Algebraic generation of minimum size orthogonal fractional factorial designs: an approach based on integer linear programming

Generation of orthogonal fractional factorial designs (OFFDs) is an important and extensively studied subject in applied statistics. In this paper we show how searching for an OFFD that satisfies a set of constraints, expressed in terms of orthogonality between simple and interaction effects, is, in many applications, equivalent to solving an integer linear programming problem.We use a recent methodology, based on polynomial counting functions and strata, that represents OFFDs as the positive integer solutions of a system of linear equations. We use this system to set up an optimization problem where the cost function to be minimized is the size of the OFFD and the constraints are represented by the system itself. Finally we search for a solution using standard integer programming techniques. Some applications are also presented in the computational results section. It is worth noting that the methodology does not put any restriction either on the number of levels of each factor or on the orthogonality constraints and so it can be applied to a very wide range of designs, including mixed orthogonal array

Evolution of clinical features in possible DLB depending on FP-CIT SPECT result

Objective: To test the hypothesis that core and suggestive features in possible dementia with Lewy bodies (DLB) would vary in their ability to predict an abnormal dopamine transporter scan and therefore a follow-up diagnosis of probable DLB. A further objective was to assess the evolution of core and suggestive features in patients with possible DLB over time depending on the 123I-FP-CIT SPECT scan result. Methods: A total of 187 patients with possible DLB (dementia plus one core or one suggestive feature) were randomized to have dopamine transporter imaging or to follow-up without scan. DLB features were compared at baseline and at 6-month follow-up according to imaging results and follow-up diagnosis. Results: For the whole cohort, the baseline frequency of parkinsonism was 30%, fluctuations 29%, visual hallucinations 24%, and REM sleep behavior disorder 17%. Clinician-rated presence of parkinsonism at baseline was significantly (p = 0.001) more frequent and Unified Parkinson’s Disease Rating Scale (UPDRS) score at baseline was significantly higher (p = 0.02) in patients with abnormal imaging. There was a significant increase in UPDRS score in the abnormal scan group over time (p < 0.01). There was relatively little evolution of the rest of the DLB features regardless of the imaging result. Conclusions: In patients with possible DLB, apart from UPDRS score, there was no difference in the evolution of DLB clinical features over 6 months between cases with normal and abnormal imaging. Only parkinsonism and dopamine transporter imaging helped to differentiate DLB from non-DLB dementia