British Journal of Radiology (2006) 79, 353-355
© 2006 British Institute of Radiology
doi: 10.1259/bjr/15389891
Implications of quality adjusted survival for clinical trials in radiation oncology
B Jones, MD, FRCR, MedFIPEM
Birmingham Cancer Centre, University Hospital Birmingham, Birmingham B15 2TH, UK
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Abstract
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Clinical trials in radiotherapy sometimes compare changes in radiation dose distribution using different radiation techniques. The use of quality adjusted survival can, in special circumstances, reduce the requirement of large patient numbers in order to show a significant difference in overall outcome. The provisos are that marginal improvements in survival or tumour control endpoints and a reduction in toxicity scores are present. The converse findings would also be amenable to this approach. Random sampling methods are used to construct a patient population where the first set of conditions is met. Further work is necessary to refine the absolute indications for this technique.
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Introduction
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The results of modern clinical trials in radiotherapy frequently show marginal changes in survival, which necessitate very large numbers of patients to demonstrate even a trend of improvement in outcomes. For example, the four-armed trial of accelerated and hyperfractionated radiotherapy conducted in the USA by Fu and colleagues [1] involved 1113 entered patients, with statistical significance probability values ranging from 0.045 to 0.067 for local tumour control and disease free survival. Separate analysis of survival and side effect statistics is the norm, often with much less detail given in terms of reporting the latter. The costs of clinical trials – in terms of human and financial resources provided by the government and charitable organizations, as well as the restrictions imposed upon patients – are considerable in advanced countries such as the UK. Better "value for money" would be achieved if trial costs could be curtailed – this would at least allow more trials to be conducted. The concept of quality adjusted survival is not new [2] and could be more frequently applied in clinical trial analysis, although it is most frequently used in cost benefit studies by health economists.
Clinical trials in oncology are usually concerned with the duration of local tumour control, survival times (both continuous variables) and the severity of side effects (normally graded as discrete variables). In the testing of new radiation therapy techniques, for example if dose distribution is changed while delivering the same total tumour dose, it might be that the same or similar local control and survival can be expected but that the quality of life may be the intended benefit [3]. Another example would be the delivery of a slightly higher radiation dose to the tumour while at the same time reducing the dose to normal tissues by means of charged particle beams [4], with a modest increase in tumour control and a reduction in side effects.
There are potential ethical difficulties about the conduct of such trials where the dose distributions (obtained using the predictions of the laws of physics) are judged to be so much better in the case of the new treatment [5]. However, past experience with "new" forms of radiotherapy required trials to demonstrate that theoretically predicted gains were not realised in practical situations [6, 7], although in these studies there was no change in dose distribution. There is also a dilemma when new treatments are phased in slowly owing to reduced treatment capacity: in such cases there might be opportunities to do randomized studies.
It would be advantageous if subtle changes in tumour control, survival and simultaneous improvements in quality of life could be found from trials that incorporate smaller numbers of patients; results should be available sooner and the financial costs of trials would be considerably reduced.
The present paper aims to demonstrate the potential advantage of quality-adjusted survival in a simulated clinical trial where the necessary conditions of marginal improvements of disease free survival and reduced complications occur.
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Methods
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The disease free survival times of a cancer patient population are simulated by random sampling techniques for the two arms of a trial that compares conventional X-ray therapy (XRT) with charged particle beam (CPB) therapy given to slightly higher dose. The assumptions made are given in Table 1
. This example is not meant to advance the cause of any particular form of therapy, but merely used to demonstrate the statistical principles. Mathematica and GraphPad Prism software are used to obtain the results.
The quality-adjusted survival is calculated by multiplying the actual survival by a factor F defined as:
In this way, toxicity scores of 0, 1, 2, 3 and 4, respectively, have F = 1, 0.8, 0.6, 0.4, 0.2.
The assumptions made are given in Table 1
, including the cumulative toxicity scores.
