COUNTING PROCESS IN SURVIVAL ANALYSIS

Öz

The survival analysis is used to analyzing survival data which are measured from well defined starting point to the occurrence of well defined any event. Survival data are consisting of the survival times and they are frequently incomplete observations due to censoring. So, ordinary statistical methods cannot be used. The survival function and the hazard rate are two basic concepts to be explained in theory of survival analysis. There are many models with different properties to explain these concepts. In this study, in the context of counting process some models that are used in the survival analysis have been considered and basically have been explained hazard rate.

Anahtar Kelimeler

• Survival analysis
• hazard rate
• Cox’s model
• counting process
• additive hazards model
• multiplicative-additive hazards model
• frailty

SAYMA SÜREÇLERİYLE YAŞAM SÜRDÜRME ANALİZİ

Öz

Yaşam sürdürme analizi (survival analysis), iyi tanımlanmış bir başlangıç noktasından itibaren ölçülen ve önceden tanımlanmış herhangi bir olayın gerçekleşmesine kadar geçen zaman sürelerinden oluşan verinin analizinde kullanılmaktadır. Yaşam sürdürme zamanlarından oluşan yaşam sürdürme verisi, çoğu zaman durdurmaya (censoring) bağlı olarak tamamlanamamıştır ve bilinen istatistiksel yöntemler kullanılamamaktadır. Yaşam sürdürme fonksiyonu ve hazard hızı, bütün yaşam sürdürme analizi teorisinde açıklanmaya çalışılan iki temel kavram olmaktadır. Bu kavramları açıklamak üzere özellikleri birbirlerinden farklı pek çok model kurulmaktadır. Bu çalışmada, temel olarak hazard hızını modelleyen ve yaşam sürdürme analizinde yaygın olarak kullanılan bazı modeller sayma süreçleri çerçevesinde incelenmeye çalışılmıştır.

Anahtar Kelimeler

• Yaşam sürdürme analizi
• hazard hızı
• Cox model
• sayma süreci
• toplamsal hazard modeli
• çarpımsal-toplamsal hazard modeli
• kırılganlık

Kaynakça

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