates to obtain probabilities of being in one of the 9 states at any age(Figure 1.4), and derive the probability of having a diagnosis of cancer, respectivelydiabetes before a given age (Figure 1.5), we found a lifetime risk of cancer of 44% for bothmen an women, and corresponding lifetime risk of diabetes of 35% for men and 33% forwomen. The lifetime risk of both diseases was 15% for men and 13% for women (Figure1.5).

Of all persons who contracted diabetes in their lifetime, 43% of men and 41% of womenhad a diagnosis of cancer too; only slightly less than the figures for the entire population.

Examining the conditional distribution given that a person was alive and free of bothdiabetes and cancer at age 50, 60 or 70 years (Figure 1.6, columns 1 & 3), we found thatthe lifetime risk of cancer were 45, 44 and 38% among men and 41, 37 and 29% amongwomen. Comparing to persons who were alive and diagnosed with diabetes only at thesame ages (Figure 1.6, columns 2 & 4), the lifetime risk of cancer were 37, 36 and 32%among men and 37, 34 and 27% among women. So the lifetime risk of cancer for a personwith diabetes at a given age is smaller than for a person without diabetes at the same age,and this risk decreases by the age considered.

1.4 Discussion

The risk of cancer increases among persons with diabetes with increasing severity of thediabetic disease. It is not clear (let alone discernible) whether this a result of thedisease-processes associated with diabetes or if latent cancers contribute to thedeterioration of the diabetic status of patients.

With the exception of liver and pancreatic cancer, it is also clear that the excess riskamong persons with diabetes is moderate, in the order of maximum 20-50% higher for


those cancers for which an increased cancer incidence has been observed and other cancertypes there is no excess risk.

When incorporating death as a competing risk to cancer incidence, the excess mortalityamong persons with diabetes is of quantitatively much larger concern that the excess ofcancers [21, 12].

Our Danish study demonstrated that the life-time cumulative risk of cancer is smalleramong persons with diabetes than among persons not suffering from diabetes. This is dueto the higher mortality rates among persons with diabetes compared to those withoutdiabetes. In general terms, persons with diabetes die earlier and thus escape developmentof some cancers.

One limitation of our register-based estimates is that the calculations were based oncross-sectional rates applied longitudinally. Nevertheless, this approach is in completeparallel to classical calculations of life expectancy, and essentially the only practicableapproach since the time-period covered by the diabetes register (1995–2012) is too short togive reliable cohort specific rates over the entire age-range.

Another limitation is that the rates were only modelled by age and calendar time nottaking duration of diabetes or cancer into account, as it is known that both incidence ratesand mortality rates are higher shortly after a diagnosis of either diabetes or cancer.However, since our focus was on cumulative measures the impact of ignoring duration ofdiabetes and cancer is likely small.

1.4.1 Conclusions

• Overall cancer incidence among persons with diabetes is 10-20% higher than amongthose without diabetes.

• The most elevated incidence rates among persons with diabetes are found for cancersof the liver or pancreas, and incidence rates of cancers of the endometrium, kidneyand colon also seem to be consistently elevated among patients with diabetes acrossstudies.

• In the general population, the lifetime risk of cancer is about 45%, and the lifetimerisk of diabetes about 35%, and the lifetime risk of both diagnoses about 15%. Forboth diseases the proportions are slightly less for women than for men.

• Persons with diabetes at a given age have a smaller lifetime risk of cancer thanpersons without diabetes at the same age. This is attributable to the highermortality rates among persons with diabetes.

• Differences in cancer occurrence between persons with diabetes and non-diabetics is aquantitatively smaller problem than the difference in mortality rates between the twogroups.

• A further decrease in mortality among persons with diabetes would be expected toincrease the fraction of persons with diabetes contracting cancer.

Article 1.4 Discussion 7

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Figure 1.1: Estimated RRs from different studies. Blue lines for men, red lines for women.Within each cancer site, estimates are from the studies mentioned in in table 1.1, in thesame order as in table 1.1.


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Figure 1.2: Transition rates in a population exposed to occurrence of diabetes and cancer.The red transitions represent cancer incidence rates and the black ones death after a cancerdiagnosis.


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Figure 1.3: Estimated age-specific incidence and mortality rates in the Danish population2005, and trends 1995–2010. The coloring of the lines refer to the state from which the ratesare. The full lines in the upper panels are cancer incidence rates, the broken line diabetesincidence rates and the black lines are the cancer-incidence rate-ratios between persons withand without diabetes. In the lower panels, the broken red lines are for cancer patients devel-oping diabetes after cancer, and the dotted red lines are for cancer patients with pre-existingdiabetes at time of diagnosis.


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Figure 1.4: Fraction of a birth cohort in each state at a given age, based on Danish ratesas of 2005. The black line is the overall survival curve, the green part represents those alivewithout diabetes or cancer, the gray those who died without any of the diseases. Blue areasare those with diabetes, red those with cancer and the purple areas those with both diseases.The white line in the purple area separates those that had diabetes before cancer (closest tothe diabetes part) from those who had cancer before diabetes.


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Figure 1.6: Fraction of a birth cohort in each state at a given age, based on Danish data.Colouring as in Figure 1.4. The three rows of graphs give the conditional probabilities giventhat a person is alive at age 50, 60 and 70, respectively. The first and 3rd columns areconditional on having neither diabetes nor cancer, the 2nd and 4th columns are conditionalon having diabetes only.

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14 BIBLIOGRAPHY Diabetes & Cancer

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[13] S. Sasazuki, H. Charvat, A. Hara, K. Wakai, C. Nagata, K. Nakamura, I. Tsuji,Y. Sugawara, A. Tamakoshi, K. Matsuo, I. Oze, T. Mizoue, K. Tanaka, M. Inoue,S. Tsugane, S. Sasazuki, S. Tsugane, M. Inoue, M. Iwasaki, T. Otani, N. Sawada,T. Shimazu, T. Yamaji, I. Tsuji, Y. Tsubono, Y. Nishino, A. Tamakoshi, K. Matsuo,H. Ito, K. Wakai, C. Nagata, T. Mizoue, and K. Tanaka. Diabetes mellitus and cancerrisk: pooled analysis of eight cohort studies in Japan. Cancer Sci., 104(11):1499–1507,Nov 2013.

[14] H. Kajüter, A.S. Geier, I. Wellmann, V. Krieg, R. Fricke, O. Heidinger, and H.-W.Hense. Kohortenstudie zur Krebsinzidenz bei Patienten mit Diabetes mellitus Typ 2.Bundesgesundheitsblatt, 57:52–59, 2014.

[15] B. B. Barone, H. C. Yeh, C. F. Snyder, K. S. Peairs, K. B. Stein, R. L. Derr, A. C.Wolff, and F. L. Brancati. Long-term all-cause mortality in cancer patients withpreexisting diabetes mellitus: a systematic review and meta-analysis. JAMA,300:2754–2764, Dec 2008.

[16] B. Carstensen, Christensen J.K., Marcussen M.M., and Borch-Johnsen K. TheNational Diabetes Register. Scandinavian Journal of Public Health, 39(7 suppl):58–61,2011.

[17] B. Carstensen, J.K. Kristensen, P. Ottosen, and K. Borch-Johnsen. The DanishNational Diabetes Register: Trends in incidence, prevalence and mortality.Diabetologia, 51:2187–2196, 2008.

[18] M. L. Gjerstorff. The Danish Cancer Registry. Scand J Public Health, 39/7Suppl):42–45, July 2011.

[19] Human Mortality Database. University of California, Berkeley (USA), and Max PlanckInstitute for Demographic Research (Germany). available at www.mortality.org orwww.humanmortality.de (data downloaded on 20 april 2014). Technical report.

[20] B Carstensen. Age-Period-Cohort models for the Lexis diagram (author’s reply).Statistics in Medicine, 27:1561–1564, 2007.

[21] J. A. Johnson, B. Carstensen, D. Witte, S. L. Bowker, L. Lipscombe, A. G. Renehan,and the Diabetes and Cancer Research Consortium. Diabetes and cancer (1):evaluating the temporal relationship between type 2 diabetes and cancer incidence.Diabetologia, 55(6):1607–1618, Jun 2012.

www.mortality.orgwww.humanmortality.de

Chapter 2

Background calculations

2.1 Comparing cancer RRs from published studies

We have collected data from other studies that on population basis has estimated theoverall RR of specific cancers among diabetes patients relative to the non-diabetic part ofthe population.

> library(Epi)> # Read the keyed-in data> oth str( oth )

'data.frame': 243 obs. of 7 variables:$ sex : Factor w/ 2 levels "F","M": 2 1 2 1 2 1 2 1 2 1 ...$ diag : Factor w/ 24 levels " Brain",..: 22 22 12 12 7 7 2 2 20 20 ...$ author: Factor w/ 7 levels "Adami","Coughlin",..: 7 7 7 7 7 7 7 7 7 7 ...$ RR : num 1.1 1.1 1.3 1 1.2 1.1 1.3 1.1 1.1 1 ...$ lo : num 1.1 1.1 1 0.7 1 1 1.1 1 0.9 0.9 ...$ hi : num 1.1 1.1 1.6 1.5 1.3 1.4 1.4 1.2 1.2 1.2 ...$ N : int 4666 4165 67 26 188 131 413 442 235 167 ...

