The AccelerAge framework: a new statistical approach to predict biological age based on time-to-event data.

Aging is a multifaceted and intricate physiological process characterized by a gradual decline in functional capacity, leading to increased susceptibility to diseases and mortality. While chronological age serves as a strong risk factor for age-related health conditions, considerable heterogeneity exists in the aging trajectories of individuals, suggesting that biological age may provide a more nuanced understanding of the aging process. However, the concept of biological age lacks a clear operationalization, leading to the development of various biological age predictors without a solid statistical foundation. This paper addresses these limitations by proposing a comprehensive operationalization of biological age, introducing the "AccelerAge" framework for predicting biological age, and introducing previously underutilized evaluation measures for assessing the performance of biological age predictors. The AccelerAge framework, based on Accelerated Failure Time (AFT) models, directly models the effect of candidate predictors of aging on an individual's survival time, aligning with the prevalent metaphor of aging as a clock. We compare predictors based on the AccelerAge framework to a predictor based on the GrimAge predictor, which is considered one of the best-performing biological age predictors, using simulated data as well as data from the UK Biobank and the Leiden Longevity Study. Our approach seeks to establish a robust statistical foundation for biological age clocks, enabling a more accurate and interpretable assessment of an individual's aging status.

Compliance-Adjusted Estimates of Aspirin Effects Among Older Persons in the ASPREE Randomized Trial.

The Aspirin in Reducing Events in the Elderly (ASPREE) Trial recruited 19,114 participants across Australia and the United States during 2010-2014. Participants were randomized to receive either 100 mg of aspirin daily or matching placebo, with disability-free survival as the primary outcome. During a median 4.7 years of follow-up, 37% of participants in the aspirin group permanently ceased taking their study medication and 10% commenced open-label aspirin use. In the placebo group, 35% and 11% ceased using study medication and commenced open-label aspirin use, respectively. In order to estimate compliance-adjusted effects of aspirin, we applied rank-preserving structural failure time models. The results for disability-free survival and most secondary endpoints were similar in intention-to-treat and compliance-adjusted analyses. For major hemorrhage, cancer mortality, and all-cause mortality, compliance-adjusted effects of aspirin indicated greater risks than were seen in intention-to-treat analyses. These findings were robust in a range of sensitivity analyses. In accordance with the original trial analyses, compliance-adjusted results showed an absence of benefit with aspirin for primary prevention in older people, along with an elevated risk of clinically significant bleeding.

Flexible parametric accelerated failure time model.

Accelerated Failure Time (AFT) models are viable alternatives to the Cox proportional hazard model, where failure times are explicitly modelled with respect to covariates. A major problem with parametric AFT models in practice is that statistical distribution used there often have a limited range of shapes, which may be inadequate to cope with real-life data. This paper presents an AFT model algorithm involving generalised lambda distributions (GLD) using maximum likelihood estimation, by extending and adapting existing work on GLD regression model and estimation, which would enhance the capabilities of AFT models owing to the rich shapes of GLDs. The proposed method is demonstrated to achieve parameter consistency and is very robust against outliers. A real-life example demonstrating the use of GLD AFT models compared to more established methods such as semi-parametric models of Buckley James regression, Accelerated Failure Time GEE model and Cox proportional hazard model is also given.

Bayesian Stacked Parametric Survival with Frailty Components and Interval-Censored Failure Times: An Application to Food Allergy Risk.

To better understand the risk of exposure to food allergens, food challenge studies are designed to slowly increase the dose of an allergen delivered to allergic individuals until an objective reaction occurs. These dose-to-failure studies are used to determine acceptable intake levels and are analyzed using parametric failure time models. Though these models can provide estimates of the survival curve and risk, their parametric form may misrepresent the survival function for doses of interest. Different models that describe the data similarly may produce different dose-to-failure estimates. Motivated by predictive inference, we developed a Bayesian approach to combine survival estimates based on posterior predictive stacking, where the weights are formed to maximize posterior predictive accuracy. The approach defines a model space that is much larger than traditional parametric failure time modeling approaches. In our case, we use the approach to include random effects accounting for frailty components. The methodology is investigated in simulation, and is used to estimate allergic population eliciting doses for multiple food allergens.

Adaptive Treatment Strategies With Survival Outcomes: An Application to the Treatment of Type 2 Diabetes Using a Large Observational Database.

