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A reduction in salivary flow and xerostomia are common side-effects after radiotherapy of head and neck tumours. Xerostomia can be modeled based on the dose to the parotid glands. To date, all spatial information has been discarded and dose-response models are usually reduced to the mean dose. We present novel morphological dose-response models and use multivariate Bayesian logistic regression to model xerostomia. We use 3D invariant statistical moments as morphometric descriptors to quantify the shape of the 3D dose distribution. As this results in a very high number of potential predictors, we apply a Bayesian variable-selection algorithm to find the best model based on any subset of all potential predictors. To do this, we determine the posterior probabilities of being the best model for all potential models and calculate the marginal probabilities that a variable should be included in a model. This was done using a Reversible Jump Markov Chain Monte Carlo algorithm. The performance of the best model was quantified using the deviance information criterion and a leave-one-out cross-validation (LOOCV). This methodology was applied to 64 head and neck cancer patients treated with either intensity-modulated radiotherapy (IMRT) or conventional radiotherapy. Results show a substantial increase in both model-fit and area under the curve (AUC) when including morphological information compared to conventional mean-dose models. The best mean-dose model for IMRT patients only resulted in an AUC of 0.63 after LOOCV while the best morphological model had an AUC of 0.90. For conventional patients the mean-dose model and the morphological model had AUC of 0.55 and 0.86 respectively. For a joint model with all patients pooled together, the mean dose model had an AUC of 0.75 and the morphological model an AUC of 0.88. We have shown that invariant statistical moments are a good morphometric descriptor and by using Bayesian variable selection we were able to identify models with a - - substantially higher predictive power than conventional mean-dose models.