The use of fractional polynomials to model continuous risk variables in epidemiology
Abstract
BACKGROUND: The traditional method of analysing continuous or ordinal risk factors by categorization or linear models may be improved. METHODS: We propose an approach based on transformation and fractional polynomials which yields simple regression models with interpretable curves. We suggest a way of presenting the results from such models which involves tabulating the risks estimated from the model at convenient values of the risk factor. We discuss how to incorporate several continuous risk and confounding variables within a single model. The approach is exemplified with data from the Whitehall I study of British Civil Servants. We discuss the approach in relation to categorization and non-parametric regression models. RESULTS: We show that non-linear risk models fit the data better than linear models. We discuss the difficulties introduced by categorization and the advantages of the new approach. CONCLUSIONS: Our approach based on fractional polynomials should be considered as an important alternative to the traditional approaches for the analysis of continuous variables in epidemiological studies.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
NfL was entered as a linear predictor term after confirming linearity of the associations with fractional polynomial analyses.
“NfL was entered as a linear predictor term after confirming linearity of the associations with fractional polynomial analyses (32).”
From A Method to Combine Neurofilament Light Measurements From Blood Serum and Plasma in Clinical and Population-Based Studies (2022) · cites this paper as [32]
Linearity in the logit was assessed with fractional polynomials.
“Linearity in the logit was assessed with fractional polynomials (35).”
From Personality, Socioeconomic Status, and All-Cause Mortality in the United States (2010) · cites this paper as [35]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1994) · doi:10.1201/9780429246593 · Cited by 40,500 · see citing works
(1990) · Choice Reviews Online · doi:10.5860/choice.27-3338 · Cited by 35,305 · see citing works
Brown, R. A., Hastie, T. J., & Tibshirani, R. J. (1991) · Biometrics · doi:10.2307/2532174 · Cited by 8,262 · see citing works
Koyak, R. A., Hastie, T. J., & Tibshirani, R. J. (1991) · Journal of the American Statistical Association · doi:10.2307/2290538 · Cited by 7,717 · see citing works
Kupper, L. L., Hosmer, D. W., & Lemeshow, S. A. (1990) · Journal of the American Statistical Association · doi:10.2307/2290035 · Cited by 7,690 · see citing works
Statistical Methods in Cancer Research
Breslow, N. E. (1980) · Cited by 6,695 · see citing works
Statistical methods in cancer research. Volume I - The analysis of case-control studies.
Breslow, N. E., & Day, N. E. (1980) · PubMed · Cited by 4,895 · see citing works
The analysis of case-control studies
Breslow, N. E., & Day, N. E. (1980) · International Agency for Research on Cancer eBooks · Cited by 2,415 · see citing works
THE IMPACT OF CONFOUNDER SELECTION CRITERIA ON EFFECT ESTIMATION
Mickey, R. M., & Greenland, S. (1989) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a115101 · Cited by 2,405 · see citing works
RE:“;THE IMPACT OF CONFOUNDER SELECTION CRITERIA ON EFFECT ESTIMATION”
Greenland, S., & Mickey, R. M. (1989) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a115409 · Cited by 2,120 · see citing works
Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling
Royston, P. J., & Altman, D. G. (1994) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.2307/2986270 · Cited by 1,843 · see citing works
Self-citationStatistical methods in cancer research. Vol. 1. The analysis of case-control studies
(1983) · Food and Chemical Toxicology · doi:10.1016/0278-6915(83)90281-8 · Cited by 1,726 · see citing works
Model Selection: An Integral Part of Inference
Buckland, S. T., Burnham, K. P., & Augustin, N. H. (1997) · Biometrics · doi:10.2307/2533961 · Cited by 1,717 · see citing works
INEQUALITIES IN DEATH—SPECIFIC EXPLANATIONS OF A GENERAL PATTERN?
Marmot, M. G., Shipley, M. J., & Rose, G. (1984) · The Lancet · doi:10.1016/s0140-6736(84)92337-7 · Cited by 1,461 · see citing works
- Statistical Models for Epidemiology
Broemeling, L. D. (2013) · Chapman & Hall/CRC eBooks · doi:10.1201/b15382-9 · Cited by 1,346 · see citing works
An Introduction to the Bootstrap.
