Abstract
BackgroundMulti-state models are being increasingly used to capture complex disease pathways. The convenient formula of the exponential multi-state model can facilitate a quick and accessible understanding of the data. However, assuming time constant transition rates is not always plausible. On the other hand, obtaining predictions from a fitted model with time-dependent transitions can be challenging. One proposed solution is to utilise a general simulation algorithm to calculate predictions from a fitted multi-state model.MethodsPredictions obtained from an exponential multi-state model were compared to those obtained from two different parametric models and to non-parametric Aalen-Johansen estimates. The first comparative approach fitted a multi-state model with transition-specific distributions, chosen separately based on the Akaike Information Criterion. The second approach was a Royston-Parmar multi-state model with 4 degrees of freedom, which was chosen as a reference model flexible enough to capture complex hazard shapes. All quantities were obtained analytically for the exponential and Aalen-Johansen approaches. The transition rates for the two comparative approaches were also obtained analytically, while all other quantities were obtained from the fitted models via a general simulation algorithm. Metrics investigated were: transition probabilities, attributable mortality (AM), population attributable fraction (PAF) and expected length of stay. This work was performed on previously analysed hospital acquired infection (HAI) data. By definition, a HAI takes three days to develop and therefore selected metrics were also predicted from time 3 (delayed entry).ResultsDespite clear deviations from the constant transition rates assumption, the empirical estimates of the transition probabilities were approximated reasonably well by the exponential model. However, functions of the transition probabilities, e.g. AM and PAF, were not well approximated and the comparative models offered considerable improvements for these metrics. They also provided consistent predictions with the empirical estimates in the case of delayed entry time, unlike the exponential model.ConclusionWe conclude that methods and software are readily available for obtaining predictions from multi-state models that do not assume constant transition rates. The multistate package in Stata facilitates a range of predictions with confidence intervals, which can provide a more comprehensive understanding of the data. User-friendly code is provided.
Highlights
Multi-state models are being increasingly used to capture complex disease pathways
Data The analysis was performed on the publicly available los.data from the R package etm [24]. This is a sample from an observational cohort study conducted to analyse the burden of hospital acquired infection (HAI) in intensive care, see Beyersmann et al [29] for details. 756 patients were admitted to hospital. 632 patients did not acquire an infection during the study, of which 475 were discharged and 157 died. 124 patients did acquire an infection, of which 90 were discharged and 34 died
It was evident that the transition rates were not constant over time and transition 2 appeared to deviate most drastically from this assumption
Summary
Multi-state models are being increasingly used to capture complex disease pathways. The convenient formula of the exponential multi-state model can facilitate a quick and accessible understanding of the data. Multi-state models are being increasingly used to investigate complex disease pathways, for example, when interest lies in subsequent and/or intermediate events as well as a primary event This unified approach facilitates a better understanding of the whole disease profile and provides clinically relevant predictions, for example, transition probabilities and expected duration in each state. Available software includes: mstate in R [14] for semi- and non-parametric methods; msm in R [10] for exponential and piecewise exponential models; flexsurv in R [15] for fitting models and obtaining predictions by numerically solving the Kolmogorov forward equations; and flexsurv in R [15] or multistate in Stata [12] for the general simulation algorithm, the latter following model fitting by merlin [16, 17]
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