Introduction: Why Do We Visualize Data and What Is This Book About?
 3.2k Downloads
Abstract
Introduction: Why do we visualize data and what is this book about? The introductory chapter describes the three rationales to visualize data: exploration, confirmation and presentation, and discusses the developments in computer hardware, software and connectivity that were instrumental for the recent increased interest in visualizing data.
The goal of this book is simple: We would like to show how mortality dynamics can be visualized in the socalled Lexis diagram. To appeal to as many potential readers as possible, we do not require any specialist knowledge. This approach may be disappointing: Demographers may have liked more information about the mathematical underpinnings of population dynamics on the Lexis surface as demonstrated, for instance, by Arthur and Vaupel in 1984. Statisticians would have probably preferred more information about the underlying smoothing methods that were used. Epidemiologists likewise might miss discussions about the etiology of diseases. Sociologists would have probably expected that our results were more embedded into theoretical frameworks….
We are aware of those potential shortcomings but believe that the current format can, nevertheless, provide interesting insights into mortality dynamics, and we hope our book can serve as a starting point to visualize data on the Lexis plane for those who have not used those techniques yet.
 1.
Exploration: John Tukey stresses that exploratory data analysis “can never be the whole story, but nothing else can serve as the foundation—as the first step” (Tukey 1977, p. 3). He uses the expression of “graphical detective work” by trying to uncover as many important details about the underlying data as possible. If one explores data only with preconceived notions and theories, it is likely that essential characteristics remain undiscovered.
 2.
Confirmation: It could be argued that the mere exploration of data without any hypotheses is a misguided endeavor. Exploration needs to be firmly distinguished from confirmatory analysis, though. While the exploration is comparable to the work of the police, this step can be seen as the task of a judge or the jury. Both are important to advance science, the first step is to gather the facts whereas the second step is of judgmental nature: Can the “facts” be interpreted to support the theory? Or do certain findings exclude some hypotheses? In this sense, confirmatory analysis represents the core of scientific progress in Popper’s sense, namely by falsifying theories.
 3.
Presentation: Presenting and communicating the findings from the data analysis to the reader, or more appropriately, to the viewer, represents the third pillar of why data visualization is important. Mixing up confirmatory analysis with the presentation of the findings is probably one of the root causes for poor scientific communication. It is a common occurrence at scientific conferences that researchers use the same graphical tools to present their results to others as they used to obtain their findings in the first place. As pointed out by Schumann and Müller (2000, p. 6), this step requires careful thought that third parties are able to understand the findings without any unnecessary difficulties.
 Hardware:

The introduction of the predecessor of all modern PCs, the IBM personal computer, in 1981 as well as of microcomputers (e.g., the “C64”) in the same era triggered a shift away from the socalled minicomputers of the 1970s^{2} to computers that could be purchased by households of average income. The speed of the processors was too slow and the size of computer memory was too small to process data as conveniently as we can nowadays, though. The first PC had an upper limit for working memory (RAM) of 256 kB, that is about 0.000778% of the first author’s current desktop workstation. If we disregard developments in cache technology, parallel processing, etc., the pure clock speed of processors is now three orders of magnitude higher than in the early 1980s. Only 20 years ago, the typical size of total RAM was about as large as the size of a single digital photo today. But even if there was enough RAM and sufficient clock speed of the CPU, data storage was another limiting factor. The first hard disk with a capacity of more than one gigabyte was introduced in 1980 and cost at least US$ 97,000.^{3} One thousand times the storage capacity is available now at less than US$ 100. This trend allowed the collection of massive data sets. To illustrate current capabilities: If we were interested in creating a data set, which contains about 1000 alphabetic characters (more than enough for the name, birth date and current residence) of any person alive, we would have to invest less than US$ 400.^{4} But, once again, even if we had the affordable computer storage of today, communicating results graphically was hindered by the low resolution combined with relatively few colors of early graphics standards such as CGA and EGA. Only with the introduction and the extension of the VGA standard, high resolution displays have become feasible.
