Çok Durumlu Modellerde Geçiş Olasılıklarının Tahmini

Abstract

The time until an event occurs is examined in survival analysis. During the time that an individual or a unit under examination passes from the starting state to the final state, other situations may occur and transitions may take between them. In multi-state models, intermediate states are involved until the final state is. Multi-state models are an extended version of the two-state analysis models. The most commonly used model in the literature is the three-state disease-death model, which includes a transitional state between the first and last states.

This study introduces the multi-state models and their general model structures. The estimation approach proposed by Zaman et al. (2012) for transition probability and standard error estimates were adapted to a three-state illness-death model. Probability and standard error adjustments were made to the Aalen-Johansen (AJ), Presmoothed Aalen-Johansen (PAJ), Lifetime Data Analysis (LIDA), Landmark (LM), Presmoothed Landmark (PLM), Landmark Aalen-Johansen (LMAJ) and Presmoothed Landmark Aalen-Johansen (PLMAJ) estimators, and probability (p_11, p_12, p_13, p_22 ve p_23) and standard error values were calculated for all transitions between states. In addition, Fleming Harrington (FH) estimator used in two-state survival analysis was adapted to the three-state illness-death models, and adjustments were made to the FH estimators. Transition probabilities and standard error values were calculated for time points during the process for all estimators, and graphs were drawn for some s points determined for p_ij(s,t) and standard errors. The variability among estimators was demonstrated by comparing the results of AJ, PAJ, LIDA, LM, PLM, LMAJ, and PLMAJ, and the FH estimators calculated using these estimators.

Colon cancer, heart transplant, breast cancer and cervical cancer data sets have been studied to demonstrate the applicability of the methods. Lower standard error values have been obtained for the adjusted/corrected estimators for AJ, PAJ, LIDA, LM, PLM, LMAJ, and PLMAJ. While FH and adjusted FH estimators generally have higher standard error values than other estimators, the adjusted FH estimators have provided lower standard error values for p_11 in breast cancer data and p_23 in cervical cancer data. Better results were obtained with the adjusted estimators for all data sets.