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A joint QoL-Survival framework with debiased estimation under truncation by death

Torben Martinussen, Klaus K. Holst, Christian Bressen Pipper, Per Kragh Andersen

TL;DR

Addresses evaluation of QoL under truncation by death by proposing a joint QoL-survival framework that jointly describes survival and QoL distributions without imputing QoL after death. The method uses assumption-lean, semiparametric estimators based on efficient influence functions to yield root-n consistent, debiased estimates while allowing machine-learning-based nuisance estimation through cross-fitting. It represents the joint distribution via a simplex, reporting both survival probability and QoL-survival probabilities instead of a single summary. The approach is validated through simulations and two real-data applications, demonstrating unbiased, efficient inference and interpretable visualization of treatment effects on survival and QoL.

Abstract

Evaluating quality-of-life (QoL) outcomes in populations with high mortality risk is complicated by truncation by death, since QoL is undefined for individuals who do not survive to the planned measurement time. We propose a framework that jointly models the distribution of QoL and survival without extrapolating QoL beyond death. Inspired by multistate formulations, we extend the joint characterization of binary health states and mortality to continuous QoL outcomes. Because treatment effects cannot be meaningfully summarized in a single one-dimensional estimand without strong assumptions, our approach simultaneously considers both survival and the joint distribution of QoL and survival with the latter conveniently displayed in a simplex. We develop assumption-lean, semiparametric estimators based on efficient influence functions, yielding flexible, root-n consistent estimators that accommodate machine-learning methods while making transparent the conditions these must satisfy. The proposed method is illustrated through simulation studies and two real-data applications.

A joint QoL-Survival framework with debiased estimation under truncation by death

TL;DR

Addresses evaluation of QoL under truncation by death by proposing a joint QoL-survival framework that jointly describes survival and QoL distributions without imputing QoL after death. The method uses assumption-lean, semiparametric estimators based on efficient influence functions to yield root-n consistent, debiased estimates while allowing machine-learning-based nuisance estimation through cross-fitting. It represents the joint distribution via a simplex, reporting both survival probability and QoL-survival probabilities instead of a single summary. The approach is validated through simulations and two real-data applications, demonstrating unbiased, efficient inference and interpretable visualization of treatment effects on survival and QoL.

Abstract

Evaluating quality-of-life (QoL) outcomes in populations with high mortality risk is complicated by truncation by death, since QoL is undefined for individuals who do not survive to the planned measurement time. We propose a framework that jointly models the distribution of QoL and survival without extrapolating QoL beyond death. Inspired by multistate formulations, we extend the joint characterization of binary health states and mortality to continuous QoL outcomes. Because treatment effects cannot be meaningfully summarized in a single one-dimensional estimand without strong assumptions, our approach simultaneously considers both survival and the joint distribution of QoL and survival with the latter conveniently displayed in a simplex. We develop assumption-lean, semiparametric estimators based on efficient influence functions, yielding flexible, root-n consistent estimators that accommodate machine-learning methods while making transparent the conditions these must satisfy. The proposed method is illustrated through simulation studies and two real-data applications.
Paper Structure (12 sections, 2 theorems, 38 equations, 4 figures, 4 tables)

This paper contains 12 sections, 2 theorems, 38 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Quantifying treatment effects on survival and QoL jointly
  3. Preliminaries
  4. Binary marker
  5. Real-valued marker
  6. Debiased learning
  7. Robust estimation and large sample results
  8. Numerical studies
  9. Simulation study
  10. Application to A Southwest Oncology Trial
  11. Application to the FLOW clinical kidney outcome trial
  12. Concluding remarks

Key Result

Theorem 3.1

The efficient influence function of $\eta_1(y)$ w.r.t. the observed data law $P$ of $O=\{T_t^*=t\wedge T^*,\Delta_t=I(T\wedge t\leq C),I(t= T_t^*),Y I(t= T_t^*),A,L\}$, assuming $C\hbox{$\perp\!\!\!\perp$} \{T,YI(t<T)\}|A,L$, is where $\tilde{D}_{\eta_1}(O,P)$ is the debiasing term: with $S(r|A,L)=P(T>r|A,L)$, $K(r|A,L)=P(C>r|A,L)$, $H=SK$ and where $M_C(r|A,L)$ is the censoring martingale at ti

Figures (4)

  • Figure 1: Simplex summarizing $\{Q_0(t), Q_1(t), Q_D(t)\}$ for a fixed $t$.
  • Figure 2: Oncology Data. Simplex summarizing $(Q_0,Q_1,Q_D)$ along with 95% confidence region for the two treatments: docetaxel plus estramustine (steel blue) and mitoxantrone plus prednisone (light green).
  • Figure 3: Oncology Data. Plot of $\eta(t,y)$ with $t$ equal to 1 year versus $y$ corresponding to HRQoL values as observed in data ranging from 0 to 100 with 0 being poor HRQoL and 100 the highest HRQoL.
  • Figure 4: Kidney Data. Simplex summarizing $(Q_0,Q_1,Q_D)$ along with 95% confidence region for the two treatments: GLP-1 RA + standard of care (steel blue) and placebo + standard of care (light green)

Theorems & Definitions (2)

  • Theorem 3.1
  • Theorem 4.1