Kimber, A., Efron, B., & Tibshirani, R. J. (1994) · Journal of the Royal Statistical Society Series D (The Statistician) · doi:10.2307/2348146 · Cited by 1,246 · see citing works
Dangers of Using "Optimal" Cutpoints in the Evaluation of Prognostic Factors
Altman, D. G., Lausen, B., Sauerbrei, W., & Schumacher, M. (1994) · JNCI Journal of the National Cancer Institute · doi:10.1093/jnci/86.11.829 · Cited by 1,143 · see citing works
Self-citationModel uncertainty, data mining and statistical inference
Chatfield, C. (1995) · Journal of the Royal Statistical Society. Series A (Statistics in Society) · doi:10.2307/2983440 · Cited by 1,103 · see citing works
Dose-Response and Trend Analysis in Epidemiology
Greenland, S. (1995) · Epidemiology · doi:10.1097/00001648-199507000-00005 · Cited by 1,086 · see citing works
Transformation of the Independent Variables
Box, G. E. P., & Tidwell, P. W. (1962) · Technometrics · doi:10.1080/00401706.1962.10490038 · Cited by 987 · see citing works
Carey, V. J., Walters, E. E., Colditz, G. A., Solomon, C. G., Willet, W. C., Rosner, B. A., Speizer, F. E., & Manson, J. E. (1997) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a009158 · Cited by 827 · see citing works
Sauerbrei, W., & Royston, P. J. (1999) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/1467-985x.00122 · Cited by 475 · see citing works
Self-citationStatistical Models in Epidemiology
Leger, A. S. S. (1994) · Journal of Epidemiology & Community Health · doi:10.1136/jech.48.6.607 · Cited by 428 · see citing works
Farnett, L. (1991) · JAMA · doi:10.1001/jama.265.4.489 · Cited by 417 · see citing works
Greenland, S. (1995) · Epidemiology · doi:10.1097/00001648-199507000-00025 · Cited by 362 · see citing works
The Use of Resampling Methods to Simplify Regression Models in Medical Statistics
Sauerbrei, W. (1999) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/1467-9876.00155 · Cited by 310 · see citing works
Self-citationStatistical Models in Epidemiology
K., M., Clayton, D. G., & Hills, M. (1995) · Population · doi:10.2307/1534207 · Cited by 272 · see citing works
Designing and analysing case-control studies to exploit independence of genotype and exposure
Umbach, D. M., & Weinberg, C. R. (1997) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19970815)16:15 · Cited by 179 · see citing works
An Improper Use of Statistical Significance Testing in Studying Covariables
DALES, L. G., & URY, H. K. (1978) · International Journal of Epidemiology · doi:10.1093/ije/7.4.373 · Cited by 169 · see citing works
The concept of residual confounding in regression models and some applications
Becher, H. (1992) · Statistics in Medicine · doi:10.1002/sim.4780111308 · Cited by 168 · see citing works
Transformation of the Independent Variables
Box, G. E. P., & Tidwell, P. W. (1962) · Technometrics · doi:10.2307/1266288 · Cited by 166 · see citing works
Tests for Trend and Dose Response: Misinterpretations and Alternatives
Madure, M., & Greenland, S. (1992) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a116206 · Cited by 154 · see citing works
Controlling for Continuous Confounders in Epidemiologic Research
Brenner, H., & Blettner, M. (1997) · Epidemiology · doi:10.1097/00001648-199707000-00014 · Cited by 151 · see citing works
Zhao, L. P., & Kolonel, L. N. (1992) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a116520 · Cited by 108 · see citing works
Binomial Regression with Monotone Splines: A Psychometric Application
Ramsay, J. O., & Abrahamowicz, M. (1989) · Journal of the American Statistical Association · doi:10.1080/01621459.1989.10478854 · Cited by 75 · see citing works
Outcome-oriented Cutpoints in Analysis of Quantitative Exposures
Schulgen, G., Lausen, B., Olsen, J. H., & Schumacher, M. C. (1994) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a117227 · Cited by 62 · see citing works
Weinberg, C. R. (1995) · PubMed · Cited by 61 · see citing works
Flexible Modeling of the Effects of Serum Cholesterol on Coronary Heart Disease Mortality
Abrahamowicz, M., du Berger, R., & Graver, S. (1997) · American Journal of Epidemiology · doi:10.1093/aje/145.8.714 · Cited by 54 · see citing works
Robertson, C., Boyle, P., Hsieh, C.-C., Macfarlane, G. J., & Maisonneuve, P. (1994) · Epidemiology · doi:10.1097/00001648-199403000-00006 · Cited by 47 · see citing works
Effect of Categorizing a Continuous Covariate on the Comparison of Survival Time
Morgan, T. M., & Elashoff, R. M. (1986) · Journal of the American Statistical Association · doi:10.1080/01621459.1986.10478350 · Cited by 42 · see citing works
Detection and Estimation of J-Shaped Risk-Response Relationship
Goetghebeur, E. J. T., & Pocock, S. (1995) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.2307/2983406 · Cited by 39 · see citing works
Greenland, S., & Poole, C. (1995) · Epidemiology · doi:10.1097/00001648-199505000-00024 · Cited by 25 · see citing works
Estimating Relative Risk Functions in Case-Control Studies Using a Nonparametric Logistic Regression
Zhao, L. P., Kristal, A. R., & White, E. (1996) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a008970 · Cited by 23 · see citing works
Effect of Categorizing a Continuous Covariate on the Comparison of Survival Time
Morgan, T. M., & Elashoff, R. M. (1986) · Journal of the American Statistical Association · doi:10.2307/2289060 · Cited by 12 · see citing works
Binomial Regression with Monotone Splines: A Psychometric Application
Ramsay, J. O., & Abrahamowicz, M. (1989) · Journal of the American Statistical Association · doi:10.2307/2290065 · Cited by 11 · see citing works
Hosmer (1997) · doi:10.1002/(sici)1097-0258(19970515)16:9
Flagged first, then by citations
Research works printed but not linked: 2
- Draper D. Assessment and propagation of model uncertainty (with discussion). J R Stat Soc, Ser B 1995;57:45-97.
