Abstract
When analyzing data from an epidemiological study, some features are rather specific for a particular study design. Those are dealt with among others in chapters “Descriptive Studies,” “Cohort Studies,” “Modern Epidemiological Study Designs,” and “Survival Analysis” of this handbook. Other features are generally relevant; see chapters “Rates, Risks, Measures of Association,” and “Impact and Confounding and Interaction.” This chapter focuses on the analysis of continuous covariates where it will be discussed how such variables can be modeled to capture their potential association with an outcome of interest and to best describe the shape of such an association. We present classical methods based on categorization and subsequent contingency table analysis. The major part of the chapter, however, deals with the analysis of continuous covariates using regression models commonly used in epidemiology (see also chapter “Regression Methods for Epidemiological Analysis” of this handbook). Each of the proposed techniques to model continuous covariates is illustrated by a real data example taken from a case-control study on laryngeal cancer and smoking as well as alcohol consumption that has been conducted in Germany during the 1990s. The chapter ends with practical recommendations and conclusions.
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References
Agresti A (2019) Categorical data analysis, 4th edn. Wiley, Hoboken
Altman DG, Lausen B, Sauerbrei W, Schumacher M (1994) Dangers of using “optimal” cutpoints in the evaluation of prognostic factors. J Natl Cancer Inst 86:829–835
Becher H (1993) The concept of residual confounding in regression models and some applications. Stat Med 11:1747–1758
Becher H, Ramroth H, Ahrens W, Risch A, Schmezer P, Dietz A (2005) Occupation, exposure to polycyclic aromatic hydrocarbons and laryngeal cancer risk. Int J Cancer 116:451–457
Becher H, Lorenz E, Royston P, Sauerbrei W (2012) Analysing covariates with spike at zero: a modified FP procedure and conceptual issues. Biom J 54:686–700
Bennette C, Vickers A (2012) Against quantiles: categorization of continuous variables in epidemiologic research, and its discontents. BMC Med Res Methodol 12:21
Bernstein S, Bernstein R (1998) Schaum’s outline of elements of statistics I: descriptive statistics and probability. McGraw-Hill, New York
Breslow N, Day N (1980) Statistical methods in cancer research. Volume I – the analysis of case-control studies. IARC scientific publications no. 32. International Agency for Research on Cancer, Lyon
Breslow N, Day N (1987) Statistical methods in cancer research. Volume II – the design and analysis of cohort studies. IARC scientific publications no. 82. International Agency for Research on Cancer, Lyon
Breslow NW, Storer BE (1985) General relative risk functions for case-control studies. Am J Epidemiol 122:149–162
Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach, 2nd edn. Springer, New York
Eilers PHC, Marx BD (1996) Flexible smoothing with B-splines and penalties. Stat Sci 11:89–121
Greenland S, Senn SJ, Rothman KJ, Carlin JB, Poole C, Goodman SN, Altman DG (2016) Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. Eur J Epidemiol 31:337–350
Hastie T, Tibshirani R (1986) Generalized additive models. Stat Sci 1:297–318
Hastie T, Tibshirani R (1990) Generalized additive models. Chapman & Hall, London
Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning: data mining, inference, and prediction, 2nd edn. Springer, New York
Heumann C, Schomaker M, Shalabh S (2016) Introduction to statistics and data analysis. Springer, Heidelberg
Jedrychowski W, Becher H, Wahrendorf J, Basa-Cierpialek Z, Gomola G (1992) Effect of tobacco smoking on various histologic types of lung cancer. J Cancer Res Clin Oncol 118:276–282
Lausen B, Schumacher M (1996) Evaluating the effect of optimized cutoff values in the assessment of prognostic factors. Comput Stat Data Ana 21:307–326
Lausen B, Lerche R, Schumacher M (2002) Maximally selected rank statistics for dose-response problems (2002). Biom J 44:131–147
Maclure M, Greenland S (1992) Tests for trend and dose response: misinterpretations and alternatives. Am J Epidemiol 135:96–104
Mantel N, Haenszel W (1959) Statistical aspects of the analysis of data from retrospective studies of disease. J Natl Cancer Inst 22:719–748
Mizon GE, Richard JF (1986) The encompassing principle and its application to testing non-nested hypothesis. Econometrica 54:657–678
Neuhäuser M, Becher H (1997) Improved odds ratio estimation by posthoc stratification of case-control data. Stat Med 16:993–1004
Olsen MK, Schafer JL (2001) A two-part random-effects model for semicontinuous longitudinal data. J Am Stat Assoc 96:730–745
Perperoglou A, Sauerbrei W, Abrahamowicz M, Schmid M, on behalf of TG2 of the STRATOS initiative (2019) A review of spline function procedures in R. BMC Med Res Methodol 19:46
Porta M, Gasull M, Pumarega J, Kiviranta H, Rantakokko P et al (2022) Plasma concentrations of persistent organic pollutants and pancreatic cancer risk. Int J Epidemiol 51:479–490
Robertson C, Boyle P, Hsieh CC, Macfarlane GJ, Maisonneuve P (1994) Some statistical considerations in the analysis of case-control studies when the exposure variables are continuous measurements. Epidemiology 5:164–170
Royston P, Altman DG (1994) Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling. Appl Stat 43:429–467
Royston P, Sauerbrei W (2008) Multivariable model-building: a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables. Wiley, Chichester
Royston P, Thompson SG (1995) Comparing non-nested regression models. Biometrics 51:114–127
Royston P, Sauerbrei W, Becher H (2010) Modelling continuous exposures with a ‘spike’ at zero: a new procedure based on fractional polynomials. Stat Med 29:1219–1227
Sauerbrei W, Perperoglou A, Schmid M, Abrahamowicz M, Becher H, Binder H, Dunkler D, Harrell FE Jr, Royston P, Heinze G, for TG2 of the STRATOS initiative (2020) State of the art in selection of variables and functional forms in multivariable analysis - outstanding issues. Diagn Progn Res 4:3
Schisterman EF, Reiser B, Faraggi D (2006) ROC analysis for markers with mass at zero. Stat Med 25:623–638
Schulgen G, Lausen B, Olsen JH, Schumacher M (1994) Outcome-oriented cutpoints in analysis of quantitative exposures. Am J Epidemiol 140:172–184
Van Calster B, Steyerberg EW, Collins GS, Smits T (2018) Consequences of relying on statistical significance: some illustrations. Eur J Clin Investig 48(5):e12912
Wood SN (2017) Generalized additive models: an introduction with R, 2nd edn. Chapman and Hall/CRC, Boca Raton
Zatonski W, Becher H, Lissowska J, Wahrendorf J (1991) Tobacco, alcohol and diet in the etiology of laryngeal cancer – a population-based case-control study. Cancer Causes Control 2:3–10
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The authors thank Bernhard Hader for corrections and proofreading.
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Becher, H., Schmid, M. (2023). Analysis of Continuous Covariates and Dose-Effect Analysis. In: Ahrens, W., Pigeot, I. (eds) Handbook of Epidemiology. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6625-3_16-1
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DOI: https://doi.org/10.1007/978-1-4614-6625-3_16-1
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