Monday, Aug 5: 2:00 PM - 3:50 PM
5066
Contributed Papers
Oregon Convention Center
Room: CC-G132
Main Sponsor
Lifetime Data Science Section
Presentations
Hazard ratios are often used to describe a treatment effect in randomized trials, but their causal interpretation is not straightforward. We discuss hazard ratios in the context of potential outcomes. We first review two classes of causal estimands. An individual-level estimand compares potential outcomes within each subject, then summarize those pairwise comparisons over the population. A population-level estimand summarizes the marginal distribution of each potential outcome first, then compares those marginal distributions. Difference-in-means estimands are both individual-level and population-level estimands, but hazard ratios are typically only population-level estimands. Practitioners rarely make a distinction between the two estimands, and as a result often confuse the causal meaning we can get from hazard ratio estimators from randomized trials. We argue that the population-level hazard ratio causal estimand is useful, but care must be made in its interpretation. This care is especially important when it appears that the hazard ratios are changing over time. We highlight this issue with an example interpreting COVID-19 vaccination efficacy over time.
Keywords
Cox regression
estimand
causal inference
randomized trial
proportional hazards
Co-Author
Fan Li, Yale School of Public Health
First Author
Michael Fay, National Institute of Allergy and Infectious Diseases
Presenting Author
Michael Fay, National Institute of Allergy and Infectious Diseases
Micro-randomized trials (MRTs) are commonly conducted for optimizing mobile health interventions such as push notifications for behavior change. In analyzing such trials, causal excursion effects are often of primary interest, and their estimation typically involves inverse probability weighting (IPW). However, in a MRT, additional treatments can often occur during the time window over which an outcome is defined, and this can greatly inflate the variance of the causal effect estimator because IPW would involve a product of numerous weights. To reduce variance and improve estimation efficiency, we propose a new estimator using a modified version of IPW, which we call "per-decision IPW". It is applicable when the outcome is binary and can be expressed as the maximum of a series of sub-outcomes defined over sub-intervals of time. We establish the estimator's consistency and asymptotic normality. Through simulation studies and real data applications, we demonstrate substantial efficiency improvement of the proposed estimator over existing estimators. The new estimator can be used to improve the precision of primary and secondary analyses for MRTs with binary outcomes.
Keywords
causal excursion effect
inverse probability weighting
log relative risk
micro-randomized trial
per-decision importance weighting
mobile health
Co-Author(s)
Lauren Bell, Medical Research Council Biostatistics Unit, University of Cambridge
Elizabeth Williamson, Department of Medical Statistics, London School of Hygiene and Tropical Medicine
Claire Garnett, Department of Behavioural Science and Health, University College London
Tianchen Qian, University of California, Irvine
First Author
Yihan Bao
Presenting Author
Yihan Bao
In a Cox model, the partial likelihood (PL), as the product of a series of conditional probabilities, is used to estimate the parameter. In practice, those conditional probabilities are approximated by risk score ratios based on a continuous time model, and thus result in parameter estimates from only an approximate PL. Through a revisit to the original PL idea, we propose an accurate PL computing method for the Cox model, which calculates the exact conditional probability using the Poisson binomial distribution (PBD). We develop new estimating and inference procedures and establish asymptotic theory for the new procedure. Although ties are common in real studies, current theory for the Cox model does not allow ties. In contrast, our new approach includes the theory for grouped data, which allows ties. Our theory for the new method is also valid for continuous data without ties, thus, providing a unified framework for computing PL for data with or without ties. From simulation and real applications in several datasets, we show that the proposed method is superior to current methods in reducing bias, especially when there are ties or when the variability in risk scores is large.