- Elswick RK Jr, Schwartz PF, Welsh JA. Interpretation of the odds ratio from logistic regression after a transformation of the covariate vector. Stat Med 1997;16:1695-703.
Cited by
Sorted by citations
Vandenbroucke, J. P., von Elm, E., Altman, D. G., Gøtzsche, P. C., Mulrow, C. D., Pocock, S. J., Poole, C., Schlesselman, J. J., Egger, M., & Initiative, F. T. S. (2007) · PLoS Medicine · doi:10.1371/journal.pmed.0040297 · Cited by 8,613 · see citing works
“Several methods exist for fi tting a non-linear relation between the exposure and outcome [82 e 84].”
Vandenbroucke, J. P., Elm, E. V., Altman, D. G., Gøtzsche, P. C., Mulrow, C. D., Pocock, S. J., Poole, C., Schlesselman, J. J., Egger, M., & initiative, F. T. S. (2007) · Annals of Internal Medicine · doi:10.7326/0003-4819-147-8-200710160-00010-w1 · Cited by 3,543 · see citing works
Multi-Ethnic Study of Atherosclerosis: Objectives and Design
Bild, D. E. (2002) · American Journal of Epidemiology · doi:10.1093/aje/kwf113 · Cited by 3,942 · see citing works
Vandenbroucke, J. P., von Elm, E., Altman, D. G., Gøtzsche, P. C., Mulrow, C. D., Pocock, S. J., Poole, C., Schlesselman, J. J., & Egger, M. (2014) · International Journal of Surgery · doi:10.1016/j.ijsu.2014.07.014 · Cited by 2,969 · see citing works
Vandenbroucke, J. P., von Elm, E., Altman, D. G., Gøtzsche, P. C., Mulrow, C. D., Pocock, S. J., Poole, C., Schlesselman, J. J., & Egger, M. (2007) · Epidemiology · doi:10.1097/ede.0b013e3181577511 · Cited by 2,779 · see citing works
Dose‐response analyses using restricted cubic spline functions in public health research
Desquilbet, L., & Mariotti, F. (2010) · Statistics in Medicine · doi:10.1002/sim.3841 · Cited by 2,006 · see citing works
Aortic Pulse Wave Velocity Improves Cardiovascular Event Prediction
Ben-Shlomo, Y., Spears, M., Boustred, C., May, M., Anderson, S. G., Benjamin, E. J., Boutouyrie, P., Cameron, J., Chen, C.-H., Cruickshank, J. K., et al. (2014) · Journal of the American College of Cardiology · doi:10.1016/j.jacc.2013.09.063 · Cited by 1,835 · see citing works
Hippisley-Cox, J., Coupland, C., & Brindle, P. (2017) · BMJ · doi:10.1136/bmj.j2099 · Cited by 1,703 · see citing works
Predicting cardiovascular risk in England and Wales: prospective derivation and validation of QRISK2
Hippisley-Cox, J., Coupland, C., Vinogradova, Y., Robson, J., Minhas, R., Sheikh, A., & Brindle, P. (2008) · BMJ · doi:10.1136/bmj.39609.449676.25 · Cited by 1,459 · see citing works
Bhaskaran, K., dos-Santos-Silva, I., Leon, D. A., Douglas, I. J., & Smeeth, L. (2018) · The Lancet Diabetes & Endocrinology · doi:10.1016/s2213-8587(18)30288-2 · Cited by 1,228 · see citing works
Chan, D. S. M., Vieira, A. R., Aune, D., Bandera, E. V., Greenwood, D. C., McTiernan, A., Navarro Rosenblatt, D., Thune, I., Vieira, R., & Norat, T. (2014) · Annals of Oncology · doi:10.1093/annonc/mdu042 · Cited by 1,165 · see citing works
Wood, A. M., Kaptoge, S., Butterworth, A. S., Willeit, P., Warnakula, S., Bolton, T., Paige, E., Paul, D. S., Sweeting, M., Burgess, S., et al. (2018) · The Lancet · doi:10.1016/s0140-6736(18)30134-x · Cited by 1,188 · see citing works
A meta-analysis of alcohol consumption and the risk of 15 diseases
Corrao, G. (2004) · Preventive Medicine · doi:10.1016/j.ypmed.2003.11.027 · Cited by 1,077 · see citing works
Hippisley-Cox, J., Coupland, C., Vinogradova, Y., Robson, J., May, M., & Brindle, P. (2007) · British medical journal · doi:10.1136/bmj.39261.471806.55 · Cited by 1,070 · see citing works
Serum lactate is associated with mortality in severe sepsis independent of organ failure and shock*
Mikkelsen, M. E., Miltiades, A., Gaieski, D. F., Goyal, M. K., Fuchs, B. D., Shah, C. V., Bellamy, S. L., & Christie, J. D. (2009) · Critical Care Medicine · doi:10.1097/ccm.0b013e31819fcf68 · Cited by 1,002 · see citing works
Red and Processed Meat and Colorectal Cancer Incidence: Meta-Analysis of Prospective Studies
Chan, D. S. M., Lau, R., Aune, D., Vieira, R., Greenwood, D. C., Kampman, E., & Norat, T. (2011) · PLoS ONE · doi:10.1371/journal.pone.0020456 · Cited by 903 · see citing works
