Survival Mixture Model Research Articles

Confidence score: a data-driven measure for inclusive systematic reviews considering unpublished preprints.

COVID-19, since its emergence in December 2019, has globally impacted research. Over 360000 COVID-19-related manuscripts have been published on PubMed and preprint servers like medRxiv and bioRxiv, with preprints comprising about 15% of all manuscripts. Yet, the role and impact of preprints on COVID-19 research and evidence synthesis remain uncertain. We propose a novel data-driven method for assigning weights to individual preprints in systematic reviews and meta-analyses. This weight termed the "confidence score" is obtained using the survival cure model, also known as the survival mixture model, which takes into account the time elapsed between posting and publication of a preprint, as well as metadata such as the number of first 2-week citations, sample size, and study type. Using 146 preprints on COVID-19 therapeutics posted from the beginning of the pandemic through April 30, 2021, we validated the confidence scores, showing an area under the curve of 0.95 (95% CI, 0.92-0.98). Through a use case on the effectiveness of hydroxychloroquine, we demonstrated how these scores can be incorporated practically into meta-analyses to properly weigh preprints. It is important to note that our method does not aim to replace existing measures of study quality but rather serves as a supplementary measure that overcomes some limitations of current approaches. Our proposed confidence score has the potential to improve systematic reviews of evidence related to COVID-19 and other clinical conditions by providing a data-driven approach to including unpublished manuscripts.

MSR113 Inferring the Proportion of Durable Responders to Targeted Oncology Therapies in Combination Regimens Using Bayesian Parametric Mixture Survival Models

MSR113 Inferring the Proportion of Durable Responders to Targeted Oncology Therapies in Combination Regimens Using Bayesian Parametric Mixture Survival Models

MSR53 Bayesian Parametric Mixture Survival Models in Immuno-Oncology Applications: Leveraging Control Arm Observations to Model Heterogeneous Response in the Experimental Arm

Heterogeneous response to an intervention is a common feature of survival patterns in randomized clinical trials (RCTs) of immuno-oncology therapies. This effect is usually inadequately represented by standard parametric models. Instead, it is desirable to employ parametric mixture models (PMMs), which represent the cohort as a combination of two latent subpopulations with distinct survival curves. However, classical PMMs are often too complex to parameterize reliably given the limited observations in RCT data.

Internalizing and externalizing pathways to high-risk substance use and geographic location in Australian adolescents.

One specific instantiation of the storm-and-stress view of adolescence is the idea that “normal” adolescence involves high-risk substance use behaviors. However, although uptake of some substance use behaviors is more common during adolescence than other life stages, it is clear that not all adolescents engage in risky substance use—and among those who do, there is much variation in emotional, behavioral, and contextual precursors of this behavior. One such set of predictors forms the internalizing pathway to substance use disorder, whereby internalizing symptoms in childhood such as negative affect and anxiety set off a chain of consequences culminating in high-risk substance use in late adolescence. However, findings linking internalizing symptoms to substance use are mixed, and it is clear that this link varies across adolescents and contexts. One heretofore unanswered question is whether and how geographic location, specifically whether the adolescent lives in an urban or rural location, moderates this link. The current report is a secondary analysis of data from the Longitudinal Study of Australian Children (LSAC; N = 2,285), in which we examined the link between internalizing symptoms in childhood and initiation of substance use through age 19. Using a multiple event process survival mixture model (MEPSUM), we identified three trajectories of substance use initiation in adolescence: one (65.7% of the sample) characterized by near-complete abstinence until late adolescence, another (27.2%) by earlier initiation of alcohol, nicotine, and cannabis, and another (7.2%) by early initiation of these substances and later initiation of more hazardous drugs such as cocaine and methamphetamine. Although childhood externalizing symptoms increased the risk of being in the second or third class, internalizing symptoms decreased risk when rural and non-rural adolescents were considered together. Few effects of rurality were found, but the negative relationship between internalizing at age 10 and high-risk substance use was only observed among non-rural adolescents. This finding, which was inconsistent with our initial predictions that rurality might confer higher risk for substance use, instead suggests a potentially protective effect of internalizing symptoms for engagement in risky substance use which may differ based on an adolescent’s geographical context.

Know Where to Invest: Platform Risk Evaluation in Online Lending

Practice- and policy-oriented abstract for “Research Spotlights” Although enjoying rapid development, online lending also endures some unusual risk, that is, platform risk. We address a new problem at the macro platform level, platform risk evaluation, and explore types of information and methods that are effective in predicting platform risk. We identify four types of information, that is, platform characteristic, risk management, commercial competition, and online word of mouth, and examine their utilities, separately and jointly, in predicting platform risk. We also propose the use of survival analysis, especially the mixture survival model, in predicting whether and when a platform will default. We carry out a cross-stage analysis using data crawled from two leading web portals for online lending in China with the two stages separated by the recent dramatic policy intervention. The results reveal the differences among the four identified factors in terms of predictive utility, the heterogeneity between the two types of default platforms, and differences between the start-up and stable periods of platform development. Based on the results, we derive some insights and examine the cross-stage changes and commonalities. We provide both lessons learned from the past and practical implications for market managers and lenders in the current online lending market.