 Software:
 Having hardware in terms of processing speed, working memory and hard disk capacity to process graphics coincided with a revolution in software in the 1990s: Similar to the introduction of home computers that gave access to almost everyone, the emergence of free software, also called open source software, allowed anyone to use software without the costs and other restrictions often imposed by software products. Examples for this development can be found in the area of

general programming languages (e.g., Python, Perl) as well as

languages tailored or at least particularly suited for statistical programming and data analysis. The invention of the S language, started in the 1970s, was instrumental.^{5} The most prominent example today is probably R (Ihaka 1998), but also other languages such as the now almost completely abandoned XLISPSTAT (de Leeuw 2005) facilitate(d) the visualization of data.^{6}

Lastly, in the area of efficient data storage, especially with the advent of “big data”. Although it might be one of the most abused buzzwords currently, data sets in the gigabyte and terabyte range, partly in nonrectangular formats, have become ubiquitous. Those data can be handled by relational and nonrelational database systems that are also available under free and open source licenses (e.g., SQLite, MySQL, Postgresql, Cassandra).

 Connectivity:

While the internet existed already for more than 20 years, the introduction and rising popularity of the world wide web (WWW) was a catalyst for the exchange of information via electronic networks. This technology allows now billions of people on earth to have almost instant access to data. The speed of the internet connection, which is crucial for the exchange of information such as downloading large data sets, has also increased by at least two orders of magnitude since the middle of the 1990s when 56 kbit/s modems were the standard.
Footnotes
 1.
This trend is probably best demonstrated by visualizing the popularity of the term “visualizing data” over time, for instance, via Google’s Ngram viewer. Google Books Ngram Viewer displays the relative frequency of a search term in a corpus of books during a given time frame. Please see, for example: https://books.google.com/ngrams/graph?content=visualizing+data+&year_start=1960&year_end=2008
 2.
As noted at https://en.wikipedia.org/wiki/Minicomputer#cite_noteSmith_19704 (last accessed on 13 June 2017), the New York Times wrote in 1970 that minicomputers were computers that cost less than US$ 25,000.
 3.
See: https://www03.ibm.com/ibm/history/exhibits/storage/storage_3380.html, last accessed on 13 June 2017.
 4.
Assuming a world population of less than eight billion, a price for a 2TB hard disk of less than US$S 100 and one byte per alphabetic letter.
 5.
Please see Appendix A in Chambers (2008) for some notes on the history of S.
 6.
It should be mentioned, though, that Matlab (Mathworks 2017), which is not published under a free/opensource license, was and is also key for the analysis and visualization of data.
References
 Abel, G. J., & Sander, N. (2014). Quantifying global international migration flows. Science, 343(6178), 1520–1522.CrossRefGoogle Scholar
 Andreev, K. F. (2002). Evolution of the Danish population from 1835 to 2000 (Odense Monographs on Population Aging, Vol. 9), Odense: University Press of Southern Denmark.Google Scholar
 Arriaga, E. E. (1984). Measuring and explaining the change in life expectancies. Demography, 21(1), 83–96.Google Scholar
 Arthur, W. B., & Vaupel, J. W. (1984). Some general relationships in population dynamics. Population Index, 50(2), 214–226.CrossRefGoogle Scholar
 Berkson, J., & Gage, R. P. (1952). Survival curve for cancer patients following treatment. Journal of the American Statistical Association, 47(259), 501–515.CrossRefGoogle Scholar
 Camarda, C. G. (2008). Smoothing methods for the analysis of mortality development. PhD thesis, Universidad Carlos III de Madrid.Google Scholar
 Camarda, C. G. (2012). MortalitySmooth: An R package for smoothing Poisson counts with Psplines. Journal of Statistical Software, 50(1), 1–24.CrossRefGoogle Scholar
 Camarda, C. G. (2015). Smoothing and forecasting Poisson counts with Psplines. http://CRAN.Rproject.org/package=MortalitySmooth, R package version 2.3.4.
