# SPLINE REGRESSION ANALYSIS WITH APPLICATION TO CLINICAL DATA: A REVIEW

## Keywords:

Cubic Spline, Knots, Panel Data, Quadratic spline, Penalized spline, Spline regressions, Traditional regression## 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.