Curriculum Vitae for Ørnulf Borgan

(Last updated 14 March 2023)

Address

Department of Mathematics
University of Oslo
P.O.Box 1053 Blindern
N-0316 Oslo, Norway
e-mail: borgan@math.uio.no

Personal facts

Born: April 1950.
Place of birth: Ski, Norway.
Citizenship: Norwegian.

Academic degrees

1984: Dr. philos. (Ph.D.) in statistics, University of Oslo.
1976: M.sc. in statistics, University of Oslo.

Positions held

Since 2020: Professor emeritus in statistics, University of Oslo.
1993 - 2020: Professor in statistics, University of Oslo.
1984 - 92: Associate professor in statistics, University of Oslo.
1983: Associate professor in statistics, Agricultural University of Norway.
1980 - 82: Research fellow in statistics, University of Oslo.
1977 - 79: Assistant professor in insurance mathematics, University of Copenhagen.
1973 - 76: Research assistant in statistics, University of Oslo.

Editorial work

2019: Guest editor Lifetime Data Analysis issue 4, volume 25.
2013: Guest editor Statistics in Medicine issue 30, volume 32.
2013 - 2017: Associate editor Biometrical Journal.
2007 - 2009: Editor Scandinavian Journal of Statistics.
1998 - 2003: Associate editor The Annals of Statistics.
1997 - 2003: Associate editor Scandinavian Journal of Statistics.

Selected professional work

2005-2006: Group leader (joint with Odd O. Aalen) for a research group on Statistical Analysis of Complex Event History Data, Centre for Advanced Study, Oslo.
2007 - 2012: Head of the University of Oslo Graduate School in Biostatistics.
2007 - 2012: Leader of the Research group in Statistics at the Department of Mathematics, University of Oslo.
2007 - 2014: Key scientist at Statistics for innovation.
2012-2015: Member of the Marie Curie initial training network MEDIASRES - Novel Statistical Methodology for Diagnostic/Prognostic and Therapeutic Studies and Systematic Reviews.
2015-2020: Member Scientific Advisory Board, NORBIS - National research school in bioinformatics, biostatistics and systems biology.

Research interests

Statistical models and methods based on counting processes.
Survival and event history analysis.
Case-control designs.

Research visits

January-June 2014: Department of Medical Statistics, London School of Hygiene and Tropical Medicine.
August-December 2013: Department of Biostatistics, Columbia University, New York.
January-June 2005: School of Mathematics and Statistics, University of Newcastle upon Tyne (UK).
September-December 2004: Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm.
August 1997-June 1998: Department of Statistics, Stanford University.
June-August 1995: Department of Preventive medicine, University of Southern California.
June-August 1993: Departments of Mathematics and Preventive medicine, University of Southern California.
July 1991-June 1992: MRC Biostatistics Unit, Cambridge (UK).
June-August 1985: Statistical Research Unit, University of Copenhagen.
January-August 1982: Department of Statistics, Stanford University.

Academic associations

Elected member of the Royal Norwegian Society of Sciences and Letters, since 2019.
Elected member of the Norwegian Academy of Science and Letters, since 2011.
Fellow of the American Statistical Association, since 2015.
Elected member of the International Statistical Institute, since 1997.
Member of the International Biometric Society, the International Society for Clinical Biostatistics, and the Norwegian Statistical Association.

Administrative positions

2010-12: Elected head, Division of Statistics, Department of Mathematics, University of Oslo.
2009-16: Member of the board, Norwegian Computing Center (NR)
2003-08: Member of the board for the bachelor program Mathematics, informatics and technology at the University of Oslo
Spring 1997: Elected head, Division of Statistics, Department of Mathematics, University of Oslo.
1994-97: Member of the Senate, Department of Mathematics, University of Oslo.
Spring 1994: Elected head, Division of Statistics, Department of Mathematics, University of Oslo.
1989-90: Elected head, Division of Statistics, Department of Mathematics, University of Oslo.
1987-91: Member of the board, Norwegian Statistical Association.
1987-90: Member of the Senate, Faculty of Mathematics and Natural Sciences, University of Oslo.
1987-90: Member of the Senate, Department of Mathematics, University of Oslo.
1984-85: Elected leader for educational matters, Division of Statistics, Department of Mathematics, University of Oslo.
Fall 1979: Elected head, Laboratory of Actuarial Mathematics, University of Copenhagen.
1977-79: Elected leader for educational matters, Laboratory of Actuarial Mathematics, University of Copenhagen.

