Surgical Oncology
Volume 19, Issue 2 , Pages 59-60, June 2010

Commentary on paper, ‘cancer survival analysis’

Department of Preventive Medicine, Keck School of Medicine, University of Southern California, 4650 Sunset Blvd, Los Angeles, CA, USA

Accepted 16 April 2010.

Article Outline

Keywords: Cure model, Survival analysis, Cox regression, Log-rank test, Proportional hazards

 

In their paper “Evolution of cancer survival analysis”, Drs. Maetani and Gamel highlight some of the differences between the most ubiquitous and well accepted methods for analyzing survival data – the Kaplan Meier (or product-limit) estimator, the logrank test, Cox regression analysis [1] – and methods based on what can be referred to as cure models, of which the Boag model [2] is probably the earliest example. Boag’s simple but useful idea was that after treatment – which at the time comprised surgery and radiation over a short period of time – cancer patients either were cured of the cancer, or were not cured and would die from the cancer at varying times, so that a statistical model could be used to predict the chance that a patient was cured as well as to describe the life expectancy of those who were not. Other similar models [3], models with extensions to add the ability to study the influence of covariables on cure rate and time to failure [4], [5], and models that relax some of the required strong assumptions [6], [7] have also since been developed.

As Drs. Maetani and Gamel point out, there may be advantages to using cure models. The logrank test and Cox regression analysis (in its strictly proportional hazards form) assume that variables such as treatment or patient age affect the same change on the failure rate early after diagnosis as they do late in follow-up. For example, one is assuming that if a patient is twice as likely to experience recurrence in the month after diagnosis with treatment A compared to treatment B, then a patient who is three years from diagnosis similarly will be twice as likely to experience recurrence in the next month with treatment A compared to treatment B. This is a fairly strong assumption, but it is valid enough in many situations, which is why Cox regression analysis is so useful and has gained such prominence in medical research. When the proportional hazards assumption is not valid, and when this is either ignored or not appreciated, a logrank test or proportion-hazards Cox regression analysis can be misleading – variables that are predictive of long-term survival or cure may not be discovered, or variables that are statistically significant may not in fact strongly influence long-term survival or cure. The latter is the case in the leukemia/6-MP example, but this does not invalidate the finding that 6-MP is an active drug in leukemia. Non-proportionality can be tested and modeled within a Cox regression analysis, but cure models can have an advantage since one can explicitly separate the influence of variables on the cure rate from their influence on early failure rate.

But cure models come with their own strong assumptions. The Boag model assumes that the log of the time to failure in patients who are not cured follows the common normal distribution. When this assumption is not valid, a cure model analysis also will be misleading. In these cases models with different statistical distributions, or which do not require distributional assumptions [6], [7] can be used. The concept of cure itself – that the disease is gone and will never come back – implies that one knows the final outcome of patients, but this is not true, since patients are followed for only finite periods of time. This means that statements about the probability of cure and what may influence it are always extrapolations past the data. It is important, therefore, when applying these models, that most patients have been followed well past the time of significant risk of recurrence. It is not wise to extrapolate beyond actual known follow-up if this follow-up is short, even if the model appears to fit the data.

The cure rate is a good measure of long-term outcome and treatment success in cancer, but it may not always be the best. In paediatric cancers, in particular hematologic malignancies and solid tumors like medulloblastoma [8], [9], [10], [11], [12], cure is achieved in the majority patients, if the meaning of cure is in the narrowest sense of simply eliminating the original neoplasm. These children are not cured in the broader sense that it is as if they had never been diagnosed and treated for cancer. Young children who are still in developmental phases are at greater risk for severe long-lasting treatment morbidity [13], [14], [15]. A more nuanced definition of cure would include measures of the impact of treatment on quality of life [16].

In older adults, death may occur directly from the cancer, from completely “natural” causes, or from treatment-related morbidity or complications, whether or not the cancer persists. The competing risks model described by Drs. Maetani and Gamel is an attempt to separate the cancer-related death causes from the others, and it will provide a good description of survival data, but its literal interpretation as accurately describing two independent causes of death will often be difficult because of ambiguity in ascribing death to cancer or other causes. Here, also, it may be important in assessing long-term outcome and treatment success to include measures of patient quality of life in analysis, and there have been attempts to do so [17], [18], [19].

Nevertheless, an important message to take away from Dr. Maetani’s and Dr. Gamel’s article is that the most commonly used methods for survival analysis – Cox regression, logrank – may not always be the best to use. It is important to understand what the most relevant measures of treatment success are for a particular clinical research question, and use the statistical models and methods that are most appropriate for these.

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PII: S0960-7404(10)00041-1

doi:10.1016/j.suronc.2010.04.002

Surgical Oncology
Volume 19, Issue 2 , Pages 59-60, June 2010

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