A Sequential Stratification Method for Estimating the Effect of a Time‐Dependent Experimental Treatment in Observational Studies

In survival analyses that include a time-dependent covariate, the standard partial likelihood approach is often complicated by the fact that the necessary observations of the time-dependent covariate are not always available for the subjects in each risk set. In this article, we consider the situation of a binary time-dependent covariate. We specify a longitudinal model for the binary covariate with missing observations and a proportional hazards model for survival time conditional on fixed covariates and the completed time-dependent covariate history. The joint posterior distribution of the missing covariates and the parameters in the covariate and hazard models is simulated using Gibbs sampling. The joint modeling approach allows the missing covariates to be generated using all of the observed covariates as well as the disease outcome and failure time information. Simulation studies show that this approach often leads to lower bias of relative risk estimates associated with the time-dependent covariate and superior coverage of interval estimates as compared to variations of approaches based on imputing missing covariate values using previous values and then performing partial likelihood analysis. Our research is motivated by a study of survival of lung cancer patients after surgery in which current smoking status is a binary time-dependent covariate. We apply the methods to data from this study and explore the advantages of the joint modeling approach. The application demonstrates that the joint modeling approach can have improved efficiency in estimating the coefficients of both the fixed and the time-dependent covariates. Moreover, it can facilitate analyses using more complicated functions of the time-dependent covariate, such as cumulative smoking, that are difficult or inappropriate to use with the comparison methods.

Background and aims: Midgut carcinoid tumours are uncommon tumours with an unpredictable clinical behaviour and few useful prognostic markers. Somatostatin analogues are widely used in treatment but a survival advantage...

ABSTRACTIntroductionMechanisms underlying kidney benefits with sodium-glucose cotransporter-2 (SGLT2) inhibition in heart failure and/or type 2 diabetes (T2D) with established cardiovascular disease are currently unclear.MethodsWe evaluated post hoc the factors mediating the effect of empagliflozin on a composite kidney outcome (first sustained estimated glomerular filtration rate ≥40% reduction from baseline, initiation of renal replacement therapy or death due to kidney disease) in EMPA-REG OUTCOME (Empagliflozin Cardiovascular Outcome Event Trial in Type 2 Diabetes Mellitus Patients). Variables, calculated as change from baseline or updated mean, were evaluated as time-dependent covariates and using a landmark approach (at Week 12) in Cox regression analyses. In multivariable analyses, variables with the greatest mediating effect were added using a step-up procedure.ResultsIn univariable time-dependent updated mean covariate analyses, the strongest mediator was hematocrit (99.5% mediation). Hemoglobin, uric acid and urine albumin-to-creatinine ratio mediated 79.4%, 33.2% and 31.0%, respectively. Multivariable analyses were not performed due to the very strong mediation effect of hematocrit. In univariable Week 12 landmark change from baseline analyses, the strongest mediators included hematocrit (40.7%), glycated hemoglobin (28.3%), systolic blood pressure (16.8%) and free fatty acids (16.5%), which yielded a combined mediation of 78.9% in multivariable analysis.ConclusionsChanges in hematocrit and hemoglobin were the strongest mediators of empagliflozin's kidney benefits in EMPA-REG OUTCOME participants with T2D and cardiovascular disease.