The Obesity Paradox: Body Mass Index and Outcomes in Patients With Heart Failure
Curtis, J. P., Selter, J. G., Wang, Y., Rathore, S. S., Jovin, I. S., Jadbabaie, F., Kosiborod, M., Portnay, E. L., Sokol, S. I., Bader, F., et al. (2005) · Archives of Internal Medicine · doi:10.1001/archinte.165.1.55 · Cited by 809 · see citing works
A meta-analysis of alcohol drinking and cancer risk
Bagnardi, V., Blangiardo, M., Vecchia, C. L., & Corrao, G. (2001) · British Journal of Cancer · doi:10.1054/bjoc.2001.2140 · Cited by 596 · see citing works
The Antiretroviral Therapy Cohort Collaboration (2010) · Clinical Infectious Diseases · doi:10.1086/652283 · Cited by 592 · see citing works
Curtis, J. P., Sokol, S. I., Wang, Y., Rathore, S. S., Ko, D. T., Jadbabaie, F., Portnay, E. L., Marshalko, S. J., Radford, M. J., & Krumholz, H. M. (2003) · Journal of the American College of Cardiology · doi:10.1016/s0735-1097(03)00789-7 · Cited by 579 · see citing works
Bouyer, J. (2003) · American Journal of Epidemiology · doi:10.1093/aje/kwf190 · Cited by 528 · see citing works
Wyld, M. L. R., Morton, R. L., Hayen, A. D., Howard, K., & Webster, A. C. (2012) · PLoS Medicine · doi:10.1371/journal.pmed.1001307 · Cited by 511 · see citing works
Hippisley‐Cox, J., & Coupland, C. A. C. (2010) · BMJ · doi:10.1136/bmj.c2197 · Cited by 511 · see citing works
Núñez, J. E., Núñez, E., Bodı́, V., Sanchís, J. M., Miñana, G., Mainar, L., Santas, E., Merlos, P., Rúmiz, E., Darmofal, H., et al. (2008) · The American Journal of Cardiology · doi:10.1016/j.amjcard.2007.11.004 · Cited by 510 · see citing works
Hospital Volume and the Outcomes of Mechanical Ventilation
Kahn, J. M., Goss, C. H., Heagerty, P. J., Kramer, A. A., O'Brien, C. R., & Rubenfeld, G. D. (2006) · New England Journal of Medicine · doi:10.1056/nejmsa053993 · Cited by 507 · see citing works
Verburg, B. O., Steegers, E. A. P., de Ridder, M. A. J., Snijders, R. J. M., Smith, E. A., Albert Hofman, D., Moll, H. A., Jaddoe, V. W. V., & Witteman, J. C. M. (2008) · Ultrasound in Obstetrics and Gynecology · doi:10.1002/uog.5225 · Cited by 505 · see citing works
Model building strategy for logistic regression: purposeful selection
Zhang, Z. (2016) · Annals of Translational Medicine · doi:10.21037/atm.2016.02.15 · Cited by 488 · see citing works
Hippisley-Cox, J., & Coupland, C. (2009) · British medical journal · doi:10.1136/bmj.b4229 · Cited by 500 · see citing works
Clive, A. O., Kahan, B. C., Hooper, C. E., Bhatnagar, R., Morley, A. J., Zahan-Evans, N. J., Bintcliffe, O. J., Boshuizen, R. C., Fysh, E. T. H., Tobin, C., et al. (2014) · Thorax · doi:10.1136/thoraxjnl-2014-205285 · Cited by 449 · see citing works
Jaddoe, V. W. V., de Jonge, L. L., Hofman, A., Franco, O. H., Steegers, E. A. P., & Gaillard, R. (2014) · BMJ · doi:10.1136/bmj.g14 · Cited by 443 · see citing works
Population-Based Analysis of Invasive Fungal Infections, France, 2001–2010
Bitar, D., Lortholary, O., Strat, Y. L., Nicolau, J., Coignard, B., Tattevin, P., Che, D., & Dromer, F. (2014) · Emerging infectious diseases · doi:10.3201/eid2007.140087 · Cited by 422 · see citing works
van Veldhuisen, D. J., Linssen, G. C. M., Jaarsma, T., van Gilst, W. H., Hoes, A. W., Tijssen, J. G. P., Paulus, W. J., Voors, A. A., & Hillege, H. L. (2013) · Journal of the American College of Cardiology · doi:10.1016/j.jacc.2012.12.044 · Cited by 415 · see citing works
Schellong, K., Schulz, S., Harder, T., & Plagemann, A. (2012) · PLoS ONE · doi:10.1371/journal.pone.0047776 · Cited by 410 · see citing works
Ye, J., Zhang, J., Mikolajczyk, R., Torloni, M., Gülmezoglu, A. M., & Betrán, A. P. (2015) · BJOG An International Journal of Obstetrics & Gynaecology · doi:10.1111/1471-0528.13592 · Cited by 404 · see citing works
Association Between Depressive Symptoms and Incident Cardiovascular Diseases
Harshfield, E. L., Pennells, L. A. M., Schwartz, J. E., Willeit, P., Kaptoge, S. K., Bell, S., Shaffer, J. A., Bolton, T. R., Spackman, S., Wassertheil‐Smoller, S., et al. (2020) · JAMA · doi:10.1001/jama.2020.23068 · Cited by 406 · see citing works