Teaching

I have:

List of publications

Books:

[B1] Andersen, P.K., Borgan, Ø., Gill, R.D., and Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer-Verlag, New York.

[B2] Aalen, O.O., Borgan, Ø., and Gjessing, H.K. (2008). Survival and Event History Analysis: A Process Point of View. Springer-Verlag, New York.

[B3] Borgan, Ø., Breslow, N.E., Chatterjee, N., Gail, M.H., Scott, A., and Wild, C.J. (eds.) (2018). Handbook of Statistical Methods for Case-Control Studies. CRC Press; Boca Raton.

Methodological papers in International Scientific Journals:

[J1] Borgan, Ø. (1979). On the theory of moving average graduation. Scand. Actuarial J. 1979, 83-105.

[J2] Borgan, Ø. (1979). Comparison of two sequential tests for two-sided alternatives. J. Royal Stat. Soc. Ser. B 41, 101-106.

[J3] Aalen, O.O, Borgan, Ø., Keiding, N., and Thorman, J. (1980). Interaction between life history events. Nonparametric analysis for prospective and retrospective data in the presence of censoring. Scand. J. Statist. 7, 161-171.

[J4] Borgan, Ø., Hoem, J.M., and Norberg, R. (1981). A nonasymptotic criterion for the evaluation of automobile bonus systems. Scand. Actuarial J. 1981, 165-178.

[J5] Borgan, Ø., Menne, T., and Green, A. (1982). Interaction between nickel allergy and hand eczema in the Danish female population. Scand. J. Statist. 9, 183-185.

[J6] Andersen, P.K., Borgan, Ø., Gill, R.D., and Keiding, N. (1982). Linear non-parametric tests for comparison of counting processes, with application to censored survival data (with discussion). Internat. Statist. Rev. 50, 219-258. Amendment 52, 225.

[J7] Borgan, Ø., Liestøl, K., and Ebbesen, P. (1984). Efficiencies of experimental designs for an illness-death model. Biometrics 40, 627-638.

[J8] Borgan, Ø. (1984). Maximum likelihood estimation in parametric counting process models, with applications to censored failure times data. Scand. J. Statist. 11, 1-16. Correction 11, 275.

[J9 ] Borgan, Ø. and Ramlau-Hansen, H. (1985). Demographic incidence rates and estimation of intensities with incomplete information. Ann. Statist. 13, 564-582.

[J10] Andersen, P.K. and Borgan, Ø. (1985). Counting process models for life history data (with discussion). Scand. J. Statist. 12, 97-158.

[J11] Bie, O., Borgan, Ø., and Liestøl, K. (1987). Confidence intervals and confidence bands for the cumulative hazard rate function and their small sample properties. Scand. J. Statist. 14, 221-233.

[J12] Borgan, Ø. and Hoem, J.M. (1988). Demographic reproduction rates and the estimation of an expected total count per person in an open population. J. Amer. Statist. Assoc. 83, 886-891.

[J13] Andersen, P.K., Borgan, Ø., Gill, R.D., and Keiding, N. (1988). Censoring, truncation and filtering in statistical models based on counting processes. Contemp. Math. 80, 19-60.

[J14] Borgan, Ø. and Liestøl, K. (1990). A note on confidence intervals and bands for the survival function based on transformations. Scand. J. Statist. 17, 35-41.

[J15] Borgan, Ø. and Langholz, B. (1993). Nonparametric estimation of relative mortality from nested case-control studies. Biometrics 49, 593-602.

[J16] Langholz, B. and Borgan, Ø. (1995). Counter-matching: A stratified nested case-control sampling method. Biometrika 82, 69-79.

[J17] Borgan, Ø., Goldstein, L., and Langholz, B. (1995). Methods for the analysis of sampled cohort data in the Cox proportional hazards model. Ann. Statist. 23, 1749-1778.

[J18] Grønnesby, J.K. and Borgan, Ø. (1996). A method for checking regression models in survival analysis based on risk score. Lifetime Data Anal. 2, 315-328.

[J19] Borgan, Ø. and Langholz, B. (1997). Estimation of excess risk from case-control data using Aalen's linear regression model. Biometrics 53, 690-697.

