Designing a Bayesian adaptive clinical trial to evaluate novel mechanical ventilation strategies in acute respiratory failure using integrated nested Laplace approximations

BACKGROUND

Adaptive trials usually require simulations to determine values for design parameters, demonstrate error rates, and establish the sample size. We designed a Bayesian adaptive trial comparing ventilation strategies for patients with acute hypoxemic respiratory failure using simulations. The complexity of the analysis would usually require computationally expensive Markov Chain Monte Carlo methods but this barrier to simulation was overcome using the Integrated Nested Laplace Approximations (INLA) algorithm to provide fast, approximate Bayesian inference.

METHODS

We simulated two-arm Bayesian adaptive trials with equal randomization that stratified participants into two disease severity states. The analysis used a proportional odds model, fit using INLA. Trials were stopped based on pre-specified posterior probability thresholds for superiority or futility, separately for each state. We calculated the type I error and power across 64 scenarios that varied the probability thresholds and the initial minimum sample size before commencing adaptive analyses. Two designs that maintained a type I error below 5%, a power above 80%, and a feasible mean sample size were evaluated further to determine the optimal design.

RESULTS

Power generally increased as the initial sample size and the futility threshold increased. The chosen design had an initial recruitment of 500 and a superiority threshold of 0.9925, and futility threshold of 0.95. It maintained high power and was likely to reach a conclusion before exceeding a feasible sample size.

CONCLUSIONS

We designed a Bayesian adaptive trial to evaluate novel strategies for ventilation using the INLA algorithm to efficiently evaluate a wide range of designs through simulation.

Statistical analyses of ordinal outcomes in randomised controlled trials: a scoping review

BACKGROUND

Randomised controlled trials (RCTs) aim to estimate the causal effect of one or more interventions relative to a control. One type of outcome that can be of interest in an RCT is an ordinal outcome, which is useful to answer clinical questions regarding complex and evolving patient states. The target parameter of interest for an ordinal outcome depends on the research question and the assumptions the analyst is willing to make. This review aimed to provide an overview of how ordinal outcomes have been used and analysed in RCTs.

METHODS

The review included RCTs with an ordinal primary or secondary outcome published between 2017 and 2022 in four highly ranked medical journals (the British Medical Journal, New England Journal of Medicine, The Lancet, and the Journal of the American Medical Association) identified through PubMed. Details regarding the study setting, design, the target parameter, and statistical methods used to analyse the ordinal outcome were extracted.

RESULTS

The search identified 309 studies, of which 144 were eligible for inclusion. The most used target parameter was an odds ratio, reported in 78 (54%) studies. The ordinal outcome was dichotomised for analysis in 47 ( 33 % ) studies, and the most common statistical model used to analyse the ordinal outcome on the full ordinal scale was the proportional odds model (64 [ 44 % ] studies). Notably, 86 (60%) studies did not explicitly check or describe the robustness of the assumptions for the statistical method(s) used.

CONCLUSIONS

The results of this review indicate that in RCTs that use an ordinal outcome, there is variation in the target parameter and the analytical approaches used, with many dichotomising the ordinal outcome. Few studies provided assurance regarding the appropriateness of the assumptions and methods used to analyse the ordinal outcome. More guidance is needed to improve the transparent reporting of the analysis of ordinal outcomes in future trials.

Efficiency of the Breslow estimator in semiparametric transformation models

Semiparametric transformation models for failure time data consist of a parametric regression component and an unspecified cumulative baseline hazard. The nonparametric maximum likelihood estimator (NPMLE) of the cumulative baseline hazard can be summarized in terms of weights introduced into a Breslow-type estimator (Weighted Breslow). At any given time point, the weights invoke an integral over the future of the cumulative baseline hazard, which presents theoretical and computational challenges. A simpler non-MLE Breslow-type estimator (Breslow) was derived earlier from a martingale estimating equation (MEE) setting observed and expected counts of failures equal, conditional on the past history. Despite much successful theoretical and computational development, the simpler Breslow estimator continues to be commonly used as a compromise between simplicity and perceived loss of full efficiency. In this paper we derive the relative efficiency of the Breslow estimator and consider the properties of the two estimators using simulations and real data on prostate cancer survival.

