A propensity score-integrated approach for leveraging external data in a randomized controlled trial with time-to-event endpoints.

In a randomized controlled trial with time-to-event endpoint, some commonly used statistical tests to test for various aspects of survival differences, such as survival probability at a fixed time point, survival function up to a specific time point, and restricted mean survival time, may not be directly applicable when external data are leveraged to augment an arm (or both arms) of an RCT. In this paper, we propose a propensity score-integrated approach to extend such tests when external data are leveraged. Simulation studies are conducted to evaluate the operating characteristics of three propensity score-integrated statistical tests, and an illustrative example is given to demonstrate how these proposed procedures can be implemented.

Disease progression based feature screening for ultrahigh-dimensional survival-associated biomarkers.

The increased availability of ultrahigh-dimensional biomarker data and the high demand of identifying biomarkers importantly related to survival outcomes made feature screening methods commonplace in the analysis of cancer genome data. When survival outcomes include endpoints of overall survival (OS) and time-to-progression (TTP), a high concordance is typically found in both endpoints in cancer studies, namely, patients' OS would most likely be extended when tumour progression is delayed. Existing screening procedures are often performed on a single survival endpoint only and may result in biased selection of features for OS in ignorance of disease progression. We propose a novel feature screening method by incorporating information of TTP into the selection of important biomarker predictors for more accurate inference of OS subsequent to disease progression. The proposal is based on the rank of correlation between individual features and the conditional distribution of OS given observations of TTP. It is advantageous for its flexible model nature, which requires no marginal model assumption for each endpoint, and its minimal computational cost for implementation. Theoretical results show its ranking consistency, sure screening and false rate control properties. Simulation results demonstrate that the proposed screener leads to more accurate feature selection than the method without considering the prior observations of disease progression. An application to breast cancer genome data illustrates its practical utility and facilitates disease classification using selected biomarker predictors.

Multiply robust estimator for the difference in survival functions using pseudo-observations.

BACKGROUND: When estimating the causal effect on survival outcomes in observational studies, it is necessary to adjust confounding factors due to unbalanced covariates between treatment and control groups. There is no study on multiple robust method for estimating the difference in survival functions. In this study, we propose a multiply robust (MR) estimator, allowing multiple propensity score models and outcome regression models, to provide multiple protection. METHOD: Based on the previous MR estimator (Han 2014) and pseudo-observation approach, we proposed a new MR estimator for estimating the difference in survival functions. The proposed MR estimator based on the pseudo-observation approach has several advantages. First, the proposed estimator has a small bias when any PS and OR models were correctly specified. Second, the proposed estimator considers the advantage pf the pseudo-observation approach, which avoids proportional hazards assumption. A Monte Carlo simulation study was performed to evaluate the performance of the proposed estimator. And the proposed estimator was used to estimate the effect of chemotherapy on triple-negative breast cancer (TNBC) in real data. RESULTS: The simulation studies showed that the bias of the proposed estimator was small, and the coverage rate was close to 95% when any model for propensity score or outcome regression is correctly specified regardless of whether the proportional hazard assumption holds, finite sample size and censoring rate. And the simulation results also showed that even though the propensity score models are misspecified, the bias of the proposed estimator was still small when there is a correct model in candidate outcome regression models. And we applied the proposed estimator in real data, finding that chemotherapy could improve the prognosis of TNBC. CONCLUSIONS: The proposed estimator, allowing multiple propensity score and outcome regression models, provides multiple protection for estimating the difference in survival functions. The proposed estimator provided a new choice when researchers have a "difficult time" choosing only one model for their studies.

Some new results on Cox-Czanner divergence and their applications in survival studies.

In the present communication, we propose a quantile-based measure for the divergence between two survival functions. This can also be used in a dynamic way where the divergence between survival functions varies with time. Several new properties of the proposed measure are investigated with suitable examples. The behavior of the measure for various reliability models is also investigated. A real data analysis is employed to compare the relative efficacy of two treatment groups using the proposed divergence measure.

A New Truncated Lindley-Generated Family of Distributions: Properties, Regression Analysis, and Applications.

We present the truncated Lindley-G (TLG) model, a novel class of probability distributions with an additional shape parameter, by composing a unit distribution called the truncated Lindley distribution with a parent distribution function G(x). The proposed model's characteristics including critical points, moments, generating function, quantile function, mean deviations, and entropy are discussed. Also, we introduce a regression model based on the truncated Lindley-Weibull distribution considering two systematic components. The model parameters are estimated using the maximum likelihood method. In order to investigate the behavior of the estimators, some simulations are run for various parameter settings, censoring percentages, and sample sizes. Four real datasets are used to demonstrate the new model's potential.