Hippisley-Cox, J., Coupland, C. A. C., Robson, J., Sheikh, A., & Brindle, P. (2009) · British medical journal · doi:10.1136/bmj.b880 · Cited by 399 · see citing works
Neonatal Vitamin D Status and Risk of Schizophrenia
McGrath, J. J., Eyles, D. W., Pedersen, C. B., Anderson, C., Ko, P., Burne, T. H. J., Nørgaard‐Pedersen, B., HOUGAARD, D. M., & Mortensen, P. B. (2010) · Archives of General Psychiatry · doi:10.1001/archgenpsychiatry.2010.110 · Cited by 360 · see citing works
Grønbæk, L., Vilstrup, H., & Jepsen, P. (2013) · Journal of Hepatology · doi:10.1016/j.jhep.2013.10.020 · Cited by 355 · see citing works
Hippisley-Cox, J., & Coupland, C. (2012) · British medical journal · doi:10.1136/bmj.e3427 · Cited by 357 · see citing works
Sauerbrei, W., Meier‐Hirmer, C., Benner, A., & Royston, P. J. (2005) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2005.07.015 · Cited by 351 · see citing works
Self-citationPrinciples for modeling propensity scores in medical research: a systematic literature review
Weitzen, S. H., Lapane, K. L., Toledano, A. Y., Hume, A. L., & Mor, V. (2004) · Pharmacoepidemiology and Drug Safety · doi:10.1002/pds.969 · Cited by 344 · see citing works
Cortisol, Testosterone, and Coronary Heart Disease: Prospective Evidence From the Caerphilly Study
Smith, G., Ben-Shlomo, Y., Beswick, A., Yarnell, J., Lightman, S., & Elwood, P. (2005) · Circulation · doi:10.1161/circulationaha.104.489088 · Cited by 348 · see citing works
Risk Factors for Surgical Site Infection After Low Transverse Cesarean Section
Olsen, M. A. A., Butler, A. M., Willers, D. M., Devkota, P., Gross, G. A., & Fraser, V. J. (2008) · Infection Control and Hospital Epidemiology · doi:10.1086/587810 · Cited by 330 · see citing works
Psychosocial predictors of energy underreporting in a large doubly labeled water study
Tooze, J. A., Subar, A. F., Thompson, F. E., Troiano, R. P., Schatzkin, A. G., & Kipnis, V. (2004) · American Journal of Clinical Nutrition · doi:10.1093/ajcn/79.5.795 · Cited by 327 · see citing works
McGurnaghan, S. J., Weir, A., Bishop, J., Kennedy, S., Blackbourn, L. A. K., McAllister, D., Hutchinson, S. J., Caparrotta, T. M., Mellor, J., Jeyam, A., et al. (2020) · The Lancet Diabetes & Endocrinology · doi:10.1016/s2213-8587(20)30405-8 · Cited by 329 · see citing works
Ladha, K. S., Melo, M. F. V., McLean, D. J., Wanderer, J. P., Grabitz, S. D., Kurth, T., & Eikermann, M. (2015) · BMJ · doi:10.1136/bmj.h3646 · Cited by 325 · see citing works
Intrauterine Cannabis Exposure Affects Fetal Growth Trajectories: The Generation R Study
Marroun, H. E., Tiemeier, H. W., Steegers, E. A. P., Jaddoe, V. W. V., Albert Hofman, D., Verhulst, F. C., van den Brink, W., & Huizink, A. C. (2009) · Journal of the American Academy of Child & Adolescent Psychiatry · doi:10.1097/chi.0b013e3181bfa8ee · Cited by 322 · see citing works
A Procedure to Tabulate and Plot Results after Flexible Modeling of a Quantitative Covariate
Orsini, N., & Greenland, S. (2011) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x1101100101 · Cited by 321 · see citing works
Ngugi, A. K., Bottomley, C., Kleinschmidt, I., Wagner, R. G., Kakooza‐Mwesige, A., Ae-Ngibise, K. A., Owusu‐Agyei, S., Masanja, H., Kamuyu, G., Odhiambo, R., et al. (2013) · The Lancet Neurology · doi:10.1016/s1474-4422(13)70003-6 · Cited by 321 · see citing works
Staley, J. R., & Burgess, S. (2017) · Genetic Epidemiology · doi:10.1002/gepi.22041 · Cited by 290 · see citing works
Kaptoge, S., Beck, T. J., Reeve, J., Stone, K. L., Hillier, T. A., Cauley, J. A., & Cummings, S. R. (2008) · Journal of Bone and Mineral Research · doi:10.1359/jbmr.080802 · Cited by 283 · see citing works
Angerås, O., Albertsson, P., Karason, K., Råmunddal, T., Matejka, G., James, S. K., Lagerqvist, B., Rosengren, A., & Ömerovic, E. (2012) · European Heart Journal · doi:10.1093/eurheartj/ehs217 · Cited by 279 · see citing works
Importance of Age of Onset in Pancreatic Cancer Kindreds