VGLM proportional odds model to infer hosts' Airbnb performance

We investigated aspects of host activities that influence and enhance host performance in an effort to achieve best results in terms of the occupancy rate and the overall rating. The occupancy rate measures the percentage of reserved days with respect to available days. The overall rating identifies the satisfaction level of guests that booked an Airbnb accommodation. We used the proportional odds model to estimate the impact of the managerial variables and the characteristics of the accommodation on host performance. Five different levels of the occupancy and the overall rating were investigated to understand which features impact them and support the effort to move from the lowest to the highest level. The analysis was carried out for Italy's most visited cities: Rome, Milan, Venice, and Florence. We focused on the year 2016. Moreover, we investigated different impact levels in terms of the overall rating during the COVID-19 pandemic to evaluate possible differences. Our findings show the relevance of some variables, such as the number of reviews, services, and typology of the rented accommodation. Moreover, the results show differences among cities and in time for the relevant impact of the COVID-19 pandemic.

Bias correction via outcome reassignment for cross-sectional data with binary disease outcome

Cross-sectionally sampled data with binary disease outcome are commonly analyzed in observational studies to identify the relationship between covariates and disease outcome. A cross-sectional population is defined as a population of living individuals at the sampling or observational time. It is generally understood that binary disease outcome from cross-sectional data contains less information than longitudinally collected time-to-event data, but there is insufficient understanding as to whether bias can possibly exist in cross-sectional data and how the bias is related to the population risk of interest. Wang and Yang (2021) presented the complexity and bias in cross-sectional data with binary disease outcome with detailed analytical explorations into the data structure. As the distribution of the cross-sectional binary outcome is quite different from the population risk distribution, bias can arise when using cross-sectional data analysis to draw inference for population risk. In this paper we argue that the commonly adopted age-specific risk probability is biased for the estimation of population risk and propose an outcome reassignment approach which reassigns a portion of the observed binary outcome, 0 or 1, to the other disease category. A sign test and a semiparametric pseudo-likelihood method are developed for analyzing cross-sectional data using the OR approach. Simulations and an analysis based on Alzheimer's Disease data are presented to illustrate the proposed methods.

Semi-supervised approach to event time annotation using longitudinal electronic health records

Large clinical datasets derived from insurance claims and electronic health record (EHR) systems are valuable sources for precision medicine research. These datasets can be used to develop models for personalized prediction of risk or treatment response. Efficiently deriving prediction models using real world data, however, faces practical and methodological challenges. Precise information on important clinical outcomes such as time to cancer progression are not readily available in these databases. The true clinical event times typically cannot be approximated well based on simple extracts of billing or procedure codes. Whereas, annotating event times manually is time and resource prohibitive. In this paper, we propose a two-step semi-supervised multi-modal automated time annotation (MATA) method leveraging multi-dimensional longitudinal EHR encounter records. In step I, we employ a functional principal component analysis approach to estimate the underlying intensity functions based on observed point processes from the unlabeled patients. In step II, we fit a penalized proportional odds model to the event time outcomes with features derived in step I in the labeled data where the non-parametric baseline function is approximated using B-splines. Under regularity conditions, the resulting estimator of the feature effect vector is shown as root-n consistent. We demonstrate the superiority of our approach relative to existing approaches through simulations and a real data example on annotating lung cancer recurrence in an EHR cohort of lung cancer patients from Veteran Health Administration.

A proportional odds model of risk behaviors associated with recurrent road traffic crashes among young adults in Kuwait

Background

The aims of this cross-sectional study were to i) assess one-year period prevalence of one, two, three or more road traffic crashes (RTCs) as an ordinal outcome and ii) identify the drivers’ characteristics associated with this ordinal outcome among young adult drivers with propensity to recurrent RTCs in Kuwait.

Methods

During December 2016, 1465 students, 17 years old or older from 15 colleges of Kuwait University participated in this cross-sectional study. A self-administered questionnaire was used for data collection. One-year period prevalence (95% confidence interval (CI)) of one, two, three or more RTCs was computed. Multivariable proportional odds model was used to identify the drivers’ attributes associated with the ordinal outcome.

