Kernel and regression spline smoothing techniques to estimate coefficient in rates model and its application in psoriasis

Data types are recurrent events in studies in which each person may experience an event at different times. One of the most popular approaches to analyze recurrent event data is obtaining an estimate of the means/rate of events at different times. In this context, determining the variability over time can help better understand the effect of factor on the response. In this study, we applied smoothing methods to estimate coefficients in time-dependent rate model, and we also showed its application in data of psoriasis patients.

In the present study, psoriasis patients who experienced relapse that led to hospitalization during 2005 and 2014 in the Dermatology Department of Imam Khomeini hospital in Tehran were examined. To investigate the rate of relapse during a year, time-dependent rate model was used and variability of the effects was assessed using Wald test. Both b-spline and kernel methods were used to estimate time varying coefficients in rates model. Finally, results from methods were compared based on the obtained estimates.

Based on the results of the Wald test, the effect of season on the occurrence of psoriasis was significantly different (p<0.01). Also according to the estimated coefficients from both b-spline and kernel methods, there was little difference between them.

In situations in which the effect of a variable is different at different times, using time-dependent coefficients rate model can lead to a better estimate of the effect of variable on the response. On the other hand, smoothing methods can smooth the effects of the variables that vary over time.