 CanudasRomo, V. (2003). Decomposition methods in demography. PhD thesis, Rijksuniversiteit Groningen, Groningen, NL.Google Scholar
 Caselli, G., & Vallin, J. (2006). Frequency surfaces and isofrequency lines. In G. Caselli, J. Vallin, & G. Wunsch (Eds.), Demography. Analysis and synthesis (Vol. I, Chap. 7, pp. 69–77). Amsterdam: Elsevier.Google Scholar
 Caselli, G., Vaupel, J. W., & Yashin, A. I. (1985). Mortality in Italy: Contours of a century of evolution. Genus, 41(1–2), 39–55.Google Scholar
 CDC/NCHS. (2015). Mortality in the United States, 2014. NCHS Data Brief, Number 229, Dec 2015. Available online as Supplementary Material at: https://www.cdc.gov/nchs/data/databriefs/db229_table.pdf#1.
 Chambers, J. (2008). Software for data analysis. New York: Springer.CrossRefGoogle Scholar
 Cho, H., Howlader, N., Mariotto, A. B., & Cronin, K. A. (2011). Estimating relative survival for cancer patients from the SEER program using expected rates based on Ederer I versus Ederer II method. Tech. Rep. 201101, National Cancer Institute.Google Scholar
 Christensen, K., Doblhammer, G., Rau, R., & Vaupel, J. (2009). Ageing populations: The challenges ahead. The Lancet, 374(9696), 1196–1208.CrossRefGoogle Scholar
 Crimmins, E. M., Preston, S. H., & Cohen, B. (Eds.). (2011). Explaining divergent levels of longevity in highincome countries. Washington, DC: The National Academies Press.Google Scholar
 Currie, I. D., Durban, M., & Eilers, P. H. (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4, 279–298.CrossRefGoogle Scholar
 Deborah, S. (1998). The da Vinci of Data. The New York Times, 30 March 1998.Google Scholar
 Delaporte, P. (1938). Évolution de la mortalité française depuis un siècle. Journal de la société de statistique de Paris, 79, 181–206.Google Scholar
 Delaporte, P. (1942). Évolution de la mortalité en Europe depuis l’origine des statisques. Journal de la société de statistique de Paris, 83, 183–203.Google Scholar
 Drefahl, S., Ahlbom, A., & Modig, K. (2014). Losing ground — Swedish life expectancy in a comparative perspective. PLOS ONE, 9(2), e88357.CrossRefGoogle Scholar
 Ederer, F., Axtell, L. M., & Cutler, S. J. (1961). The relative survival rate: A statistical methodology (Chap. 6, pp. 101–121). National Cancer Institute Monograph, National Cancer Institute.Google Scholar
 Eilers, P. H. C., & Marx, B. D. (1996). Flexible Smoothing with Bsplines and Penalties. Statistical Science, 11(2), 89–102.CrossRefGoogle Scholar
 Eilers, P. H. C., Gampe, J., Marx, B. D., & Rau, R. (2008). Modulation models for seasonal incidence tables. Statistics in Medicine, 27(17), 3430–3441.CrossRefGoogle Scholar
 EurowinterGroup. (1997). Cold exposure and winter mortality from ischaemic heart disease, cerebrovascular disease, respiratory disease, and all causes in warm and cold regions of Europe. Lancet, 349, 1341–1346.Google Scholar
 EurowinterGroup. (2000). Winter mortality in relation to climate. International Journal of Circumpolar Health, 59, 154–159.Google Scholar
 Feinstein, C. A. (2002). Seasonality of deaths in the U.S. by age and cause. Demographic Research, 6, 469–486.CrossRefGoogle Scholar
 Few, S. (2014). Why do we visualize quantitative data? Available Online At: http://www.perceptualedge.com/blog/?p=1897, Visual Business Intelligence. A blog by Stephen Few. Last verification: 14 June 2017.
