Cox regression is a well-known approach for modeling censored survival data. However, the model has an assumption of proportional hazards which requires an attention. In this study, we examine weighted estimation in Cox regression model under nonproportional hazards. Our aim is to propose various weighting functions that are more appropriate than existing ones. The proposed and existing weighting functions are applied to a data set in breast cancer in order to analyze their effects on the analysis results. In order to analyze the performance and effect of proposed and existing weighting functions, a wide simulation study, covering different censoring rates and tied observations, is carried out.