Clarify all-future model interpretation
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all_future_model_interpretation.tex
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all_future_model_interpretation.tex
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\documentclass[11pt]{ctexart}
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\usepackage[margin=1in]{geometry}
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\usepackage{amsmath, amssymb}
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\usepackage{booktabs}
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\usepackage{enumitem}
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\usepackage{hyperref}
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\title{Interpreting the All-Future DeepHealth Model\\
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all-future DeepHealth 模型的解释边界}
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\author{}
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\date{}
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\begin{document}
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\maketitle
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\begin{abstract}
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The all-future DeepHealth model should be interpreted as a
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history-conditioned incident disease and mortality risk model. At a query time
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\(t\), the hidden state \(h(t)\) summarizes the observed history up to that
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time, and the model estimates future first-occurrence risks for diseases in the
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model vocabulary, together with future mortality risk. The model does not
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directly estimate current clinical disease burden, organ damage, frailty,
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disease severity, recurrence risk, or disease-specific weights. Those
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quantities require labels, mappings, weights, or supervision that are not part
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of the present model.
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\medskip
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all-future DeepHealth 模型应被解释为一个基于既往轨迹的未来新发疾病和死亡风险模型。
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在查询时刻 \(t\)，隐含状态 \(h(t)\) 汇总了截至该时刻的已观测历史；模型输出的是
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模型词表内各疾病的未来首次发生风险，以及未来死亡风险。当前模型并不直接估计当前
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临床疾病负担、器官损伤、衰弱程度、疾病严重度、复发风险或疾病特异性权重。这些量
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都需要当前模型之外的标签、映射、权重或额外监督。
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\end{abstract}
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\section{English}
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\subsection{Model object}
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For individual \(i\), let \(\mathcal{H}_i(t)\) denote the observed history up to
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query time \(t\). The all-future model produces
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\[
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h_i(t) = f_\theta(\mathcal{H}_i(t)),
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\]
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and, for each disease token \(d\) in the modeled disease vocabulary
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\(\mathcal{D}\), estimates a future first-occurrence risk over a horizon
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\(\tau\):
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\[
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p_{i,d}(t,\tau)
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=
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P_\theta\!\left(T_{i,d}\in(t,t+\tau]\mid h_i(t)\right),
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\]
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where \(T_{i,d}\) is the first observed occurrence time of disease \(d\). If the
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model includes a death endpoint, it also estimates
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\[
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p_{i,\mathrm{death}}(t,\tau)
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=
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P_\theta\!\left(T_{i,\mathrm{death}}\in(t,t+\tau]\mid h_i(t)\right).
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\]
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The disease sequence is a first-occurrence sequence. Therefore, from the input
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history itself we know
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\[
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m_{i,d}(t)=\mathbf{1}\{T_{i,d}\le t\}.
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\]
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This historical indicator is not learned by the model; it is read directly from
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the event history.
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\subsection{Masking already occurred diseases}
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For a disease that has already occurred before or at \(t\), the model output for
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that disease should not be interpreted as recurrence risk or current disease
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activity. For future incident disease summaries, already occurred diseases
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should be masked:
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\[
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p^{\mathrm{new}}_{i,d}(t,\tau)
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=
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\left[1-m_{i,d}(t)\right]p_{i,d}(t,\tau).
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\]
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\subsection{Directly supported model-derived quantities}
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The current model directly supports the following quantities.
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\paragraph{Disease-specific future first-occurrence risk.}
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For each modeled disease \(d\),
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\[
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p^{\mathrm{new}}_{i,d}(t,\tau)
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\]
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is the estimated risk that disease \(d\) newly appears within the next
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\(\tau\) years, conditional on the history summarized by \(h_i(t)\).
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\paragraph{Future mortality risk.}
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\[
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p_{i,\mathrm{death}}(t,\tau)
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\]
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is the estimated probability of death within the next \(\tau\) years. Death is a
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terminal endpoint and should not be treated as an ordinary disease burden
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weight.
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\paragraph{Probability of being alive with no new modeled disease.}
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Using the model's disease-specific and death risks, one can summarize the
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probability of no new modeled disease and survival over the next \(\tau\) years:
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\[
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S^{\mathrm{all}}_i(t,\tau)
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=
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\left[1-p_{i,\mathrm{death}}(t,\tau)\right]
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\prod_{d\in\mathcal{D}}
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\left[1-p^{\mathrm{new}}_{i,d}(t,\tau)\right].