Finite mixture survival model for examining the variability of urban arterial travel time for buses, passenger cars and taxis

Examining the travel time variability (TTV) of buses, passenger cars and taxis is essential to obtain reliable travel time in urban daily trips. TTV analyses of three travel modes are conducted using travel time data collected on two urban arterial roads in Xi'an City. Firstly, the TTV is evaluated using statistical indexes. The results reveal that the TTV differs from vehicle to vehicle, period to period and site to site. Secondly, the finite mixture survival model is proposed to address the heterogeneity of travel time data by decomposing the population into several sub-populations. Wasserstein distance and Kolmogorov–Smirnov test are used to further compare the sub-populations of different vehicle types during different periods on different roads. Finally, based on the model analysis, it can be found that the finite mixture survival model is an accurate tool to examine the variability by capturing the heterogeneity of travel time data. The difference among the sub-populations suggests different travel behaviours. It concludes that more diverse travel behaviours result in higher TTV. An accurate investigation on TTV is valuable for travellers’ mode choices and transportation management agencies to obtain reliable travel time information and improve traffic efficiency.

Incident Instrumental Activities of Daily Living Difficulty in Older Adults: Which Comes First? Findings From the Advanced Cognitive Training for Independent and Vital Elderly Study.

Introduction: Instrumental activities of daily living (IADLs) are complex daily tasks important for independent living. Many older adults experience difficulty with IADLs as their physical and/or cognitive function begins to decline. However, it is unknown in what order IADLs become difficult.Methods: Participants from the Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE) study who were free of IADL difficulty at baseline (N = 1,277) were followed up to 10 years until first reported IADL difficulty. A total of 19 IADL tasks were grouped into seven task categories. A discrete-time multiple-event process survival mixture model (MEPSUM) was used to generate hazard estimates of incident IADL difficulty in seven groups from ages 65 to 80. Hazard estimates were compared in the three intervention groups (memory, inductive reasoning, and speed of information processing) vs. the no-contact control group.Results: A total of 887 (69.5%) participants reported incident difficulty in at least one IADL task category. Compared to individuals who remained free of IADL difficulty, those who reported incident difficulty were more likely to be older, female, and have lower Short Form 36 general health scores. The IADL task categories to first become difficult were housework, managing health care, and phone use. There were no differences by intervention group in the hazard estimates of incident IADL difficulty.Conclusion: Managing health care and phone use are more cognitively demanding IADLs, and individuals who experience difficulty in these tasks first may be more likely to experience cognitive decline. Recognizing early difficulty in managing health care may allow for implementation of compensation strategies to minimize unintentional medication misuse, increased adverse medical events, and unnecessary hospitalization. Training of a specific cognitive domain may not influence ordering of IADL difficulty because IADL tasks require proficiency in, and integration of, multiple cognitive domains.

Identifying diverse life transition patterns from adolescence to young adulthood: The influence of early socioeconomic context

The purposes of the present study are to investigate: (1) the heterogeneity in life transition patterns of youth from adolescence to young adulthood (ages 18–30) involving the timing and sequence of four transition events (college graduation, full-time employment, marriage, and parenthood), (2) the influence of early socioeconomic adversity on life transition patterns from adolescence to young adulthood, and (3) the influence of gender and race/ethnicity on these transition patterns. Using a multivariate discrete-time mixture survival model with a sample of 14,503 adolescents from the National Longitudinal Study of Adolescent to Adult Health (Add Health), the study identified four life transition patterns and found that early socioeconomic adversity shapes disrupted life transition patterns from adolescence to young adulthood. Gender and race/ethnicity differences are discussed. These results highlight the need for prevention and intervention programs that selectively target at-risk youth beginning in adolescence and continuing through subsequent transition periods.

Legislative success in open sky congresses: weak gatekeeping prerogatives and the loss of majority support

ABSTRACTIn legislatures with weak gatekeeping institutions and constrained plenary time, scheduling rules and majority requirements explain inter-party differences in the consideration and approval of law initiatives. In this paper a mixture survival model is used to analyse legislative success in a legislature with very weak gatekeeping prerogatives, the House of Representatives of Uruguay. Evidence is provided that the loss of majority support depletes plenary time more rapidly and yields an ideological drift that benefits the median voter of the House. The results inform recent debates on the endogenous formation of a plenary schedule in open sky legislatures.

