Censoring and collinearity in the log-linear exponential regression model

In medicine, sometimes it is necessary to evaluate if a variable represents a risk factor, which implies estimating parameters and making tests of hypothesis. When collinearity among the variables exists, statistical tests lose power which may lead to take wrong decisions. The effect of collinearity and censoring on the maximum likelihood estimates of the survival log-linear exponential regression model was studied. A simulation was conducted involving four factors: censoring level, degree of collinearity, number of variables and orientation of the vector of parameters. Simulation involved the aforemenhined factors and analyzed their effect on the scaled condition number of the observed information matrix, the mean square error and the sum of squares of prediction. The scaled condition numbers were affected by the number of variates and degree of collinearity. The mean square error of the estimated coefficients increased with collinearity; this effect was stronger in the estimated parameters involved in the collinear relationship. A similar effect was found for the censoring level: as the censoring level increased, the mean square error. However, in this case the effect was similar in all the variables in the model. The sum of squares of prediction was affected by the number of variables, orientation of the vector of parameters, and the censoring level.