Effects of Categorizing Continuous Variables in Decision-Analytic Models
Faculty of Arts and Sciences, Harvard University, Cambridge, Massachusetts, USA. Medical Decision Making
(Impact Factor: 3.24).
08/2009; 29(5):549-56. DOI: 10.1177/0272989X09340238
When using continuous predictor variables in discrete-state Markov modeling, it is necessary to create categories of risk and assume homogeneous disease risk within categories, which may bias model outcomes. This analysis assessed the tradeoffs between model bias and complexity and/or data limitations when categorizing continuous risk factors in Markov models.
The authors developed a generic Markov cohort model of disease, defining bias as the percentage change in life expectancy gain from a hypothetical intervention when using 2 to 15 risk factor categories as compared with modeling the risk factor as a continuous variable. They evaluated the magnitude and sign of bias as a function of disease incidence, disease-specific mortality, and relative difference in risk among categories.
Bias was positive in the base case, indicating that categorization overestimated life expectancy gains. The bias approached zero as the number of risk factor categories increased and did not exceed 4% for any parameter combinations or numbers of categories considered. For any given disease-specific mortality and disease incidence, bias increased with relative risk of disease. For any given relative risk, the relationship between bias and parameters such as disease-specific mortality or disease incidence was not always monotonic.
Under the assumption of a normally distributed risk factor and reasonable assumption regarding disease risk and moderate values for the relative risk of disease given risk factor category, categorizing continuously valued risk factors in Markov models is associated with less than 4% absolute bias when at least 2 categories are used.
Available from: Tanya G K Bentley
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ABSTRACT: When using state-transition Markov models to simulate risk of recurrent events over time, incorporating dependence on higher numbers of prior episodes can increase model complexity, yet failing to capture this event history may bias model outcomes. This analysis assessed the tradeoffs between model bias and complexity when evaluating risks of recurrent events in Markov models.
The authors developed a generic episode/relapse Markov cohort model, defining bias as the percentage change in events prevented with 2 hypothetical interventions (prevention and treatment) when incorporating 0 to 9 prior episodes in relapse risk versus a model with 10 such episodes. Magnitude and sign of bias were evaluated as a function of event and recovery risks, disease-specific mortality, and risk function.
Bias was positive in the base case for a prevention strategy, indicating that failing to fully incorporate dependence on event history overestimated the prevention's predicted impact. For treatment, the bias was negative, indicating an underestimated benefit. Bias approached zero as the number of tracked prior episodes increased, and the average bias over 10 tracked episodes was greater with the exponential compared with linear functions of relapse risk and with treatment compared with prevention strategies. With linear and exponential risk functions, absolute bias reached 33% and 78%, respectively, in prevention and 52% and 85% in treatment.
Failing to incorporate dependence on prior event history in subsequent relapse risk in Markov models can greatly affect model outcomes, overestimating the impact of prevention and treatment strategies by up to 85% and underestimating the impact in some treatment models by up to 20%. When at least 4 prior episodes are incorporated, bias does not exceed 26% in prevention or 11% in treatment.
Medical Decision Making 12/2010; 30(6):651-60. DOI:10.1177/0272989X10363480 · 3.24 Impact Factor
Available from: Alison J. Hayes
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ABSTRACT: Recent studies have demonstrated that measures of health-related quality of life can predict complications and mortality in patients with diabetes, even after adjustment for clinical risk factors.
The authors developed a simulation model of disease progression in type 2 diabetes to investigate the impact of patient quality of life on lifetime outcomes and its potential response to therapy. Changes in health utility over time are captured as a result of complications and aging. All risk equations, model parameter estimates, and input data were derived from patient-level data from the Fenofibrate Intervention and Event Lowering in Diabetes (FIELD) trial.
Healthier patients with type 2 diabetes enjoy more life years, quality-adjusted life years (QALYs), and more life years free of complications. A 65-year-old patient at full health (utility = 1) can expect to live approximately 2 years longer and achieve 6 more QALYs than a patient at average health (utility = 0.8), given similar clinical risk factors. For patients with higher EQ-5D utility, the additional years lived without complications contribute more to longer life expectancy than years lived with complications.
The authors have developed a model for progression of disease in diabetes that has a number of novel features; it captures the observed relationships between measures of quality of life and future outcomes, the number of states have been minimized, and it can be parameterized with just 4 risk equations. Underlying the simple model structure is important patient-level heterogeneity in health and outcomes. The simulations suggest that differences in patients' EQ-5D utility can account for large differences in QALYs, which could be relevant in cost-utility analyses.
Medical Decision Making 06/2011; 31(4):559-70. DOI:10.1177/0272989X11409049 · 3.24 Impact Factor
Available from: ars.els-cdn.com
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ABSTRACT: State-transition modeling (STM) is an intuitive, flexible, and transparent approach of computer-based decision-analytic modeling, including both Markov model cohort simulation as well as individual-based (first-order Monte Carlo) microsimulation. Conceptualizing a decision problem in terms of a set of (health) states and transitions among these states, STM is one of the most widespread modeling techniques in clinical decision analysis, health technology assessment, and health-economic evaluation. STMs have been used in many different populations and diseases, and their applications range from personalized health care strategies to public health programs. Most frequently, state-transition models are used in the evaluation of risk factor interventions, screening, diagnostic procedures, treatment strategies, and disease management programs.
Medical Decision Making 09/2012; 32(5):690-700. DOI:10.1177/0272989X12455463 · 3.24 Impact Factor
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