Results

One-year period prevalence (%) of one, two and three or more RTCs respectively was 23.1 (95% CI: 21.2, 25.6), 10.9 (95% CI: 9.4, 12.6), and 4.6 (95% CI: 3.6, 5.9). Participants were significantly (p < 0.05) more likely to be in higher RTCs count category than their current or lower RCTs count, if they habitually violated speed limit (adjusted proportional odds ratio (pOR_adjusted) = 1.40; 95% Cl: 1.13, 1.75), ran through red lights (pOR_adjusted = 1.64; 95%CI: 1.30, 2.06), frequently (≥ 3) received multiple (> 3) speeding tickets (pOR_adjusted = 1.63; 95% CI: 1.12, 2.38), frequently (> 10 times) violated no-parking zone during the past year (pOR_adjusted = 1.64; 95% CI: 1.06, 2.54) or being a patient with epilepsy (pOR_adjusted = 4.37; 95% CI: 1.63, 11.70).

Conclusion

High one-year period prevalence of one, two and three or more RTCs was recorded. Targeted education based on identified drivers’ attributes and stern enforcement of traffic laws may reduce the recurrent RTCs incidence in this and other similar populations in the region.

Population exposure-response model of 131I in patients with benign thyroid disease

PURPOSE

The study aimed to explore the relationship of different exposure measures with ¹³¹I therapy response in patients with benign thyroid disease, estimate the variability in the response, investigate possible covariates, and discuss dosing implications of the results.

METHODS

A population exposure-response analysis was performed using nonlinear mixed-effects modelling. Data from 95 adult patients with benign thyroid disease were analysed. Evaluated exposure parameters were: administered radioactivity dose (Aa) [MBq], total absorbed dose (ABD) [Gy], maximum of absorbed dose-rate (MXR) [Gy/h] and biologically effective dose (BED) [Gy]. The response was modelled as ordered categorical data: hyper-, eu- and hypothyroidism. The final model performance was evaluated by a visual predictive check.

RESULTS

The probability of the outcome following ¹³¹I therapy was best described by a proportional-odds model, including the log-linear model of ¹³¹I effect and the exponential model of the response-time relationship. All exposure measures were statistically significant with p<0.001, with BED and ABD being statistically better than the other two. Nevertheless, as BED resulted in the lowest AIC value, it was included in the final model. Accordingly, BED value of 289.7 Gy is associated with 80% probability of successful treatment outcome 12 months after ¹³¹I application in patients with median thyroid volume (32.28 mL). The target thyroid volume was a statistically significant covariate. The visual predictive check of the final model showed good model performance.

CONCLUSION

Our results imply that BED formalism could aid in therapy individualisation. The larger thyroid volume is associated with a lower probability of a successful outcome.

Joint modeling of longitudinal continuous, longitudinal ordinal, and time-to-event outcomes

In this paper, we propose an innovative method for jointly analyzing survival data and longitudinally measured continuous and ordinal data. We use a random effects accelerated failure time model for survival outcomes, a linear mixed model for continuous longitudinal outcomes and a proportional odds mixed model for ordinal longitudinal outcomes, where these outcome processes are linked through a set of association parameters. A primary objective of this study is to examine the effects of association parameters on the estimators of joint models. The model parameters are estimated by the method of maximum likelihood. The finite-sample properties of the estimators are studied using Monte Carlo simulations. The empirical study suggests that the degree of association among the outcome processes influences the bias, efficiency, and coverage probability of the estimators. Our proposed joint model estimators are approximately unbiased and produce smaller mean squared errors as compared to the estimators obtained from separate models. This work is motivated by a large multicenter study, referred to as the Genetic and Inflammatory Markers of Sepsis (GenIMS) study. We apply our proposed method to the GenIMS data analysis.

Concordance probability as a meaningful contrast across disparate survival times

The performance of time-to-event models is frequently assessed in part by estimating the concordance probability, which evaluates the probabilistic pairwise ordering of the model-based risk scores and survival times. The standard definition of this probability conditions on any survival time pair ordering, irrespective of whether the times are meaningfully separated. Inclusion of survival times that would be deemed clinically similar attenuates the concordance and moves the estimate away from the contrast-of-interest: comparing the risk scores between individuals with disparate survival times. In this manuscript, we propose a concordance definition and corresponding method to estimate the probability conditional on survival times being separated by at least a minimum difference. The proposed estimate requires direct input from the analyst to identify a separable survival region and, in doing so, is analogous to the clinically defined subgroups used for binary outcome area under the curve estimates. The method is illustrated in two cancer examples: a prognostic score in clear cell renal cell carcinoma and two biomarkers in metastatic prostate cancer.