 Friendly, M. (2008). A brief history of data visualization. In C. H. Chen, W. K. Härdle, & A. Unwin (Eds.), Handbook of data visualization (Springer Handbooks of Computational Statistics, Chap. I, pp. 15–56). Berlin/Heidelberg: Springer.Google Scholar
 Galilei, G. (1613). Istoria e dimostrazioni intorno alle macchie solari. Rome.Google Scholar
 Gambill, B. A., & Vaupel, J. W. (1985). The LEXIS program for creating shaded contour maps of demographic surfaces. Tech. Rep. RR–85–94. International Institute for Applied Systems Analysis (IIASA), Laxenburg, A.Google Scholar
 Hippocrates. (400BC). On airs, waters, and places. Translated by Francis Adams. Available online at: http://classics.mit.edu/Hippocrates/airwatpl.html.
 Huynen, M. M., Martens, P., Schram, D., Weijenberg, M. P., & Kunst, A. E. (2001). The impact of heat waves and cold spells on mortality rates in the Dutch population. Environmental Health Perspectives, 109, 463–470.CrossRefGoogle Scholar
 Ihaka, R. (1998). R: Past and future history. Available online at https://cran.rproject.org/doc/html/interface98paper/paper.html.
 Jacobsen, R., Keiding, N., & Lynge, E. (2002). Long term mortality trends behind low life expectancy of Danish women. Journal of Epidemiology and Community Health, 56, 205–208.CrossRefGoogle Scholar
 Jacobsen, R., Von Euler, M., Osler, M., Lynge, E., & Keiding, N. (2004). Women’s death in Scandinavia—What makes Denmark different? European Journal of Epidemiology, 19(2), 117–121.CrossRefGoogle Scholar
 Jacobsen, R., Keiding, N., & Lynge, E. (2006). Causes of death behind low life expectancy of Danish women. Scandinavian Journal of Social Medicine, 34(4), 432–436.Google Scholar
 Janssen, F., Nusselder, W. J., Looman, C., Mackenbach, J. P., & Kunst, A. E. (2003). Stagnation in mortality decline among elders in the Netherlands. Gerontologist, 43(5), 722–734.CrossRefGoogle Scholar
 Jdanov, D. A., Jasilionis, D., Soroko, E. L., Rau, R., & Vaupel, J. W. (2008). Beyond the KannistoThatcher database on old age mortality: An assessment of data quality at advanced ages. Working paper MPIDR Working Paper WP20083013, Max Planck Institute for Demographic Research, Rostock, Germany.Google Scholar
 Kannisto, V. (1994). Development of oldestold mortality, 1950–1990: Evidence from 28 developed countries (Monographs on Population Aging, Vol. 1). Odense: Odense University Press.Google Scholar
 Kannisto, V., Lauritsen, J., Thatcher, A. R., & Vaupel, J. W. (1994). Reductions in mortality at advanced ages: Several decades of evidence from 27 countries. Population and Development Review, 20, 793–810.CrossRefGoogle Scholar
 Keyfitz, N. (1977). Applied mathematical demography. New York: John Wiley & Sons.Google Scholar
 Kintner, H. J. (2004). The life table. In J. B. Siegel & D. A. Swanson (Eds.), The methods and materials of demography (2nd ed., Chap. 13, pp. 301–340). San Diego: Elsevier.Google Scholar
 Kunst, A., Looman, C., & Mackenbach, J. (1990). The decline in winter excess mortality in the Netherlands. International Journal of Epidemiology, 20, 971–977.CrossRefGoogle Scholar
 Lang, D. T., & the CRAN team. (2015). RCurl: General Network (HTTP/FTP/…) Client Interface for R. http://CRAN.Rproject.org/package=RCurl, R package version 1.954.7.