Sequences of treatments that adapt to a patient's changing condition over time are often needed for the management of chronic diseases. An adaptive treatment strategy (ATS) consists of personalized treatment rules to be applied through the course of a disease that input the patient's characteristics at the time of decision-making and output a recommended treatment. An optimal ATS is the sequence of tailored treatments that yields the best clinical outcome for patients sharing similar characteristics. Methods for estimating optimal adaptive treatment strategies, which must disentangle short- and long-term treatment effects, can be theoretically involved and hard to explain to clinicians, especially when the outcome to be optimized is a survival time subject to right-censoring. In this paper, we describe dynamic weighted survival modeling, a method for estimating an optimal ATS with survival outcomes. Using data from the Clinical Practice Research Datalink, a large primary-care database, we illustrate how it can answer an important clinical question about the treatment of type 2 diabetes. We identify an ATS pertaining to which drug add-ons to recommend when metformin in monotherapy does not achieve the therapeutic goals.

Spatial patterns in prostate Cancer-specific mortality in Pennsylvania using Pennsylvania Cancer registry data, 2004-2014.

BACKGROUND: Spatial heterogeneity of prostate cancer-specific mortality in Pennsylvania remains unclear. We utilized advanced geospatial survival regressions to examine spatial variation of prostate cancer-specific mortality in PA and evaluate potential effects of individual- and county-level risk factors. METHODS: Prostate cancer cases, aged ≥40 years, were identified in the 2004-2014 Pennsylvania Cancer Registry. The 2018 County Health Rankings data and the 2014 U.S. Environmental Protection Agency's Environmental Quality Index were used to extract county-level data. The accelerated failure time models with spatial frailties for geographical correlations were used to assess prostate cancer-specific mortality rates for Pennsylvania and by the Penn State Cancer Institute (PSCI) 28-county catchment area. Secondary assessment based on estimated spatial frailties was conducted to identify potential health and environmental risk factors for mortality. RESULTS: There were 94,274 cases included. The 5-year survival rate in PA was 82% (95% confidence interval, CI: 81.1-82.8%), with the catchment area having a lower survival rate 81% (95% CI: 79.5-82.6%) compared to the non-catchment area rate of 82.3% (95% CI: 81.4-83.2%). Black men, uninsured, more aggressive prostate cancer, rural and urban Appalachia, positive lymph nodes, and no definitive treatment were associated with lower survival. Several county-level health (i.e., poor physical activity) and environmental factors in air and land (i.e., defoliate chemical applied) were associated with higher mortality rates. CONCLUSIONS: Spatial variations in prostate cancer-specific mortality rates exist in Pennsylvania with a higher risk in the PSCI's catchment area, in particular, rural-Appalachia. County-level health and environmental factors may contribute to spatial heterogeneity in prostate cancer-specific mortality.

Parametric and semiparametric estimation methods for survival data under a flexible class of models.

In survival analysis, accelerated failure time models are useful in modeling the relationship between failure times and the associated covariates, where covariate effects are assumed to appear in a linear form in the model. Such an assumption of covariate effects is, however, quite restrictive for many practical problems. To incorporate flexible nonlinear relationship between covariates and transformed failure times, we propose partially linear single index models to facilitate complex relationship between transformed failure times and covariates. We develop two inference methods which handle the unknown nonlinear function in the model from different perspectives. The first approach is weakly parametric which approximates the nonlinear function globally, whereas the second method is a semiparametric quasi-likelihood approach which focuses on picking up local features. We establish the asymptotic properties for the proposed methods. A real example is used to illustrate the usage of the proposed methods, and simulation studies are conducted to assess the performance of the proposed methods for a broad variety of situations.

Are we assuming too much with our statistical assumptions? Lessons learned from the ALTTO trial.

BACKGROUND: Design, conduct, and analysis of randomized clinical trials (RCTs) with time to event end points rely on a variety of assumptions regarding event rates (hazard rates), proportionality of treatment effects (proportional hazards), and differences in intensity and type of events over time and between subgroups. DESIGN AND METHODS: In this article, we use the experience of the recently reported Adjuvant Lapatinib and/or Trastuzumab Treatment Optimization (ALTTO) RCT, which enrolled 8381 patients with human epidermal growth factor 2-positive early breast cancer between June 2007 and July 2011, to highlight how routinely applied statistical assumptions can impact RCT result reporting. RESULTS AND CONCLUSIONS: We conclude that (i) futility stopping rules are important to protect patient safety, but stopping early for efficacy can be misleading as short-term results may not imply long-term efficacy, (ii) biologically important differences between subgroups may drive clinically different treatment effects and should be taken into account, e.g. by pre-specifying primary subgroup analyses and restricting end points to events which are known to be affected by the targeted therapies, (iii) the usual focus on the Cox model may be misleading if we do not carefully consider non-proportionality of the hazards. The results of the accelerated failure time model illustrate that giving more weight to later events (as in the log rank test) can affect conclusions, (iv) the assumption that accruing additional events will always ensure gain in power needs to be challenged. Changes in hazard rates and hazard ratios over time should be considered, and (v) required family-wise control of type 1 error ≤ 5% in clinical trials with multiple experimental arms discourages investigations designed to answer more than one question. TRIAL REGISTRATION: clinicaltrials.gov Identifier NCT00490139.