Maximum likelihood estimation for the proportional odds model with mixed interval-censored failure time data

This article discusses regression analysis of mixed interval-censored failure time data. Such data frequently occur across a variety of settings, including clinical trials, epidemiologic investigations, and many other biomedical studies with a follow-up component. For example, mixed failure times are commonly found in the two largest studies of long-term survivorship after childhood cancer, the datasets that motivated this work. However, most existing methods for failure time data consider only right-censored or only interval-censored failure times, not the more general case where times may be mixed. Additionally, among regression models developed for mixed interval-censored failure times, the proportional hazards formulation is generally assumed. It is well-known that the proportional hazards model may be inappropriate in certain situations, and alternatives are needed to analyze mixed failure time data in such cases. To fill this need, we develop a maximum likelihood estimation procedure for the proportional odds regression model with mixed interval-censored data. We show that the resulting estimators are consistent and asymptotically Gaussian. An extensive simulation study is performed to assess the finite-sample properties of the method, and this investigation indicates that the proposed method works well for many practical situations. We then apply our approach to examine the impact of age at cranial radiation therapy on risk of growth hormone deficiency in long-term survivors of childhood cancer.

General regression model for the subdistribution of a competing risk under left-truncation and right-censoring

Left-truncation poses extra challenges for the analysis of complex time-to-event data. We propose a general semiparametric regression model for left-truncated and right-censored competing risks data that is based on a novel weighted conditional likelihood function. Targeting the subdistribution hazard, our parameter estimates are directly interpretable with regard to the cumulative incidence function. We compare different weights from recent literature and develop a heuristic interpretation from a cure model perspective that is based on pseudo risk sets. Our approach accommodates external time-dependent covariate effects on the subdistribution hazard. We establish consistency and asymptotic normality of the estimators and propose a sandwich estimator of the variance. In comprehensive simulation studies we demonstrate solid performance of the proposed method. Comparing the sandwich estimator with the inverse Fisher information matrix, we observe a bias for the inverse Fisher information matrix and diminished coverage probabilities in settings with a higher percentage of left-truncation. To illustrate the practical utility of the proposed method, we study its application to a large HIV vaccine efficacy trial dataset.

Comparison of an ordinal endpoint to time-to-event, longitudinal, and binary endpoints for use in evaluating treatments for severe influenza requiring hospitalization

Background/aims

The Food and Drug Administration recommends research into developing well-defined and reliable endpoints to evaluate treatments for severe influenza requiring hospitalization. A novel 6-category ordinal endpoint of patient health status after 7 days that ranges from death to hospital discharge with resumption of normal activities is being used in a randomized placebo-controlled trial of intravenous immunoglobulin (IVIG) for severe influenza (FLU-IVIG). We compare the power of the ordinal endpoint under a proportional odds model to other types of endpoints as a function of various trial parameters.

Methods

We used closed-form analysis and empirical simulation to compare the power of the ordinal endpoint to time-to-event, longitudinal, and binary endpoints. In the simulation setting, we varied the treatment effect and the distribution of the placebo group across the follow-up period with consideration of adjustment for baseline health status.

Results

In the analytic setting, ordinal endpoints of high granularity provided greater power than time-to-event endpoints when most patients in the placebo group had either naturally progressed to the category of hospital discharge by day 7 or were far from hospital discharge on day 7. In the simulation setting, adjustment for baseline health status universally raised power for the proportional odds model. Across different placebo group distributions of the ordinal endpoint regardless of adjustment for baseline health status, only time-to-event endpoints yielded higher power than the ordinal endpoint for certain treatment effects.

Conclusions

In this case study, the FLU-IVIG ordinal endpoint provided greater power than time-to-event, binary, and longitudinal endpoints for most scenarios of the treatment effect and placebo group distribution, including the target population studied for FLU-IVIG. The ordinal endpoint was only surpassed by the time-to-event endpoint when many patients in the placebo group were on the cusp of hospital discharge on day 7 and the follow-up period for the time-to-event endpoint was extended to allow for additional events. Our general approach for evaluating the power of several potential endpoints for an influenza trial can be used for designing other influenza trials with different target populations and for other trials in other disease areas.

