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The Lognormal Distribution as a Model for Survival Time in Cancer, With an Emphasis on Prognostic Factors

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  • P. Royston

Abstract

Despite their long history, parametric survival‐time models have largely been neglected in the modern biostatistical and medical literature in favour of the Cox proportional hazards model. Here, I present a case for the use of the lognormal distribution in the analysis of survival times of breast and ovarian cancer patients, specifically in modelling the effects of prognostic factors. The lognormal provides a completely specified probability distribution for the observations and a sensible estimate of the variation explained by the model, a quantity that is controversial for the Cox model. I show how imputation of censored observations under the model may be used to inspect the data using familiar graphical and other technques. Results from the Cox and lognormal models are compared and shown apparently to differ to some extent. However, it is hard to judge which model gives the more accurate estimates. It is concluded that provided the lognormal model fits the data adequately, it may be a useful approach to the analysis of censored survival data.

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  • P. Royston, 2001. "The Lognormal Distribution as a Model for Survival Time in Cancer, With an Emphasis on Prognostic Factors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(1), pages 89-104, March.
    • Handle: RePEc:bla:stanee:v:55:y:2001:i:1:p:89-104
    DOI: 10.1111/1467-9574.00158
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    Cited by:

    1. Patrick Royston, 2007. "Multiple imputation of missing values: further update of ice, with an emphasis on interval censoring," Stata Journal, StataCorp LP, vol. 7(4), pages 445-464, December.
    2. Chrys Caroni, 2022. "Regression Models for Lifetime Data: An Overview," Stats, MDPI, vol. 5(4), pages 1-11, December.
    3. Warisa Thangjai & Suparat Niwitpong, 2020. "Comparing particulate matter dispersion in Thailand using the Bayesian Confidence Intervals for ratio of coefficients of variation," Statistics in Transition New Series, Polish Statistical Association, vol. 21(5), pages 41-60, December.
    4. Shirin Moghaddam & John Newell & John Hinde, 2022. "A Bayesian Approach for Imputation of Censored Survival Data," Stats, MDPI, vol. 5(1), pages 1-19, January.
    5. Nicholas Longford, 2008. "Inference with the lognormal distribution," Economics Working Papers 1104, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Sun Eric & Jena Anupam B & Lakdawalla Darius & Reyes Carolina & Philipson Tomas J & Goldman Dana, 2010. "The Contributions of Improved Therapy and Earlier Detection to Cancer Survival Gains, 1988-2000," Forum for Health Economics & Policy, De Gruyter, vol. 13(2), pages 1-22, February.
    7. Selamawit Endale Gurmu, 2018. "Assessing Survival Time of Women with Cervical Cancer Using Various Parametric Frailty Models: A Case Study at Tikur Anbessa Specialized Hospital, Addis Ababa, Ethiopia," Annals of Data Science, Springer, vol. 5(4), pages 513-527, December.
    8. Leon Chen, L. & Beck, Christian, 2008. "A superstatistical model of metastasis and cancer survival," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3162-3172.

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