> levels(oth$author)

[1] "Adami" "Coughlin" "Johnson" "Kajuter" "Sasazuki" "Vecchia" "Wiederoff"

> oth oth$author head( oth )

sex diag author RR lo hi N1 M All malignant neoplasms Wiederoff 1.1 1.1 1.1 46662 F All malignant neoplasms Wiederoff 1.1 1.1 1.1 41653 M Oesophagus Wiederoff 1.3 1.0 1.6 674 F Oesophagus Wiederoff 1.0 0.7 1.5 265 M Stomach Wiederoff 1.2 1.0 1.3 1886 F Stomach Wiederoff 1.1 1.0 1.4 131

> # Clean up the site names> nn nn nn oth$diag nn nn

[1] "All malignant neoplasms" "Oesophagus"[3] "Stomach" "Colon"[5] "Rectum " "Liver"[7] "Pancreas" "Lung, bronchus and pleura"

15

16 Background calculations Diabetes & Cancer

[9] "Melanoma of skin" "Other skin"[11] "Breast" "Cervix uteri"[13] "Corpus uteri" "Ovary, fallopian tube etc."[15] "Prostate" "Testis"[17] "Kidney" "Urinary bladder"[19] "Brain" "Thyroid"[21] "Hodgkins lymphoma" "Non-Hodgkin lymphoma"[23] "Multiple myeloma" "Leukaemia"

> # Make sure they are in the correct order> oth$diag levels( oth$diag )

[1] "All malignant neoplasms" "Oesophagus"[3] "Stomach" "Colon"[5] "Rectum " "Liver"[7] "Pancreas" "Lung, bronchus and pleura"[9] "Melanoma of skin" "Other skin"[11] "Breast" "Cervix uteri"[13] "Corpus uteri" "Ovary, fallopian tube etc."[15] "Prostate" "Testis"[17] "Kidney" "Urinary bladder"[19] "Brain" "Thyroid"[21] "Hodgkins lymphoma" "Non-Hodgkin lymphoma"[23] "Multiple myeloma" "Leukaemia"

> # Turn it into a 4-dimensional array for plotting> xxx xxx[xxx==0] dimnames(xxx)[[1]]

[1] "Adami" "Coughlin" "Johnson" "Kajuter" "Sasazuki" "Wiederoff"

> # dimnames(xxx)[[2]][8] # dimnames(xxx)[[2]][8]> nd # Get the data from the DK study> load( file="../../data/ana1i.Rdata" )> dimnames(res)[[1]] str( res )

num [1:29, 1:2, 1:4, 1:3] 1.19 1.27 1.25 1.32 1.4 ...- attr(*, "dimnames")=List of 4..$ diag: chr [1:29] "All malignant neoplasms" "Oesophagus" "Stomach" "Colon incl. rectosigmoideum" .....$ sex : chr [1:2] "M" "F"..$ type: chr [1:4] "DM/noIns" "DM/Ins" "Ins vs. noIns" "DM"..$ est : chr [1:3] "Est" "lo" "hi"

> data.frame( 1:29, dimnames(res)[[1]] )

X1.29 dimnames.res...1..1 1 All malignant neoplasms2 2 Oesophagus3 3 Stomach4 4 Colon incl. rectosigmoideum5 5 Ascending colon6 6 Transverse colon7 7 Descending and sigmoid colon8 8 Other colon (unspec. or multiple)9 9 Rectum10 10 Colorectal cancer11 11 Liver12 12 Pancreas13 13 Lung, bronchus and pleura14 14 Melanoma of skin15 15 Breast16 16 Cervix uteri

Background calculations 2.1 Comparing cancer RRs from published studies 17

17 17 Corpus uteri18 18 Ovary, fallopian tube etc.19 19 Prostate20 20 Testis21 21 Kidney22 22 Urinary bladder23 23 Brain24 24 Thyroid25 25 Hodgkin's lymphoma26 26 Non-Hodgkin lymphoma27 27 Multiple myeloma28 28 Leukaemia29 29 Other

> # Check which ones belong to the ones from the keyed-in data> wh cbind( dimnames(res)[[1]][wh], dimnames(xxx)[[2]] )

[,1] [,2][1,] "All malignant neoplasms" "All malignant neoplasms"[2,] "Oesophagus" "Oesophagus"[3,] "Stomach" "Stomach"[4,] "Colon incl. rectosigmoideum" "Colon"[5,] "Rectum" "Rectum "[6,] "Liver" "Liver"[7,] "Pancreas" "Pancreas"[8,] "Lung, bronchus and pleura" "Lung, bronchus and pleura"[9,] "Melanoma of skin" "Melanoma of skin"[10,] "Breast" "Breast"[11,] "Cervix uteri" "Cervix uteri"[12,] "Corpus uteri" "Corpus uteri"[13,] "Ovary, fallopian tube etc." "Ovary, fallopian tube etc."[14,] "Prostate" "Prostate"[15,] "Testis" "Testis"[16,] "Kidney" "Kidney"[17,] "Urinary bladder" "Urinary bladder"[18,] "Brain" "Brain"[19,] "Thyroid" "Thyroid"[20,] "Hodgkin's lymphoma" "Hodgkins lymphoma"[21,] "Non-Hodgkin lymphoma" "Non-Hodgkin lymphoma"[22,] "Multiple myeloma" "Multiple myeloma"[23,] "Leukaemia" "Leukaemia"

> # Extract the corresponding ones from data> cwf # Nullify male breast cancer> xxx[,"Breast","M",] cwf["Breast","M",,] # Combine to one array> ( dnam


$sex[1] "F" "M"

[[4]][1] "RR" "lo" "hi"

> dnam[["author"]] XXX XXX[-1,,,] str( cwf )

num [1:23, 1:2, 1:4, 1:3] 1.19 1.27 1.25 1.32 1.11 ...- attr(*, "dimnames")=List of 4..$ diag: chr [1:23] "All malignant neoplasms" "Oesophagus" "Stomach" "Colon incl. rectosigmoideum" .....$ sex : chr [1:2] "M" "F"..$ type: chr [1:4] "DM/noIns" "DM/Ins" "Ins vs. noIns" "DM"..$ est : chr [1:3] "Est" "lo" "hi"

> str( XXX[1,,,] )

num [1:23, 1:2, 1:3] NA NA NA NA NA NA NA NA NA NA ...- attr(*, "dimnames")=List of 3..$ diag: chr [1:23] "All malignant neoplasms" "Oesophagus" "Stomach" "Colon" .....$ sex : chr [1:2] "F" "M"..$ : chr [1:3] "RR" "lo" "hi"

> str( cwf[,2:1,4,] )

num [1:23, 1:2, 1:3] 1.202 0.979 1.344 1.204 0.996 ...- attr(*, "dimnames")=List of 3..$ diag: chr [1:23] "All malignant neoplasms" "Oesophagus" "Stomach" "Colon incl. rectosigmoideum" .....$ sex : chr [1:2] "F" "M"..$ est : chr [1:3] "Est" "lo" "hi"

> XXX[1,,,] str( XXX )

num [1:7, 1:23, 1:2, 1:3] 1.2 1.1 NA NA NA ...- attr(*, "dimnames")=List of 4..$ author: chr [1:7] "Carstensen" "Adami" "Coughlin" "Johnson" .....$ diag : chr [1:23] "All malignant neoplasms" "Oesophagus" "Stomach" "Colon" .....$ sex : chr [1:2] "F" "M"..$ : chr [1:3] "RR" "lo" "hi"

> RRCa str( RRCa )

num [1:7, 1:23, 1:2, 1:3] 1 1.1 NA NA 1.21 ...- attr(*, "dimnames")=List of 4..$ author: chr [1:7] "Adami" "Wiederoff" "Coughlin" "Johnson" .....$ diag : chr [1:23] "All malignant neoplasms" "Oesophagus" "Stomach" "Colon" .....$ sex : chr [1:2] "M" "F"..$ : chr [1:3] "RR" "lo" "hi"

> save( RRCa, file="./data/RRCa.Rda" )

With this array set up, we can make a comprehensive forest plot of estimates

> # Plot to compare the studies results to the previous ones.> par( mar=c(3,1,1,1), mgp=c(3,1,0)/1.6 )> plotEst( RRCa[1,,"M",1:3], y=nd:1, col="transparent", lwd=1,+ xlog=T, xlim=c(0.5,5), grid=c(5:19/10,4:10/2),+ vref=1, ylim=c(1,nd),+ xtic=c(0.5,0.7,1,1.5,2:5), xlab="RR, DM vs. non-DM" )> nst for( i in 1:nst )+ {+ pointsEst( RRCa[i,,"M",1:3], y=nd:1+(0+i)/(2.3*nst), col="blue",+ lwd=1.5, cex=0.8 )+ pointsEst( RRCa[i,,"F",1:3], y=nd:1+(i-nst+1)/(2.3*nst), col="red",+ lwd=1.5, cex=0.8 )+ }


For reference purposes we also print the collected estimates too:

> load( file="./data/RRCa.Rda" )> dimnames( RRCa )[[2]] round( ftable( RRCa, row.vars=2:1 ), 2 )

sex M FRR lo hi RR lo hi

diag authorAll malign Adami 1.00 0.90 1.10 1.10 1.00 1.10

Wiederoff 1.10 1.10 1.10 1.10 1.10 1.10Coughlin NA NA NA NA NA NAJohnson NA NA NA NA NA NACarstensen 1.21 1.19 1.23 1.20 1.18 1.23Sasazuki 1.21 1.15 1.28 1.18 1.08 1.30Kajuter NA NA NA NA NA NA

Oesophagus Adami 1.60 1.00 2.40 0.80 0.40 1.60Wiederoff 1.30 1.00 1.60 1.00 0.70 1.50Coughlin 1.20 0.94 1.53 NA NA NAJohnson NA NA NA NA NA NACarstensen 1.27 1.12 1.44 0.98 0.77 1.24Sasazuki 1.07 0.79 1.44 4.70 1.12 19.71Kajuter NA NA NA NA NA NA

Stomach Adami 0.80 0.70 1.00 0.90 0.70 1.20Wiederoff 1.20 1.00 1.30 1.10 1.00 1.40Coughlin 0.99 0.77 1.27 1.25 0.90 1.73Johnson NA NA NA NA NA NACarstensen 1.28 1.15 1.43 1.34 1.14 1.58Sasazuki 1.03 0.84 1.25 1.22 0.95 1.57Kajuter NA NA NA NA NA NA

Colon Adami 1.20 0.90 1.40 1.00 0.80 1.20Wiederoff 1.30 1.10 1.40 1.10 1.00 1.20Coughlin 1.20 1.06 1.37 1.24 1.07 1.43Johnson 1.24 1.14 1.35 1.24 1.14 1.35Carstensen 1.32 1.24 1.40 1.20 1.13 1.28Sasazuki 1.58 1.32 1.89 0.92 0.66 1.29Kajuter 1.00 0.89 1.12 0.85 0.73 0.98

Rectum Adami 1.30 1.10 1.70 0.90 0.70 1.20Wiederoff 1.10 0.90 1.20 1.00 0.90 1.20Coughlin 1.07 0.75 1.51 0.90 0.57 1.42Johnson NA NA NA NA NA NACarstensen 1.11 1.03 1.20 1.00 0.89 1.11Sasazuki 1.05 0.80 1.36 1.48 0.76 2.89Kajuter NA NA NA NA NA NA