Addressing Extreme Propensity Scores in Estimating Counterfactual Survival Functions via the Overlap Weights.

The inverse probability of treatment weighting (IPTW) approach is popular for evaluating causal effects in observational studies, but extreme propensity scores could bias the estimator and induce excessive variance. Recently, the overlap weighting approach has been proposed to alleviate this problem, which smoothly down-weights the subjects with extreme propensity scores. Although advantages of overlap weighting have been extensively demonstrated in literature with continuous and binary outcomes, research on its performance with time-to-event or survival outcomes is limited. In this article, we propose estimators that combine propensity score weighting and inverse probability of censoring weighting to estimate the counterfactual survival functions. These estimators are applicable to the general class of balancing weights, which includes IPTW, trimming, and overlap weighting as special cases. We conduct simulations to examine the empirical performance of these estimators with different propensity score weighting schemes in terms of bias, variance, and 95% confidence interval coverage, under various degrees of covariate overlap between treatment groups and censoring rates. We demonstrate that overlap weighting consistently outperforms IPTW and associated trimming methods in bias, variance, and coverage for time-to-event outcomes, and the advantages increase as the degree of covariate overlap between the treatment groups decreases.

Propensity score-integrated approach to survival analysis: leveraging external evidence in single-arm studies.

External data, referred to as data external to the traditional clinical study being planned, include but are not limited to real-world data (RWD) and data collected from clinical studies being conducted in the past or in other countries. The external data are sometimes leveraged to augment a single-arm, prospectively designed study when appropriate. In such an application, recently developed propensity score-integrated approaches including PSPP and PSCL can be used for study design and data analysis when the clinical outcomes are binary or continuous. In this paper, the propensity score-integrated Kaplan-Meier (PSKM) method is proposed for a similar situation but the outcome of interest is time-to-event. The propensity score methodology is used to select external subjects that are similar to those in the current study in terms of baseline covariates and to stratify the selected subjects from both data sources into more homogeneous strata. The stratum-specific PSKM estimators are obtained based on all subjects in the stratum with the external data being down-weighted, and then these estimators are combined to obtain an overall PSKM estimator. A simulation study is conducted to assess the performance of the PSKM method, and an illustrative example is presented to demonstrate how to implement the proposed method.

AccPDIA6 from Apis cerana cerana plays important roles in antioxidation.

PDIA6 is a member of the protein disulfide isomerase (PDI) family, shows disulfide isomerase activity and oxidoreductase activity, and can act as a molecular chaperone. Its biological functions include modulating apoptosis, regulating the proliferation and invasion of cancer cells, supporting thrombosis and modulating insulin secretion. However, the roles of PDIA6 in Apis cerana cerana are poorly understood. Herein, we obtained the PDIA6 gene from A. cerana cerana (AccPDIA6). We investigated the expression patterns of AccPDIA6 in response to oxidative stress induced by H2O2, UV, HgCl2, extreme temperatures (4 °C, 42 °C) and pesticides (thiamethoxam and hexythiazox) and found that AccPDIA6 was upregulated by these treatments. Western blot analysis indicated that AccPDIA6 was also upregulated by oxidative stress at the protein level. In addition, a survival test demonstrated that the survival rate of E. coli cells expressing AccPDIA6 increased under oxidative stress, suggesting a possible antioxidant function of AccPDIA6. In addition, we tested the transcripts of other antioxidant genes and found that some of them were downregulated in AccPDIA6 knockdown samples. It was also discovered that the antioxidant enzymatic activity of superoxide dismutase (SOD) decreased in AccPDIA6-silenced bees. Moreover, the survival rate of AccPDIA6 knockdown bees decreased under oxidative stress, implying that AccPDIA6 may function in the oxidative stress response by enhancing the viability of honeybees. Taken together, these results indicated that AccPDIA6 may play an essential role in counteracting oxidative stress.

Nonparametric Bayesian inference for mean residual life functions in survival analysis.