Semiparametric competing risks regression under interval censoring using the R package intccr

BACKGROUND AND OBJECTIVE

Competing risk data are frequently interval-censored in real-world applications, that is, the exact event time is not precisely observed but is only known to lie between two time points such as clinic visits. This type of data requires special handling because the actual event times are unknown. To deal with this problem we have developed an easy-to-use open-source statistical software.

METHODS

An approach to perform semiparametric regression analysis of the cumulative incidence function with interval-censored competing risks data is the sieve maximum likelihood method based on B-splines. An important feature of this approach is that it does not impose restrictive parametric assumptions. Also, this methodology provides semiparametrically efficient estimates. Implementation of this methodology can be easily performed using our new R package intccr.

RESULTS

The R package intccr performs semiparametric regression analysis of the cumulative incidence function based on interval-censored competing risks data. It supports a large class of models including the proportional odds and the Fine-Gray proportional subdistribution hazards model as special cases. It also provides the estimated cumulative incidence functions for a particular combination of covariate values. The package also provides some data management functionality to handle data sets which are in a long format involving multiple lines of data per subject.

CONCLUSIONS

The R package intccr provides a convenient and flexible software for the analysis of the cumulative incidence function based on interval-censored competing risks data.

An item response theory based integrated model of headache, nausea, photophobia, and phonophobia in migraine patients

This study developed an integrated model of severity scores of migraine headache and the incidence of nausea, photophobia, and phonophobia to predict the natural time course of migraine symptoms, which are likely to occur by a common disease progression mechanism. Data were acquired from two phase 3 clinical trials conducted during the development of eletriptan. Only the placebo arm was used for analysis. A conventional proportional odds model was compared with an item response theory (IRT) based approach. Results suggested that the IRT based approach led to a better model fit, successfully revealing the difference in relief rates among different symptoms, which was the fastest in phonophobia and the slowest in headache. Simulation with the developed model suggested that using headache scores at 4 h post-dose attained greatest statistical power, yielding sample size of 100 per arm given drug effect of 40%, as compared to that of 200 per arm when 2 h post-dose scores were used as in the original eletriptan protocol. This work demonstrated the usefulness of an IRT based model as applied to analyzing multidimensional migraine symptoms and designing clinical trials. Our model can be similarly applied to analyzing other multiple endpoints sharing a common underlying mechanism.

Factors associated with asthma control: MOSAR study (Multicenter Observational Study of Asthma in Rabat-Morocco)

BACKGROUND

The purpose of the study is to describe the profile of patients with asthma and to identify the signifiant risks and the protective factors associated with asthma control.

METHODS

A prospective epidemiological study was conducted in three hospitals of Rabat-Morocco and included 396 patients with asthma. Differences in characteristics across the levels of asthma control were compared by the one-way analysis of variance for continuous variables, and chi-square test was used for categorical variables. The risk and protective factors associated with the asthma control levels were determined by Proportional Odds Model (POM) for bivariate and multivariate ordinal logistic regression, also expressed as Odds Ratios (OR) and 95% Confidence Intervals (95% CI).

RESULTS

From 7440 patients screened by 28 physicians, 396 were included in study. 53% of the particiants sufferd controlled, 18% had partly controlled and 29% had uncontrolled asthma symptoms. A multivariate ordinal logistic regression analysis showed that having respiratory infections (AOR = 5.71), suffering from concomitant diseases (AOR = 3.36) and being allergic to animals (AOR = 2.76) were positively associated with poor control of asthma. However, adherence to treatement (AOR = 0.07), possession of health insurance (AOR = 0.41) and having more than 2 children (AOR = 0.47) were associated with good asthma control.

CONCLUSION

The study established a clinical-epidemiological profile of asthmatic patients in Rabat region in Morocco. By ordinal logistic regression we found that 6 factors - respiratory infections, concomitant diseases, animals allergy, adherence to treatment, health insurance and having more than two children - were associated with asthma control.