Keywords
Breslow Estimator
Efron Estimator
Survival Data with/without Ties
Kalbfleisch-Prentice Correction
Proportional Hazards Model
Period-prevalent cohorts are often used for their cost-saving potential in observational survival analyses. Under this design, prevalent patients allow for evaluations of long-term survival outcomes without the need for long follow-up windows, whereas incident patients allow for evaluations of short-term survival outcomes without the issue of left-truncation. In practice, most period-prevalent survival analyses are designed to achieve an overall target sample size, and there is no rigorous methodology available to quantify how the relative frequencies of prevalent and incident patients impact the efficiency of the estimation and inference. In response to this gap, we propose a new method to identify the optimal mix of prevalent and incident patients that maximizes precision over the estimated survival curve, subject to a flexible weighting scheme. In addition, we derive an analytic formula for the optimal incident patient proportion that maximizes the power of the weighted log-rank test and Cox model. Simulations confirm the validity of the optimization criteria and show that substantial efficiency gains are achieved by recruiting the optimal mix of prevalent and incident patients.
Keywords
Cox Proportional Hazards Model
Epidemiology
Kaplan-Meier Estimator
Left Truncation
Study Design
The nested case-control (NCC) design is useful in biomarker discovery for rare diseases, particularly when potential biomarkers may be difficult or expensive to collect. By including all events and a subsample of controls, the NCC design maximizes information while reducing the number of subjects requiring full covariate information. Because the NCC design uses fewer controls compared to the full cohort analysis, however, it also reduces the number of patients from underrepresented groups included in the sample, further exacerbating the issue of underrepresenation in clinical research. To help alleviate this problem, we propose a weighted NCC (WNCC) sampling design that allows for oversampling of subpopulations, thereby maximizing precision for estimated covariate effects in these subpopulations. We extend the Samuelsen estimator to correct for weighted sampling and propose corrected estimation and inferential methods when oversampling is based upon both binary and continuous covariates. We apply our proposed method to data from the NIH-funded National Alzheimer's Coordinating Center (NACC) where we consider differential associations between amyloid beta and the risk of Alzheimer's disease between Black and non-Black populations.
Keywords
survival analysis
efficient sampling
weighted sampling
effect modification
Alzheimer's disease
biomarkers
Nonproportionality can come from various sources under the Cox's model, and it is well known that omission of a balancing yet unobservable covariate could be one such cause. The nonproportionality could introduce a substantial bias in the main effect estimate in the model. The unobservable nonproportionality-inducing covariate could be a biomarker positivity, an overlooked binary stratification factor, or a continuous covariate as a strong prognostic factor whose distributions are also unbalanced between treatment groups. Frailty models have been utilized to derive the optimal weights for the weighted log-rank tests and also to quantify the bias in the estimators under Cox's model. We revisit the relevant literature on the topic of the frailty model and bias in the hazard ratio, extend the existing results, and propose a remedy to correct the bias partially.
Keywords
Bias
Proportional hazards model
Gamma frailty
Hazard ratio
Two-point frailty
First Author
Jong-Hyeon Jeong, National Institutes of Health/National Cancer Institute
Presenting Author
Jong-Hyeon Jeong, National Institutes of Health/National Cancer Institute
Multiple imputation is one of the most common approaches to analyze incomplete data. Additional challenges arise when missingness is observed in covariates collected longitudinally, and the outcome of interest is interval-censored event time. A complete case analysis will result in reduced efficiency and could even generate biased parameter estimates. This paper proposes a time-sequential imputation method based on the idea of fully conditional specification to multiply impute missing time-dependent covariates in studies with interval-censored outcomes. In addition to covariates of interest, the imputation model also utilizes cumulative hazard estimated iteratively, risk status, and observance of failure in subjects' subsequent visits. Extensive simulation studies demonstrated improved performance over existing methods with reduced bias, improved efficiency, and valid inference. The proposed method was applied to the cohort data from the Atherosclerosis Risk in Communities (ARIC) study to assess the risk of hypertension with potential predictors.
Keywords
Cohort studies
Fully conditional specification
Interval-censored
Missing data
Time-sequential