Survival analysis of time to cure on multi-drug resistance tuberculosis patients in Amhara region, Ethiopia.

BACKGROUND: Multidrug-resistant tuberculosis (MDR-TB) is caused by bacteria that are resistant to the most effective anti-tuberculosis drug. The MDR-TB is an increasing global problem and the spread of MDR-TB has different recovery time for different patients. Therefore, this study aimed to investigate the recovery time of MDR-TB patients in Amhara region, Ethiopia. METHOD: A retrospective study was carried out in seven hospitals having MDR-TB treatment center of Amhara region, Ethiopia from September 2015 to February 2018. An accelerated failure time and parametric shared frailty models were employed. RESULTS: The study revealed that the recovery time of MDR-TB patients in Amhara region was 21 months. Out of the total MDR-TB patients, 110 (35.4%) censored and 201 (64.6%) cured of MDR-TB. The clustering effect of frailty model was hospitals and the Weibull-gamma shared frailty model was selected among all and hence used for this study. The study showed that extra pulmonary MDR-TB patients had longer recovery time than that of seamier pulmonary MDR-TB patients in Amhara region, Ethiopia. According to this study, male MDR-TB patients, MDR-TB patients with co-morbidity and clinical complication were experiencing longer recovery time than that of the counter groups. This study also showed that MDR-TB patients with poor adherence had longer recovery time than those with good adherence MDR-TB patients. CONCLUSION: Among different factors considered in this study, MDR-TB type, clinical complication, adherence, co-morbidities, sex, and smoking status had a significant effect on recovery time of MDR-TB patients in Amhara region, Ethiopia. In conclusion, the Regional and Federal Government of Ethiopia should take immediate steps to address causes of recovery time of MDR-TB patients in Amhara region through encouraging adherence, early case detection, and proper handling of drug-susceptibility according to WHO guidelines.

Exponentiated Weibull regression for time-to-event data.

The Weibull, log-logistic and log-normal distributions are extensively used to model time-to-event data. The Weibull family accommodates only monotone hazard rates, whereas the log-logistic and log-normal are widely used to model unimodal hazard functions. The increasing availability of lifetime data with a wide range of characteristics motivate us to develop more flexible models that accommodate both monotone and nonmonotone hazard functions. One such model is the exponentiated Weibull distribution which not only accommodates monotone hazard functions but also allows for unimodal and bathtub shape hazard rates. This distribution has demonstrated considerable potential in univariate analysis of time-to-event data. However, the primary focus of many studies is rather on understanding the relationship between the time to the occurrence of an event and one or more covariates. This leads to a consideration of regression models that can be formulated in different ways in survival analysis. One such strategy involves formulating models for the accelerated failure time family of distributions. The most commonly used distributions serving this purpose are the Weibull, log-logistic and log-normal distributions. In this study, we show that the exponentiated Weibull distribution is closed under the accelerated failure time family. We then formulate a regression model based on the exponentiated Weibull distribution, and develop large sample theory for statistical inference. We also describe a Bayesian approach for inference. Two comparative studies based on real and simulated data sets reveal that the exponentiated Weibull regression can be valuable in adequately describing different types of time-to-event data.

Sample size planning of two-arm superiority and noninferiority survival studies with discrete follow-up.

In clinical trials using lifetime as primary outcome variable, it is more the rule than the exception that even for patients who are failing in the course of the study, survival time does not become known exactly since follow-up takes place according to a restricted schedule with fixed, possibly long intervals between successive visits. In practice, the discreteness of the data obtained under such circumstances is plainly ignored both in data analysis and in sample size planning of survival time studies. As a framework for analyzing the impact of making no difference between continuous and discrete recording of failure times, we use a scenario in which the partially observed times are assigned to the points of the grid of inspection times in the natural way. Evaluating the treatment effect in a two-arm trial fitting into this framework by means of ordinary methods based on Cox's relative risk model is shown to produce biased estimates and/or confidence bounds whose actual coverage exhibits marked discrepancies from the nominal confidence level. Not surprisingly, the amount of these distorting effects turns out to be the larger the coarser the grid of inspection times has been chosen. As a promising approach to correctly analyzing and planning studies generating discretely recorded failure times, we use large-sample likelihood theory for parametric models accommodating the key features of the scenario under consideration. The main result is an easily implementable representation of the expected information and hence of the asymptotic covariance matrix of the maximum likelihood estimators of all parameters contained in such a model. In two real examples of large-scale clinical trials, sample size calculation based on this result is contrasted with the traditional approach, which consists of applying the usual methods for exactly observed failure times. Copyright © 2017 John Wiley & Sons, Ltd.

