No abstract

Blocking is often used to reduce known variability in designed experiments by collecting together homogeneous experimental units. A common modelling assumption for such experiments is that responses from units within a block are dependent. Accounting for such dependencies in both the design of the experiment and the modelling of the resulting data when the response is not normally distributed can be challenging, particularly in terms of the computation required to find an optimal design. The application of copulas and marginal modelling provides a computationally efficient approach for estimating population-average treatment effects. Motivated by an experiment from materials testing, we develop and demonstrate designs with blocks of size two using copula models. Such designs are also important in applications ranging from microarray experiments to experiments on human eyes or limbs with naturally occurring blocks of size two. We present methodology for design selection, make comparisons to existing approaches in the literature and assess the robustness of the designs to modelling assumptions.

Background Far too often, one meets patients who went for years or even decades from doctor to doctor, without getting a valid diagnosis. This brings pain to millions of patients and their families, not to speak of the enormous costs. Often patients do not know well enough which factors (or combinations thereof) trigger their problems. Results If conventional methods fail, we propose the use of statistics and algebra to give doctors much more precise inputs from patients. We propose statistical regression for independent triggering factors for medical problems, and “balanced incomplete block designs” for non-independent factors. These methods might change a useless statement like “I feel very tired after meals” to a much more valuable “After a meal with many carbohydrates, but few vegetables, a moderate physical activity will usually force me into a wheel-chair”. In order to show that these methods do work, we briefly describe a real case in which these methods helped to solve a 60 year old problem in a patient, and give some more examples where these methods might be very useful. Discussion In this paper, we present a way of getting medical diagnoses when the methods in medicine are insufficient, too time consuming, or very expensive. By asking the patient to conduct tests (often at home) according to a very well-prepared schedule, statistics can use regression analysis to identify the factors (or combinations thereof) which trigger or worsen the patient’s problems. This (very inexpensive) analysis can often give the patient’s doctor(s) a very good and precise input for their diagnosis. Conclusions While regression is used in clinical medicine, it seems to be widely unknown among diagnosing doctors. In finding the reason(s) of rare diseases, doctors face very tough problems. So they deserve to know all tools which could offer some help. This can save the health systems much money, and the patients also a lot of pain.

Far too often, one meets patients who went for years or even decades from doctor to doctor without obtaining a valid diagnosis. This brings pain to millions of patients and their families, not to speak of the enormous costs. Often patients cannot tell precisely enough which factors (or combinations thereof) trigger their problems. If conventional methods fail, we propose the use of statistics and algebra to provide doctors much more useful inputs from patients. We use statistical regression for triggering factors of medical problems, and in particular, “balanced incomplete block designs” for factors detection. These methods can supply doctors with much more valuable inputs and can also find combinations of multiple factors through very few tests. In order to show that these methods do work, we briefly describe a case in which these methods helped to solve a 60-year-old problem in a patient and provide some more examples where these methods might be particularly useful. As a conclusion, while regression is used in clinical medicine, it seems to be widely unknown in diagnosing. Statistics and algebra can save the health systems much money, as well as the patients a lot of pain.