 de Leeuw, J. (2005). On abandoning XLISPSTAT. Journal of Statistical Software, 13(7), 1–5.CrossRefGoogle Scholar
 Leon, D. A., Chenet, L., Shkolnikov, V. M., Zakharov, S., Shapiro, J., Rakhmanova, G., Vassin, S., & McKee, M. (1997). Huge variation in Russian mortality rates 1984–1994: Artefact, alcohol, or what? The Lancet, 350(9075), 383–388. https://doi.org/10.1016/S01406736(97)033606, http://www.sciencedirect.com/science/article/pii/S0140673697033606.
 LindahlJacobsen, R., Rau, R., Jeune, B., CanudasRomo, V., Lenart, A., Christensen, K., & Vaupel, J. W. (2016). Rise, stagnation, and rise of Danish women’s life expectancy. Proceedings of the National Academy of Sciences, 113(15), 4015–4020. DOI 10.1073/pnas.1602783113, http://www.pnas.org/content/113/15/4015.abstract, http://www.pnas.org/content/113/15/4015.full.pdf.
 Luy, M. (2004). Mortality differences between Western and Eastern Germany before and after Reunification. A macro and micro level analysis of developments and responsible factors. Genus, 60(3/4), 99–141.Google Scholar
 Mackenbach, J., Kunst, A., & Looman, C. (1992). Seasonal variation in mortality in the Netherlands. Journal of Epidemiology and Community Health, 46, 261–265.CrossRefGoogle Scholar
 Marrero, O. (1983). The performance of several statistical tests for seasonality in monthly data. Journal of Computational Statistics and Simulation, 17, 275–296.CrossRefGoogle Scholar
 Mathworks. (2017). Matlab. Available at www.mathworks.com.
 Max Planck Institute for Demographic Research (Germany) and Vienna Institute of Demography (Austria). (2017). Human fertility database. Available at http://www.humanfertility.org.
 McDowall, M. (1981). Long term trends in seasonal mortality. Population Trends, 26, 16–19.Google Scholar
 Meslé, F. (2004). Mortality in Central and Eastern Europe: Longterm trends and recent upturns. Demographic Research Special Collection, 2, 45–70.CrossRefGoogle Scholar
 Meslé, F. (2006). Medical causes of death. In G. Caselli, J. Vallin, & G. Wunsch (Eds.), Demography. Analysis and synthesis (Vol. II, Chap. 42, pp. 29–44). Amsterdam: Elsevier.Google Scholar
 Meslé, F., & Vallin, J. (1996). Reconstructing longterm series of causes of death. Historical Methods, 29, 72–87.CrossRefGoogle Scholar
 Meslé, F., & Vallin, J. (2006a). Diverging trends in female oldage mortality: The United States and the Netherlands versus France and Japan. Population and Development Review, 32, 123–145.Google Scholar
 Meslé, F., & Vallin, J. (2006b). The health transition: Trends and prospects. In G. Caselli, J. Vallin, & G. Wunsch (Eds.), Demography. Analysis and synthesis (Vol. II, Chap. 57, pp. 247–259). Amsterdam: Elsevier.Google Scholar
 Moore, T. B., & Hurvitz, C. G. (2009). Cancers in childhood. In D. A. Casciato & M. C. Territo (Eds.), Manual of clinical oncology (Chap. 18, p. 397). Philadelphia: Lippincott Williams & Wilkins.Google Scholar
 National Bureau of Economic Research. (1959–2015). Mortality data — Vital statistics NCHS’ multiple cause of death data, 1959–2015. http://www.nber.org/data/vitalstatisticsmortalitydatamultiplecauseofdeath.html.
 National Cancer Institute. (2017). NCI dictionary of cancer terms. Available Online at https://www.cancer.gov/publications/dictionaries/cancerterms.Google Scholar
 National Center for Health Statistics. (1959–2015). Mortality multiple cause files. Available online at https://www.cdc.gov/nchs/data_access/vitalstatsonline.htm#Mortality_Multiple.
