Estimating treatment effects with observational data is very difficult because of contextual confounding, imbalanced case and control group size and etc. In this paper, we present the causal inference methods (propensity score matching estimate and propensity score weighting estimate) that can help to address these problems, aiming at providing unbiased estimates of treatment effects by controlling other possible factors to perform a randomized experiment. Based on the data collected from 773 participants in Personal Genome Project database, we employ the causal inference methods to estimate the treatment effects of high cholesterol on myopia. In our approach, we first estimate the average treatment effect for treated group (high cholesterol participants) on myopia by conducting two causal inference methods. Afterwards, we verify our estimation by performing pseudo treatment and sensitivity analysis. Based on our research, participants with high cholesterol have a chance of getting myopia 10% higher than if they did not have high cholesterol. Our findings lead to a new path for biomedical researchers to discover the novel genome-wide causation, from which the causal effect of high cholesterol on myopia is derived.

Abstract In this paper, a new method is presented for representing conics precisely using NURBS of degree two. The method requires only four control vertices to represent a full circle using the full circumscribing square‐based representation, which is less than the number required with the other methods using the square control vertex configuration.9, 10, 13 The paper also derives a new condition for NURBS to represent conics precisely and shows the sufficient and necessary conditions for representation of a circular arc, and gives the definition and the knot vector formulae of a periodic NURBS curve.