To the Editor: We read with interest “Effect of cumulative bortezomib dose on survival in multiple myeloma patients receiving bortezomib–melphalan–prednisone in the phase III VISTA study” 1. Mateos et al. reported a retrospective post hoc analysis by using data from a randomized phase III trial, VISTA 2, which showed improved outcomes of patients with newly diagnosed myeloma who were ineligible for high-dose therapy by adding bortezomib to melphalan–prednisone. Furthermore, Mateos et al. found that the transplant-ineligible myeloma patients who received a cumulative bortezomib dose of more than the median (39 mg/m2) had better overall survival (OS). This study provides new evidence that an increased cumulative bortezomib dose could improve OS in transplant-ineligible untreated myeloma patients. However, according to protocol, patients had to survive at least 151 days to have a cumulative bortezomib dose of 39 mg/m2. If the data was analyzed by using a log-rank test or time-independent Cox proportional hazards model, it would be likely that an “immortal time bias” could interfere with these results 3-6. “Immortal time” implies to a time interval during the follow-up period in which death cannot occur because of exposure definition. For instance, mortality “cannot” occur in the first five months of follow-up in the patients who had received at least 30 doses of protocol bortezomib. In conventional survival analysis using the likelihood ratio or log-rank tests, the immortal time bias can confer a spurious survival advantage to patients with a higher cumulative dose. The authors further performed a landmark analysis of OS that was conducted at 180 days post-randomization that might be unable to avoid this bias. In contrast, the results should be analyzed by using time-dependent analysis 3, 6, such as Cox regression with the cumulative dose of bortezomib as a time-dependent covariate. Furthermore, the planned dose of bortezomib in the VISTA trial was 67.6 mg/m2 2. Patients who had a cumulative bortezomib dose of less than 39 mg/m2 had higher probability of serious adverse effects and disease progression, both of which were correlated to death. Obviously, patients who had better response to bortezomib can live longer and have a chance to receive more doses of bortezomib. Reverse causality means that Y might exert a causal effect on X, in addition to the effects of X on Y 7. In this study, a longer OS might also offer a causal effect on higher cumulative dose of bortezomib, which could not be solved by a 180-day landmark or time-dependent analysis. We believe that the best way to evaluate the effect of cumulative dose of bortezomib on survival of multiple myeloma patients is a randomized controlled study while the cut-off value of the cumulative dose was best determined by receiver operating characteristic curve analysis. Pei-Ying Hsieh,1 Chia-Jen Liu,2,3,4 and Chung-Jen Teng1,2,3* 1Division of Oncology and Hematology, Department of Medicine, Far Eastern Memorial Hospital, New Taipei City, Taiwan; 2School of Medicine, National Yang-Ming University, Taipei, Taiwan; 3Institute of Public Health, National Yang-Ming University, Taipei, Taiwan; 4Division of Hematology and Oncology, Department of Medicine, Taipei Veterans General Hospital, Taipei, Taiwan

SummaryThe transitional phase of menopause induces significant hormonal fluctuations, exerting a profound influence on the long-term well-being of women. In an extensive longitudinal investigation of women’s health during mid-life and beyond, known as the Study of Women’s Health Across the Nation (SWAN), hormonal biomarkers are repeatedly assessed, following an asynchronous schedule compared to other error-prone covariates, such as physical and cardiovascular measurements. We conduct a subgroup analysis of the SWAN data employing a semiparametric mixture regression model, which allows us to explore how the relationship between hormonal responses and other time-varying or time-invariant covariates varies across subgroups. To address the challenges posed by asynchronous scheduling and measurement errors, we model the time-varying covariate trajectories as functional data with reduced-rank Karhunen–Loéve expansions, where splines are employed to capture the mean and eigenfunctions. Treating the latent subgroup membership and the functional principal component (FPC) scores as missing data, we propose an Expectation-Maximization algorithm to effectively fit the joint model, combining the mixture regression for the hormonal response and the FPC model for the asynchronous, time-varying covariates. In addition, we explore data-driven methods to determine the optimal number of subgroups within the population. Through our comprehensive analysis of the SWAN data, we unveil a crucial subgroup structure within the aging female population, shedding light on important distinctions and patterns among women undergoing menopause.

Panel count data occur in many clinical and observational studies and in some situations the observation process is informative. In this article, we propose a new joint model for the analysis of panel count data with time-dependent covariates and possibly in the presence of informative observation process via two latent variables. For the inference on the proposed model, a class of estimating equations is developed and the resulting estimators are shown to be consistent and asymptotically normal. In addition, a lack-of-fit test is provided for assessing the adequacy of the model. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies which suggest that the proposed approach works well for practical situations. Also an illustrative example is provided.