[J20] Langholz, B. and Borgan, Ø. (1997). Estimation of absolute risk from nested case-control data. Biometrics 53, 767-774. Correction 59, 451.

[J21] Borgan, Ø. and Olsen, E.F. (1999). The efficiency of simple and counter-matched nested case-control sampling. Scand. J. Statist. 26, 493-509.

[J22] Zhang, J. and Borgan, Ø. (1999). Aalen's linear model for sampled risk set data: a large sample study. Lifetime Data Anal. 5, 351-369.

[J23] Borgan, Ø., Langholz, B., Samuelsen, S.O., Goldstein, L. and Pogoda, J. (2000). Exposure stratified case-cohort designs. Lifetime Data Anal. 6, 39-58.

[J24] Aalen, O.O, Borgan, Ø., and Fekjær, H. (2001). Covariate adjustment of event histories estimated from Markov chains: The additive approach. Biometrics 57, 993-1001. Correction 59, 452-453.

[J25] Borgan, Ø. (2002). Estimation of covariate-dependent Markov transition probabilities from nested case-control data. Statist. Meth. Med. Res. 11, 183-202. Correction 12, 124.

[J26] Aalen, O.O, Fosen, J., Wedon-Fekjær, H., Borgan, Ø., and Husebye, E. (2004). Dynamic analysis of multivariate failure time data. Biometrics 60, 764-773.

[J27] Fosen, J., Borgan, Ø., Weedon-Fekjær, H., and Aalen, O.O. (2006). Dynamic analysis of recurrent event data using the additive hazard model. Biometrical J. 48, 381-398.

[J28] Fosen, J., Ferkingstad, E., Borgan, Ø., and Aalen, O.O. (2006). Dynamic path analysis - a new approach to analyzing time-dependent covariates. Lifetime Data Anal. 12, 143-167.

[J29] Borgan, Ø., Fiaccone, R.L, Henderson, R., and M. L. Barreto, M.L. (2007). Dynamic analysis of recurrent event data with missing observations, with application to infant diarrhoea in Brazil. Scand. J. Statist. 34, 53-69.

[J30] Gunnes, N., Borgan, Ø. and Aalen, O.O. (2007). Estimating stage occupation probabilities in non-Markov models. Lifetime Data Anal. 13, 211-240.

[J31] Bøvelstad, H. M., Nygård, S., Størvold, H.L., Aldrin, M., Borgan, Ø., Frigessi, A. and Lingjærde, O.C. (2007). Predicting survival from microarray data - a comparative study. Bioinformatics 23, 2080-2087.

[J32] Moger, T.A., Pawitan, Y. and Borgan, Ø. (2008). Case-cohort methods for survival data on families from routine registers. Stat. Med. 27, 1062-1074.

[J33] Nygård, S., Borgan, Ø., Lingjærde, O.C. and Størvold, H.L. (2008). Partial least squares Cox regression for genome-wide data. Lifetime Data Anal. 14, 179-195.

[J34] Aalen, O. O., Andersen, P. K., Borgan, Ø., Gill, R. D.; Keiding, N. (2009). History of applications of martingales in survival analysis. Journal Électronique d'Histoire des Probabililtés et de la Statistique 5, 1-28.

[J35] Bøvelstad, H. M., Nygård, S. and Borgan, Ø. (2009). Survival prediction from clinico-genomic models - a comparative study. BMC Bioinformatics 10:413 (online).

[J36] Moger, T. A., Haugen, M., Yip, B. H. K., Gjessing, H. K. and Borgan, Ø. (2011). A hierarchical frailty model applied to two-generation melanoma data. Lifetime Data Anal. 17, 445-460.

[J37] Bøvelstad, H. M. and Borgan, Ø. (2011). Assessment of evaluation criteria for survival prediction from genomic data. Biometrical J. 53, 202-216.

[J38] Paulsen, J., Lien, T. G., Sandve, G. K, Holden, L., Borgan, Ø., Glad, I. K. and Hovig, E. (2013). Handling realistic assumptions in hypothesis testing of 3D co-localization of genomic elements. Nucleic Acids Research 41, 5164-5174.

[J39] Nilsen, G., Borgan, Ø., Liestøl, K. and Lingjærde, O.C. (2013). Identifying clusters in genomics data by recursive partitioning. Statistical Applications in Genetics and Molecular Biology 12, 637-652.

