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Fitting Smooth-in-Time Prognostic Risk Functions via Logistic Regression

Author

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  • Hanley James A

    (McGill University)

  • Miettinen Olli S

    (McGill University)

Abstract

When considering treatment options, a physician ideally has access to prognoses for various spans of prospective time, meaning known risks specific for these and also for both treatment and the profile of the patient. Accordingly, investigators ideally would report estimates of such risks from clinical trials and their non-experimental counterparts. To the extent that such risk estimates have been reported at all, they have mainly been based on the semi-parametric regression model of Cox. We focus on a family of fully-parametric hazard models of an attractive, versatile form that readily allows for non-proportionality, yet models that have not been easy to fit with standard statistical software. We elaborate an approach, recently proposed, to fitting such hazard functions via logistic regression. From the fitted hazard function, cumulative incidence and, thus, risk functions of time, treatment and profile can be derived. This approach accommodates any log-linear hazard function of prognostic time, treatment, and the prognostic indicators defining the patient's prognostic profile.

Suggested Citation

  • Hanley James A & Miettinen Olli S, 2009. "Fitting Smooth-in-Time Prognostic Risk Functions via Logistic Regression," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-25, January.
    • Handle: RePEc:bpj:ijbist:v:5:y:2009:i:1:n:3
    DOI: 10.2202/1557-4679.1125
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    References listed on IDEAS

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    1. Murray Aitkin & David Clayton, 1980. "The Fitting of Exponential, Weibull and Extreme Value Distributions to Complex Censored Survival Data Using Glim," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(2), pages 156-163, June.
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    Cited by:

    1. Olli Saarela & Elja Arjas, 2015. "Non-parametric Bayesian Hazard Regression for Chronic Disease Risk Assessment," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 609-626, June.
    2. Olli Saarela, 2016. "A case-base sampling method for estimating recurrent event intensities," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 589-605, October.
    3. Olli Saarela & James A. Hanley, 2015. "Case-base methods for studying vaccination safety," Biometrics, The International Biometric Society, vol. 71(1), pages 42-52, March.

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