 Pampel, F. C. (2001). Cigarette diffusion and sex differences in smoking. Journal of Health and Social Behavior, 42, 388–404.CrossRefGoogle Scholar
 Parkin, D., & Hakulinen, T. (1991). Analysis of survival. In O. Jensen, D. Parkin, R. MacLennan, C. Muir, & R. Skeet (Eds.), Cancer registration: Principles and methods (Chap. 12, pp. 159–176). No. 95 in IARC Scientific Publication, International Agency for Research on Cancer (IARC).Google Scholar
 Pechholdová, M. (2009). Results and observations from the reconstruction of continuous time series of mortality by cause of death: Case of West Germany, 1968–1997. Demographic Research, 21, 535–568.CrossRefGoogle Scholar
 Peters, F. (2015). Deviating trends in Dutch life expectancy. PhD thesis, Erasmus University Rotterdam, Rotterdam, NL.Google Scholar
 Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography. Measuring and modeling population processes. Oxford, UK: Blackwell Publishers.Google Scholar
 Pullum, T. W. (1980). Separating age, period, and cohort effects in white US fertility, 1920–1970. Social Science Research, 9(3), 225–244.CrossRefGoogle Scholar
 Quetelet, A. (1838). De l’influence des saisons sur la mortalité aux différens ages dans la Belgique. M. Hayez, Bruxelles, B.Google Scholar
 R Development Core Team. (2015). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, http://www.Rproject.org, ISBN:3900051070.Google Scholar
 Rau, R. (2007). Seasonality in human mortality. A demographic approach (Demographic research monographs). Heidelberg: Springer.Google Scholar
 Rau, R., & Doblhammer, G. (2003). Seasonal mortality in Denmark. The role of sex and age. Demographic Research, 9, 197–222.CrossRefGoogle Scholar
 Rau, R., & Riffe, T. (2015). ROMIplot: Plots surfaces of rates of mortality improvement. R package version 1.0.Google Scholar
 Rau, R., Jasilionis, D., Soroko, E. L., & Vaupel, J. W. (2008). Continued reductions in mortality at advanced ages. Population & Development Review, 34(4), 747–768.CrossRefGoogle Scholar
 van Rossum, G. (1995). Python reference manual. Tech. rep., CWI (Centre for Mathematics and Computer Science), Amsterdam, The Netherlands.Google Scholar
 Rutherford, M. J., Dickman, P. W., & Lambert, P. C. (2012). Comparison of methods for calculating relative survival in populationbased studies. Cancer Epidemiology, 36(1), 16–21.CrossRefGoogle Scholar
 Schumann, H., & Müller, W. (2000). Visualisierung. Grundlagen und allgemeine Methoden. Berlin/Heidelberg: Springer.Google Scholar
 Seretakis, D., Lagiou, P., Lipworth, L., Signorello, L. B., Rothman, K. J., & Trichopoulos, D. (1997). Changing seasonality of mortality from coronary heart disease. Journal of the American Medical Association, 278, 1012–1014.CrossRefGoogle Scholar
 Shkolnikov, V. M., Andreev, E. M., McKee, M., & Leon, D. A. (2013). Components and possible determinants of decrease in Russian mortality in 2004–2010. Demographic Research, 28(32), 917–950.CrossRefGoogle Scholar
 Surveillance, Epidemiology, and End Results (SEER) Program. (2014). Research data (1973–2011). Available online at www.seer.cancer.gov. National Cancer Institute, DCCPS, Surveillance Research Program, released April 2014, based on the November 2013 submission.
