Biostatistics Research Group, Department of Health Sciences, University of Leicester, George Davies Centre, University Road, Leicester, LE1 7RH, UK.
Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Box 281, Stockholm, 17177, Sweden.
BMC Med Res Methodol. 2021 Jan 11;21(1):16. doi: 10.1186/s12874-020-01192-8.
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. 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.
Predictions 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).
Despite 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.
We 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.
多状态模型正越来越多地用于捕捉复杂的疾病途径。指数多状态模型的方便公式可以促进对数据的快速和易于理解。然而，假设时间不变的转移率并不总是合理的。另一方面，从具有时变转移的拟合模型中获得预测可能具有挑战性。一种提出的解决方案是利用通用模拟算法从拟合的多状态模型中计算预测。
比较了从指数多状态模型获得的预测值与从两个不同的参数模型和非参数 Aalen-Johansen 估计值获得的预测值。第一种比较方法拟合了具有特定于转移的分布的多状态模型，这些分布是根据赤池信息量准则（Akaike Information Criterion）分别选择的。第二种方法是具有 4 个自由度的 Royston-Parmar 多状态模型，该模型被选为足够灵活以捕捉复杂危险形状的参考模型。所有数量都是通过解析方法获得的，适用于指数和 Aalen-Johansen 方法。两个比较方法的转移率也是通过解析方法获得的，而所有其他数量都是通过通用模拟算法从拟合模型中获得的。研究的指标包括：转移概率、归因死亡率（Attributable Mortality，AM）、人群归因分数（Population Attributable Fraction，PAF）和预期住院时间（Length of Stay，LOS）。这项工作是在以前分析的医院获得性感染（Hospital Acquired Infection，HAI）数据上进行的。根据定义，HAI 需要三天才能发展，因此选择的指标也从时间 3（延迟进入）进行预测。
尽管与恒定转移率假设存在明显偏差，但指数模型对转移概率的经验估计值进行了合理的近似。然而，转移概率的函数，例如 AM 和 PAF，没有得到很好的近似，比较模型在这些指标上提供了很大的改进。它们还在延迟进入时间的情况下与经验估计值提供了一致的预测，而不像指数模型那样。
我们得出结论，有现成的方法和软件可用于从不假设恒定转移率的多状态模型中获得预测。Stata 中的多状态包方便了具有置信区间的各种预测，这可以提供对数据的更全面理解。提供了用户友好的代码。