Panel count data occur in many fields including clinical, demographical and industrial studies and an extensive literature has been established for their regression analysis. However, most of the existing methods apply only to the situations where both covariates and their effects are constant or one of them may be time-dependent. In the first part of this dissertation, we consider a situation where both covariates and their effects may be time-dependent and an estimating equation-based approach is developed for estimating those time-varying effects. In the method, B-spline functions are employed to approximate time-dependent coefficients and the asymptotic properties of the proposed estimators are established. To assess the performance of the proposed approach, an extensive simulation study is conducted and suggests that it works well in practical situations. An application to the China Health and Nutrition Survey (CHNS) study is provided. In practice, there could exist more than one type of event of interest, such as two types of tumor recurrence, leading to multivariate panel count data. The second part of this dissertation considers marginal mean model for multivariate panel count data with time-dependent coefficient and covariate effects, which has limited previous research. Based on the conditional estimating equation method developed for time-dependent covariates, we approximate the coefficients by B-splines, hence allow both coefficients and covariates to be time-dependent. Simulation studies show that the proposed estimation procedures work well for practical situations. The methodology is again applied to the China Health and Nutrition Survey (CHNS) study. When we consider time-varying covariates and coefficients effects, most of the previous study focused on the proportional mean model because the likelihood function under the rate model involves intractable integration. However, the rate model is more realistic and efficient. Hence, in the third part of this dissertation, we propose a semi-parametric MLE method under the rate model for panel count data with time-dependent covariates and time-varying effects. B-spline functions are employed again to approximate time-dependent coefficients and an efficient Expectation-Maximization-type algorithm is developed to overcome the computational difficulty. The resulting estimators are shown to be consistent and asymptotically efficient. Monte Carlo simulation studies demonstrate that the proposed method enjoys desirable finite-sample properties. An application to The Young Women's Project (YWP) is provided.

Recurrent event data analyses are usually conducted under the assumption that the censoring time is independent of the recurrent event process. In many applications the censoring time can be informative about the underlying recurrent event process, especially in situations where a correlated failure event could potentially terminate the observation of recurrent events. In this article, we consider a semiparametric model of recurrent event data that allows correlations between censoring times and recurrent event process via frailty. This flexible framework incorporates both time-dependent and time-independent covariates in the formulation, while leaving the distributions of frailty and censoring times unspecified. We propose a novel semiparametric inference procedure that depends on neither the frailty nor the censoring time distribution. Large sample properties of the regression parameter estimates and the estimated baseline cumulative intensity functions are studied. Numerical studies demonstrate that the proposed methodology performs well for realistic sample sizes. An analysis of hospitalization data for patients in an AIDS cohort study is presented to illustrate the proposed method.

SummaryWe develop a new approach to using estimating equations to estimate marginal regression models for longitudinal data with time-dependent covariates. Our approach classifies time-dependent covariates into three types—types I, II and III. The type of covariate determines what estimating equations can be used involving the covariate. We use the generalized method of moments to make optimal use of the estimating equations that are made available by the covariates. Previous literature has suggested the use of generalized estimating equations with the independent working correlation when there are time-dependent covariates. We conduct a simulation study that shows that our approach can provide substantial gains in efficiency over generalized estimating equations with the independent working correlation when a time-dependent covariate is of types I or II, and our approach remains consistent and comparable in efficiency with generalized estimating equations with the independent working correlation when a time-dependent covariate is of type III. We apply our approach to analyse the relationship between the body mass index and future morbidity among children in the Philippines.

Overall Survival and Its Interplay with Allogeneic Stem Cell Transplant and Age in Newly Diagnosed AML Patients Treated with Ven/Aza

To conduct an assessment of time-dependent covariates related to dental caries of the permanent dentition among a low socioeconomic status, understudied cohort of children, incorporating time-dependent covariates through the application of extended Cox proportional hazards modeling. This study modeled the time to first cavitated dental caries in permanent teeth among school-aged children and assessed factors associated with this event. A cohort of 98 low socioeconomic status African-American children with mean age of 5.85 years at baseline was recruited in Uniontown, Alabama and followed prospectively for 6 years. None of these children had dental caries on permanent teeth at baseline, and oral examinations were performed annually. Caries-free survival curves were generated to describe time to event (having first decayed, filled, or missing permanent surface). Bivariate and multivariable extended Cox hazards modeling was used to assess the relationships between time-dependent and time-independent covariates and time to event. Twenty-eight children (28.6 percent) had their first permanent tooth caries event during the 6-year follow-up. Multivariable results showed that greater consumption of water was associated with lower dental caries hazard, while previous primary tooth caries experience was associated with greater dental caries hazard after adjustment for frequency of consumptions of milk, added-sugar beverages, and 100 percent juice. There was a global/overall significant caries protective effect of water consumption during the school-age period of child development.

