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Logistic Regression and Related Methods

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Principles and Practice of Clinical Trials

Abstract

Inference on binary outcomes is a common goal in clinical trials and case-control studies. Logistic regression is the usual approach to estimate treatment effect adjusted for categorical and continuous confounding variables. In this chapter, model building, interpretation of parameters, diagnostics, and inference to small sample sizes are discussed. At last, a case study is presented applying the proposed analytic strategies.

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References

  • Agresti A (2003) Categorical data analysis. Wiley, Hoboken

    MATH  Google Scholar 

  • Anderson JA, Richardson SC (1979) Logistic discrimination and bias correction in maximum likelihood estimation. Technometrics 21(1):71–78

    Article  MATH  Google Scholar 

  • Becher H (1992) The concept of residual confounding in regression models and some applications. Stat Med 11(13):1747–1758

    Article  Google Scholar 

  • Berkson J (1944) Application of the logistic function to bio-assay. J Am Stat Assoc 39(227):357–365

    Google Scholar 

  • Berkson J (1951) Why I prefer logits to probits. Biometrics 7(4):327–339

    Article  Google Scholar 

  • Bowman KO, Shenton LR (1998) Asymptotic skewness and the distribution of maximum likelihood estimators. Commun Stat Theory Methods 27(11):2743–2760

    Article  MATH  Google Scholar 

  • Brookes ST, Whitely E, Egger M, Smith GD, Mulheran PA, Peters TJ (2004) Subgroup analyses in randomized trials: risks of subgroup-specific analyses: power and sample size for the interaction test. J Clin Epidemiol 57(3):229–236

    Article  Google Scholar 

  • Buettner P, Garbe c, Guggenmoos-Holzmann I (1997) Problems in defining cutoff points of continuous prognostic factors: example of tumor thickness in primary cutaneous melanoma. J Clin Epidemiol 50(11):1201–1210

    Article  Google Scholar 

  • Cleveland WS (1979) Robust locally weighted regression and smoothing scatterplots. J Am Stat Assoc 74(368):829–836

    Article  MathSciNet  MATH  Google Scholar 

  • Copas JB (1983) Plotting p against x. Appl Stat 32(1):25–31

    Article  Google Scholar 

  • Cox DR (1969) Analysis of binary data. Chapman and Hall, London

    Google Scholar 

  • Cox DR, Snell EJ (1968) A general definition of residuals. J Royal Statistical Soc Ser B (Methodological) 30(2):248–275

    Article  MathSciNet  MATH  Google Scholar 

  • Cramer JS (2002) The origins of logistic regression. Technical Report 2002-119/4, Tinbergen Institute Working Paper. Available at SSRN: https://ssrn.com/abstract=360300 or https://doi.org/10.2139/ssrn.360300

  • Farewell V (1979) Some results on the estimation of logistic models based on retrospective data. Biometrika 66(1):27–32

    Article  MathSciNet  MATH  Google Scholar 

  • Firth D (1993) Bias reduction of maximum likelihood estimates. Biometrika 80(1):27–38

    Article  MathSciNet  MATH  Google Scholar 

  • Gail M, Wieand S, Piantadosi S (1984) Biased estimates of treatment effect in randomized trials. Control Clin Trials 5(3):303

    Article  MATH  Google Scholar 

  • Gail M, Tan W-Y, Piantadosi S (1988) Tests for no treatment effect in randomized clinical trials. Biometrika 75(1):57–64

    Article  MathSciNet  MATH  Google Scholar 

  • Harrell F (2015) Regression modeling strategies: with applications to linear models, logistic and ordinal regression, and survival analysis. Springer series in statistics. Springer International Publishing, Cham

    Book  MATH  Google Scholar 

  • Hernández AV, Steyerberg EW, Habbema JDF (2004) Covariate adjustment in randomized controlled trials with dichotomous outcomes increases statistical power and reduces sample size requirements. J Clin Epidemiol 57(5):454–460

    Article  Google Scholar 

  • Hosmer DW, Lemesbow S (1980) Goodness of fit tests for the multiple logistic regression model. Commun Stat Theory Methods 9(10):1043–1069

    Article  MATH  Google Scholar 

  • Hosmer D, Lemeshow S (2000) Applied logistic regression, 2nd edn. Wiley, New York

    Book  MATH  Google Scholar 

  • Hosmer DW, Hosmer T, Le Cessie S, Lemeshow S (1997) A comparison of goodness-of-fit tests for the logistic regression model. Stat Med 16(9):965–980

    Article  MATH  Google Scholar 

  • Jiang H, Kulkarni PM, Mallinckrodt CH, Shurzinske L, Molenberghs G, Lipkovich I (2017) Covariate adjustment for logistic regression analysis of binary clinical trial data. Stat Biopharm Res 9(1):126–134

