SPLINE REGRESSION ANALYSIS WITH APPLICATION TO CLINICAL DATA: A REVIEW

Abstract

Building reliable multivariable regression models is a major concern in many application areas, when one or more of
the predictor(s) is/are continuous, the question arises of how to represent the relationship meaningfully following
substantive background knowledge. In this paper, we review and present in epidemiological context polynomial
regressions splines with applications in real-life clinical data. We also investigate if the added complexity of the spline
regression models is justified by a significantly better fit (under certain conditions). Assumptions of constant variance,
zero mean and many other properties were examined using residual versus fitted values plot. We imposed the
assumption of no discontinuity at the spline knot respectively. Following the outcome of the scattered plot of survival
time data for cancer patients, our data structures follow a quadratic relationship, based on all criteria. Also, the cubic
polynomial regression model and cubic spline revealed that indeed the regression diagnostic tools such as the Normal
Q-Q plot do not show a serious departure from the normality assumption. However, by assessing the contribution of
the cubic effect parameter, the cubic model is inadequate to fit the data, Hence, employing regression diagnostics
visualization plot/ techniques alone for assessing the quality of the fit of the data to a model is good but not sufficient
enough to judge the suitability and adequacy of a model.