Brune, K. A., Lau, B., Palmisano, E., Canto, M., Goggins, M. G., Hruban, R. H., & Klein, A. P. (2010) · JNCI Journal of the National Cancer Institute · doi:10.1093/jnci/djp466 · Cited by 257 · see citing works
Generic, Simple Risk Stratification Model for Heart Valve Surgery
Ambler, G., Omar, R. Z., Royston, P., Kinsman, R., Keogh, B. E., & Taylor, K. M. (2005) · Circulation · doi:10.1161/circulationaha.104.515049 · Cited by 279 · see citing works
Self-citationAbbas, S., Linseisen, J., Slanger, T. E., Kropp, S., Mutschelknauss, E. J., Flesch‐Janys, D., & Chang-Claude, J. C. (2007) · Carcinogenesis · doi:10.1093/carcin/bgm240 · Cited by 279 · see citing works
Applications of simulation within the healthcare context
Katsaliaki, K., & Mustafee, N. (2010) · Journal of the Operational Research Society · doi:10.1057/jors.2010.20 · Cited by 276 · see citing works
Bagnardi, V. (2004) · American Journal of Epidemiology · doi:10.1093/aje/kwh142 · Cited by 270 · see citing works
Rituximab in Steroid-Dependent or Frequently Relapsing Idiopathic Nephrotic Syndrome
Ruggenenti, P. L., Ruggiero, B., Cravedi, P., Vivarelli, M., Massella, L., Marasà, M., Chianca, A., Rubis, N., Ene‐Iordache, B., Rudnicki, M., et al. (2014) · Journal of the American Society of Nephrology · doi:10.1681/asn.2013030251 · Cited by 269 · see citing works
Obradović, J., Long, J. D., Cutuli, J. J., Chan, C.-K., Hinz, E., Heistad, D., & Masten, A. S. (2009) · Development and Psychopathology · doi:10.1017/s0954579409000273 · Cited by 259 · see citing works
Alcohol consumption and the risk of cancer: a meta-analysis.
Bagnardi, V., Blangiardo, M., Vecchia, C. L., & Corrao, G. (2001) · PubMed Central · Cited by 257 · see citing works
Roerecke, M., & Rehm, J. (2012) · Addiction · doi:10.1111/j.1360-0443.2012.03780.x · Cited by 249 · see citing works
Vinogradova, Y., Coupland, C., & Hippisley-Cox, J. (2020) · British medical journal · doi:10.1136/bmj.m3873 · Cited by 221 · see citing works
dos Reis, F. J. C., Wishart, G. C., Dicks, E., Greenberg, D. C., Rashbass, J., Schmidt, M. K., van den Broek, A. J., Ellis, I. O., Green, A. R., Rakha, E. A., et al. (2017) · Breast Cancer Research · doi:10.1186/s13058-017-0852-3 · Cited by 251 · see citing works
Britton, A. R., Ben‐Shlomo, Y., Benzeval, M., Kuh, D. J., & Bell, S. (2015) · BMC Medicine · doi:10.1186/s12916-015-0273-z · Cited by 246 · see citing works
Dwyer, T., Pezic, A., Sun, C., Cochrane, J., Venn, A., Srikanth, V., Jones, G., Shook, R., Sui, X., Ortaglia, A., et al. (2015) · PLOS ONE · doi:10.1371/journal.pone.0141274 · Cited by 239 · see citing works
To, M. S., Skentou, C., Royston, P. J., Yu, C.-S., & Nicolaides, K. H. (2006) · Ultrasound in Obstetrics and Gynecology · doi:10.1002/uog.2773 · Cited by 237 · see citing works
Self-citationAir Pollution During Pregnancy and Childhood Cognitive and Psychomotor Development
Guxens, M., García‐Esteban, R., Giorgis-Allemand, L., Forns, J., Badaloní, C., Ballester, F., Beelen, R. M. J., Cesaroni, G., Chatzi, L., Agostini, M. D., et al. (2014) · Epidemiology · doi:10.1097/ede.0000000000000133 · Cited by 228 · see citing works
Multivariable Modeling with Cubic Regression Splines: A Principled Approach
Royston, P. J., & Sauerbrei, W. (2007) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x0700700103 · Cited by 227 · see citing works
Self-citationStatistical primer: multivariable regression considerations and pitfalls†
Grant, S. W., Hickey, G. L., & Head, S. J. (2018) · European Journal of Cardio-Thoracic Surgery · doi:10.1093/ejcts/ezy403 · Cited by 227 · see citing works
Incidence and natural course of fatty liver in the general population: The Dionysos study
Bedogni, G., Miglioli, L., Masutti, F., Castiglione, A., Crocè, L. S., Tiribelli, C., & Bellentani, S. (2007) · Hepatology · doi:10.1002/hep.21827 · Cited by 224 · see citing works
Hickey, G. L., Dunning, J., Seifert, B., Sodeck, G. H., Carr, M., Burger, H. U., & Beyersdorf, F. (2015) · European Journal of Cardio-Thoracic Surgery · doi:10.1093/ejcts/ezv168 · Cited by 221 · see citing works