    Article  Google Scholar 

  • Kahan BC, Rushton H, Morris TP, Daniel RM (2016) A comparison of methods to adjust for continuous covariates in the analysis of randomised trials. BMC Med Res Methodol 16(1):42

    Article  Google Scholar 

  • le Cessie S, van Houwelingen JC (1991) A goodness-of-fit test for binary regression models, based on smoothing methods. Biometrics 47(4):1267–1282

    Article  MATH  Google Scholar 

  • Magalhães TM, Botter DA, Sandoval MC, Pereira GHA, Cordeiro GM (2019) Skewness of maximum likelihood estimators in the varying dispersion beta regression model. Commun Stat Theory Methods 48(17):4250–4260

    Article  MathSciNet  Google Scholar 

  • Nastri AC d SS, de Mello Malta F, Diniz MA, Yoshino A, Abe-Sandes K, dos Santos SEB, de Castro Lyra A, Carrilho FJ, Pinho JRR (2016) Association of ifnl3 and ifnl4 polymorphisms with hepatitis c virus infection in a population from southeastern Brazil. Arch Virol 161(6):1477–1484

    Article  Google Scholar 

  • Pocock SJ, Assmann SE, Enos LE, Kasten LE (2002) Subgroup analysis, covariate adjustment and baseline comparisons in clinical trial reporting: current practice and problems. Stat Med 21(19):2917–2930

    Article  Google Scholar 

  • Polson NG, Scott JG, Windle J (2013) Bayesian inference for logistic models using pólya–gamma latent variables. J Am Stat Assoc 108(504):1339–1349

    Article  MATH  Google Scholar 

  • Pregibon D et al (1981) Logistic regression diagnostics. Ann Stat 9(4):705–724

    Article  MathSciNet  MATH  Google Scholar 

  • Prentice RL, Pyke R (1979) Logistic disease incidence models and case-control studies. Biometrika 66(3):403–411

    Article  MathSciNet  MATH  Google Scholar 

  • Robinson LD, Jewell NP (1991) Some surprising results about covariate adjustment in logistic regression models. Int Stat Rev/Revue Int Stat 59(2):227–240

    Article  MATH  Google Scholar 

  • Rothwell PM (2005) Subgroup analysis in randomised controlled trials: importance, indications, and interpretation. Lancet 365(9454):176–186

    Article  Google Scholar 

  • Royston P (1992) The use of cusums and other techniques in modelling continuous covariates in logistic regression. Stat Med 11(8):1115–1129

    Article  MathSciNet  Google Scholar 

  • Royston P, Altman DG, Sauerbrei W (2006) Dichotomizing continuous predictors in multiple regression: a bad idea. Stat Med 25(1):127–141

    Article  MathSciNet  Google Scholar 

  • Sand S, Victorin K, Filipsson AF (2008) The current state of knowledge on the use of the benchmark dose concept in risk assessment. J Appl Toxicol 28(4):405–421

    Article  Google Scholar 

  • Schaefer RL (1983) Bias correction in maximum likelihood logistic regression. Stat Med 2(1):71–78

    Article  Google Scholar 

  • Tsiatis AA (1980) A note on a goodness-of-fit test for the logistic regression model. Biometrika 67(1):250–251

    Article  MATH  Google Scholar 

  • Wang R, Lagakos SW, Ware JH, Hunter DJ, Drazen JM (2007) Statistics in medicine – reporting of subgroup analyses in clinical trials. N Engl J Med 357(21):2189–2194

    Article  Google Scholar 

  • Wilson EB, Worcester J (1943) The determination of ld 50 and its sampling error in bio-assay. Proc Natl Acad Sci 29(2):79–85

    Article  Google Scholar 

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Correspondence to Márcio A. Diniz .

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Diniz, M.A., Magalhães, T.M. (2020). Logistic Regression and Related Methods. In: Piantadosi, S., Meinert, C. (eds) Principles and Practice of Clinical Trials. Springer, Cham. https://doi.org/10.1007/978-3-319-52677-5_122-2

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  • DOI: https://doi.org/10.1007/978-3-319-52677-5_122-2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52677-5

  • Online ISBN: 978-3-319-52677-5

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Chapter history

  1. Latest

    Logistic Regression and Related Methods
    Published:
    26 February 2020

    DOI: https://doi.org/10.1007/978-3-319-52677-5_122-2

  2. Original

    Logistic Regression and Related Methods
    Published:
    06 February 2020

    DOI: https://doi.org/10.1007/978-3-319-52677-5_122-1