On the role of Volterra integral equations in self-consistent, product-limit, inverse probability of censoring weighted, and redistribution-to-the-right estimators for the survival function.

This paper reconsiders several results of historical and current importance to nonparametric estimation of the survival distribution for failure in the presence of right-censored observation times, demonstrating in particular how Volterra integral equations help inter-connect the resulting estimators. The paper begins by considering Efron's self-consistency equation, introduced in a seminal 1967 Berkeley symposium paper. Novel insights provided in the current work include the observations that (i) the self-consistency equation leads directly to an anticipating Volterra integral equation whose solution is given by a product-limit estimator for the censoring survival function; (ii) a definition used in this argument immediately establishes the familiar product-limit estimator for the failure survival function; (iii) the usual Volterra integral equation for the product-limit estimator of the failure survival function leads to an immediate and simple proof that it can be represented as an inverse probability of censoring weighted estimator; (iv) a simple identity characterizes the relationship between natural inverse probability of censoring weighted estimators for the survival and distribution functions of failure; (v) the resulting inverse probability of censoring weighted estimators, attributed to a highly influential 1992 paper of Robins and Rotnitzky, were implicitly introduced in Efron's 1967 paper in its development of the redistribution-to-the-right algorithm. All results developed herein allow for ties between failure and/or censored observations.

Confounding-adjustment methods for the causal difference in medians.

BACKGROUND: With continuous outcomes, the average causal effect is typically defined using a contrast of expected potential outcomes. However, in the presence of skewed outcome data, the expectation (population mean) may no longer be meaningful. In practice the typical approach is to continue defining the estimand this way or transform the outcome to obtain a more symmetric distribution, although neither approach may be entirely satisfactory. Alternatively the causal effect can be redefined as a contrast of median potential outcomes, yet discussion of confounding-adjustment methods to estimate the causal difference in medians is limited. In this study we described and compared confounding-adjustment methods to address this gap. METHODS: The methods considered were multivariable quantile regression, an inverse probability weighted (IPW) estimator, weighted quantile regression (another form of IPW) and two little-known implementations of g-computation for this problem. Methods were evaluated within a simulation study under varying degrees of skewness in the outcome and applied to an empirical study using data from the Longitudinal Study of Australian Children. RESULTS: Simulation results indicated the IPW estimator, weighted quantile regression and g-computation implementations minimised bias across all settings when the relevant models were correctly specified, with g-computation additionally minimising the variance. Multivariable quantile regression, which relies on a constant-effect assumption, consistently yielded biased results. Application to the empirical study illustrated the practical value of these methods. CONCLUSION: The presented methods provide appealing avenues for estimating the causal difference in medians.

Discussion on "Instrumental variable estimation of the causal hazard ratio," by Linbo Wang, Eric Tchetgen Tchetgen, Torben Martinussen, and Stijn Vansteelandt.

We propose and study an augmented variant of the estimator proposed by Wang, Tchetgen Tchetgen, Martinussen, and Vansteelandt.

Assessing the robustness of results from clinical trials and meta-analyses with the fragility index.

The fragility index has been increasingly used to assess the robustness of the results of clinical trials since 2014. It aims at finding the smallest number of event changes that could alter originally statistically significant results. Despite its popularity, some researchers have expressed several concerns about the validity and usefulness of the fragility index. It offers a comprehensive review of the fragility index's rationale, calculation, software, and interpretation, with emphasis on application to studies in obstetrics and gynecology. This article presents the fragility index in the settings of individual clinical trials, standard pairwise meta-analyses, and network meta-analyses. Moreover, this article provides worked examples to demonstrate how the fragility index can be appropriately calculated and interpreted. In addition, the limitations of the traditional fragility index and some solutions proposed in the literature to address these limitations were reviewed. In summary, the fragility index is recommended to be used as a supplemental measure in the reporting of clinical trials and a tool to communicate the robustness of trial results to clinicians. Other considerations that can aid in the fragility index's interpretation include the loss to follow-up and the likelihood of data modifications that achieve the loss of statistical significance.

Assessing mortality differences across acute respiratory failure management strategies in Covid-19.

PURPOSE: Prolonged observation could avoid invasive mechanical ventilation (IMV) and related risks in patients with Covid-19 acute respiratory failure (ARF) compared to initiating early IMV. We aimed to determine the association between ARF management strategy and in-hospital mortality. MATERIALS AND METHODS: Patients in the Weill Cornell Covid-19 registry who developed ARF between March 5 - March 25, 2020 were exposed to an early IMV strategy; between March 26 - April 1, 2020 to an intermediate strategy; and after April 2 to prolonged observation. Cox proportional hazards regression was used to model in-hospital mortality and test an interaction between ARF management strategy and modified sequential organ failure assessment (mSOFA). RESULTS: Among 632 patients with ARF, 24% of patients in the early IMV strategy died versus 28% in prolonged observation. At lower mSOFA, prolonged observation was associated with lower mortality compared to early IMV (at mSOFA = 0, HR 0.16 [95% CI 0.04-0.57]). Mortality risk increased in the prolonged observation strategy group with each point increase in mSOFA score (HR 1.29 [95% CI 1.10-1.51], p = 0.002). CONCLUSION: In Covid-19 ARF, prolonged observation was associated with a mortality benefit at lower mSOFA scores, and increased mortality at higher mSOFA scores compared to early IMV.