Brodbelt, D. C., Pfeiffer, D. U., Young, L. E., & Wood, J. L. N. (2007) · British Journal of Anaesthesia · doi:10.1093/bja/aem229 · Cited by 220 · see citing works
Fisher, D. J., Carpenter, J. R., Morris, T. P., Freeman, S. C., & Tierney, J. F. (2017) · BMJ · doi:10.1136/bmj.j573 · Cited by 212 · see citing works
de Vienne, C. M., Creveuil, C., & Dreyfus, M. (2009) · European Journal of Obstetrics & Gynecology and Reproductive Biology · doi:10.1016/j.ejogrb.2009.08.006 · Cited by 215 · see citing works
Hippisley‐Cox, J., & Coupland, C. A. C. (2017) · BMJ · doi:10.1136/bmj.j5019 · Cited by 218 · see citing works
Predicting Stuttering Onset by the Age of 3 Years: A Prospective, Community Cohort Study
Reilly, S., Onslow, M., Packman, A., Wake, M. A., Bavin, E. L., Prior, M. R., Eadie, P. A., Cini, E., Bolzonello, C., & Ukoumunne, O. C. (2008) · PEDIATRICS · doi:10.1542/peds.2007-3219 · Cited by 215 · see citing works
Mikkelsen, M. E., Shah, C. V., Meyer, N. J., Gaieski, D. F., Lyon, S. M., Miltiades, A., Goyal, M. K., Fuchs, B. D., Bellamy, S. L., & Christie, J. D. (2013) · Shock · doi:10.1097/shk.0b013e3182a64682 · Cited by 215 · see citing works
Maternal Low-Level Lead Exposure and Fetal Growth
Zhu, M., Fitzgerald, E. F., Gelberg, K. H., Lin, S., & Druschel, C. M. (2010) · Environmental Health Perspectives · doi:10.1289/ehp.0901561 · Cited by 211 · see citing works
Cigarette smoking and gastric cancer in the Stomach Cancer Pooling (StoP) Project
Praud, D., Rota, M., Pelucchi, C., Bertuccio, P., Rosso, T., Galeone, C., Zhang, Z., Matsuo, K., Ito, H. M., Hu, J., et al. (2016) · European Journal of Cancer Prevention · doi:10.1097/cej.0000000000000290 · Cited by 211 · see citing works
Phan, H., Blizzard, C. L., Reeves, M. J., Thrift, A. G., Cadilhac, D. A.-M., Sturm, J. W., Heeley, E. L., Otáhal, P., Vemmos, K. N., Anderson, C. S., et al. (2017) · Circulation Cardiovascular Quality and Outcomes · doi:10.1161/circoutcomes.116.003436 · Cited by 221 · see citing works
Hippisley-Cox, J., & Coupland, C. (2012) · British Journal of General Practice · doi:10.3399/bjgp12x616355 · Cited by 208 · see citing works
Night-shift work and risk of breast cancer: a systematic review and meta-analysis
Kamdar, B. B., Tergas, A. I., Mateen, F. J., Bhayani, N. H., & Oh, J. (2013) · Breast Cancer Research and Treatment · doi:10.1007/s10549-013-2433-1 · Cited by 209 · see citing works
Influence of Paternal Age on the Risk of Spontaneous Abortion
Slama, R., Bouyer, J., Windham, G. C., Fenster, L., Werwatz, A., & Swan, S. H. (2005) · American Journal of Epidemiology · doi:10.1093/aje/kwi097 · Cited by 206 · see citing works
Systemic inflammatory markers in COPD: results from the Bergen COPD Cohort Study
Eagan, T., Ueland, T., Wagner, P. D., Hardie, J. A., Mollnes, T. E., Damås, J. K., Aukrust, P., & Bakke, P. S. (2009) · European Respiratory Journal · doi:10.1183/09031936.00088209 · Cited by 203 · see citing works
Jaddoe, V. W. V., Verburg, B. O., de Ridder, M. A. J., Hofman, A., Mackenbach, J. P., Moll, H. A., Steegers, E. A. P., & Witteman, J. C. M. (2007) · American Journal of Epidemiology · doi:10.1093/aje/kwm014 · Cited by 202 · see citing works
Lodi, S., Phillips, A. N., Touloumi, G., Geskus, R. B., Meyer, L., Thiébaut, R., Pantazis, N., del Amo, J., Johnson, A. M., Babiker, A. G., et al. (2011) · Clinical Infectious Diseases · doi:10.1093/cid/cir494 · Cited by 199 · see citing works
Personality, Socioeconomic Status, and All-Cause Mortality in the United States
Chapman, B. P., Fiscella, K., Kawachi, I., & Duberstein, P. R. (2010) · American Journal of Epidemiology · doi:10.1093/aje/kwp323 · Cited by 198 · see citing works
Building Multivariable Regression Models with Continuous Covariates in Clinical Epidemiology
Sauerbrei, W., & Royston, P. J. (2005) · Methods of Information in Medicine · doi:10.1055/s-0038-1634008 · Cited by 198 · see citing works
Self-citationA Frailty Index for UK Biobank Participants
