Fisher信息的一种分解方法以确定开发公平且精确的临床预测模型的样本量——第二部分：时间-事件结局
A decomposition of Fisher's information to inform sample size for developing fair and precise clinical prediction models -- Part 2: time-to-event outcomes
AI总结：
本研究提出分解Fisher信息矩阵的方法，以确定开发公平且精确的时间-事件结局临床预测模型所需的样本量，并通过六步流程和闭式解实现。该方法有助于提高个体预测的信任度、可靠性和公平性。
摘要：
背景：在利用时间-事件数据开发临床预测模型时，以往的研究侧重于最小化过拟合和精确估计总体风险的样本量。然而，个体水平风险估计的不稳定性可能仍然很大。方法：我们提出对Fisher信息矩阵进行分解，以检验和计算开发旨在获得精确且公平的风险估计的模型所需的样本量。我们提出了一个六步流程，可在数据收集前或已有数据集时使用。步骤(1)至(5)要求研究者指定目标人群在感兴趣的关键时间点的总体风险；一个假设的实用'核心模型'，形式为指数回归模型；该模型中包含的核心预测因子的（预期）联合分布；以及任何删失的分布。结果：我们推导出闭式解，将个体估计事件率的方差分解为Fisher单位信息矩阵、预测因子值和总样本量；这使得研究者能够计算和检验指定样本量下个体风险估计周围的 uncertainty 分布和误分类概率。我们提供了一个乳腺癌的示例，并强调了临床背景的重要性，包括用于决策的风险阈值，并检验了绝经前和绝经后女性的公平性问题。最后，在两项实证评估中，我们证明了基于我们方法的 uncertainty 区间宽度接近使用更灵活模型的结果。结论：我们的方法允许用户通过pmstabilityss模块识别开发时间-事件结局预测模型所需的（目标）样本量。它旨在促进在个体水平预测中具有改进的信任度、可靠性和公平性的模型。
英文摘要：
Background: When developing a clinical prediction model using time-to-event data, previous research focuses on the sample size to minimise overfitting and precisely estimate the overall risk. However, instability of individual-level risk estimates may still be large. Methods: We propose a decomposition of Fisher's information matrix to examine and calculate the sample size required for developing a model that aims for precise and fair risk estimates. We propose a six-step process which can be used before data collection or when an existing dataset is available. Steps (1) to (5) require researchers to specify the overall risk in the target population at a key time-point of interest; an assumed pragmatic 'core model' in the form of an exponential regression model; the (anticipated) joint distribution of core predictors included in that model; and the distribution of any censoring. Results: We derive closed-form solutions that decompose the variance of an individual's estimated event rate into Fisher's unit information matrix, predictor values and total sample size; this allows researchers to calculate and examine uncertainty distributions around individual risk estimates and misclassification probabilities for specified sample sizes. We provide an illustrative example in breast cancer and emphasise the importance of clinical context, including risk thresholds for decision making, and examine fairness concerns for pre- and post-menopausal women. Lastly, in two empirical evaluations, we provide reassurance that uncertainty interval widths based on our approach are close to using more flexible models. Conclusions: Our approach allows users to identify the (target) sample size required to develop a prediction model for time-to-event outcomes, via the pmstabilityss module. It aims to facilitate models with improved trust, reliability and fairness in individual-level predictions.
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