Liver Adami 1.80 1.40 2.30 1.30 1.00 1.60Wiederoff 4.00 3.50 4.60 2.10 1.60 2.70Coughlin 2.19 1.76 2.72 1.37 0.94 2.00Johnson NA NA NA NA NA NACarstensen 3.90 3.50 4.35 1.77 1.43 2.19Sasazuki 2.25 1.83 2.76 1.84 1.30 2.60Kajuter 1.88 1.42 2.43 1.82 1.15 2.73

Pancreas Adami 1.40 1.10 1.80 1.50 1.20 1.80Wiederoff 1.70 1.50 2.00 1.60 1.40 1.90Coughlin 1.48 1.27 1.73 1.44 1.21 1.72Johnson NA NA NA NA NA NACarstensen 2.86 2.64 3.10 2.65 2.43 2.88Sasazuki 1.72 1.30 2.28 2.27 1.33 3.85Kajuter 1.42 1.09 1.82 1.83 1.44 2.30

Lung, bron Adami 1.00 0.80 1.10 1.10 0.80 1.50Wiederoff 1.00 0.90 1.10 0.90 0.80 1.10Coughlin 1.05 0.97 1.14 1.11 0.98 1.25Johnson 1.14 1.06 1.24 1.14 1.06 1.24Carstensen 1.17 1.12 1.23 1.14 1.07 1.20Sasazuki 1.01 0.83 1.22 1.08 0.76 1.54Kajuter 1.20 1.08 1.33 1.25 1.05 1.48

Melanoma o Adami 1.00 0.50 1.60 0.70 0.40 1.20Wiederoff 1.00 0.70 1.20 1.00 0.80 1.30Coughlin 0.93 0.64 1.36 NA NA NA


Johnson NA NA NA NA NA NACarstensen 0.92 0.83 1.03 0.78 0.69 0.89Sasazuki NA NA NA NA NA NAKajuter NA NA NA NA NA NA

Breast Adami NA NA NA 0.90 0.80 1.10Wiederoff NA NA NA 1.10 1.10 1.20Coughlin NA NA NA 1.27 1.11 1.45Johnson NA NA NA 1.00 0.92 1.10Carstensen NA NA NA 1.04 1.00 1.09Sasazuki NA NA NA 0.98 0.69 1.38Kajuter NA NA NA 0.91 0.82 1.01

Cervix ute Adami NA NA NA 0.70 0.40 1.10Wiederoff NA NA NA 0.90 0.70 1.10Coughlin NA NA NA NA NA NAJohnson NA NA NA 1.50 1.26 1.77Carstensen NA NA NA 1.08 0.92 1.27Sasazuki NA NA NA 2.08 1.02 4.27Kajuter NA NA NA NA NA NA

Corpus ute Adami NA NA NA 1.50 1.20 1.80Wiederoff NA NA NA 1.40 1.20 1.60Coughlin NA NA NA 1.33 0.92 1.90Johnson NA NA NA 1.63 1.33 1.99Carstensen NA NA NA 1.58 1.45 1.71Sasazuki NA NA NA 1.69 0.87 3.31Kajuter NA NA NA 1.34 1.08 1.65

Ovary, fal Adami NA NA NA 0.90 0.60 1.10Wiederoff NA NA NA 0.90 0.70 1.00Coughlin NA NA NA 1.02 0.80 1.29Johnson NA NA NA 1.19 0.93 1.53Carstensen NA NA NA 1.08 0.97 1.20Sasazuki NA NA NA 1.68 0.68 4.07Kajuter NA NA NA NA NA NA

Prostate Adami 0.70 0.70 0.90 NA NA NAWiederoff 0.90 0.80 1.00 NA NA NACoughlin 0.90 0.80 1.02 NA NA NAJohnson 0.88 0.82 0.95 NA NA NACarstensen 0.94 0.91 0.98 NA NA NASasazuki 0.98 0.70 1.36 NA NA NAKajuter 0.72 0.65 0.79 NA NA NA

Testis Adami 1.00 0.40 2.00 NA NA NAWiederoff 1.00 0.60 1.50 NA NA NACoughlin NA NA NA NA NA NAJohnson NA NA NA NA NA NACarstensen 0.78 0.58 1.06 NA NA NASasazuki NA NA NA NA NA NAKajuter NA NA NA NA NA NA

Kidney Adami 1.10 0.80 1.40 1.60 1.20 2.00Wiederoff 1.40 1.20 1.60 1.70 1.40 1.90Coughlin 0.82 0.61 1.10 1.12 0.80 1.58Johnson NA NA NA NA NA NACarstensen 1.53 1.38 1.71 1.83 1.59 2.10Sasazuki 1.48 0.67 3.29 1.28 0.46 3.55Kajuter NA NA NA NA NA NA

Urinary bl Adami 1.00 0.80 1.30 0.90 0.60 1.30Wiederoff 1.00 0.90 1.10 0.90 0.80 1.10Coughlin 1.43 1.14 1.80 1.30 0.85 2.00Johnson NA NA NA NA NA NACarstensen 1.20 1.13 1.27 1.03 0.91 1.16Sasazuki 1.30 0.89 1.91 1.45 0.65 3.22Kajuter NA NA NA NA NA NA

Brain Adami NA NA NA NA NA NAWiederoff 1.10 0.90 1.40 1.10 0.80 1.30Coughlin 0.96 0.72 1.29 1.03 0.74 1.43Johnson NA NA NA NA NA NACarstensen 1.15 1.01 1.31 1.26 1.09 1.47Sasazuki NA NA NA NA NA NA


Kajuter NA NA NA NA NA NAThyroid Adami 1.30 0.50 2.80 1.00 0.60 1.80

Wiederoff 1.30 0.60 2.30 1.20 0.70 1.80Coughlin NA NA NA NA NA NAJohnson 1.29 0.87 1.91 1.29 0.87 1.91Carstensen 1.38 0.96 1.99 1.22 0.92 1.62Sasazuki NA NA NA NA NA NAKajuter NA NA NA NA NA NA

Hodgkins l Adami NA NA NA NA NA NAWiederoff NA NA NA NA NA NACoughlin NA NA NA NA NA NAJohnson NA NA NA NA NA NACarstensen 1.86 1.37 2.53 1.69 1.12 2.55Sasazuki NA NA NA NA NA NAKajuter 0.72 0.51 1.00 0.93 0.67 1.26

Non-Hodgki Adami NA NA NA NA NA NAWiederoff NA NA NA NA NA NACoughlin 1.21 0.99 1.48 0.93 0.71 1.21Johnson NA NA NA NA NA NACarstensen 1.16 1.04 1.29 1.16 1.02 1.32Sasazuki 1.73 0.94 3.18 2.16 0.88 5.32Kajuter NA NA NA NA NA NA

Multiple m Adami NA NA NA NA NA NAWiederoff 1.00 0.80 1.40 1.30 1.00 1.70Coughlin 1.27 0.98 1.66 0.87 0.62 1.24Johnson NA NA NA NA NA NACarstensen 1.06 0.91 1.23 1.02 0.84 1.23Sasazuki NA NA NA NA NA NAKajuter NA NA NA NA NA NA

Leukaemia Adami NA NA NA NA NA NAWiederoff 1.10 0.90 1.30 1.10 0.90 1.40Coughlin 0.88 0.71 1.10 1.10 0.85 1.44Johnson NA NA NA NA NA NACarstensen 1.03 0.92 1.16 1.17 1.02 1.34Sasazuki NA NA NA NA NA NAKajuter NA NA NA NA NA NA

> round( ftable( RRCa, row.vars=1:2 ), 2 )

sex M FRR lo hi RR lo hi

author diagAdami All malign 1.00 0.90 1.10 1.10 1.00 1.10

Oesophagus 1.60 1.00 2.40 0.80 0.40 1.60Stomach 0.80 0.70 1.00 0.90 0.70 1.20Colon 1.20 0.90 1.40 1.00 0.80 1.20Rectum 1.30 1.10 1.70 0.90 0.70 1.20Liver 1.80 1.40 2.30 1.30 1.00 1.60Pancreas 1.40 1.10 1.80 1.50 1.20 1.80Lung, bron 1.00 0.80 1.10 1.10 0.80 1.50Melanoma o 1.00 0.50 1.60 0.70 0.40 1.20Breast NA NA NA 0.90 0.80 1.10Cervix ute NA NA NA 0.70 0.40 1.10Corpus ute NA NA NA 1.50 1.20 1.80Ovary, fal NA NA NA 0.90 0.60 1.10Prostate 0.70 0.70 0.90 NA NA NATestis 1.00 0.40 2.00 NA NA NAKidney 1.10 0.80 1.40 1.60 1.20 2.00Urinary bl 1.00 0.80 1.30 0.90 0.60 1.30Brain NA NA NA NA NA NAThyroid 1.30 0.50 2.80 1.00 0.60 1.80Hodgkins l NA NA NA NA NA NANon-Hodgki NA NA NA NA NA NAMultiple m NA NA NA NA NA NALeukaemia NA NA NA NA NA NA

Wiederoff All malign 1.10 1.10 1.10 1.10 1.10 1.10Oesophagus 1.30 1.00 1.60 1.00 0.70 1.50Stomach 1.20 1.00 1.30 1.10 1.00 1.40


Colon 1.30 1.10 1.40 1.10 1.00 1.20Rectum 1.10 0.90 1.20 1.00 0.90 1.20Liver 4.00 3.50 4.60 2.10 1.60 2.70Pancreas 1.70 1.50 2.00 1.60 1.40 1.90Lung, bron 1.00 0.90 1.10 0.90 0.80 1.10Melanoma o 1.00 0.70 1.20 1.00 0.80 1.30Breast NA NA NA 1.10 1.10 1.20Cervix ute NA NA NA 0.90 0.70 1.10Corpus ute NA NA NA 1.40 1.20 1.60Ovary, fal NA NA NA 0.90 0.70 1.00Prostate 0.90 0.80 1.00 NA NA NATestis 1.00 0.60 1.50 NA NA NAKidney 1.40 1.20 1.60 1.70 1.40 1.90Urinary bl 1.00 0.90 1.10 0.90 0.80 1.10Brain 1.10 0.90 1.40 1.10 0.80 1.30Thyroid 1.30 0.60 2.30 1.20 0.70 1.80Hodgkins l NA NA NA NA NA NANon-Hodgki NA NA NA NA NA NAMultiple m 1.00 0.80 1.40 1.30 1.00 1.70Leukaemia 1.10 0.90 1.30 1.10 0.90 1.40