Investigating Progression in Substance Use Initiation Using a Discrete-Time Multiple Event Process Survival Mixture (MEPSUM) Approach.

The order and timing of substance initiation has significant implications for later problematic patterns of use. Despite the need to study initiation from a multivariate framework, survival analytic methods typically cannot accommodate more than two substances in one model. The Discrete-Time Multiple Event Process Survival Mixture (MEPSUM; Dean, Bauer, & Shanahan, 2014) model represents an advance by incorporating more than two outcomes and enabling establishment of latent classes within a multivariate hazard distribution. Employing a MEPSUM approach, we evaluated patterns of tobacco, alcohol, and cannabis initiation in the National Longitudinal Study of Adolescent to Adult Health (N=18,923). We found four classes that differed in their ages and ordering of peak initiation risk. Demographics, externalizing psychopathology, and personality significantly predicted class membership. Sex differences in the association between delinquency and initiation patterns also emerged. Findings support the utility of the MEPSUM approach in elucidating developmental pathways underlying clinically relevant phenomena.

Delineating prototypical patterns of substance use initiations over time.

The purpose of this paper is to discover patterns of drug use initiations over time through a multiple event process survival mixture model (MEPSUM model), a novel approach for substance use and prevention research. The MEPSUM model combines survival analysis and mixture modeling-specifically latent class analysis-to examine individual differences in the timing of initiation and cumulative risk of substance use over time, and is applied to cross-sectional survey data on drug initiations. Data are drawn from the 2009 National Survey on Drug Use and Health. The survey includes responses from 55 772 individuals (52.05% female). The age of first use of nine different types of substances are examined, including alcohol, tobacco, cocaine and non-medical use of prescription drugs. It is argued that six patterns parsimoniously describe the population's risk of initiating different substances over time, described colloquially as general abstainers; early, late and progressive soft drug users; and early and late hard drug users. Both gender and ethnicity significantly predict the patterns, with Caucasians and males having a higher risk for the hard drug-using patterns. The MEPSUM model produced stable results in this application, as the patterns are validated in a split-sample design. The MEPSUM model provides a statistical framework from which to evaluate patterns of risk for drug initiations over time and predict substance use trajectories relevant to public health interventions. The patterns that result from the model can be used as outcomes for subsequent investigations of etiological and mediating mechanisms.

Mixture Model of the Exponential, Gamma and Weibull Distributions to Analyse Heterogeneous Survival Data

Aims: In this study a survival mixture model of three components is considered to analyse survival data of heterogeneous nature.The survival mixture model is of the Exponential, Gamma and Weibull distributions.Methodology: The proposed model was investigated and the Maximum Likelihood (ML) estimators of the parameters of the model were evaluated by the application of the Expectation Maximization Algorithm (EM).Graphs, log likelihood (LL) and the Akaike Information Criterion (AIC) were used to compare the proposed model with the pure classical parametric survival models corresponding to each component using real survival data.The model was compared with the survival mixture models corresponding to each component.Results: The graphs, LL and AIC values showed that the proposed model fits the real data better than the pure classical survival models corresponding to each component.Also the proposed model fits the real data better than the survival mixture models corresponding to each component. Conclusion: The proposed model showed that survival mixture models are flexible and maintain the features of the pure classical survival model and are better option for modelling heterogeneous survival data.

A discrete-time Multiple Event Process Survival Mixture (MEPSUM) model.

Traditional survival analysis was developed to investigate the occurrence and timing of a single event, but researchers have recently begun to ask questions about the order and timing of multiple events. A multiple event process survival mixture model is developed here to analyze nonrepeatable events measured in discrete-time that may occur at the same point in time. Building on both traditional univariate survival analysis and univariate survival mixture analysis, the model approximates the underlying multivariate distribution of hazard functions via a discrete-point finite mixture in which the mixing components represent prototypical patterns of event occurrence. The model is applied in an empirical analysis concerning transitions to adulthood, where the events under study include parenthood, marriage, beginning full-time work, and obtaining a college degree. Promising opportunities, as well as possible limitations of the model and future directions for research, are discussed.

A discrete-time Multiple Event Process Survival Mixture (MEPSUM) model.

A discrete-time Multiple Event Process Survival Mixture (MEPSUM) model.