[J40] Günther, C-C., Tvete I. F., Aas, K., Sandnes, G. I. and Borgan, Ø. (2014). Modelling and predicting customer churn from an insurance company. Scand. Actuarial J. 2014, 58-71.

[J41] Borgan, Ø. and Zhang, Y. (2015). Using cumulative sums of martingale residuals for model checking in nested case-control studies. Biometrics 71, 696-703.

[J42] Borgan, Ø. and Keogh, R. (2015). Nested case-control studies: should one break the matching? Lifetime Data Anal. 21, 517-541.

[J43] Susanne, S., Røysland, K., Hoff, R., Borgan, Ø., Pedersen, T. R. and Aalen, O. O. (2015). Dynamic path analysis - a useful tool to investigate mediation processes in clinical survival trials. Stat. Med..34, 3866- 3887 .

[J44] Kvamme, H., Borgan, Ø. and Scheel, I. (2019).Time-to-event prediction with neural networks and Cox regression. Journal of Machine Learning Research. 20, 1-30.

[J45] Lingjærde, C., Lien, T.G., Borgan, Ø., Bergholtz, H. and Glad, I.K. (2021). Tailored graphical lasso for data integration in gene network reconstruction. BMC Bioinformatics. 22, 498.

[J46] Kvamme, H. and Borgan, Ø. (2021). Continuous and discrete-time survival prediction with neural networks. Lifetime Data Anal. 27, 710–736.

[J47] Kvamme, H. and Borgan, Ø. (2023).The Brier score under administrative censoring: Problems and a solution. Journal of Machine Learning Research. 24, 1-26.

[J48] Borgan, Ø., Keogh, R.H. and Njøs, A. (2023). Use of multiple imputation in supersampled nested case-control and case-cohort studies. Scand. J. Statist. 50, 13-37.

Substance matter papers in International Scientific Journals:

[S1] Menne, T., Borgan, Ø., and Green, A. (1982). Nickel allergy and hand dermatitis in a stratified sample of the Danish female population. An epidemiological study including a statistical appendix. Acta Dermatovener. (Stockholm) 62, 35-41.

[S2] Ebbesen, P., Borgan, Ø., and Liestøl, K. (1983). Decreasing luekemia risk in old AKR mice. Exp. Geront. 18, 347-353.

[S3] Stavem, K., Bjørtuft, Ø., Borgan, Ø., Geiran, O., and Boe, J. (2006). Lung transplantation in patients with chronic obstructive pulmonary disease in a national cohort is without obvious survival benefit. J. Heart and Lung Transpl. 25, 75-84.

[S4] Langerød, A., Zhao, H., Borgan, Ø., Nesland, J.M., Bukholm, I.R.K., Ikdahl, T., Kåresen, R., Børresen-Dale, A.-L. and Jeffery, S.S. (2007). TP53 mutation status and gene expression profiles are powerful prognostic markers of breast cancer. Breast Cancer Research 9, R30 (online).

[S5] Aldrin, M., Lyngstad. T. M., Kristoffersen, A. B., Storvik, B., Borgan, Ø. and Jansen, P. A. (2011). Modelling the spread of infectious salmon anaemia among salmon farms based on seaway distances between farms and genetic relationships between infectious salmon anaemia virus isolates. J. R. Soc. Interface 8, 1346-1356.

[S6] Gran, J.M., Lie, S.A., Øyeflaten, I., Borgan, Ø. and Aalen, O.O. (2015). Causal inference in multi-state models --sickness absence and work for 1145 participants after work rehabilitation. BMC Public Health 15, 1082 (online). DOI:10.1186/s12889-015-2408-8

[S7] Lien, T.G., Borgan, Ø., Reppe, S., Gautvik, K.M., and & Glad, I.K. (2018). Integrated analysis of DNA-methylation and gene expression using high-dimensional penalized regression: a cohort study on bone mineral density in postmenopausal women. BMC Medical Genomics 11:24.

[S8] Ergon, T., Borgan, Ø., Nater, C.R., and Vindenes, Y. (2018). The utility of mortality hazard rates in population analyses. Methods in Ecology and Evolution. 9, 2046-2056.