Coughlin All malign NA NA NA NA NA NAOesophagus 1.20 0.94 1.53 NA NA NAStomach 0.99 0.77 1.27 1.25 0.90 1.73Colon 1.20 1.06 1.37 1.24 1.07 1.43Rectum 1.07 0.75 1.51 0.90 0.57 1.42Liver 2.19 1.76 2.72 1.37 0.94 2.00Pancreas 1.48 1.27 1.73 1.44 1.21 1.72Lung, bron 1.05 0.97 1.14 1.11 0.98 1.25Melanoma o 0.93 0.64 1.36 NA NA NABreast NA NA NA 1.27 1.11 1.45Cervix ute NA NA NA NA NA NACorpus ute NA NA NA 1.33 0.92 1.90Ovary, fal NA NA NA 1.02 0.80 1.29Prostate 0.90 0.80 1.02 NA NA NATestis NA NA NA NA NA NAKidney 0.82 0.61 1.10 1.12 0.80 1.58Urinary bl 1.43 1.14 1.80 1.30 0.85 2.00Brain 0.96 0.72 1.29 1.03 0.74 1.43Thyroid NA NA NA NA NA NAHodgkins l NA NA NA NA NA NANon-Hodgki 1.21 0.99 1.48 0.93 0.71 1.21Multiple m 1.27 0.98 1.66 0.87 0.62 1.24Leukaemia 0.88 0.71 1.10 1.10 0.85 1.44

Johnson All malign NA NA NA NA NA NAOesophagus NA NA NA NA NA NAStomach NA NA NA NA NA NAColon 1.24 1.14 1.35 1.24 1.14 1.35Rectum NA NA NA NA NA NALiver NA NA NA NA NA NAPancreas NA NA NA NA NA NALung, bron 1.14 1.06 1.24 1.14 1.06 1.24Melanoma o NA NA NA NA NA NABreast NA NA NA 1.00 0.92 1.10Cervix ute NA NA NA 1.50 1.26 1.77Corpus ute NA NA NA 1.63 1.33 1.99Ovary, fal NA NA NA 1.19 0.93 1.53Prostate 0.88 0.82 0.95 NA NA NATestis NA NA NA NA NA NAKidney NA NA NA NA NA NAUrinary bl NA NA NA NA NA NABrain NA NA NA NA NA NAThyroid 1.29 0.87 1.91 1.29 0.87 1.91Hodgkins l NA NA NA NA NA NANon-Hodgki NA NA NA NA NA NAMultiple m NA NA NA NA NA NALeukaemia NA NA NA NA NA NA


Carstensen All malign 1.21 1.19 1.23 1.20 1.18 1.23Oesophagus 1.27 1.12 1.44 0.98 0.77 1.24Stomach 1.28 1.15 1.43 1.34 1.14 1.58Colon 1.32 1.24 1.40 1.20 1.13 1.28Rectum 1.11 1.03 1.20 1.00 0.89 1.11Liver 3.90 3.50 4.35 1.77 1.43 2.19Pancreas 2.86 2.64 3.10 2.65 2.43 2.88Lung, bron 1.17 1.12 1.23 1.14 1.07 1.20Melanoma o 0.92 0.83 1.03 0.78 0.69 0.89Breast NA NA NA 1.04 1.00 1.09Cervix ute NA NA NA 1.08 0.92 1.27Corpus ute NA NA NA 1.58 1.45 1.71Ovary, fal NA NA NA 1.08 0.97 1.20Prostate 0.94 0.91 0.98 NA NA NATestis 0.78 0.58 1.06 NA NA NAKidney 1.53 1.38 1.71 1.83 1.59 2.10Urinary bl 1.20 1.13 1.27 1.03 0.91 1.16Brain 1.15 1.01 1.31 1.26 1.09 1.47Thyroid 1.38 0.96 1.99 1.22 0.92 1.62Hodgkins l 1.86 1.37 2.53 1.69 1.12 2.55Non-Hodgki 1.16 1.04 1.29 1.16 1.02 1.32Multiple m 1.06 0.91 1.23 1.02 0.84 1.23Leukaemia 1.03 0.92 1.16 1.17 1.02 1.34

Sasazuki All malign 1.21 1.15 1.28 1.18 1.08 1.30Oesophagus 1.07 0.79 1.44 4.70 1.12 19.71Stomach 1.03 0.84 1.25 1.22 0.95 1.57Colon 1.58 1.32 1.89 0.92 0.66 1.29Rectum 1.05 0.80 1.36 1.48 0.76 2.89Liver 2.25 1.83 2.76 1.84 1.30 2.60Pancreas 1.72 1.30 2.28 2.27 1.33 3.85Lung, bron 1.01 0.83 1.22 1.08 0.76 1.54Melanoma o NA NA NA NA NA NABreast NA NA NA 0.98 0.69 1.38Cervix ute NA NA NA 2.08 1.02 4.27Corpus ute NA NA NA 1.69 0.87 3.31Ovary, fal NA NA NA 1.68 0.68 4.07Prostate 0.98 0.70 1.36 NA NA NATestis NA NA NA NA NA NAKidney 1.48 0.67 3.29 1.28 0.46 3.55Urinary bl 1.30 0.89 1.91 1.45 0.65 3.22Brain NA NA NA NA NA NAThyroid NA NA NA NA NA NAHodgkins l NA NA NA NA NA NANon-Hodgki 1.73 0.94 3.18 2.16 0.88 5.32Multiple m NA NA NA NA NA NALeukaemia NA NA NA NA NA NA

Kajuter All malign NA NA NA NA NA NAOesophagus NA NA NA NA NA NAStomach NA NA NA NA NA NAColon 1.00 0.89 1.12 0.85 0.73 0.98Rectum NA NA NA NA NA NALiver 1.88 1.42 2.43 1.82 1.15 2.73Pancreas 1.42 1.09 1.82 1.83 1.44 2.30Lung, bron 1.20 1.08 1.33 1.25 1.05 1.48Melanoma o NA NA NA NA NA NABreast NA NA NA 0.91 0.82 1.01Cervix ute NA NA NA NA NA NACorpus ute NA NA NA 1.34 1.08 1.65Ovary, fal NA NA NA NA NA NAProstate 0.72 0.65 0.79 NA NA NATestis NA NA NA NA NA NAKidney NA NA NA NA NA NAUrinary bl NA NA NA NA NA NABrain NA NA NA NA NA NAThyroid NA NA NA NA NA NAHodgkins l 0.72 0.51 1.00 0.93 0.67 1.26


Non-Hodgki NA NA NA NA NA NAMultiple m NA NA NA NA NA NALeukaemia NA NA NA NA NA NA

Background calculations 2.2 Overview of rate computation 25

2.2 Overview of rate computation

2.2.1 Data

We merged the diabetes register and the cancer register, restricting the cancer register tothe first primary tumour in a person, and excluding non-melanoma skin cancers.

Thus the resulting data set has one record per person, and comprises persons that have adiagnosis of either cancer or diabetes (or both). Thus we have follow-up (and deaths) ofpatients in the Danish population corresponding to all boxes in figure 1.2 except the “Well”state.

From the human mortality database we extract the no. of deaths in 1-year Lexistriangles. We also extract the population size, which is used for calculation of person-yearsin 1-year Lexis triangles. Thus we have deaths and risk time for the total population. Wecan obtain the figures for the “Well” state by subtraction of risk time and deaths in thepatient population from that in the total population.

First we need to attach the relevant packages:

library( foreign )library( Epi )library( RCurl )# A function to fish out data from the HMDBsource( "C:/stat/R/BxC/Examples/HMD2R.r" )# HMD2R

2.2.2 Total population follow-up

Along the same lines we can derive the number of deaths in the class (“Well”,“DK”) bysubtracting the number of deaths in all other classes from the total number of deaths in thepopulation. To that end we first retrieve the total number of deaths from the humanmortality database:

2.2.2.1 Mortality data from Human Mortality Database

In order to fetch mortality from the HMD in 1× 1 Lexis triangles we need to provide a userid and a password, which is hidden in the output here; but they are put in the variablesHMDBusr and HMDBpwd, respctively.

We can now get the mortality data for Denmark, and reshape them to our purpose. Firstwe get the deaths in Lexis triangles; note that we also compute the average age andcalendar time in the Lexis triangles, since this is going to be used in the modelling:

DK


names( DK )


The data frame Y.dk now have the amount of follow-up time in Lexis triangles between1995-01-01 and 2008-12-31 in the ages between 0 and 100. The function N2Y automaticallyreturns the mean age and period in A and P.

2.2.2.3 Total population data

We can merge the two dataframe to one; recall that the variable A and P refer to Lexistriangles, and are coded as the mean age and period in the triangles:

All.dk


11 * Set the entry and exit dates for the entire follow-up endeavour ;12 %let truncdate = '01JAN1995'd ;13 %let censdate = '31DEC2009'd ;14 * Just to check it all wemt well ;15 %put validdate = &validdate.16 truncdate = &truncdate.17 censdate = &censdate. ;validdate = '01JAN1995'd truncdate = '01JAN1995'd censdate = '31DEC2009'd18 * Set the selector of subgroups to analyse ;19 %let dgrp = 21,22,241,242,243,249,251,26,28,20 33,21 51,22 70,23 82,83,84,24 91,92,25 101,103,26 113,27 121,28 131,132,133,139 ;29 %let diagselect = diag in (&dgrp.) ;30 * Variable names for tabulation purposes, note DX and D259 here ;31 %let dvars = D0 D99932 D21 D22 D241 D242 D243 D249 D251 D259 D26 D2833 D3334 D5135 D7036 D82 D83 D8437 D91 D9238 D101 D10339 D11340 D12141 D131 D132 D133 D139 ;4243 * Get the formats and the Lexis macro ;44 options nosource2 ;45 %inc "c:\bendix\steno\DM-register\NDR\projects\Cancer\sas\CRG-fmts.sas" ;NOTE: Format SEX has been output.NOTE: Format DIAG has been output.