Comparison of hypertabastic survival model with other unimodal hazard rate functions using a goodness-of-fit test.

We studied the problem of testing a hypothesized distribution in survival regression models when the data is right censored and survival times are influenced by covariates. A modified chi-squared type test, known as Nikulin-Rao-Robson statistic, is applied for the comparison of accelerated failure time models. This statistic is used to test the goodness-of-fit for hypertabastic survival model and four other unimodal hazard rate functions. The results of simulation study showed that the hypertabastic distribution can be used as an alternative to log-logistic and log-normal distribution. In statistical modeling, because of its flexible shape of hazard functions, this distribution can also be used as a competitor of Birnbaum-Saunders and inverse Gaussian distributions. The results for the real data application are shown. Copyright © 2017 John Wiley & Sons, Ltd.

Bayesian random effects selection in mixed accelerated failure time model for interval-censored data.

In many medical problems that collect multiple observations per subject, the time to an event is often of interest. Sometimes, the occurrence of the event can be recorded at regular intervals leading to interval-censored data. It is further desirable to obtain the most parsimonious model in order to increase predictive power and to obtain ease of interpretation. Variable selection and often random effects selection in case of clustered data become crucial in such applications. We propose a Bayesian method for random effects selection in mixed effects accelerated failure time (AFT) models. The proposed method relies on the Cholesky decomposition on the random effects covariance matrix and the parameter-expansion method for the selection of random effects. The Dirichlet prior is used to model the uncertainty in the random effects. The error distribution for the accelerated failure time model has been specified using a Gaussian mixture to allow flexible error density and prediction of the survival and hazard functions. We demonstrate the model using extensive simulations and the Signal Tandmobiel Study(®).

Randomized Controlled Trials 7: On Contamination and Estimating the Actual Treatment Effect.

The intention-to-treat analysis is the gold standard for evaluating the efficacy in a randomized controlled trial. However, when non-adherence to randomized treatments is high the actual treatment effect may be underestimated. The impact of drop-out from the intervention group or drop-in to the control group may be controlled by trial design, increasing the sample size, effective study execution, and a pre-specified analytical plan to take contamination into account.These analyses may include censoring at the time of co-interventions associated with stopping treatment, lag censoring which allows an additional period after discontinuation of study treatment to account for residual treatment effects, inverse probability of censoring weights (IPCW), accelerated failure time models, and contamination adjusted intent-to-treat analysis . These methods are particularly useful in assessing the "prescribed efficacy" of the study treatment, which can aid clinical decision-making .

[Application of conditional inference forest in time-to-event data analysis].

OBJECTIVE: To explore the application and advantages of conditional inference forest in survival analysis. METHODS: We used simulated experiment and actual data to compare the predictive performance of 4 models, including Coxproportional hazards model, accelerated failure time model, random survival forest model and conditional inference forest model based on their Brier scores. RESULTS: Simulation experiment suggested that both of the two forest models had more accurate and robust predictive performance than the other two regression models. Conditional inference forest model was superior to the other models in analyzing time-to-event data with polytomous covariates, collinearity or interaction, especially for a large sample size and a high censoring rate. The results of actual data analysis demonstrated that conditional inference forest model had the best predictive performance among the 4 models. CONCLUSIONS: Compared with the commonly used survival analysis methods, conditional inference forest model performs better especially when the data contain polytomous covariates with collinearity and interaction.

Shared parameter models for joint analysis of longitudinal and survival data with left truncation due to delayed entry - Applications to cystic fibrosis.

Many longitudinal studies observe time to occurrence of a clinical event such as death, while also collecting serial measurements of one or more biomarkers that are predictive of the event, or are surrogate outcomes of interest. Joint modeling can be used to examine the relationship between the biomarker and the event, and also as a way of adjusting analyses of the biomarker for non-ignorable dropout. In settings such as registry studies, an additional complexity is caused when follow-up of subjects is delayed, referred to as left-truncation of follow-up in the survival analysis setting. If not adjusted for, this can cause bias in estimation of parameters of the survival distribution for the clinical event and in parameters of the longitudinal outcome such as the profile or rate of change over time because subjects may die or have the clinical event before follow-up starts. This paper illustrates how a broad class of shared parameter models can be used to jointly model a time to event outcome along with a longitudinal marker using available nonlinear mixed modeling software, when follow-up times are left truncated. Methods are applied to jointly model survival and decline in lung function in cystic fibrosis patients.