[S9] Riiser, E.S., Haverkamp, T.H.A., Borgan, Ø., Jakobsen, K.S., Jentoft, S., and Star, B. (2018) A single Vibrionales 16S rRNA oligotype dominates the intestinal microbiome in two geographically separated Atlantic cod populations. Frontiers in Microbiology 9:1561.

[S10] Borgan, Ø. and Keilman, N. (2019). Do Japanese and Italian Women Live Longer than Women in Scandinavia? European Journal of Population. 35, 87-99.

[S11] Riiser, E.S., Haverkamp, T.H.A., Varadharajan, S., Borgan, Ø., Jakobsen, K.S. Jentoft, S. and & Star, B. (2019).Switching on the light: using metagenomic shotgun sequencing to characterize the intestinal microbiome of Atlantic cod. Environmental Microbiology 21, 2576-2594.

[S12] Pladsen, A.V., Nilsen, G., Rueda, O.M., Aure, M.R., Borgan, Ø., Liestøl, K., Vitelli, V., Frigessi, A., Langerød, A., Mathelier, A., Engebråten, O., Kristensen, V.N., Wedge, D.C., Van Loo, P., Caldas, C., Børresen-Dale, A.-L., Russnes, H.E.G. and Lingjærde, O.C. (2020).DNA copy number motifs are strong and independent predictors of survival in breast cancer. Communications Biology 3: 153.

[S13] Riiser, E.S., Haverkamp, T.H.A., Varadharajan, S., Borgan, Ø., Jakobsen, K.S., Jentoft, S. and Star, B. (2020). Metagenomic shotgun analyses reveal complex patterns of intra- and interspecific variation in the intestinal microbiomes of codfishes. Applied and Environmental Microbiology. 86:6.

[S14] Nedkvitne, E. N., Borgan, Ø., Eriksen, D.Ø. and Rui, H.M.V. (2021). Variation in chemical composition of MSWI fly ash and dry scrubber residues. Waste Management. 126, 623–631.

Encyclopedia entries:

[E1] Borgan, Ø. (1998). Aalen-Johansen estimator. Encyclopedia of Biostatistics (eds. P. Armitage and T. Colton), vol 1, pp. 5-10. Wiley, Chichester. Revised version published 2018 in Wiley StatsRef: Statistics Reference Online (eds. N. Balakrishnan, P. Brandimarte, B.S. Everitt, G. Molenberghs, W.W. Piegorsch, and F. Ruggeri).

[E2] Borgan, Ø. (1998). Kaplan-Meier estimator. Encyclopedia of Biostatistics (eds. P. Armitage and T. Colton), vol 3, pp. 2154-60. Wiley, Chichester.

[E3] Borgan, Ø. (1998). Nelson-Aalen estimator. Encyclopedia of Biostatistics (eds. P. Armitage and T. Colton), vol 4, pp. 2967-72. Wiley, Chichester.

[E4] Borgan, Ø. (1999). Countermatched sampling. Encyclopedia of Statistical Sciences (eds. S. Kotz, C.B. Read and D.L. Banks), update vol 3, pp. 129-31. Wiley, New York.

[E5] Borgan, Ø. (1999). Nested case-control sampling (sampling from the risk sets). Encyclopedia of Statistical Sciences (eds. S. Kotz, C.B. Read and D.L. Banks), update vol 3, pp. 523-28. Wiley, New York.

[E6] Borgan, Ø. (2004). Sverdrup, Erling (1917-1994). Encyclopedia of Actiarial Sciences (eds. J.L. Teugels and B. Sundt), vol 3, pp. 1665-1666. Wiley, Chichester.

Miscellaneous:

[M1] Borgan, Ø. (1980). Applications of non-homogeneous Markov chains to medical studies. Nonparametric analysis for prospective and retrospective data. Pages 102-115 in Explorative Datenanalyse, Frühjahrstagung, München, 1980, Proceedings (eds. N. Victor, W. Lehmacher and W. van Eimeren). Springer's series Medizinische Informatik und Statistik vol. 26.

[M2] Borgan, Ø. (1989). Discussion contribution to E. Arjas' paper "Survival models and martingale dynamics". Scand. J. Statist. 16, 214-215.

[M3] Borgan, Ø. (1990). Lecture notes in life history analysis. Statistical Memoir no 1/90, Department of Mathematics, University of Oslo.