 Talbäck, M., & Dickman, P. W. (2011). Estimating expected survival probabilities for relative survival analysis—Exploring the impact of including cancer patient mortality in the calculations. European Journal of Cancer, 47(17), 2626–2632.CrossRefGoogle Scholar
 Thatcher, R. A., Kannisto, V., & Vaupel, J. W. (1998). The force of mortality at ages 80 to 120 (Monographs on population aging, Vol. 3). Odense: Odense University Press.Google Scholar
 Tufte, E. R. (2001). The visual display of quantitative data (2nd ed.). Cheshire: Graphics Press.Google Scholar
 Tufte, E. R. (2003). The cognitive style of PowerPoint. Cheshire: Graphics Press.Google Scholar
 Tukey, J. W. (1977). Exploratory data analysis. Reading, MA: AddisonWesley.Google Scholar
 University of California, Berkeley (USA), and Max Planck Institute for Demographic Research, Rostock, (Germany). (2007). Methods protocol for the human mortality database. Available at http://www.mortality.org/Public/Docs/MethodsProtocol.pdf.
 University of California, Berkeley (USA), and Max Planck Institute for Demographic Research, Rostock, (Germany). (2017). Human mortality database. Available at http://www.mortality.org.
 Van Den Berg, G. J. (1860). Befolknings statistik in: Underdaniga berattelse for dren 1856–1860, ny folijd II, 3. Stockholm, Statistika CentralByrans.Google Scholar
 Vandeschrick, C. (2001). The Lexis diagram, a misnomer. Demographic Research, 4(3), 97–124. DOI 10.4054/DemRes.2001.4.3, http://www.demographicresearch.org/volumes/vol4/3/.CrossRefGoogle Scholar
 Vaupel, J. W., Gambill, B. A., & Yashin, A. I. (1985a). Contour maps of population surfaces. Tech. Rep. RR–85–47, International Institute for Applied Systems Analysis (IIASA), Laxenburg, A.Google Scholar
 Vaupel, J. W., Gambill, B. A., & Yashin, A. I., Bernstein, A. J. (1985b). Contour maps of demographic surfaces. Tech. Rep. RR–85–33, International Institute for Applied Systems Analysis (IIASA), Laxenburg, A.Google Scholar
 Vaupel, J. W., Gambill, B. A., & Yashin, A. I. (1987). Thousands of data at a glance: Shaded contour maps of demographic surfaces. Tech. Rep. RR–87–16, International Institute for Applied Systems Analysis (IIASA), Laxenburg, A.Google Scholar
 Vaupel, J. W., Zhenglian, W., Andreev, K. F., & Yashin, A. I. (1997). Population data at a glance: Shaded contour maps of demographic surfaces over age and time (Odense Monographs on Population Aging, Vol. 4). Odense: University Press of Southern Denmark.Google Scholar
 Wang, H., & Preston, S. H. (2009). Forecasting United States mortality using cohort smoking histories. Proceedings of the National Academy of Sciences, 106(2), 393–398. DOI 10.1073/pnas.0811809106, http://www.pnas.org/content/106/2/393.abstract, http://www.pnas.org/content/106/2/393.full.pdf.
 Wilmoth, J. R. (2006). Ageperiodcohort models in demography. In G. Caselli, J. Vallin, & G. Wunsch (Eds.), Demography. Analysis and synthesis (Vol. I, Chap. 18, pp. 227–236). Elsevier, Amsterdam.Google Scholar
 Yen, C. J., Chao, C. L., Sung, F. C., Chen, W. J., Liau, C. S., & Lee, Y. T. (2000). Seasonal effects on cardiovascular mortality in older patients. Age & Ageing, 29, 186–187.CrossRefGoogle Scholar
Copyright information
Open Access This chapter is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, a link is provided to the Creative Commons license, and any changes made are indicated.
The images or other third party material in this book are included in the work’s Creative Commons license, unless indicated otherwise in the credit line; if such material is not included in the work’s Creative Commons license and the respective action is not permitted by statutory regulation, users will need to obtain permission from the license holder to duplicate, adapt or reproduce the material.