Bayesian analysis of a disability model for lung cancer survival.

Bayesian reasoning, survival analysis and multi-state models are used to assess survival times for Stage IV non-small-cell lung cancer patients and the evolution of the disease over time. Bayesian estimation is done using minimum informative priors for the Weibull regression survival model, leading to an automatic inferential procedure. Markov chain Monte Carlo methods have been used for approximating posterior distributions and the Bayesian information criterion has been considered for covariate selection. In particular, the posterior distribution of the transition probabilities, resulting from the multi-state model, constitutes a very interesting tool which could be useful to help oncologists and patients make efficient and effective decisions.

A Comparison between Accelerated Failure-time and Cox Proportional Hazard Models in Analyzing the Survival of Gastric Cancer Patients.

BACKGROUND: Gastric cancer is the one of the most prevalent reason of cancer-related death in the world. Survival of patients after surgery involves identifying risk factors. There are various models to detect the effect of risk factors on patients' survival. The present study aims at evaluating these models. METHODS: Data from 330 gastric cancer patients diagnosed at the Iran cancer institute during 1995-99 and followed up the end of 2011 were analyzed. The survival status of these patients in 2011 was determined by reopening the files as well as phone calls and the effect of various factors such as demographic, clinical, treatment, and post-surgical on patients' survival was studied. To compare various models of survival, Akaike Information Criterion and Cox-Snell Residuals were used. STATA 11 was used for data analyses. RESULTS: Based on Cox-Snell Residuals and Akaike Information Criterion, the exponential (AIC=969.14) and Gompertz (AIC=970.70) models were more efficient than other accelerated failure-time models. Results of Cox proportional hazard model as well as the analysis of accelerated failure-time models showed that variables such as age (at diagnosis), marital status, relapse, number of supplementary treatments, disease stage, and type of surgery were among factors affecting survival (P<0.05). CONCLUSION: Although most cancer researchers tend to use proportional hazard model, accelerated failure-time models in analogous conditions - as they do not require proportional hazards assumption and consider a parametric statistical distribution for survival time - will be credible alternatives to proportional hazard model.

Risk factors associated with persistence of Salmonella shedding in finishing pigs.

The objective of this study was to identify risk factors associated with persistence of Salmonella shedding in finishing swine. A longitudinal study was conducted in 18 cohorts of pigs from three finishing sites of one swine production company. Among the 446 Salmonella isolates (isolated from 187 pigs), there were 18 distinct serovars. The six most common serovars were S. enterica serovar Derby (47.3%), S. Agona (27.4%), S. Johannesburg (10.5%), S. Schwarzengrund (2.7%), S. Litchfield (2.5%) and S. Mbandaka (2.2%). Survival analysis techniques, Kaplan-Meier methods and Log-rank test were used to estimate the duration of Salmonella shedding in days and to evaluate differences in shedding associated with risk factors at different organizational levels: isolate (serovar), pig, cohort and site. The risk factors at the pig-level were: sex, age and individual health status; and the risk factors at the cohort-level were: health risk, treatment and "at risk pigs" proportions, nursery and barn environment Salmonella status and prior exposure to the same serovar in the nursery or barn environment. Survival analysis using acceleration failure time models, with a log-normal distribution, was applied to investigate risk factors associated with Salmonella persistence (175 pigs) and serovar-specific persistence (151 pigs) during the study period. Pigs detected Salmonella positive for the first time at 10 weeks of age had a longer duration of shedding, than pigs first detected at an older age. The duration of shedding was shorter among pigs infected with S. Derby, S. Johannesburg and other serovars as compared to pigs infected with S. Agona. A significant difference was observed among sites. Cohorts with pig treatment proportions greater than the median were more likely to have a shorter duration of Salmonella shedding. Pigs from cohorts with nursery positive pools greater than the overall mean had a longer duration of Salmonella shedding as compared to pigs from cohorts with nursery pools less than or equal to the mean. These results suggest that the duration of Salmonella shedding may depend on Salmonella serovar, pig age at the time of infection, farm site and cohort-level risk factors. Identification of risk factors associated with the duration of shedding may allow more targeted interventions for the control Salmonella by evaluation of control measures not only for prevalence reduction, but also to decrease the duration of shedding. Such measures may decrease the risk of contamination of pork and subsequent risk of foodborne illness.