We review methodological challenges in the observational studies of the patterns and outcomes of drug utilization. First, we address issues related to design and data collection in different studies that rely on administrative databases, discuss their limitations in accounting for clinical indication bias, and outline new opportunities created by the emergence of the integrated electronic patient records. Then, we focus on the different analytical issues related to such complexities as prescriber effects, assessing the impact of policy changes on drug utilization, description and classification of longitudinal patterns of medication use, alternative methods of measuring time‐dependent exposure status and medication dose, use of nonparametric modeling to represent time‐varying, lagged and/or nonlinear effects of exposure.

Survival analyses have been used to overcome some of the limitations encountered with other statistical analyses. Although extended Cox hazard modeling with time-dependent variables has been utilized in several medical studies, it has never been utilized in assessing the complex relationship between mutans streptococci (MS) acquisition (time-dependent covariate) and time to having dental caries (outcome). This study involved secondary analyses of data from a prospective study conducted at the University of Alabama at Birmingham. Low socioeconomic status, African-American preschool children from Perry County, AL, USA (n = 95) had dental examinations at age 1 year and annually thereafter until age 6 years by three calibrated dentists. Salivary MS tests were done at ages 1, 1.5, 2, 2.5, 3, and 4 years. The patterns of and relationship between initial MS detection (time-dependent covariate) and dental caries experience occurrence were assessed, using extended Cox hazard modeling. The median time without MS acquisition (50% of the children not having positive MS test) was 2 years. Approximately 79% of the children had positive salivary MS tests by the age of 4 years. The median caries experience survival (50% of the children not having dental caries) was 4 years. During the follow-up period, 65 of the children (68.4%) had their initial primary caries experience. Results of the extended Cox hazard modeling showed a significant overall/global relationship between initial caries experience event at any given time during the follow-up period and having a positive salivary MS test at any time during the follow-up period (hazard ratio = 2.25, 95% CI 1.06-4.75). In conclusion, the extended Cox modeling was used for the first time and its results showed a significant global/overall relationship between MS acquisition and dental caries. Further research using causal mediation analysis with survival data is necessary, where the mediator “presence of MS” is treated as a time-dependent variable.

Role of B Cell Recovery in Relapse Risk and CD19 Phenotype Following Real-World Use of Tisagenlecleucel for Pediatric B-Acute Lymphoblastic Leukemia: A Multi-Institutional Retrospective Study

Background/Objectives: Research on the association between change from baseline in patient-reported outcomes (PROs) and overall survival (OS) in patients with advanced non-small-cell lung cancer (NSCLC) exists. This study evaluated the association between post-baseline PROs and OS in patients with advanced NSCLC who received first-line cemiplimab-based therapy. Methods: We evaluated PRO data from two phase III studies (EMPOWER-Lung 1 [NCT03088540] and EMPOWER-Lung 3 [NCT03409614]) using a Cox proportional hazards model. Twelve pre-specified PRO scales from the European Organisation for Research and Treatment of Cancer Quality of Life Questionnaire Core 30 and Quality of Life Questionnaire Lung Cancer 13 module were evaluated. Landmark analyses were conducted at 3, 6, 9, and 12 months. Time-dependent analyses using change from baseline PROs as a time-dependent covariate were conducted to evaluate the association of post-baseline PRO improvement with OS. Results: At the 3-month landmark, we observed a 56% reduction in the risk of death (HR = 0.44; 95% CI: 0.32-0.62; nominal p < 0.0001) among stable/improved vs. worsened/unobserved PROs for global health status (GHS)/quality of life (QoL). Results at the 6-, 9-, and 12-month landmarks of GHS/QoL were consistent with those at the 3-month landmark. Time-dependent analyses showed that every 10-point improvement in GHS/QoL was associated with a 31% reduction in the risk of death (HR = 0.69; 95% CI: 0.64-0.75; nominal p < 0.0001). Conclusions: In patients with advanced NSCLC who received first-line cemiplimab-based therapy, improvements in post-baseline PROs are associated with improved OS. These results may inform endpoint selection and interpretation of future clinical trials.