NOTE: PROCEDURE FORMAT used (Total process time):real time 0.07 secondscpu time 0.03 seconds

130 libname DMCA "c:\bendix\steno\DM-register\NDR\projects\Cancer\data" ;NOTE: Libref DMCA was successfully assigned as follows:

Engine: V9Physical Name: c:\bendix\steno\DM-register\NDR\projects\Cancer\data

131132 *----------------------------------------------------------------------;133 * Preprocessing of the cancer register to first primary tumours only ;134135 * First take the cancer registry, remove all non-cancers ;136 data cancer ;137 set DMCA.cancer ;138 doca = d_diagnosedato ;139 * Remove 'not counted as cancer' and non-melanoma skin cancer ;140 if ( diag in (52,150) ) then delete ;141 * Recode the leukaemias to one group (139 is a not used value in formats) ;142 if diag in (134,135,136,137) then diag = 139 ;143 * Recode the colon cancers to the three separate subsites and the rest ;144 * 24.1 Ascending colon C18.0, C18.1, C18.2145 * 24.2 Transverse colon C18.3, C18.4, C18.5146 * 24.3 Descending and sigmoid colon C18.6, C18.7, C19, C19.9147 * 24.9 Other colon (unspec. or multiple)148 * 25.1 Rectum (excl. anus) C20, C209149 * This means that colorectal cancers are to be taken as the sum of these150 * 5 groups, but also that the group 24.9 is NOT of interest per se ;151 if( diag eq 24 ) then diag = 249 ;152 if( icdpyrs in ("C180","C181","C182") ) then diag = 241 ;153 if( icdpyrs in ("C183","C184","C185") ) then diag = 242 ;154 if( icdpyrs in ("C186","C187","C19","C199") ) then diag = 243 ;155 if( icdpyrs in ("C20","C209") ) then diag = 251 ;156 * Finally make a single code for the sites not among those to be anlysed ;157 if not ( diag in ( &dgrp. ) ) then diag = 999 ;158 run ;

NOTE: There were 1748815 observations read from the data set DMCA.CANCER.NOTE: The data set WORK.CANCER has 1286419 observations and 32 variables.NOTE: DATA statement used (Total process time):

real time 8.51 secondscpu time 1.70 seconds

159160 * Sort by id and date of diagnosis ;161 proc sort data = cancer ;162 by id doCA ;163 run ;


NOTE: There were 1286419 observations read from the data set WORK.CANCER.NOTE: The data set WORK.CANCER has 1286419 observations and 32 variables.NOTE: PROCEDURE SORT used (Total process time):


164165 * Then merge with the diabetes register ;166 data DMCR;167 merge cancer168 DMCA.diabetes ;169 by id ;170 keep id sex diag171 doBT doDM doCA doDD ;172 * Demografic dates collected from CRG and NDR ;173 doBT = min( D_foddto , D_fdsdato ) ;174 doDD = min( D_statdato, D_dodsdto ) ;175 * Event-dates ;176 doDM = D_inkldto ;177 doI = D_ins ;178 doCA = D_diagnosedato ;179 * If date of diabetes or cancer is equal to date of death, remove it ;180 if doDD gt .z then do;181 if doDM ge doDD then doDM = . ;182 if doCA ge doDD then doCA = . ;183 end ;184 * If date of diabetes and cancer is the same, diabetes first ;185 if doDM eq doCA then doDM = doCA - 2 ;186 if doDM > .z or doCA > .z ;187 * Only persons alive on 1.1.1995 (or born later) ;188 if doDD gt '31DEC94'd or doDD le .z ;189 * Only persons with one or the other disease ;190 if doDM > .z or doCA > .z ;191 run ;

NOTE: Missing values were generated as a result of performing an operation on missing values.Each place is given by: (Number of times) at (Line):(Column).463041 at 174:10 62702 at 185:36

NOTE: There were 1286419 observations read from the data set WORK.CANCER.NOTE: There were 437593 observations read from the data set DMCA.DIABETES.NOTE: The data set WORK.DMCR has 912764 observations and 7 variables.NOTE: DATA statement used (Total process time):


192193 * The dataset DMCR now has a record for each person who has either a194 * a diabetes diagnosis or a cancer diagnosis. Persons with more than195 * one recorded tumour are represented by a record for each tumour ;196 * We then construct the records of follow-up in different states ;197198 data toLex ;199 set DMCR ;200 id = _n_ ;201 keep id sex diag202 doBT doCa doDM doDD203 entry exit en_st ex_st ;204 length en_st ex_st $5 ;205 *** Only Cancer ;206 if ( doDM le .z ) then do ;207 entry = max( doCa, &truncdate. ) ;208 en_st = "Ca" ;209 exit = min( doDD, &censdate ) ;210 if exit eq doDD then ex_st = "Dead" ; else211 ex_st = en_st ;212 if entry lt exit then output ;213 end ;214 *** Only diabetes ;215 else216 if ( doCa le .z ) then do ;217 entry = max( doDM, &truncdate. ) ;218 en_st = "DM" ;219 exit = min( doDD, &censdate ) ;220 if exit eq doDD then ex_st = "Dead" ; else221 ex_st = en_st ;222 if entry lt exit then output ;223 end ;224 *** DM before Cancer ;225 else226 if ( doCa gt doDM ) then do ;227 * from DM to Ca ;228 entry = max( doDM, &truncdate. ) ;229 en_st = "DM" ;230 exit = min( doCa, &censdate ) ;231 if exit eq doCa then ex_st = "DM-Ca" ; else232 ex_st = en_st ;


233 if entry lt exit then output ;234 * from Ca to end ;235 entry = max( doCa, &truncdate. ) ;236 en_st = ex_st ;237 exit = min( doDD, &censdate ) ;238 if exit eq doDD then ex_st = "Dead" ; else239 ex_st = en_st ;240 if entry lt exit then output ;241 end ;242 *** Cancer before DM ;243 else244 if ( doCa lt doDM ) then do ;245 * from Ca to DM ;246 entry = max( doCa, &truncdate. ) ;247 en_st = "Ca" ;248 exit = min( doDM, &censdate ) ;249 if exit eq doDM then ex_st = "Ca-DM" ; else250 ex_st = en_st ;251 if entry lt exit then output ;252 * from DM to end ;253 entry = max( doDM, &truncdate. ) ;254 en_st = ex_st ;255 exit = min( doDD, &censdate ) ;256 if exit eq doDD then ex_st = "Dead" ; else257 ex_st = en_st ;258 if entry lt exit then output ;259 end ;260 run ;

NOTE: There were 912764 observations read from the data set WORK.DMCR.NOTE: The data set WORK.TOLEX has 981476 observations and 11 variables.NOTE: DATA statement used (Total process time):


261262 libname allPT xport '../data/allPT.xpt' ;NOTE: Libref ALLPT was successfully assigned as follows:

Engine: XPORTPhysical Name: C:\Bendix\Steno\DM-register\NDR\projects\Cancer\papers\EpiDMCa\data\allPT.xpt

263 proc copy in = work264 out = allPT ;265 select toLex ;266 run;

NOTE: Copying WORK.TOLEX to ALLPT.TOLEX (memtype=DATA).NOTE: There were 981476 observations read from the data set WORK.TOLEX.NOTE: The data set ALLPT.TOLEX has 981476 observations and 11 variables.NOTE: PROCEDURE COPY used (Total process time):


NOTE: SAS Institute Inc., SAS Campus Drive, Cary, NC USA 27513-2414NOTE: The SAS System used:


The dataset is generated in Lexis-ready-format, so that it can be put into a Lexis objectanfter a bit of name-grooming and transformaton of the dates to fractions of calendaryears:

dc


wh


2.2.4 Setting up the analysis data frame

Before we can analyze rates of cancer and diabetes we must include the part of thepopulation that is without any of the two diseases. We have the total amount ofperson-years and no. of deaths in the data frame All.dk. But we must then subtract allrisk time and deaths that occur subsequent to either DM or Cancer in order to get theright amount of deaths and PY in the “Well” state.

2.2.4.1 Patient follow-up

In order to get the risk time among patients obtain this we must split the follow-up in thepatients by age and calendar time. This is done the classical way, by successivelyaggreating the risk time and events in tabular form.

The aggredated data frame must be classified by the relevant factors, and must allowcounting of events of cancer, diabetes and death.

Agg


load( file="./data/Agg.Rda" )Ptt.dk


Finally we merge in the number of DM cancer diagnoses from the “Well” state:

str( Well )

'data.frame': 6000 obs. of 10 variables:$ A : num 0.333 0.333 0.333 0.333 0.333 ...$ P : num 1996 1996 1997 1997 1998 ...$ sex : Factor w/ 2 levels "M","F": 2 1 2 1 2 1 2 1 2 1 ...$ U : int 0 0 0 0 0 0 0 0 0 0 ...$ Y.tot: num 16972 17961 16425 17392 16402 ...$ D.tot: num 137 179 134 189 152 172 132 142 95 156 ...$ Y.ptt: num 1.136 2.738 2.567 0.936 2.197 ...$ D.ptt: num 0 3 2 0 4 0 0 0 0 0 ...$ Y : num 16971 17958 16423 17391 16399 ...$ D.dd : num 137 176 132 189 148 172 132 142 95 156 ...

str( Inc )

'data.frame': 5972 obs. of 6 variables:$ sex : Factor w/ 2 levels "M","F": 1 2 1 2 1 2 1 2 1 2 ...$ A : num 0.333 0.333 1.333 1.333 2.333 ...$ P : num 1996 1996 1996 1996 1996 ...$ U : num 0 0 0 0 0 0 0 0 0 0 ...$ D.dm: num 1 0 4 2 5 1 3 1 5 1 ...$ D.ca: num 4 3 7 4 3 4 5 2 1 1 ...