Williams, D. M., Jylhävä, J., Pedersen, N. L., & Hägg, S. (2018) · The Journals of Gerontology Series A · doi:10.1093/gerona/gly094 · Cited by 193 · see citing works
Stingele, R., Berger, J., Alfke, K., Eckstein, H., Fraedrich, G., Allenberg, J. R., Hartmann, M., Ringleb, P. A., & Fiehler, J. (2008) · The Lancet Neurology · doi:10.1016/s1474-4422(08)70024-3 · Cited by 195 · see citing works
Early childhood aetiology of mental health problems: a longitudinal population-based study
Bayer, J. K., Hiscock, H., Ukoumunne, O. C., Price, A., & Wake, M. (2008) · Journal of Child Psychology and Psychiatry · doi:10.1111/j.1469-7610.2008.01943.x · Cited by 193 · see citing works
Magnussen, C. G., Venn, A., Thomson, R. J., Juonala, M., Srinivasan, S. R., Viikari, J. S. A., Berenson, G. S., Dwyer, T., & Raitakari, O. T. (2009) · Journal of the American College of Cardiology · doi:10.1016/j.jacc.2008.09.061 · Cited by 192 · see citing works
Gilbert Syndrome and the Development of Antiretroviral Therapy–Associated Hyperbilirubinemia
Rotger, M., Taffé, P., Bleiber, G., Günthard, H. F., Furrer, H., Vernazza, P., Drechsler, H., Bernasconi, E., Rickenbach, M., Telenti, A., et al. (2005) · The Journal of Infectious Diseases · doi:10.1086/466531 · Cited by 194 · see citing works
Howe, L., Tilling, K., Matijasevich, A., Petherick, E., Santos, A., Fairley, L., Wright, J., Santos, I., Barros, A., Martin, R. M., et al. (2013) · Statistical Methods in Medical Research · doi:10.1177/0962280213503925 · Cited by 193 · see citing works
Vandenbroucke, J. P., von Elm, E. B., Altman, D. G., Gøtzsche, P. C., Mulrow, C. D., Pocock, S., Poole, C., Schlesselman, J. J., & Egger, M. (2009) · Gaceta Sanitaria · doi:10.1016/j.gaceta.2008.12.001 · Cited by 203 · see citing works
Collins, P. G. S., & Altman, D. G. (2009) · BMJ · doi:10.1136/bmj.b2584 · Cited by 192 · see citing works
Splines for Trend Analysis and Continuous Confounder Control
Howe, C. J., Cole, S. R., Westreich, D. J., Greenland, S., Napravnik, S., & Eron, J. J. (2011) · Epidemiology · doi:10.1097/ede.0b013e31823029dd · Cited by 189 · see citing works
Survival Analysis Part IV: Further concepts and methods in survival analysis
Clark, T. G., Bradburn, M. J., Love, S., & Altman, D. G. (2003) · British Journal of Cancer · doi:10.1038/sj.bjc.6601117 · Cited by 187 · see citing works
Sapir‐Pichhadze, R., Wang, Y., Famure, O., Li, Y., & Kim, S. J. (2013) · Kidney International · doi:10.1038/ki.2013.465 · Cited by 185 · see citing works
Wen, X., KLEINMAN, K. P., Gillman, M. W., Rifas‐Shiman, S. L., & Taveras, E. M. (2012) · BMC Medical Research Methodology · doi:10.1186/1471-2288-12-38 · Cited by 183 · see citing works
- Authors
- Royston, P., Ambler, G., & Sauerbrei, W.
- Affiliations
- Imperial College London (GB)
- Hammersmith Hospital (GB)
- University of Freiburg (DE)
- Venue
- International Journal of Epidemiology
- Publisher
- Oxford University Press (OUP)
- Published
- 1999-10-01
- Volume
- 28
- Issue
- 5
- Pages
- 964-974
- ISSN
- 0300-5771 (ISSN-L)
- 1464-3685
- OpenAlex
- W2105087430
- Cited by
- 1,066
- References
- 44
- Citations by year
- 2026: 15 · 2025: 26 · 2024: 30 · 2023: 31 · 2022: 36 · 2021: 51 · 2020: 51 · 2019: 41 · 2018: 67 · 2017: 80 · 2016: 46 · 2015: 66 · 2014: 63 · 2013: 67 · 2012: 56
- FWCI
- 8.54
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- International Journal of Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- UCL Discovery (University College London) (submittedVersion)
- FreiDok plus (Universitätsbibliothek Freiburg) (submittedVersion)
- Funders
- Wellcome Trust
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Keywords
- fractional polynomials, risk transformation, risk curves, confounding variables, nonparametric regression, British civil servants
- MeSH terms
- Coronary Disease, Cross-Sectional Studies, Epidemiologic Methods, United Kingdom, Humans, Male, Models, Cardiovascular, Mortality, Neoplasms, Prospective Studies, Risk Factors, Sensitivity and Specificity, Linear Models, Odds Ratio, Risk Assessment, Stroke
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