Conditional maximum likelihood estimation in semiparametric transformation model with LTRC data

Left-truncated data often arise in epidemiology and individual follow-up studies due to a biased sampling plan since subjects with shorter survival times tend to be excluded from the sample. Moreover, the survival time of recruited subjects are often subject to right censoring. In this article, a general class of semiparametric transformation models that include proportional hazards model and proportional odds model as special cases is studied for the analysis of left-truncated and right-censored data. We propose a conditional likelihood approach and develop the conditional maximum likelihood estimators (cMLE) for the regression parameters and cumulative hazard function of these models. The derived score equations for regression parameter and infinite-dimensional function suggest an iterative algorithm for cMLE. The cMLE is shown to be consistent and asymptotically normal. The limiting variances for the estimators can be consistently estimated using the inverse of negative Hessian matrix. Intensive simulation studies are conducted to investigate the performance of the cMLE. An application to the Channing House data is given to illustrate the methodology.

Autoregressive transitional ordinal model to test for treatment effect in neurological trials with complex endpoints

BACKGROUND

A number of potential therapeutic approaches for neurological disorders have failed to provide convincing evidence of efficacy, prompting pharmaceutical and health companies to discontinue their involvement in drug development. Limitations in the statistical analysis of complex endpoints have very likely had a negative impact on the translational process.

METHODS

We propose a transitional ordinal model with an autoregressive component to overcome previous limitations in the analysis of Upper Extremity Motor Scores, a relevant endpoint in the field of Spinal Cord Injury. Statistical power and clinical interpretation of estimated treatment effects of the proposed model were compared to routinely employed approaches in a large simulation study of two-arm randomized clinical trials. A revisitation of a key historical trial provides further comparison between the different analysis approaches.

RESULTS

The proposed model outperformed all other approaches in virtually all simulation settings, achieving on average 14 % higher statistical power than the respective second-best performing approach (range: -1 %, +34 %). Only the transitional model allows treatment effect estimates to be interpreted as conditional odds ratios, providing clear interpretation and visualization.

CONCLUSION

The proposed model takes into account the complex ordinal nature of the endpoint under investigation and explicitly accounts for relevant prognostic factors such as lesion level and baseline information. Superior statistical power, combined with clear clinical interpretation of estimated treatment effects and widespread availability in commercial software, are strong arguments for clinicians and trial scientists to adopt, and further extend, the proposed approach.

In silico approaches and proportional odds model towards identifying selective ADAM17 inhibitors from anti-inflammatory natural molecules

ADAM metallopeptidase domain 17 (ADAM17) is an attractive target for the development of new anti-inflammatory drugs. We aimed to identify selective inhibitors of ADAM17 against matrix metalloproteinase enzymes (MMP-1, MMP-2, MMP-3, MMP-7, MMP-8, MMP-9, MMP-13, and MMP-16) which have substantial structural similarity. Target proteins were docked with 29 anti-inflammatory natural molecule ligands and a known selective inhibitor IK682. The ligands were screened based on Lipinski rules, interaction with the ADAM17 active site cavity, and then ranked using the proportional odds model multinomial logistic regression. Silymarin was the most selective inhibitor of ADAM17 exhibiting H-bonding with Glu 406, Gly 349, Glu 398, Asn 447, Tyr 433, and Lys 432. Molecular dynamics simulations were carried out for 10ns. The root mean square deviation (RMSD), root mean squared fluctuations (RMSF), radius of gyration (Rg), solvent accessible surface area (SASA), and H-bonding indicated the induced metastability. A comparison of the principal component analysis revealed that the silymarin complex also explored lesser region compared to IK682 complex. A control study on ADAM17 protein (2OI0) is included. These observations present silymarin (widely present in plants such as milk thistle (Silybum maianum), wild artichokes (Cynara cardunculus), turmeric (Curcuma longa) roots, coriander (Coriandrum sativum) seeds, etc.) as a promising natural template for development of ADAM17 selective drugs.

Methods for Multilevel Ordinal Data in Prevention Research

This paper discusses statistical models for multilevel ordinal data that may be more appropriate for prevention outcomes than models that assume continuous measurement and normality. Prevention outcomes often have distributions that make them inappropriate for many popular statistical models that assume normality and are more appropriately considered ordinal outcomes. Despite this, the modeling of ordinal outcomes is often not well understood. This article discusses ways to analyze multilevel ordinal outcomes that are clustered or longitudinal, including the proportional odds regression model for ordinal outcomes, which assumes that the covariate effects are the same across the levels of the ordinal outcome. The article will cover how to test this assumption and what to do if it is violated. It will also discuss application of these models using computer software programs.