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\]
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Equivalently, if the model is represented through cumulative hazards
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\(\Lambda_{i,d}(t,\tau)=-\log[1-p_{i,d}(t,\tau)]\),
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\[
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S^{\mathrm{all}}_i(t,\tau)
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=
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\exp\left(
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-\Lambda_{i,\mathrm{death}}(t,\tau)
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-\sum_{d\in\mathcal{D}}
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[1-m_{i,d}(t)]\Lambda_{i,d}(t,\tau)
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\right).
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\]
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\paragraph{Probability of being alive with no new disease in a specified set.}
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For any analyst-specified subset of disease tokens \(G\subseteq\mathcal{D}\),
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\[
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S^{G}_i(t,\tau)
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=
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\left[1-p_{i,\mathrm{death}}(t,\tau)\right]
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\prod_{d\in G}
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\left[1-p^{\mathrm{new}}_{i,d}(t,\tau)\right].
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\]
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This is a subset-level future disease-free survival summary. If \(G\) is called
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an organ system, the disease-to-organ grouping is external to the model and
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must not be described as a learned organ score.
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\subsection{Historical counts are not model-derived burden}
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One may count observed historical diseases:
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\[
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B^{\mathrm{history}}_i(t)
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=
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\sum_{d\in\mathcal{D}}m_{i,d}(t).
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\]
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This quantity is a direct count from the input sequence. It does not require the
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model and should not be presented as a model-derived disease burden score.
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Without disease severity labels or disease weights, it treats all disease
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tokens equally.
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\subsection{What the current model does not estimate}
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The current model does not directly estimate:
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\begin{itemize}[leftmargin=1.5em]
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\item current clinical disease burden;
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\item organ damage, organ age, or organ functional reserve;
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\item frailty or frailty weights;
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\item severity of a newly diagnosed disease;
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\item recurrence risk after first occurrence;
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\item relative clinical importance of different disease tokens.
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\end{itemize}
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These interpretations require additional labels, mappings, weights, or model
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training objectives. Using the present all-future model to claim these
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quantities would be over-interpretation.
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\subsection{Post-onset prognosis for the same new disease}
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For a disease \(d\) that newly occurs at time \(T_{i,d}\), the model cannot
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infer the clinical severity of that disease itself. However, after the disease
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has entered the history, one may query the model again and compare subsequent
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future risks:
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\[
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p^{\mathrm{new}}_{i,e}(T_{i,d},\tau),\quad e\ne d,
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\qquad
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p_{i,\mathrm{death}}(T_{i,d},\tau).
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\]
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This supports a prognosis-oriented statement: the same incident diagnosis may
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be followed by different future disease and mortality risk profiles in people
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with different prior trajectories. It should not be described as direct disease
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severity.
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\subsection{Future extension with reliable recurrence data}
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The above interpretation is constrained by the first-occurrence nature of the
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current disease sequence. UK Biobank does not provide a reliable longitudinal
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record of disease recurrence, relapse, repeated admissions, treatment
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escalation, or episode-level severity for the modeled disease tokens. Therefore,
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the present model cannot be used to estimate recurrence risk or ongoing disease
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activity after first onset.
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If reliable recurrence or repeated-event data were available, one could define a
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different modeling target. Let \(N_{i,d}(t)\) be the counting process for all
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episodes of disease \(d\), not only its first occurrence. A recurrence-aware
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model could estimate the future increment
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\[
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P_\theta\!\left(N_{i,d}(t+\tau)-N_{i,d}(t)>0 \mid h_i(t)\right),
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\]
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or the expected number of future episodes
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\[
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E_\theta\!\left[N_{i,d}(t+\tau)-N_{i,d}(t)\mid h_i(t)\right].
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\]
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For individuals with \(m_{i,d}(t)=1\), this would support a genuine
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post-onset interpretation of future recurrence or disease activity. For
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individuals with \(m_{i,d}(t)=0\), it would remain an incident disease risk.
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With such data, the model could also separate three clinically different
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quantities:
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\begin{itemize}[leftmargin=1.5em]
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\item incident risk: the first future onset of a disease not yet observed;
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\item recurrence or repeated-event risk: future episodes after a disease has
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already occurred;
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\item mortality risk: a terminal endpoint that competes with future
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non-fatal events.
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\end{itemize}
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If recurrence episodes were linked to reliable episode-level severity labels,
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such as hospitalization intensity, treatment escalation, or validated severity
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grades, then a further supervised model could learn severity-aware prognosis.
