Markov models to estimate and describe survival time and experience in cohorts with high euthanasia frequency

Abstract

Unique to survival analysis of veterinary clinical data is classification of observations from euthanized animals. The first study highlighted limitations of Kaplan-Meier product limit analysis (KM) of veterinary clinical data. Three data sets with different outcome proportions (alive, lost-to-follow-up, dead due to disease, dead due to other, euthanized due to disease, euthanized due to other) were used. Different classifications of observations from euthanized animals caused inconsistent conclusions of significant differences between strata within data sets. At times, ranking of median survival time estimates for strata was reversed. The KM was found inappropriate to evaluate observations from euthanized animals. This finding, coupled with restriction of KM to two-state description of disease (alive to outcome), prompted exploration of an alternate analysis method. Markov models allow modeling of multiple health states and outcomes. A 5-state, time-homogeneous, Markov chain was used for a cohort of 64 dogs with generalized lymphoma. The model contained two transient (WELL, TOXIC) and three absorbing (DEAD, EUTHANASIA, LOST-TO-FOLLOWUP) states. The transition probability matrix (P) was used to iterate future transitions and survival probabilities. Matrix solution and Monte Carlo simulation were used to estimate survival time. Estimates appeared reliable. Markov modeling was extended for comparison of vaccine-associated sarcoma progression after treatment in a cohort of 294 cats. For a 5-state model, transition probabilities derived from exponential transformation of incidence rates were used to construct P for each treatment - NONE (no surgery), SX (surgery) and SX+RAD (surgery and radiation). Monte Carlo estimates of durations in transient states and expected survival showed SX+RAD prolonged expected survival significantly longer than SX than NONE. Commitment to repeated treatment with surgery and radiation did prolong expected survival of cats with vaccine-associated sarcoma. Assumptions of Markov modeling did not appear prohibitive for analysis of veterinary clinical data and further exploration is warranted.