Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
A Multi-State Markov Model for the Progression of Chronic Kidney Disease
Kronik Böbrek Hastalığının Progresyonunda Çok Durumlu Markov Modeli
Gurprit GROVERa, Alka SABHARWALb, Shrawan KUMARb, Arpan Kumar THAKURa
aDepartment of Statistics, University of Delhi,
bDepartment of Statistics, Kirori Mal College, University of Delhi, India
Turkiye Klinikleri J Biostat. 2019;11(1):1-14
doi: 10.5336/biostatic.2018-62156
Article Language: EN
Full Text
ABSTRACT
 Objective: The main goal of this study is to develop a stochastic model for the progression of Chronic Kidney Disease (CKD) into different stages based on estimated Glomerular Filtration Rate (eGFR). Material and Methods: The present study is a retrospective study of 117 patients suffering from CKD during the period March 2006 to October 2016. The prognostic factors such as gender, age, body mass index, diabetes, hypertension, hemoglobin, urea, serum creatinine, albumin and duration of the disease were recorded for each patient. We have applied the continuous time homogeneous multistate model based on Markov processes. The deterioration of disease is continuous in time and the probability of transition from one state to another state depends on the length of time and is independent of time on which transition takes place. Also, Cox proportional hazard model has been used to examine the effects of prognostic factors on the transition rates. Results: The probabilities of staying in the same state in first five years i.e. stage 1, stage2, stage 3, stage 4 and stage 5 are 0.6126, 0.5508, 0.5631, 0.0596 and 1 respectively. The probabilities of moving to the next state are also computed for first five and ten years. The prognostic factors age, hypertension, diabetes, hemoglobin, urea, serum creatinine are significant factors for the progression of CKD into different stages. Conclusions: The mean sojourn times along with p-next probabilities provide more intuitive parametric information of continuous time multistate model based on Markov processes than crude transition intensities.

Keywords: Chronic kidney disease; multi-state markov model; end stage renal disease; glomerular filtration rate; transition intensity
ÖZET
 Amaç: Bu çalışmanın amacı tahmin edilen Glomerüler filtrasyon hızına (eGFR) bağlı olarak kronik böbrek hastalığının (CKD) farklı evrelerdeki progresyonu için stokastik model geliştirmektir. Yöntem: Bu çalışma Mart 2006 - Ekim 2016 döneminde CKD geçiren 117 hastaya ait retrospektif bir çalışmadır. Her bir hastaya ait cinsiyet, yaş, beden kitle indeksi, diyabet, hipertansiyon, üre, serum kreatinin, albümin ve hastalık süresi gibi prognostik faktörler kaydedilmiştir. Markov süreçlerine göre sürekli zamanlı homojen çok durumlu model uyguladık. Zamana bağlı olarak hastalık sürekli kötüleşmekte ve durumlar arası geçiş olasılığı geçişin gerçekleştiği zamandan bağımsızdır. Ayrıca geçiş hızlarındaki prognostik faktör etkilerini incelemek için Cox orantısal hazard modeli kullanılmıştır. Bulgular: İlk beş yılda aynı evrede kalma olasılıkları örneğin evre 1, evre 2, evre 3, evre 4 ve evre 5 sırasıyla 0.6126, 0.5508, 0.5631, 0.0596 ve 1'dir. Bir sonraki duruma ilerleme olasılıkları da ilk beş ve on yıl için hesaplanmıştır. CKD progresyonunun farklı evrelerinde yaş, hipertansiyon, diyabet, hemoglobin, üre ve serum kreatinin anlamlı faktörler olarak bulunmuştur. Sonuç: p-sonraki olasılıklarla birlikte ortalama konukluk süreleri, Markov sürecine dayalı sürekli zaman çok durumlu modelinin sezgisel parametrik bilgisini ham geçiş yoğunluğundan daha fazla sağlamaktadır.

Anahtar Kelimeler: Kronik böbrek hastalığı; Çok durumlu Markov modeli; Son dönem böbrek hastalığı; Glomerüler filtrasyon hızı; Geçiş yoğunluğu
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