Modeling and inference for survival analysis problems typically revolves around different functions related to the survival distribution. Here, we focus on the mean residual life (MRL) function, which provides the expected remaining lifetime given that a subject has survived (i.e. is event-free) up to a particular time. This function is of direct interest in reliability, medical, and actuarial fields. In addition to its practical interpretation, the MRL function characterizes the survival distribution. We develop general Bayesian nonparametric inference for MRL functions built from a Dirichlet process mixture model for the associated survival distribution. The resulting model for the MRL function admits a representation as a mixture of the kernel MRL functions with time-dependent mixture weights. This model structure allows for a wide range of shapes for the MRL function. Particular emphasis is placed on the selection of the mixture kernel, taken to be a gamma distribution, to obtain desirable properties for the MRL function arising from the mixture model. The inference method is illustrated with a data set of two experimental groups and a data set involving right censoring. The supplementary material available at Biostatistics online provides further results on empirical performance of the model, using simulated data examples.

Survival model methods for analyses of cancer incidence trends in young adults.

Recent studies have reported increases in cancer incidence in adults under 50 years. However, there remains uncertainty about whether these are true increases or a result of incidental findings from increased medical imaging. To evaluate these trends, we propose an alternative method to age-period-cohort analyses based on survival modeling. Simulations show that our method is capable of quantifying cohort effects within various backgrounds including increasing medical imaging. We applied the method to analyze the changes in cancer incidence rates for 44 anatomic sites, stratified by sex, by birth cohort for individuals born from 1945 to 1969 in the US based on incidence data from the Surveillance, Epidemiology, and End Results (SEER) program, and tested the validity of our models using later birth cohorts (1970-1974 and 1975-1979). We found that cancer risks have increased significantly in 15 sites (9 in men and 11 in women) for 25-49 year-olds. These results were consistent with previous findings from age-period-cohort analyses. Furthermore, based on our simulations, these increases were independent of increased medical imaging and support substantial, increased extrinsic risks in the identified cancers. Although our approach has several limitations including the restriction to the younger age range and requirement of complete data for all ages of interest, we demonstrate many advantages of our approach including the ease in implementation and interpretation of cohort effects, robustness to various period backgrounds, and ability to make predictions. Our approach should help epidemiologists evaluate cohort effects using incidence data for cancer or other diseases.

Prognostic score matching methods for estimating the average effect of a non-reversible binary time-dependent treatment on the survival function.

In evaluating the benefit of a treatment on survival, it is often of interest to compare post-treatment survival with the survival function that would have been observed in the absence of treatment. In many practical settings, treatment is time-dependent in the sense that subjects typically begin follow-up untreated, with some going on to receive treatment at some later time point. In observational studies, treatment is not assigned at random and, therefore, may depend on various patient characteristics. We have developed semi-parametric matching methods to estimate the average treatment effect on the treated (ATT) with respect to survival probability and restricted mean survival time. Matching is based on a prognostic score which reflects each patient's death hazard in the absence of treatment. Specifically, each treated patient is matched with multiple as-yet-untreated patients with similar prognostic scores. The matched sets do not need to be of equal size, since each matched control is weighted in order to preserve risk score balancing across treated and untreated groups. After matching, we estimate the ATT non-parametrically by contrasting pre- and post-treatment weighted Nelson-Aalen survival curves. A closed-form variance is proposed and shown to work well in simulation studies. The proposed methods are applied to national organ transplant registry data.

Bias-adjusted Kaplan-Meier survival curves for marginal treatment effect in observational studies.

For time-to-event outcomes, the Kaplan-Meier estimator is commonly used to estimate survival functions of treatment groups and to compute marginal treatment effects, such as the difference in survival rates between treatments at a landmark time. The derived estimates of the marginal treatment effect are uniformly consistent under general conditions when data are from randomized clinical trials. For data from observational studies, however, these statistical quantities are often biased due to treatment-selection bias. Propensity score-based methods estimate the survival function by adjusting for the disparity of propensity scores between treatment groups. Unfortunately, misspecification of the regression model can lead to biased estimates. Using an empirical likelihood (EL) method in which the moments of the covariate distribution of treatment groups are constrained to equality, we obtain consistent estimates of the survival functions and the marginal treatment effect. Equating moments of the covariate distribution between treatment groups simulate the covariate distribution that would have been obtained if the patients had been randomized to these treatment groups. We establish the consistency and the asymptotic limiting distribution of the proposed EL estimators. We demonstrate that the proposed estimator is robust to model misspecification. Simulation is used to study the finite sample properties of the proposed estimator. The proposed estimator is applied to a lung cancer observational study to compare two surgical procedures in treating early-stage lung cancer patients.

General single-index survival regression models for incident and prevalent covariate data and prevalent data without follow-up.