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These extensions would require new data and new training targets; they are not
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available from the current all-future first-occurrence model.
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\section{中文}
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\subsection{模型对象}
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对于个体 \(i\)，令 \(\mathcal{H}_i(t)\) 表示查询时刻 \(t\) 之前已经观测到的历史。
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all-future 模型产生
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\[
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h_i(t)=f_\theta(\mathcal{H}_i(t)),
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\]
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并且对模型疾病词表 \(\mathcal{D}\) 中的每个疾病 \(d\)，估计未来 \(\tau\) 年内的首次
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发生风险：
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\[
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p_{i,d}(t,\tau)
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=
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P_\theta\!\left(T_{i,d}\in(t,t+\tau]\mid h_i(t)\right),
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\]
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其中 \(T_{i,d}\) 是疾病 \(d\) 的首次观测发生时间。如果模型包含死亡终点，则同时估计
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\[
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p_{i,\mathrm{death}}(t,\tau)
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=
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P_\theta\!\left(T_{i,\mathrm{death}}\in(t,t+\tau]\mid h_i(t)\right).
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\]
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当前疾病序列是 first-occurrence 序列。因此，从输入历史本身即可得到
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\[
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m_{i,d}(t)=\mathbf{1}\{T_{i,d}\le t\}.
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\]
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这个历史发生指示量不是模型学出来的，而是直接从事件历史中读出的。
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\subsection{已经发生疾病的 mask}
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如果某个疾病在 \(t\) 之前或 \(t\) 时已经发生，那么该疾病对应的模型输出不应解释为复发
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风险，也不应解释为当前疾病活跃程度。在汇总未来新发疾病风险时，应对已经发生过的疾病
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进行 mask：
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\[
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p^{\mathrm{new}}_{i,d}(t,\tau)
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=
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\left[1-m_{i,d}(t)\right]p_{i,d}(t,\tau).
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\]
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\subsection{当前模型直接支持的派生量}
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当前模型直接支持以下几类量。
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\paragraph{疾病层面的未来首次发生风险。}
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对每个模型内疾病 \(d\)，
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\[
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p^{\mathrm{new}}_{i,d}(t,\tau)
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\]
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表示在 \(h_i(t)\) 所总结的历史条件下，疾病 \(d\) 在未来 \(\tau\) 年内新发生的风险。
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\paragraph{未来死亡风险。}
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\[
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p_{i,\mathrm{death}}(t,\tau)
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\]
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表示未来 \(\tau\) 年内死亡的概率。死亡是终末结局，不应作为普通疾病负担权重加入疾病
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负担求和。
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\paragraph{未来无新病且存活的概率。}
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利用疾病层面风险和死亡风险，可以汇总未来 \(\tau\) 年内无任何模型内新病且存活的概率：
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\[
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S^{\mathrm{all}}_i(t,\tau)
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=
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\left[1-p_{i,\mathrm{death}}(t,\tau)\right]
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\prod_{d\in\mathcal{D}}
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\left[1-p^{\mathrm{new}}_{i,d}(t,\tau)\right].
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\]
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如果用累计 hazard 表示，令
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\(\Lambda_{i,d}(t,\tau)=-\log[1-p_{i,d}(t,\tau)]\)，则
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\[
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S^{\mathrm{all}}_i(t,\tau)
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=
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\exp\left(
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-\Lambda_{i,\mathrm{death}}(t,\tau)
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-\sum_{d\in\mathcal{D}}
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[1-m_{i,d}(t)]\Lambda_{i,d}(t,\tau)
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\right).
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\]
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\paragraph{未来无指定疾病集合新发且存活的概率。}
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对于任意由分析者预先指定的疾病 token 集合 \(G\subseteq\mathcal{D}\)，可以定义
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\[
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S^{G}_i(t,\tau)
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=
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\left[1-p_{i,\mathrm{death}}(t,\tau)\right]
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\prod_{d\in G}
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\left[1-p^{\mathrm{new}}_{i,d}(t,\tau)\right].
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\]
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这只是指定疾病集合层面的未来 disease-free survival 汇总。如果将 \(G\) 称为某个器官系统，
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那么疾病到器官的分组来自模型外部，不能描述为模型学到的器官评分。
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\subsection{历史计数不是模型派生的疾病负担}
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可以计算历史已经发生过多少个模型内疾病：
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\[
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B^{\mathrm{history}}_i(t)
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=
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\sum_{d\in\mathcal{D}}m_{i,d}(t).
