Background and Objective <p>A primary elective total knee replacement is routinely used for patients with advanced osteoarthritis. Knee implants differ in characteristics (constraint, fixation, mobility), costs, need for revisions and other health outcomes, and so models evaluating their relative cost effectiveness are required to optimise decision making. Economic modelling approaches differ in complexity, the simplest in use being discrete time Markov models (DTMMs). Continuous-time Markov models (CTMMs) can capture transition timing in finer detail, and can more flexibly relax the constant hazard assumption. Multistate microsimulation can more easily capture patient history and time dependence. This paper aims to explore how the choice of modelling approach influences the cost effectiveness of various implant types for a total knee replacement. Based on the frequency of implant use in the National Joint Registry, 12 commonly used implants were included in the analysis.</p> Methods <p>We compared four different models of increasing complexity for male and female individuals in five age categories undergoing a total knee replacement. The DTMM and constant hazard CTMM assumed fixed revision probabilities over time. The individual-level CTMM with splines were semi-Markov, allowing time-varying rates of first revision surgery. The multistate microsimulation incorporated time-dependent splines for all revision rates but also dependence on time spent in previous health states. All revision rates were estimated using data from the National Joint Registry. The models were implemented using the <i>hesim</i> package in R.</p> Results <p>Under the constant hazard assumption, DTMM and CTMM yielded similar results, identifying the most commonly used implant as the most cost effective. However, using the spline-based hazard CTMM and patient history informed multistate microsimulation, other implants were identified as the most cost-effective options. The increased model complexity required high-performance computing facilities for CTMMs and multistate microsimulation.</p> Conclusions <p>This study shows that the choice of model can impact cost-effectiveness results. The multistate microsimulation model, which incorporates time-dependent transitions, provides a realistic representation of patient pathways over time, but is computationally complex and may be preferable only when time-varying risks are a key factor. The CTMM or DTMM models may be more efficient when data are limited or computational resources are constrained. Improving the accuracy and applicability of economic models can improve healthcare decision making. Future research should extend these methodologies to other disease areas, refine continuous-time models and explore their impact across diverse healthcare contexts.</p>