Well


$ U : num 0 0 0 0 0 0 0 0 0 0 ...$ sex : Factor w/ 2 levels "M","F": 1 2 1 2 1 2 1 2 1 2 ...$ state: Factor w/ 6 levels "Well","DM","DM-Ca",..: 1 1 1 1 1 1 1 1 1 1 ...$ Y : num 17958 16971 17391 16423 17362 ...$ D.ca : num 4 3 2 3 1 3 4 6 4 3 ...$ D.dm : num 1 0 0 4 1 0 2 0 1 1 ...$ D.dd : num 176 137 189 132 172 148 142 132 156 95 ...

cbind(xtabs( cbind( D.ca, D.dm, D.dd ) ~ state, data=dcd ), round(xtabs( Y/1000 ~ state, data=dcd ), 1 ) )

D.ca D.dm D.ddWell 382959 289438 431103 75450.8DM 40854 0 93885 2446.8DM-Ca 0 0 28648 97.5Ca 0 27958 289131 2468.4Ca-DM 0 0 18465 138.5Dead 0 0 0 0.0

save( dcd, file="./data/dcd.Rda" )


2.3 Modelling of rates

First we load the data and chek the number of events of different types from differentstates:

> library( Epi )> clear()> load( file="./data/dcd.Rda" )> addmargins( xtabs( cbind(D.dm,D.ca,D.dd) ~ state, data=dcd ), 1 )

state D.dm D.ca D.ddWell 289438 382959 431103DM 0 40854 93885DM-Ca 0 0 28648Ca 27958 0 289131Ca-DM 0 0 18465Dead 0 0 0Sum 317396 423813 861232

From the table we see that we have events for estimating 9 different rates, and also that wehave ample data for estimating them. To decide how to distribute knots im modelling ofthe age-effects, we make histograms of the age-distribution of the events:

> par( mfrow=c(5,3), mar=c(3,1,1,1), mgp=c(3,1,0)/1.6 )> par( mfg=c(1,1) ) ; with( subset( dcd, state=="Well" ),> hist( rep(A,D.dm), breaks=0:100,+ col="black", main="", yaxt="n",+ ylab="", xlab="DM | Well" ) )> par( mfg=c(1,2) ) ; with( subset( dcd, state=="Well" ),> hist( rep(A,D.ca), breaks=0:100,+ col="black", main="", yaxt="n",+ ylab="", xlab="Ca | Well" ) )> par( mfg=c(1,3) ) ; with( subset( dcd, state=="Well" ),> hist( rep(A,D.dd), breaks=0:100,+ col="black", main="", yaxt="n",+ ylab="", xlab="Dead | Well" ) )> par( mfg=c(2,2) ) ; with( subset( dcd, state=="DM" ),> hist( rep(A,D.ca), breaks=0:100,+ col="black", main="", yaxt="n",+ ylab="", xlab="Ca | DM" ) )> par( mfg=c(2,3) ) ; with( subset( dcd, state=="DM" ),> hist( rep(A,D.dd), breaks=0:100,+ col="black", main="", yaxt="n",+ ylab="", xlab="Dead | DM" ) )> par( mfg=c(3,3) ) ; with( subset( dcd, state=="DM-Ca" ),> hist( rep(A,D.dd), breaks=0:100,+ col="black", main="", yaxt="n",+ ylab="", xlab="Dead | DM-Ca" ) )> par( mfg=c(4,1) ) ; with( subset( dcd, state=="Ca" ),> hist( rep(A,D.dm), breaks=0:100,+ col="black", main="", yaxt="n",+ ylab="", xlab="DM | Ca" ) )> par( mfg=c(4,3) ) ; with( subset( dcd, state=="Ca" ),> hist( rep(A,D.dd), breaks=0:100,+ col="black", main="", yaxt="n",+ ylab="", xlab="Dead | Ca" ) )> par( mfg=c(5,3) ) ; with( subset( dcd, state=="Ca-DM" ),> hist( rep(A,D.dd), breaks=0:100,+ col="black", main="", yaxt="n",+ ylab="", xlab="Dead | Ca-DM" ) )

2.3.1 Prerequisites for the natural splines

Background calculations 2.3 Modelling of rates 37

> library( Epi )> library( splines )> ( a.kn ( p.kn ( c.kn # Men> cm.w2dm cm.w2ca cm.w2dd cm.dm2ca cm.dm2dd cm.ca2dm cm.ca2dd # Women> cf.w2dm cf.w2ca cf.w2dd cf.dm2ca cf.dm2dd cf.ca2dm cf.ca2dd # Men> pm.w2dm pm.w2ca pm.w2dd pm.dm2ca pm.dm2dd pm.ca2dm pm.ca2dd # Women> pf.w2dm pf.w2ca pf.w2dd pf.dm2ca pf.dm2dd pf.ca2dm pf.ca2dd round( ci.exp( pf.w2ca ), 3 )


exp(Est.) 2.5% 97.5%(Intercept) 0.000 0.000 0.000Ns(A, knots = a.kn)1 2.095 1.832 2.397Ns(A, knots = a.kn)2 5.856 5.384 6.370Ns(A, knots = a.kn)3 14.181 13.128 15.318Ns(A, knots = a.kn)4 37.612 35.108 40.295Ns(A, knots = a.kn)5 72.677 67.891 77.801Ns(A, knots = a.kn)6 121.710 113.823 130.142Ns(A, knots = a.kn)7 191.942 178.685 206.184Ns(A, knots = a.kn)8 82.470 72.671 93.590Ns(A, knots = a.kn)9 170.229 155.709 186.103Ns(P, knots = p.kn)1 1.047 1.029 1.066Ns(P, knots = p.kn)2 1.425 1.378 1.474Ns(P, knots = p.kn)3 1.192 1.178 1.207

> round( ci.exp( pm.ca2dd, subset="state" ), 3 )

exp(Est.) 2.5% 97.5%stateCa 0.497 0.489 0.506stateCa-DM 0.457 0.446 0.470

> round( ci.exp( pf.ca2dd, subset="state" ), 3 )

exp(Est.) 2.5% 97.5%stateCa 0.428 0.420 0.436stateCa-DM 0.415 0.404 0.426

2.3.2 Computing the state probabilities

If we want to compute the fraction of persons in a given state at a given time that is in anyof the other possible states.

Since we have restricted ourselves to a scenery where we have only one time scale,namely age we can do the clculations in closed form by setting up the transition probabilitymatrix for small intervals (of length int years. For the sake of completeness we also wealso set up s asimilar matrix for the RR by period; mainly for showing the estimated RRsby period / cohort:

> int a.pt p.pt c.pt ( states pnam


> p.ref = 2005> c.ref = 1950> aM pR cR pA cA pM cM TR["Well" ,"DM" ,,"Cross","M",] TR["Well" ,"Ca" ,,"Cross","M",] TR["Well" ,"D-W" ,,"Cross","M",] TR["DM" ,"DM-Ca",,"Cross","M",] TR["DM" ,"D-DM" ,,"Cross","M",] TR["Ca" ,"Ca-DM",,"Cross","M",] TR["Ca" ,"D-Ca" ,,"Cross","M",] TR["DM-Ca","D-DC" ,,"Cross","M",] TR["Ca-DM","D-CD" ,,"Cross","M",] TR["Well" ,"DM" ,,"Cross","F",] TR["Well" ,"Ca" ,,"Cross","F",] TR["Well" ,"D-W" ,,"Cross","F",] TR["DM" ,"DM-Ca",,"Cross","F",] TR["DM" ,"D-DM" ,,"Cross","F",] TR["Ca" ,"Ca-DM",,"Cross","F",] TR["Ca" ,"D-Ca" ,,"Cross","F",] TR["DM-Ca","D-DC" ,,"Cross","F",] TR["Ca-DM","D-CD" ,,"Cross","F",] TR["Well" ,"DM" ,,"Long" ,"M",] TR["Well" ,"Ca" ,,"Long" ,"M",] TR["Well" ,"D-W" ,,"Long" ,"M",] TR["DM" ,"DM-Ca",,"Long" ,"M",] TR["DM" ,"D-DM" ,,"Long" ,"M",] TR["Ca" ,"Ca-DM",,"Long" ,"M",] TR["Ca" ,"D-Ca" ,,"Long" ,"M",] TR["DM-Ca","D-DC" ,,"Long" ,"M",] TR["Ca-DM","D-CD" ,,"Long" ,"M",] TR["Well" ,"DM" ,,"Long" ,"F",] TR["Well" ,"Ca" ,,"Long" ,"F",] TR["Well" ,"D-W" ,,"Long" ,"F",] TR["DM" ,"DM-Ca",,"Long" ,"F",] TR["DM" ,"D-DM" ,,"Long" ,"F",] TR["Ca" ,"Ca-DM",,"Long" ,"F",] TR["Ca" ,"D-Ca" ,,"Long" ,"F",] TR["DM-Ca","D-DC" ,,"Long" ,"F",] TR["Ca-DM","D-CD" ,,"Long" ,"F",] rt round( (exp( log( rt[2,]/rt[1,] ) / 30 )-1)*100, 1 )

M F10.6 7.2


2.3.4 Secular trends

We the use almost the same code to fill in the RRs associated with period:

> pRR["Well" ,"DM" ,,"Cross","M",] pRR["Well" ,"Ca" ,,"Cross","M",] pRR["Well" ,"D-W" ,,"Cross","M",] pRR["DM" ,"DM-Ca",,"Cross","M",] pRR["DM" ,"D-DM" ,,"Cross","M",] pRR["Ca" ,"Ca-DM",,"Cross","M",] pRR["Ca" ,"D-Ca" ,,"Cross","M",] pRR["DM-Ca","D-DC" ,,"Cross","M",] pRR["Ca-DM","D-CD" ,,"Cross","M",] pRR["Well" ,"DM" ,,"Cross","F",] pRR["Well" ,"Ca" ,,"Cross","F",] pRR["Well" ,"D-W" ,,"Cross","F",] pRR["DM" ,"DM-Ca",,"Cross","F",] pRR["DM" ,"D-DM" ,,"Cross","F",] pRR["Ca" ,"Ca-DM",,"Cross","F",] pRR["Ca" ,"D-Ca" ,,"Cross","F",] pRR["DM-Ca","D-DC" ,,"Cross","F",] pRR["Ca-DM","D-CD" ,,"Cross","F",] cRR["Well" ,"DM" ,,"Long" ,"M",] cRR["Well" ,"Ca" ,,"Long" ,"M",] cRR["Well" ,"D-W" ,,"Long" ,"M",] cRR["DM" ,"DM-Ca",,"Long" ,"M",] cRR["DM" ,"D-DM" ,,"Long" ,"M",] cRR["Ca" ,"Ca-DM",,"Long" ,"M",] cRR["Ca" ,"D-Ca" ,,"Long" ,"M",] cRR["DM-Ca","D-DC" ,,"Long" ,"M",] cRR["Ca-DM","D-CD" ,,"Long" ,"M",] cRR["Well" ,"DM" ,,"Long" ,"F",] cRR["Well" ,"Ca" ,,"Long" ,"F",] cRR["Well" ,"D-W" ,,"Long" ,"F",] cRR["DM" ,"DM-Ca",,"Long" ,"F",] cRR["DM" ,"D-DM" ,,"Long" ,"F",] cRR["Ca" ,"Ca-DM",,"Long" ,"F",] cRR["Ca" ,"D-Ca" ,,"Long" ,"F",] cRR["DM-Ca","D-DC" ,,"Long" ,"F",] cRR["Ca-DM","D-CD" ,,"Long" ,"F",] rates2RR