Collective effects of human genomic variation on microbiome function.

Studies of the impact of host genetics on gut microbiome composition have mainly focused on the impact of individual single nucleotide polymorphisms (SNPs) on gut microbiome composition, without considering their collective impact or the specific functions of the microbiome. To assess the aggregate role of human genetics on the gut microbiome composition and function, we apply sparse canonical correlation analysis (sCCA), a flexible, multivariate data integration method. A critical attribute of metagenome data is its sparsity, and here we propose application of a Tweedie distribution to accommodate this. We use the TwinsUK cohort to analyze the gut microbiomes and human variants of 250 individuals. Sparse CCA, or sCCA, identified SNPs in microbiome-associated metabolic traits (BMI, blood pressure) and microbiome-associated disorders (type 2 diabetes, some neurological disorders) and certain cancers. Both common and rare microbial functions such as secretion system proteins or antibiotic resistance were found to be associated with host genetics. sCCA applied to microbial species abundances found known associations such as Bifidobacteria species, as well as novel associations. Despite our small sample size, our method can identify not only previously known associations, but novel ones as well. Overall, we present a new and flexible framework for examining host-microbiome genetic interactions, and we provide a new dimension to the current debate around the role of human genetics on the gut microbiome.

Fragility indices for only sufficiently likely modifications.

The fragility index is a clinically meaningful metric based on modifying patient outcomes that is increasingly used to interpret the robustness of clinical trial results. The fragility index relies on a concept that explores alternative realizations of the same clinical trial by modifying patient measurements. In this article, we propose to generalize the fragility index to a family of fragility indices called the incidence fragility indices that permit only outcome modifications that are sufficiently likely and provide an exact algorithm to calculate the incidence fragility indices. Additionally, we introduce a far-reaching generalization of the fragility index to any data type and explain how to permit only sufficiently likely modifications for nondichotomous outcomes. All of the proposed methodologies follow the fragility index concept.

Changes in SARS-CoV-2 viral load and mortality during the initial wave of the pandemic in New York City.

Public health interventions such as social distancing and mask wearing decrease the incidence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, but it is unclear whether they decrease the viral load of infected patients and whether changes in viral load impact mortality from coronavirus disease 2019 (COVID-19). We evaluated 6923 patients with COVID-19 at six New York City hospitals from March 15-May 14, 2020, corresponding with the implementation of public health interventions in March. We assessed changes in cycle threshold (CT) values from reverse transcription-polymerase chain reaction tests and in-hospital mortality and modeled the impact of viral load on mortality. Mean CT values increased between March and May, with the proportion of patients with high viral load decreasing from 47.7% to 7.8%. In-hospital mortality increased from 14.9% in March to 28.4% in early April, and then decreased to 8.7% by May. Patients with high viral loads had increased mortality compared to those with low viral loads (adjusted odds ratio 2.34). If viral load had not declined, an estimated 69 additional deaths would have occurred (5.8% higher mortality). SARS-CoV-2 viral load steadily declined among hospitalized patients in the setting of public health interventions, and this correlated with decreases in mortality.

On clinical trial fragility due to patients lost to follow up.

BACKGROUND: Clinical trials routinely have patients lost to follow up. We propose a methodology to understand their possible effect on the results of statistical tests by altering the concept of the fragility index to treat the outcomes of observed patients as fixed but incorporate the potential outcomes of patients lost to follow up as random and subject to modification. METHODS: We reanalyse the statistical results of three clinical trials on coronary artery bypass grafting (CABG) to study the possible effect of patients lost to follow up on the treatment effect statistical significance. To do so, we introduce the LTFU-aware fragility indices as a measure of the robustness of a clinical trial's statistical results with respect to patients lost to follow up. RESULTS: The analyses illustrate that clinical trials can either be completely robust to the outcomes of patients lost to follow up, extremely sensitive to the outcomes of patients lost to follow up, or in an intermediate state. When a clinical trial is in an intermediate state, the LTFU-aware fragility indices provide an interpretable measure to quantify the degree of fragility or robustness. CONCLUSIONS: The LTFU-aware fragility indices allow researchers to rigorously explore the outcomes of patients who are lost to follow up, when their data is the appropriate kind. The LTFU-aware fragility indices are sensitivity measures in a way that the original fragility index is not.

The fragility index can be used for sample size calculations in clinical trials.

OBJECTIVE: The fragility index is a clinically interpretable metric increasingly used to interpret the robustness of clinical trials results that is generally not incorporated in sample size calculation and applied post-hoc. In this manuscript, we propose to base the sample size calculation on the fragility index in a way that supplements the classical prefixed alpha and power cutoffs and we provide a dedicated R software package for the design and analysis tools. STUDY DESIGN AND SETTING: This approach follows from a novel hypothesis testing framework that is based on the fragility index and builds on the classical testing approach. As case studies, we re-analyse the design of two important trials in cardiovascular medicine, the FAME and FAMOUS-NSTEMI trials. RESULTS: The analyses show that approach returns sample sizes which results in a higher power for the P value based test and most importantly a lower and context dependent Type I error rate for the fragility index based test compared to standard tests. CONCLUSION: Our method allows clinicians to control for the fragility index during clinical trial design.