The proportional odds cumulative incidence model for competing risks

We suggest an estimator for the proportional odds cumulative incidence model for competing risks data. The key advantage of this model is that the regression parameters have the simple and useful odds ratio interpretation. The model has been considered by many authors, but it is rarely used in practice due to the lack of reliable estimation procedures. We suggest such procedures and show that their performance improve considerably on existing methods. We also suggest a goodness-of-fit test for the proportional odds assumption. We derive the large sample properties and provide estimators of the asymptotic variance. The method is illustrated by an application in a bone marrow transplant study and the finite-sample properties are assessed by simulations.

Score Estimating Equations from Embedded Likelihood Functions under Accelerated Failure Time Model

The semiparametric accelerated failure time (AFT) model is one of the most popular models for analyzing time-to-event outcomes. One appealing feature of the AFT model is that the observed failure time data can be transformed to identically independent distributed random variables without covariate effects. We describe a class of estimating equations based on the score functions for the transformed data, which are derived from the full likelihood function under commonly used semiparametric models such as the proportional hazards or proportional odds model. The methods of estimating regression parameters under the AFT model can be applied to traditional right-censored survival data as well as more complex time-to-event data subject to length-biased sampling. We establish the asymptotic properties and evaluate the small sample performance of the proposed estimators. We illustrate the proposed methods through applications in two examples.

Efficient semiparametric estimation of short-term and long-term hazard ratios with right-censored data

The proportional hazards assumption in the commonly used Cox model for censored failure time data is often violated in scientific studies. Yang and Prentice (2005) proposed a novel semiparametric two-sample model that includes the proportional hazards model and the proportional odds model as sub-models, and accommodates crossing survival curves. The model leaves the baseline hazard unspecified and the two model parameters can be interpreted as the short-term and long-term hazard ratios. Inference procedures were developed based on a pseudo score approach. Although extension to accommodate covariates was mentioned, no formal procedures have been provided or proved. Furthermore, the pseudo score approach may not be asymptotically efficient. We study the extension of the short-term and long-term hazard ratio model of Yang and Prentice (2005) to accommodate potentially time-dependent covariates. We develop efficient likelihood-based estimation and inference procedures. The nonparametric maximum likelihood estimators are shown to be consistent, asymptotically normal, and asymptotically efficient. Extensive simulation studies demonstrate that the proposed methods perform well in practical settings. The proposed method successfully captured the phenomenon of crossing hazards in a cancer clinical trial and identified a genetic marker with significant long-term effect missed by using the proportional hazards model on age-at-onset of alcoholism in a genetic study.

A Unified Approach to Semiparametric Transformation Models under General Biased Sampling Schemes

We propose a unified estimation method for semiparametric linear transformation models under general biased sampling schemes. The new estimator is obtained from a set of counting process-based unbiased estimating equations, developed through introducing a general weighting scheme that offsets the sampling bias. The usual asymptotic properties, including consistency and asymptotic normality, are established under suitable regularity conditions. A closed-form formula is derived for the limiting variance and the plug-in estimator is shown to be consistent. We demonstrate the unified approach through the special cases of left truncation, length-bias, the case-cohort design and variants thereof. Simulation studies and applications to real data sets are presented.

An extension of the Wilcoxon Rank-Sum test for complex sample survey data

In complex survey sampling, a fraction of a finite population is sampled. Often, the survey is conducted so that each subject in the population has a different probability of being selected into the sample. Further, many complex surveys involve stratification and clustering. For generalizability of the sample to the finite population, these features of the design are usually incorporated in the analysis. While the Wilcoxon rank sum test is commonly used to compare an ordinal variable in bivariate analyses, no simple extension of the Wilcoxon rank sum test has been proposed for complex survey data. With multinomial sampling of independent subjects, the Wilcoxon rank-sum test statistic equals the score test statistic for the group effect from a proportional odds cumulative logistic regression model for an ordinal outcome. Using this regression framework, for complex survey data, we formulate a similar proportional odds cumulative logistic regression model for the ordinal variable, and use an estimating equations score statistic for no group effect as an extension of the Wilcoxon test. The proposed method is applied to a complex survey designed to produce national estimates of the health care use, expenditures, sources of payment, and insurance coverage.