> clr # clr ylm rrr par( mfrow=c(2,2), mar=c(3,2,1,3), oma=c(1,2,1,0),+ mgp=c(3,1,0)/1.6, bty="n", las=1 )> # Cancer incidence among men> ciw cid diw rrw rrd rrD plci plci()> text( rep(23,3), (ylm[2]/5)*0.7^(3:2),+ c("Well","DM"), col=clr[1:2], adj=0, font=2 )> # Cancer incidence among women> ciw cid diw rrw rrd rrD plci()> # Mortality among men> mtw mtd mtc mtcd mtdc rrw rrd rrc rrcd rrdc plmt


+ lwd=rep(c(3,1,1),2), lty=rep(c(1:3),c(9,3,3)),+ col=rep(clr[c(1:3,3,3)],each=3),type="l" )+ axis( side=4, at=5:20/10 * rrr, labels=FALSE, tcl=-0.3 )+ axis( side=4, at=c(0.5,1,2) * rrr, labels=c(0.5,1,2) )+ axis( side=4, at=3 * rrr, labels="RR", tcl=0 )+ axis( side=1, at=seq( 20,100, 5), labels=F )+ axis( side=1, at=seq( 20,100,20) )+ axis( side=1, at=seq(105,120,5), labels=F )+ axis( side=1, at=seq(110,120,10), labels=c(2000,2010) )+ mtext( c("Age","Date"), at=c(60,112.5), side=1, line=3/1.6 )+ }> plmt()> text( rep(23,3), ylm[2]*0.7^(3:1),+ c("Well","DM","Cancer"), col=clr[1:3], adj=0, font=2 )> # Mortality among women> mtw mtd mtc mtcd mtdc rrw rrd rrc rrcd rrdc plmt()> mtext( "DM / Cancer incidence rates per 1000 PY",+ side=2, line=1/1.6, at=0.75, las=0, outer=TRUE )> mtext( "Mortality rates per 1000 PY",+ side=2, line=1/1.6, at=0.25, las=0, outer=TRUE )> mtext( "Men" , side=3, line=-1, at=0.25, las=0, outer=TRUE )> mtext( "Women", side=3, line=-1, at=0.75, las=0, outer=TRUE )

2.3.6 Transition probabilities

Now we have the transition rates corresponding to 1/10 year in the array TR, but we needto fill in the diagonals to get a proper transition matrix. To this ens we need a functionthat does this properly; note that the entries in TR are cumulative rates corresponding to aperiod of length 1/10 year (well, formally int). Thus if transition cumulatieve rates from agiven state are, say, Λ1, Λ2 Λ3, the the diagonal element in the row must beexp

(−(Λ1 + Λ2 + Λ3)

)and the off-diagonal elements in the row must be be multiplied by(

1− exp(−(Λ1 + Λ2 + Λ3)

))/(Λ1 + Λ2 + Λ3). We wrap this calculation in a small function:

> ci2pr


> TR print.table( round( TR[,,800,1,1] *10^3 ), zero.print="." )

tofrom Well DM DM-Ca Ca Ca-DM D-W D-DM D-Ca D-DC D-CDWell . 2 . 4 . 5 . . . .DM . . 4 . . . 9 . . .DM-Ca . . . . . . . . 30 .Ca . . . . 4 . . 18 . .Ca-DM . . . . . . . . . 19D-W . . . . . . . . . .D-DM . . . . . . . . . .D-Ca . . . . . . . . . .D-DC . . . . . . . . . .D-CD . . . . . . . . . .

> print.table( round( ci2pr( TR[,,800,1,1] )*10^3 ), zero.print="." )

tofrom Well DM DM-Ca Ca Ca-DM D-W D-DM D-Ca D-DC D-CDWell 990 2 . 4 . 5 . . . .DM . 987 4 . . . 9 . . .DM-Ca . . 971 . . . . . 29 .Ca . . . 979 4 . . 17 . .Ca-DM . . . . 981 . . . . 19D-W . . . . . 1000 . . . .D-DM . . . . . . 1000 . . .D-Ca . . . . . . . 1000 . .D-DC . . . . . . . . 1000 .D-CD . . . . . . . . . 1000

> TRp dim( TRp )

[1] 100 1020 2 2

> # Note that apply does not recognize the dim attribute of FUN argument> dim( TRp ) dimnames( TRp ) print.table( round( TRp[,,800,1,1]*10^3 ), zero.print="." )

tofrom Well DM DM-Ca Ca Ca-DM D-W D-DM D-Ca D-DC D-CDWell 990 2 . 4 . 5 . . . .DM . 987 4 . . . 9 . . .DM-Ca . . 971 . . . . . 29 .Ca . . . 979 4 . . 17 . .Ca-DM . . . . 981 . . . . 19D-W . . . . . 1000 . . . .D-DM . . . . . . 1000 . . .D-Ca . . . . . . . 1000 . .D-DC . . . . . . . . 1000 .D-CD . . . . . . . . . 1000

The just printed matrix is the transition matrix (multiplied by 1000) from age 80 to 80.1,so in order to get the probability distribution at 80.1, we just multiply thestate-distribution at time 80.0 (as a row vector) with the transition matrix; this must ofcourse be looped over all the other dimensions of TR:

> names( dimnames( TRp ) )

[1] "from" "to" "age" "scene" "sex"

> for( sc in dimnames(TRp)[["scene"]] )+ for( sx in dimnames(TRp)[["sex"]] )+ {+ # Initialize at age 0+ PR[,1,sc,sx]


+ for( ag in 1:dim(TRp)[3] )+ {+ PR[,ag,sc,sx] summary( PR )

Min. 1st Qu. Median Mean 3rd Qu. Max.0.0000000 0.0003761 0.0116500 0.1000000 0.0746800 0.9997000

> summary( apply( PR, 2:4, sum ) )

Min. 1st Qu. Median Mean 3rd Qu. Max.1 1 1 1 1 1

Now we have the distribution of the persons in the different states under various scenarios,and we can plot the resulting distribution of the states as function of time; for eeach of the4 combinations of scenario and sex we can plot the probabilities of being in each of the 10states, but we must put them in the right order:

> round( t(PR[,600+1:5,1,1])*100, 1 )

Stateage Well DM DM-Ca Ca Ca-DM D-W D-DM D-Ca D-DC D-CD60.05 71.4 10.7 0.5 4.2 0.2 7.1 1.6 3.8 0.4 0.160.15 71.2 10.8 0.5 4.2 0.2 7.1 1.7 3.9 0.4 0.160.25 71.0 10.8 0.5 4.3 0.2 7.1 1.7 3.9 0.4 0.160.35 70.8 10.9 0.5 4.3 0.2 7.2 1.7 4.0 0.4 0.160.45 70.6 10.9 0.5 4.3 0.2 7.2 1.7 4.0 0.4 0.1

> perm round( t(PR[perm,600+1:5,1,1])*100, 1 )

Stateage DM DM-Ca Ca-DM Ca Well D-W D-Ca D-CD D-DC D-DM60.05 10.7 0.5 0.2 4.2 71.4 7.1 3.8 0.1 0.4 1.660.15 10.8 0.5 0.2 4.2 71.2 7.1 3.9 0.1 0.4 1.760.25 10.8 0.5 0.2 4.3 71.0 7.1 3.9 0.1 0.4 1.760.35 10.9 0.5 0.2 4.3 70.8 7.2 4.0 0.1 0.4 1.760.45 10.9 0.5 0.2 4.3 70.6 7.2 4.0 0.1 0.4 1.7

> CR str( PR )

num [1:10, 1:1020, 1:2, 1:2] 1.00 1.13e-05 0.00 2.72e-05 0.00 ...- attr(*, "dimnames")=List of 4..$ State: chr [1:10] "Well" "DM" "DM-Ca" "Ca" .....$ age : chr [1:1020] "0.05" "0.15" "0.25" "0.35" .....$ scene: chr [1:2] "Cross" "Long"..$ sex : chr [1:2] "M" "F"

> str( CR )

num [1:10, 1:1020, 1:2, 1:2] 1.13e-05 1.13e-05 1.13e-05 3.85e-05 1.00 ...- attr(*, "dimnames")=List of 4..$ : chr [1:10] "DM" "DM-Ca" "Ca-DM" "Ca" .....$ age : chr [1:1020] "0.05" "0.15" "0.25" "0.35" .....$ scene: chr [1:2] "Cross" "Long"..$ sex : chr [1:2] "M" "F"

> ftable( round( apply( PR, c(1,3,4), max )*100, 1 ), col.vars=1 )

State Well DM DM-Ca Ca Ca-DM D-W D-DM D-Ca D-DC D-CDscene sexCross M 100.0 13.4 1.7 6.9 1.3 35.7 20.1 29.2 9.6 5.4

F 100.0 12.7 1.9 9.1 1.7 36.5 19.8 29.7 7.9 5.6Long M 99.8 15.5 5.4 11.1 6.4 21.6 12.9 25.5 19.7 11.3

F 99.8 16.2 4.9 11.9 6.2 16.9 10.5 26.2 20.6 12.1

> ftable( round( apply( CR, c(1,3,4), max )*100, 1 ), col.vars=1 )


DM DM-Ca Ca-DM Ca Well D-W D-Ca D-CD D-DC D-DMscene sexCross M 13.4 14.7 15.5 22.4 100.0 100.0 100.0 100.0 100.0 100.0

F 12.7 14.4 15.9 24.9 100.0 100.0 100.0 100.0 100.0 100.0Long M 15.5 19.2 23.8 34.6 99.8 100.0 100.0 100.0 100.0 100.0

F 16.2 20.7 26.5 37.2 99.8 100.0 100.0 100.0 100.0 100.0

> round( t( CR[,800+1:5,"Cross","M"] )*100, 1 )

age DM DM-Ca Ca-DM Ca Well D-W D-Ca D-CD D-DC D-DM80.05 8.6 10.1 11.4 17.1 39.6 60.5 80.2 82.7 88.6 10080.15 8.5 10.0 11.3 17.0 39.3 60.2 80.0 82.5 88.6 10080.25 8.5 9.9 11.2 16.9 38.9 60.0 79.9 82.4 88.5 10080.35 8.4 9.9 11.2 16.7 38.6 59.7 79.7 82.3 88.4 10080.45 8.3 9.8 11.1 16.6 38.2 59.5 79.6 82.2 88.3 100

