Non-linear effects in dose-time analyses: application of modern statistical techniques.
OBJECTIVE
The non-linear effect of overall treatment time and total dose on the outcome of fractionated head and neck radiotherapy is of interest. This and other non-linear effects can be investigated using recently developed statistical techniques. This article provides an illustration of the ability of these statistical methods.


METHODS
Recently developed statistical methods (Hastie, T.J. and Tibshirani, R.J. Generalised Additive Models. Chapman-Hall, London, 1990), called generalized additive models, are applied to data from the patterns of fractionation study (Withers, H.R., Peters, L.J., Taylor, J.M.G., Owen, J.B., Morrison, W.H., Schultheiss, T.E., Keane, T., O'Sullivan, B., van Dyk, J., Gupta, N., Wang, C.C., Jones, C.U., Doppke, K.P., Myint, S., Thompson, M., Parsons, J.T., Mendenhall, W.M., Dische, S., Aird, E.G.A., Henk, J.M., Bidmead, M.A.M., Svoboda, V., Chon, Y., Hanlon, A.L., Peters, T.L. and Hanks, G.E. Local control of carcinoma of the tonsil by radiation therapy: an analysis of patterns of fractionation in nine institutions. Int. J. Radiat. Oncol. Biol. Phys. 33: 549-562, 1995) of tonsil cancer. These techniques enable one to develop models which more accurately represent the relationship between multivariate predictor variables and the outcome variable in a regression analysis. These data driven methods allow the effect of each predictor variable on the outcome to be non-linear and estimated from the data. This is achieved by replacing the standard linear model combination of predictor variables, such as 'alpha0 + alpha1dose + alpha2time' by 'S1(dose) + S2(time)', where S1 and S2 are smooth non-linear functions of dose and time, respectively, which are estimated from the data.


RESULTS
In the pattern of fractionation study these methods indicate that the effect of total dose on the probability of local recurrence is linear, but there is a suggestion that the effect of overall treatment time is non-linear. There is no effect of dose and time on the latency time to recurrence of those who do recur, but there is a weak suggestion of a non-linear effect of patients age, with younger patients recurring earlier.


CONCLUSIONS
Generalized additive models provide a flexible and powerful means of exploring non-linear effects in experimental data.
Taylor
J M
JM
Department of Radiation Oncology, UCLA School of Medicine, Los Angeles, CA 90095-1772, USA.
Zhang
F
F
Withers
H R
HR
D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D004307:Dose-Response Relationship, Radiation; D005500:Follow-Up Studies; D006801:Humans; D015994:Incidence; D008875:Middle Aged; D015233:Models, Statistical; D009364:Neoplasm Recurrence, Local; D011882:Radiotherapy, High-Energy / Q000706:statistics & numerical data*; D012189:Retrospective Studies; D015996:Survival Rate; D014067:Tonsillar Neoplasms / Q000401:mortality / Q000532:radiotherapy*; D016896:Treatment Outcome