This article mainly focuses on analyzing covariate data from incident and prevalent cohort studies and a prevalent sample with only baseline covariates of interest and truncation times. Our major task in both research streams is to identify the effects of covariates on a failure time through very general single-index survival regression models without observing survival outcomes. With a strict increase of the survival function in the linear predictor, the ratio of incident and prevalent covariate densities is shown to be a non-degenerate and monotonic function of the linear predictor under covariate-independent truncation. Without such a structural assumption, the conditional density of a truncation time in a prevalent cohort is ensured to be a non-degenerate function of the linear predictor. In light of these features, some innovative approaches, which are based on the maximum rank correlation estimation or the pseudo least integrated squares estimation, are developed to estimate the coefficients of covariates up to a scale factor. Existing theoretical results are further used to establish the n -consistency and asymptotic normality of the proposed estimators. Moreover, extensive simulations are conducted to assess and compare the finite-sample performance of various estimators. To illustrate the methodological ideas, we also analyze data from the Worcester Heart Attack Study and the National Comorbidity Survey Replication.

Relationship between combination antiretroviral therapy regimens and diabetes mellitus-related comorbidities among HIV patients in Gaborone Botswana.

BACKGROUND: Combination antiretroviral therapy (cARTs) regiments are known to prolong the recipients' life even though they are risk factors for diabetes mellitus-related comorbidities (DRCs). We sought to: (i) examine cART relationship with DRCs among patients attending HIV clinics in Gaborone, Botswana (which cART regimens are associated with shorter/longer time to the event), (ii) characterize patients' underlying biomedical and demographic risk factors of DRC and identify the most important, (iii) investigate survival of patients on different cART regimens in the presence of these risk factors. METHODS: Data from two major HIV clinics in Botswana were reviewed. Relationships between different cART regimens and DRCs were investigated among 531 recipients. Recipients' DRC risk factors were identified. Cox regression model was run. Unadjusted and adjusted hazard ratios were computed, and hazard and survival functions for different cART regimens were plotted. RESULTS: Major findings were: patients on second- and third-line cART were less likely to develop DRCs earlier than those on first-line cART. Patients with CD4 count ≤ 200 cells/mm3 at cART initiation were more likely to develop DRCs earlier than those who had CD4 count > 200 cells/mm3. Overweight patients at cART initiation had a higher risk of developing DRCs earlier than those who had normal body mass index. Males had a lower risk of developing DRCs earlier than females. CONCLUSION: The risk of new onset of DRC among cART recipients is a function of the type of cART regimen, duration of exposure and patients' underlying biomedical and demographic DRC risk factors. The study has provided a survival model highlighting DRCs' significant prognostic factors to guide clinical care, policy and management of recipients of cARTs. Further studies in the same direction will likely improve the survival to the development of DRC of every cART recipient in this community.

Partitioned log-rank tests for the overall homogeneity of hazard rate functions.

In survival analysis, it is routine to test equality of two survival curves, which is often conducted by using the log-rank test. Although it is optimal under the proportional hazards assumption, the log-rank test is known to have little power when the survival or hazard functions cross. To test the overall homogeneity of hazard rate functions, we propose a group of partitioned log-rank tests. By partitioning the time axis and taking the supremum of the sum of two partitioned log-rank statistics over different partitioning points, the proposed test gains enormous power for cases with crossing hazards. On the other hand, when the hazards are indeed proportional, our test still maintains high power close to that of the optimal log-rank test. Extensive simulation studies are conducted to compare the proposed test with existing methods, and three real data examples are used to illustrate the commonality of crossing hazards and the advantages of the partitioned log-rank tests.

On the restricted mean survival time curve in survival analysis.

For a study with an event time as the endpoint, its survival function contains all the information regarding the temporal, stochastic profile of this outcome variable. The survival probability at a specific time point, say t, however, does not transparently capture the temporal profile of this endpoint up to t. An alternative is to use the restricted mean survival time (RMST) at time t to summarize the profile. The RMST is the mean survival time of all subjects in the study population followed up to t, and is simply the area under the survival curve up to t. The advantages of using such a quantification over the survival rate have been discussed in the setting of a fixed-time analysis. In this article, we generalize this approach by considering a curve based on the RMST over time as an alternative summary to the survival function. Inference, for instance, based on simultaneous confidence bands for a single RMST curve and also the difference between two RMST curves are proposed. The latter is informative for evaluating two groups under an equivalence or noninferiority setting, and quantifies the difference of two groups in a time scale. The proposal is illustrated with the data from two clinical trials, one from oncology and the other from cardiology.

Bias and variance reduction in nonparametric estimation of time-dependent accuracy measures.

