We discuss the issue of identifiability of models for multiple dichotomous diagnostic tests in the absence of a gold standard (GS) test. Data arise as multinomial or product-multinomial counts depending upon the number of populations sampled. Models are generally posited in terms of population prevalences, test sensitivities and specificities, and test dependence terms. It is commonly believed that if the degrees of freedom in the data meet or exceed the number of parameters in a fitted model then the model is identifiable. Goodman (1974, Biometrika 61, 215-231) established that this was not the case a long time ago. We discuss currently available models for multiple tests and argue in favor of an extension of a model that was developed by Dendukuri and Joseph (2001, Biometrics 57, 158-167). Subsequently, we further develop Goodman's technique, and make geometric arguments to give further insight into the nature of models that lack identifiability. We present illustrations using simulated and real data.

Highlights Wider sensor availability and miniaturisation are pushing speed/resolution limits. Small surgical datasets exist in many specialities but no standard format. Data-driven analysis avoids modelling, improves speed, addresses uncertainty. RGB-based functional imaging could exploit existing cameras, chip-on-tip devices. Clinical validation with standardised devices and data needed for translation.

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Multispectral imaging (MSI) can potentially assist the intra-operative assessment of tissue structure, function and viability, by providing information about oxygenation. In this paper, we present a novel technique for recovering intrinsic MSI measurements from endoscopic RGB images without custom hardware adaptations. The advantage of this approach is that it requires no modification to existing surgical and diagnostic endoscopic imaging systems. Our method uses a radiometric color calibration of the endoscopic camera's sensor in conjunction with a Bayesian framework to recover a per-pixel measurement of the total blood volume (THb) and oxygen saturation (SO) in the observed tissue. The sensor's pixel measurements are modeled as weighted sums over a mixture of Poisson distributions and we optimize the variables SO and THb to maximize the likelihood of the observations. To validate our technique, we use synthetic images generated from Monte Carlo physics simulation of light transport through soft tissue containing sub-surface blood vessels. We also validate our method on in vivo data by comparing it to a MSI dataset acquired with a hardware system that sequentially images multiple spectral bands without overlap. Our results are promising and show that we are able to provide surgeons with additional relevant information by processing endoscopic images with our modeling and inference framework.

Multispectral imaging (MSI) can provide information about tissue oxygenation, perfusion and potentially function during surgery. In this paper we present a novel, near real-time technique for intrinsic measurements of total haemoglobin (THb) and blood oxygenation (SO2) in tissue using only RGB images from a stereo laparoscope. The high degree of spectral overlap between channels makes inference of haemoglobin concentration challenging, non-linear and under constrained. We decompose the problem into two constrained linear sub-problems and show that with Tikhonov regularisation the estimation significantly improves, giving robust estimation of the THb. We demonstrate by using the co-registered stereo image data from two cameras it is possible to get robust SO2 estimation as well. Our method is closed from, providing computational efficiency even with multiple cameras. The method we present requires only spectral response calibration of each camera, without modification of existing laparoscopic imaging hardware. We validate our technique on synthetic data from Monte Carlo simulation and further, in vivo, on a multispectral porcine data set.