For the results shown in Figure 1, the survival log rank test provides p = 0.062 for a one tailed study. The side effect profile is separately analysed to give 
2 (with four degrees of freedom) = 9.04, p = 0.061. When the quality-adjusted survival is assessed, then p<0.001, which is a substantial reduction. Essentially this is the same approximate result as would be obtained by multiplying the two probabilities, i.e. the probability of the null hypothesis being accepted for the uncorrected survival and for the side effect profile being the same in both arms of the trial (p = 0.061 x 0.001
0.001).
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Figure 1. Kaplan-Meier plot of a simulated clinical trial comparing conventional X-ray therapy(XRT) with charged particle beam (CPB) therapy. There are 100 patients in each treatment arm and the assumptions made are given in Table 1.
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Rather than use the classical 2 test with n–1 degrees of freedom, where n is the number of categorical variables, the 2 test for trend can be used with only one degree of freedom, which inevitably reduces the p-value. By use of this test, the results given in Table 1 yield a p = 0.003, which is significant without combining with the disease free survival results. However, the necessary condition for the use of this test is that the outcome variable must be well ordered; this condition will not be satisfied in trials where there might be less grade 0 than grade 1 toxicity.
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Discussion
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At present there is some dissatisfaction with the constraints imposed by standard clinical trials in radiotherapy [8]. A wider spectrum of research methods, such as observational studies and mathematical modelling, is required to solve at least some of the problems confronted in a complicated discipline such as radiation oncology, where trials may not be appropriate, or considered unethical [9].
The relatively simple exercise presented in this paper demonstrates proof of principle that fusion of survival with quality of life end points may very substantially reduce the numbers of patients required to show that a new treatment confers significant overall benefits. The number of patients required to confirm marginal benefits in radiation oncology is discussed further by Bentzen [10]. To use the quality adjusted approach, certain safeguards would be required: e.g. that the "survival" trend is superior, with a suggested p-value of <0.1; also that the side effect profile is directionally correct, i.e. that there would be reduced numbers of toxicity scores in each toxicity category >0 for the test treatment with statistical confirmation of a trend with p<0.1 Further sensitivity analysis along these lines should be performed by expert statisticians, with more complex calculations of the expected numbers required to achieve the required level of statistical confidence using the adjusted survival [10, 11]; recommendations of acceptable p-value ranges from the primary end point analyses might also be helpful. Quality adjusted survival must be regarded as either a primary or a secondary endpoint, to be used in special circumstances: this technique might even have a place where survival is unchanged, since further endpoints such as local tumour control or disease free survival may show significant differences when adjusted for quality of life.
The quality survival concept has been applied elsewhere in oncology and some statisticians have already advocated this approach [11]. For example, in leukaemia [12], where four clinical states (viz. toxicity, treatment free of toxicity, no treatment nor symptoms, relapse) were defined. The average times spent in each state were weighted by utility coefficients that reflect relative value according to quality of life. This represents a much more complex process, which also acknowledges the reversible nature of some of the treatment-related side effects.
However, in radiotherapy the serious side effects tend to be chronic and cumulative with time; consequently, such a sophisticated approach would seem to be unnecessary. The use of extant grading systems in oncology can be used in toxicity grade allocation [13] and in crude quality adjusted survival. Actuarial assessment of each side effect grade could be used, but again the numbers of patients and events may be so small that no significant differences would be found, as would be the case for grades 3–4 in Table 1.
The present emphasis on obtaining improved survival in clinical trials ignores the quest for testing improved quality of life. The main funding agencies do not normally support or encourage: primary quality of life endpoint studies in which there is no expectation of enhanced tumour control; observational studies of more complex or newer forms of therapy; large multicentre non-randomized studies that allow convergence of technique and good quality assurance as a prerequisite for multicentre trials. Testing of new radiotherapy techniques – such as charged particle beams – that are specifically designed to reduce side effects, yet either maintain or increase tumour control, might need to utilize quality based end points in trial analysis given that the conventional clinical trial end points may not be sufficiently sensitive where subtle changes in multiple outcomes occur.
It is hoped that this paper will stimulate discussion and lead to better and more cost effective studies within the UK National Cancer Research Institute as well as in other countries.
Received for publication May 23, 2005.
Revision received July 27, 2005.
Accepted for publication October 7, 2005.
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References
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Abstract
Introduction
