Estimation of the transition probabilities of multi-state models in survival analysis and an application

Abstract

The time until an event occurs is examined in survival analysis. During the time from the starting point of an individual or a unit under study to the endpoint, other events may occur, and transitions between states are possible. Multi-state survival analysis models are an extension of the classical two-state survival analysis models. The most commonly used multi-state model in the literature is the three-state model. In this study, the three-state model structure is briefly presented and the predictive approach used for transition probabilities and standard error estimates in the two-state model is adapted to the three-state model. Adjustments are made to Aalen-Johansen, presmoothed Aalen-Johansen, lifetime data analysis, Landmark, presmoothed Landmark, Landmark Aalen-Johansen, and presmoothed Landmark Aalen-Johansen estimators used to estimate transition probabilities and probabilities and standard error values for all transitions between states are calculated.To demonstrate and compare the applicability of the methods, colon cancer data available in the R program Survidm package is used. Adjusted estimators have provided lower standard error values.

Keywords

• Multi-state model
• transition probabilities
• survival analysis

Yaşam çözümlemesinde çok durumlu modellerin geçiş olasılıklarının tahmini ve bir uygulama

Abstract

Yaşam çözümlemesinde, tanımlanan bir olay gerçekleşene kadar geçen süre incelenmektedir. Bireyin ya da incelenen birimin başlangıç noktasından son noktaya varıncaya kadar geçirdiği sürede başka durumların yaşanması ve durumlar arasında geçişlerin olması söz konusudur. Çok durumlu yaşam çözümlemesi modelleri iki durumlu klasik yaşam çözümlemesi modellerinin genişletilmiş biçimidir. Literatürde en çok kullanılan çok durumlu model, üç durumlu modeldir. Bu çalışma ile üç durumlu model tanıtılmış ve iki durumlu modelde geçiş olasılığı ve standart hata tahminlerinde kullanılan tahmin edici yaklaşımı üç durumlu modele uyarlanmıştır. Geçiş olasılıklarının tahmin edilmesinde kullanılan Aalen-Johansen, ön düzgünleştirilmiş Aalen-Johansen, yaşam verisi analizi, Landmark, ön düzgünleştirilmiş Landmark, Landmark Aalen-Johansen ve ön düzgünleştirilmiş Landmark Aalen-Johansen tahmin edicilerine düzeltme yapılmış ve durumlar arası bütün geçişler için olasılık ve standart hata değerleri hesaplanmıştır. Yöntemlerin uygulanabilirliğini göstermek ve karşılaştırmak amacıyla R programında yer alan kolon kanseri verileri ile çalışılmıştır. Düzeltilmiş tahmin edicilerin standart hata değerleri daha düşük elde edilmiştir.

Keywords

• Çok durumlu model
• geçiş olasılıkları
• yaşam çözümlemesi

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