Measurement of the effects of radiosensitising drugs and evaluation of their statistical significance - PDF version
Despite advances in radiotherapy delivery, which permit dose escalation for many tumours, the intrinsic radio-resistance of cancer cells often remains a barrier to curative treatment. Accordingly, much effort is being invested into the development of drugs that are capable of selectively disarming the defences used by cancer cells, with a view to administering them alongside radiotherapy. The identification of promising radiosensitising drugs depends upon robust pre-clinical experimentation and careful interpretation of the findings.
The gold standard in vitro method used to measure radiosensitisation is the clonogenic assay, in which long-term survival and clonogenicity following exposure to radiation is compared between experimental conditions. The response of cells treated with radiation can be described using an elegant mathematical relationship: the linear quadratic (LQ) equation. Analysis of LQ-derived parameters enhances robustness by reducing the influence of experimental noise that is associated with comparison of individual data points. The ability to analyse these models downstream is therefore a great advantage to our field of research.
Accordingly, LQ-derived parameters are widely used to quantify the activity of candidate radiosensitisers. Most methods use the LQ models that are determined for drug- and control-treated cells to calculate a ratio, and this provides a numerical representation of the additional killing mediated by the interaction of drug and radiation. Ratios are commonly computed for iso-effective doses of radiation (dose-modifying ratio, DMR) or as the ratio of surviving fractions that result from a given dose (iso-dose, radiation-enhancement ratio, RER). Values >1 indicate radiosensitisation.
However, this field has suffered greatly from a lack of consensus among scientists over the naming of the parameters of radiosensitisation. More importantly, iso-effect and iso-dose measures that vary with response level are often reported in the literature at only a single level, disregarding International Commission on Radiation Units and Measurements (ICRU) guidance.
To improve on this situation, we strongly recommend adoption of the nomenclature and approach reviewed by Subiel et al (2016). Furthermore, we specifically advocate use of the sensitiser-enhancement ratio (SER) to quantify the magnitude of radiosensitisation. This parameter, determined from the ratio of the mean inactivation dose of each LQ model, captures the size of the radiosensitising effect in a single, objective value. Adoption of the SER method by experimental scientists has been limited, however. We speculate that this lack of uptake might be exacerbated by the requirement for advanced mathematical operations (i.e. integration of the LQ equation), which cannot be performed by widely used software packages such as Excel and GraphPad. More advanced mathematical or statistical packages such as ‘R’ or MatLab are well suited to the SER methodology but require some knowledge of programming languages.
Also, while extremely informative, the article by Subiel et al does not address the challenge of calculating the statistical significance of radiosensitisation effects. As always, replicated experiments must be combined to account for biological variability. But determining a single ratio from the mean of replicated data precludes statistical comparison of radiosensitisation. At the same time, taking the mean of the ratios obtained for each biological replicate is statistically problematic, because of the (usually incorrect) assumption that data are paired. When dealing with the natural scale, one must remember that ‘the mean of the ratios’ and ‘the ratio of the means’ are not equivalent.
To overcome both these issues, we are currently developing a statistically robust methodology for the determination of radiosensitisation parameters such as SER from replicated biological data. The methodology applies a ratio-specific statistical test to replicate measures of radiosensitivity, and our aim is to create a user-friendly, freely available web-based application into which any radiobiology researcher could enter data to generate plots and statistical parameters suitable for publication.
As radiation biologists we proudly proclaim the clonogenic assay as the ‘gold-standard’, which indeed it is, but only if the subsequent data processing and interpretation is executed to the same high standard.
DMR0.37 1.49 RER2Gy 1.58 SER 1.48
DMR0.10 1.44 RER4Gy 3.74
Mark Jackson & Anthony Chalmers
Institute of Cancer Sciences
University of Glasgow, UK
Mark Jackson
Anthony Chalmers
References:
Subiel A, Ashmore R, Schettino G, Theranostics. 2016; 6(10): 1651–1671
NB. In this paper, the analytical form for determination of SER given by equation (4) is incorrect. Numerical computation of the mean inactivation doses is the method of choice, as implemented in our forthcoming application.