A new nonparametric approach is developed to estimate the time-dependent accuracy measure curves, which are defined on the cumulative cases and dynamic controls, for censored survival data. Based on an estimable survival process, the main intention of this study is to reduce the finite-sample biases of nearest neighbor estimators. The asymptotic variances of some retrospective accuracy measure estimators are further reduced by applying a smoothing technique to the underlying process of a marker. Meanwhile, practically feasible and theoretically valid procedures are proposed for bandwidth selection in the presented estimators. In addition, the proposed methodology can be reasonably extended to accommodate stratified survival data and survival data with multiple markers. As shown in the simulations, our new estimators outperform the nearest neighbor and inverse censoring weighted estimators. Data from the AIDS Clinical Trials Group study 175 and an angiographic coronary artery disease study are also used to illustrate the proposed methodology. Copyright © 2016 John Wiley & Sons, Ltd.

Comparison of under-five mortality for 2000, 2005 and 2011 surveys in Ethiopia.

BACKGROUND: Though the socio-economic situation of the Ethiopian household is improving along with the decrease in under-five child mortality. But, under-five mortality is still one of the major problems. Identification of the risk factors change over time which mismatches with the diminishing rate of under-five mortality is important to address the problems. METHODS: The survey data used for this research was taken from three different Ethiopian Demographic and Health Surveys (2000, 2005 and 2011). This data was used to identify the effect of time varying under-five mortality risk factors. The Cox proportional hazard model was adapted for the analysis. RESULTS: The effect of respondent's current age, age at first birth and educational level on the under-five mortality rate significantly diminishes in the recent surveys. On the other hand, the effect of the number of births in the last 5 years increases more in 2011 than in the earlier two surveys. Similarly, number of household members in the house and the number of under-five children in the house demonstrated a difference through years. Regarding total children ever born, child death is more for the year 2000 followed by 2005 and 2011. CONCLUSION: Based on the study, our findings confirmed that under-five mortality is a serious problem in the country. The analysis displayed that the hazard of under-five mortality has a decreasing pattern in years. The result for regions showed that there was an increase in years for some of the regions. This research work gives necessary information to device improved teaching for family planning and children health care to change the child mortality circumstance in the country. Our study suggests that the impact of demographic characteristics and socio-economic factors on child mortality should account for their integral changes over time.

Cost effectiveness of cancer treatment in Taiwan.

BACKGROUND/PURPOSE: This study aims to examine the cost effectiveness of treating major cancers compared with other major illnesses in Taiwan. METHODS: We collected data on 395,330 patients with cancer, 125,277 patients with end-stage renal disease, and 50,481 patients under prolonged mechanical ventilation during 1998-2007. They were followed for 10-13 years to estimate lifetime survival functions using a semiparametric method. EuroQol five-dimension was used to measure the quality of life for 6189 cancer patients and 1401 patients with other illnesses. The mean utility values and healthcare costs reimbursed by the National Health Insurance were multiplied with the corresponding survival probabilities to estimate quality-adjusted life expectancies and lifetime costs, respectively. Data of 22,344 cancer patients under hospice care (considered as a comparison group) were used to conduct a cost-effectiveness analysis. Sensitivity analysis was conducted by assuming patients without treatment survived for 2 years with a quality of life value of 0.5. RESULTS: The costs of care for patients under prolonged mechanical ventilation and those with end-stage renal disease were US$41,780-53,708 per quality-adjusted life year (QALY) and US$18,222-18,465 per QALY, respectively, which are equivalent to 2.17-2.79 gross domestic product (GDP) per capita per QALY and 1.18-1.25 GDP per capita per QALY. The costs of care for the nine different cancers were less than 1 GDP per capita per QALY, with those of lung, esophagus, and liver cancers being the highest. Sensitivity analysis showed the same conclusion. Lifetime risks of six out of nine cancer sites show an increased trend. CONCLUSION: Cancer care in Taiwan seemed cost effective compared with that of other illnesses, but prevention is necessary to make the National Health Insurance more sustainable.

Estimating the survival function based on the semi-Markov model for dependent censoring.

In this paper, we study a nonparametric maximum likelihood estimator (NPMLE) of the survival function based on a semi-Markov model under dependent censoring. We show that the NPMLE is asymptotically normal and achieves asymptotic nonparametric efficiency. We also provide a uniformly consistent estimator of the corresponding asymptotic covariance function based on an information operator. The finite-sample performance of the proposed NPMLE is examined with simulation studies, which show that the NPMLE has smaller mean squared error than the existing estimators and its corresponding pointwise confidence intervals have reasonable coverages. A real example is also presented.