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\]
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但这个量只是从输入序列直接计数，不需要模型，因此不应表述为模型派生的疾病负担评分。
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在没有疾病严重度标签或疾病权重时，它默认所有疾病 token 等价。
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\subsection{当前模型不能估计什么}
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当前模型不能直接估计：
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\begin{itemize}[leftmargin=1.5em]
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\item 当前临床疾病负担；
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\item 器官损伤、器官年龄或器官功能储备；
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\item 衰弱程度或衰弱权重；
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\item 某个新发疾病本身的严重程度；
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\item 首次发生后的复发风险；
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\item 不同疾病 token 之间的相对临床重要性。
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\end{itemize}
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这些解释都需要额外标签、映射、权重或新的训练目标。用当前 all-future 模型直接声称这些量，
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属于过分解读。
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\subsection{同一新发疾病后的预后差异}
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对于在 \(T_{i,d}\) 时刻新发生的疾病 \(d\)，模型不能推断这个疾病本身的临床严重程度。
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但是，当该疾病已经进入历史之后，可以再次查询模型，并比较之后的未来风险：
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\[
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p^{\mathrm{new}}_{i,e}(T_{i,d},\tau),\quad e\ne d,
|
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\qquad
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p_{i,\mathrm{death}}(T_{i,d},\tau).
|
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\]
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这支持一种预后层面的表述：同一个新发诊断出现在不同既往轨迹的人身上，可能对应不同的
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后续新病和死亡风险结构。但这不应被表述为模型直接判断了疾病严重度。
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\subsection{如果有可靠复发数据，未来可以做什么}
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上述解释受到当前 first-occurrence 疾病序列的限制。UK Biobank 并没有为模型词表中的
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疾病提供可靠的纵向复发、复燃、重复住院、治疗升级或 episode 层面严重程度记录。因此，
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当前模型不能用于估计首次发病后的复发风险或持续疾病活动。
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如果未来有可靠的复发或重复事件数据，可以定义一个不同的建模目标。令 \(N_{i,d}(t)\)
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表示疾病 \(d\) 的所有事件计数过程，而不只是首次发生。一个考虑复发的模型可以估计未来
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事件增量：
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||||
\[
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P_\theta\!\left(N_{i,d}(t+\tau)-N_{i,d}(t)>0 \mid h_i(t)\right),
|
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\]
|
||||
或者估计未来事件次数的期望：
|
||||
\[
|
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E_\theta\!\left[N_{i,d}(t+\tau)-N_{i,d}(t)\mid h_i(t)\right].
|
||||
\]
|
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对于 \(m_{i,d}(t)=1\) 的个体，这才可以支持真正的发病后复发风险或疾病活动解释；对于
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\(m_{i,d}(t)=0\) 的个体，它仍然对应未来首次发病风险。
|
||||
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在这样的数据条件下，模型可以区分三个临床上不同的量：
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\begin{itemize}[leftmargin=1.5em]
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||||
\item 新发风险：尚未发生疾病的未来首次发生风险；
|
||||
\item 复发或重复事件风险：疾病已经发生后的未来 episode 风险；
|
||||
\item 死亡风险：与非致死事件竞争的终末结局风险。
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\end{itemize}
|
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如果复发 episode 还带有可靠的 episode 层面严重程度标签，例如住院强度、治疗升级或经过
|
||||
验证的严重程度分级，那么还可以进一步训练有监督的严重程度相关预后模型。但这些扩展都
|
||||
需要新的数据和新的训练目标，并不是当前 all-future first-occurrence 模型已经具备的能力。
|
||||
|
||||
\section{Recommended wording}
|
||||
|
||||
\paragraph{English.}
|
||||
The all-future model is a history-conditioned incident disease and mortality
|
||||
risk model. Its outputs support future disease-free survival summaries over the
|
||||
modeled disease vocabulary, but do not directly quantify current disease
|
||||
burden, organ damage, frailty, or disease severity.
|
||||
|
||||
\paragraph{中文。}
|
||||
all-future 模型是基于既往轨迹的未来新发疾病和死亡风险模型。它的输出可以支持模型词表
|
||||
范围内的未来无新病且存活概率汇总，但不能直接量化当前疾病负担、器官损伤、衰弱程度或
|
||||
疾病严重度。
|
||||
|
||||
\end{document}
|
||||
Reference in New Issue
Block a user