In order to plot the different probabilities we use the polygon trick, and in order tovisualize the joint occurrence of diabetes and cancer we define semi-transparent colors

> nul sx sc aa par( mfrow=c(1,2), mar=c(2,2,1,3), oma=c(2,2,0,0), mgp=c(3,1,0)/1.6, las=1 )> for( sc in dimnames(CR)[[3]][1] )+ for( sx in dimnames(CR)[[4]] )+ {+ plot( NA, xlim=c(50,100), ylim=c(0,100),+ xlab="", ylab="", xaxs="i", yaxs="i" )+ axis( side=4, lwd=0, lwd.ticks=1 )+ axis( side=4, lwd=0, lwd.ticks=1, at=seq(10,90,10), labels=F, tcl=-0.4 )+ axis( side=4, lwd=0, lwd.ticks=1, at=seq( 5,95, 5), labels=F, tcl=-0.3 )+ axis( side=4, lwd=0, lwd.ticks=1, at=1:99, labels=F, tcl=-0.2 )+ polygon( c(aa,rev(aa)), c(CR[1,,sc,sx],rev(nul))*100,+ col = clr[2], border="transparent")+ polygon( c(aa,rev(aa)), c(CR[1,,sc,sx],+ rev(CR[3,,sc,sx]))*100,+ col = clr[4], border="transparent")+ polygon( c(aa,rev(aa)), c(CR[3,,sc,sx],+ rev(CR[4,,sc,sx]))*100,+ col = clr[3], border="transparent")+ polygon( c(aa,rev(aa)), c(CR[4,,sc,sx],+ rev(CR[5,,sc,sx]))*100,+ col = clr[1], border="transparent")+ polygon( c(aa,rev(aa)), c(CR[5,,sc,sx],+ rev(CR[6,,sc,sx]))*100,+ col = "gray", border="transparent")+ polygon( c(aa,rev(aa)), c(CR[6,,sc,sx],+ rev(CR[7,,sc,sx]))*100,+ col = clr[3], border="transparent")+ polygon( c(aa,rev(aa)), c(CR[7,,sc,sx],+ rev(CR[9,,sc,sx]))*100,+ col = clr[4], border="transparent")+ polygon( c(aa,rev(aa)), c(CR[9,,sc,sx],+ rev(CR[10,,sc,sx]))*100,+ col = clr[2], border="transparent")+ matlines( aa, 100*t(CR[c(2,5,8),,sc,sx]),+ lty=1, col=c("white","black")[c(1,2,1)], lwd=c(1,3,1), type="l" )+ text( 55, 70, sx, font=2, cex=1.5, col="white" )+ mtext( "Age (years)", side=1, outer=TRUE )+ }> mtext( "Fraction of persons (%)", side=2, outer=TRUE, las=0 )

We also want to see the cumulative risks of getting DM, cancer and both before a givenage, so we make graphs of this for men and women


> dimnames(PR)[[1]]

[1] "Well" "DM" "DM-Ca" "Ca" "Ca-DM" "D-W" "D-DM" "D-Ca" "D-DC" "D-CD"

> dmlev calev dclev dimnames(PR)[[1]][dmlev]

[1] "DM" "DM-Ca" "Ca-DM" "D-DM" "D-DC" "D-CD"

> dimnames(PR)[[1]][calev]

[1] "DM-Ca" "Ca" "Ca-DM" "D-Ca" "D-DC" "D-CD"

> dimnames(PR)[[1]][dclev]

[1] "DM-Ca" "Ca-DM" "D-DC" "D-CD"

> par( mfrow=c(1,2), mar=c(2,2,1,3), oma=c(2,2,0,0), mgp=c(3,1,0)/1.6, las=1 )> for( sc in dimnames(CR)[[3]][1] )+ for( sx in dimnames(CR)[[4]] )+ {+ plot( NA, xlim=c(50,100), ylim=c(0,50),+ xlab="", ylab="", xaxs="i", yaxs="i" )+ axis( side=4, lwd=0, lwd.ticks=1 )+ axis( side=4, lwd=0, lwd.ticks=1, at=seq(10,90,10), labels=F, tcl=-0.4 )+ axis( side=4, lwd=0, lwd.ticks=1, at=seq( 5,95, 5), labels=F, tcl=-0.3 )+ axis( side=4, lwd=0, lwd.ticks=1, at=1:99, labels=F, tcl=-0.2 )+ text( 55, 40, sx, font=2 )+ matlines( aa, cbind( apply( PR[dmlev,,sc,sx]*100, 2, sum ),+ apply( PR[calev,,sc,sx]*100, 2, sum ),+ apply( PR[dclev,,sc,sx]*100, 2, sum ) ),+ col=clr[2:4], lty=1, lwd=5 )+ mtext( "Age (years)", side=1, outer=TRUE )+ mtext( "Fraction of persons (%)", side=2, outer=TRUE, las=0 )+ }

We can of course also make the same exercise conditional being alive at age 50, 60 etc,but as is seen from figure 2.6 the ultimate distribution of the fraction of persons that get thetwo diseases is not dramatically changed by condtioning on survival to ages 50, 60 or 70.

We set up the machinery in parallel for the three conditioning ages

> DM50


For further comparisons we print the distribution on states at age 102 years:

> round( ww round( ww[c(7:10),], 1 )

M F M F M F M FD-DM 20.1 19.8 18.6 18.4 16.3 17.3 12.8 14.5D-Ca 29.2 29.7 30.1 29.0 30.5 26.9 28.5 22.6D-DC 9.6 7.9 8.6 6.4 6.8 5.2 4.1 3.2D-CD 5.4 5.6 5.9 5.6 6.1 4.9 5.5 3.5

> round( apply(ww[c(8,9,10),],2,sum), 1 )

M F M F M F M F44.1 43.2 44.6 41.0 43.5 37.0 38.1 29.3

> round( apply(ww[c(7,9,10),],2,sum), 1 )

M F M F M F M F35.1 33.4 33.1 30.4 29.3 27.4 22.4 21.2

> round( apply(ww[c( 9,10),],2,sum), 1 )

M F M F M F M F15.0 13.6 14.5 12.0 13.0 10.1 9.6 6.7

We con compute the fraction of those without disease at different age and who eventuallygets a DM diagnosis, who also have a cancer diagnosis:

> round( ww[c(7,9,10),], 1 )

M F M F M F M FD-DM 20.1 19.8 18.6 18.4 16.3 17.3 12.8 14.5D-DC 9.6 7.9 8.6 6.4 6.8 5.2 4.1 3.2D-CD 5.4 5.6 5.9 5.6 6.1 4.9 5.5 3.5

> round( apply(ww[ 9:10 ,],2,sum)/+ apply(ww[c(7,9:10),],2,sum)*100, 1 )

M F M F M F M F42.7 40.6 43.7 39.5 44.3 36.9 42.8 31.6

We can see how the overall fraction of a birth cohort that gets cancer compares to thefraction among those with diabetes at a given age that contracts cancer:

> round( cbind( PR[,1020,"Cross",],+ DM50[,1020,"Cross",],+ DM60[,1020,"Cross",],+ DM70[,1020,"Cross",] )*100, 1 )


M F M F M F M FWell 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.0DM 0.0 0.1 0.0 0.1 0.0 0.1 0.0 0.1DM-Ca 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Ca 0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0Ca-DM 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0D-W 35.7 36.5 0.0 0.0 0.0 0.0 0.0 0.0D-DM 20.1 19.8 63.5 62.9 63.5 66.1 67.9 73.4D-Ca 29.2 29.7 0.0 0.0 0.0 0.0 0.0 0.0D-DC 9.6 7.9 36.5 37.0 36.4 33.8 32.0 26.5D-CD 5.4 5.6 0.0 0.0 0.0 0.0 0.0 0.0

We can now plot the comparison between the life-long outloook of a person with andwithout diabetes:

> CRpl for( sc in dimnames(CR)[[3]][1] )+ for( sx in dimnames(CR)[[4]] )+ {+ CRpl( PR50, sc, sx, 1:500 )+ CRpl( PR60, sc, sx, 1:600 )+ CRpl( PR70, sc, sx, 1:700 )+ CRpl( DM50, sc, sx, 1:500, "transparent" )+ CRpl( DM60, sc, sx, 1:600, "transparent" )+ CRpl( DM70, sc, sx, 1:700, "transparent" )


+ }> mtext( "Age (years)", side=1, outer=TRUE )> mtext( "Fraction of persons (%)", side=2, outer=TRUE, las=0 )> mtext( "Men, no DM" , side=3, outer=TRUE, las=0, at=1/8 )> mtext( "Men, DM" , side=3, outer=TRUE, las=0, at=3/8 )> mtext( "Women, no DM", side=3, outer=TRUE, las=0, at=5/8 )> mtext( "Women, DM" , side=3, outer=TRUE, las=0, at=7/8 )


0.5 0.7 1.0 1.5 2.0 3.0 4.0 5.0

RR, DM vs. non−DM

Leukaemia

Multiple myeloma

Non−Hodgkin lymphoma

Hodgkins lymphoma

Thyroid

Brain

Urinary bladder

Kidney

Testis

Prostate

Ovary, fallopian tube etc.

Corpus uteri

Cervix uteri

Breast

Melanoma of skin

Lung, bronchus and pleura

Pancreas

Liver

Rectum

Colon

Stomach

Oesophagus

All malignant neoplasms ●

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Figure 2.1: Estimated RRs from different studies. Blue lines for men, red lines for women.Within each group of estimates they are from the studies, in the same order as in table 1.1.


Well0 0

DM2,447.4

382,477 247,428

DM−Ca97.5

2,030 14,230

Ca2,470.8

522,493 204,878

Ca−DM138.6

5,661 15,132

Dead0 430,993

40,856(16.7)

94,193(38.5)

28,656(293.8)

27,964(11.3)

289,651(117.2)

18,493(133.5)

Well0 0

DM2,447.4

382,477 247,428

DM−Ca97.5

2,030 14,230

Ca2,470.8

522,493 204,878

Ca−DM138.6

5,661 15,132

Dead0 430,993

Well0 0

DM2,447.4

382,477 247,428

DM−Ca97.5

2,030 14,230

Ca2,470.8

522,493

The Epidemiology of Diabetes and Cancer Detailed...

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Transcript of The Epidemiology of Diabetes and Cancer Detailed...