[M4] Borgan, Ø. and Langholz, B. (1998). Risk set sampling designs for proportional hazards models. Chapter 4 in Statistical Analysis of Medical Data. New Developments (eds. B. S. Everitt and G. Dunn). Arnold, London.

[M5] Borgan, Ø. (1999). Review of "Applied Survival Analysis" by C.T Le. Statist. Med. 18, 492-494.

[M6] Borgan, Ø. (2001). Review of "Modeling Survival Data: Extending the Cox Model" by T. M. Therneau and P. M. Grambsch. Statist. Med. 20, 2053-2054.

[M7] Borgan, Ø. (2001). Cohort sampling in epidemiological studies. Bulletin of the International Statistical Institute 53(1), 369-372.

[M8] Borgan, Ø. (2003). Review of "The Statistical Analysis of Failure Time Data (2nd ed.)" by J. D. Kalbfleisch and R. D. Prentice. J. Amer. Statist. Assoc. 98, 1084-1085.

[M9] Borgan, Ø. and Samuelsen, S.O. (2003). A review of cohort sampling designs for Cox's regression model: Potentials in epidemiology. Norsk epidemiologi (Norwegian Journal of Epidemiology) 13, 239-248.

[M10] Borgan, Ø. (2006). Discussion contribution to C. P. Farrington and H. J. Whitaker's paper "Semiparametric analysis of case series data". Appl. Statist. 55, 589.

[M11] Borgan, Ø. and Lindqvist, B. (2007). Editorial. Scand. J. Statist. 34, 1-2.

[M12] Borgan, Ø. and Langholz, B. (2007). Using martingale residuals to assess goodness-of-fit for sampled risk set data. Chapter 4 in Advances in statistical modeling and inference. Essays in honor of Kjell A Doksum (ed. V. Nair). World Scientific, Singapore.

[M13] Borgan, Ø. (2007). Discussion contribution to D. Zeng and D.Y. Lin's paper "Maximum likelihood estimation in semiparametric regression models with censored data". J. Royal Stat. Soc. Ser. B 69, 545.

[M14] Borgan, Ø. (2007). Event history analysis: An overview and some areas of current research. Pages 60-64 in Consilience (ed. W. Østreng). Centre for Advanced Study at the Norwegian Academy of Science and Letters.

[M15] Borgan, Ø. (2009). Inference and prediction in multi-state models: The additive approach. Bulletin of the International Statistical Institute 57,

[M16] Borgan, Ø. and Samuelsen, S. O. (2013). Nested case-control and case-cohort studies. Chapter 17 in Handbook of Survival Analysis (eds. J. P. Klein, J. G. Ibrahim, T. Scheike and J. C. van Houwelingen). Chapman & Hall/CRC Press, Boca Raton.

[M17] Aalen, O. O., Borgan, Ø, and Kvaløy, J. T. (2013). Medical statistics - a subject of increasing breadth and importance. (Preface to special issue from the 33rd annual conference of the International Society for Clinical Biostatistics.) Stat. Med. 32, 5221.

[M18] Günther, C-C., Tvete I. F., Aas, K., Hagen, J. A., Kvifte, L. and Borgan, Ø. (2014). Predicting future claims among high risk policyholders using random effects. Chapter 11 in Modern Problems in Insurance Mathematics (eds. D. Silvestrov and A. Martin-Löf). Springer-Verlag, Heidelberg.

[M19] Borgan, Ø. and Samuelsen, S.O. (2018). Cohort sampling for time-to-event data: An overview. Chapter 16 in Handbook of Statistical Methods for Case-Control Studies. (eds. Ø Borgan., N.E. Breslow, N. Chatterjee, M.H. Gail, A. Scott, and C.J. Wild). Chapman & Hall/CRC Press, Boca Raton.

[M20] Borgan, Ø. (2018). Nested case-control studies: A counting process approach. Chapter 18 in Handbook of Statistical Methods for Case-Control Studies. (eds. Ø Borgan., N.E. Breslow, N. Chatterjee, M.H. Gail, A. Scott, and C.J. Wild). Chapman & Hall/CRC Press, Boca Raton.

[M21] Aalen, O.O.,  Andersen, P.K., Borgan,  Ø., Gill, R.D. and Keiding, N. (2022). Martingales in survival analysis. Chapter 13 in The Splendors and Miseries of Martingales (eds. L. Mazliak and G. Shafer). Birkhäuser, Basel.