Semiparametric mixture survival model with application to MRFIT study

Semiparametric mixture survival model with application to MRFIT study

Different pathways towards dropout: the role of engagement in early school leaving

In this study, we examine the development of student engagement in relation to dropout. We focus on different growth trajectories of engagement between groups of students and on whether these trajectories lead to differences in the survival of the student. The development of behavioural and emotional engagement of 4063 graduates and 541 (11.7%) dropouts is examined from Year 7 to Year 12 and this development is linked to the probability of dropping out in each grade by means of a discrete-time survival mixture model. For emotional engagement, results point to a model with two different subgroups: one group starting at a high level of engagement and following a (relatively) stable pattern and the other group starting at a lower level of engagement and following a decreasing trend. For behavioural engagement, the results indicate that a three-class model showed the best fit: a high and (relatively) stable group, a high and decreasing group and a low and stable group. In terms of dropout, the unstable and low groups demonstrate a significantly higher probability of dropping out, as evidenced in the steep, declining survival curves. Different background variables are included to gain more insight into engagement and dropout, and to predict membership in the low and decreasing class.

A Comparative Study of the Estimation Methods on Frailty Mixture Survival Model

Frailty mixture survival models are statistical models which allow for a cured fraction and frailty. The cured fraction refers to a proportion of individuals who are expected not to experience the event of interest, while frailty refers to unobserved information amongst the individuals who experience the event of interest. In this study, we extend the frailty mixture survival model by including covariates into the frailty part of the model. We also employed both semiparametric and parametric methods in Gamma frailty mixture model. Using parametric method, the baseline survival function is assumed to follow Weibull distribution, while using semiparametric method, the cummulative baseline hazard function is assumed to be unknown since in some cases a parametric assumtionis diffuclt to justify. Estimation methods based on EM-algorithm and newton-raphson are utilized to obtain the maximum likelihood estimates of the unknown model parameters involved in both the semiparametric and parametric model. The study aims to compare the performance of estimators using these two methods in terms of their accuracy and efficiency measures.

Can we distinguish between infertility and subfertility when predicting natural conception in couples with an unfulfilled child wish?

Can mixture survival models help distinguish infertility from subfertility in couples with an unexplained unfulfilled child wish? Mixture models estimated that 47% of the couples were infertile; female age and previous pregnancy were significantly related to infertility, whereas duration of child wish was associated with a longer time to pregnancy for subfertile couples. To differentiate between couples who require assisted conception and couples who still have good chances of natural, i.e. unassisted, conception, several prediction models of natural conception have been developed. Prognostic factors in these models are usually assessed by Cox proportional hazard models that cannot differentiate between couples with an unfulfilled child wish who are subfertile, i.e. have reduced ability to conceive naturally, and couples who are really infertile, i.e. are completely unable to conceive naturally. We evaluated whether a mixture survival model can make such a distinction. Consecutive couples presenting at the fertility clinics of 38 centres in the Netherlands between January 2002 and February 2004 joined a prospective cohort study. Of the 7860 couples in the cohort, 3917 couples met our inclusion criteria. The median follow-up was 219 days, with a maximum of 5 years. Couples had to present with an unexplained cause of an unfulfilled child wish. A mixture model was used to estimate the proportion of couples who were infertile and the time to pregnancy for the subfertile couples. During the follow-up, 794 couples conceived naturally. The mixture model estimated that 47% [95% confidence interval (CI): 33-56%] of couples were infertile, despite the absence of objective factors indicating a cause for infertility. Of the evaluated prognostic factors, female age, duration of child wish, previous pregnancy, semen quality, BMI and cycle length, female age [odds ratio (OR): 1.11, 95% CI: 1.03-1.19] and previous pregnancy (0.22, 95% CI: 0.07-0.67) were significant predictors of infertility. Among subfertile couples, a longer duration of a child wish (FFR: 0.72, 95% CI: 0.61-0.85) was a significant prognostic factor for time to pregnancy. In the Cox models, all variables except BMI were significant predictors of time to pregnancy. The mixture model had limited power due to a low number of couples at the end of the follow-up period. Mixture model analyses on external, long-term follow-up data are necessary to validate our results. Mixture models could be a useful tool in selecting couples who require assisted reproductive technology because the effects of prognostic factors can be subdivided into effects on the fraction of infertile couples and effects on the time to pregnancy for subfertile couples, which is not possible in conventional models. This study was supported by grant 945/12/002 from ZonMw, the Netherlands Organization for Health Research and Development, The Hague, the Netherlands.

Patterns of 12-Year Change in Physical Activity Levels in Community-Dwelling Older Women: Can Modest Levels of Physical Activity Help Older Women Live Longer?

Few studies have addressed changes in physical activity participation over time among the elderly. The authors hypothesized that there were distinct trajectories of physical activity level over time and identifiable predictors of such trajectories, as well as that the maintenance of regular physical activity, even below recommended levels, was associated with lower mortality risk. Using longitudinal data (1994-2009) from 433 initially high-functioning older women aged 70-79 years at baseline, a joint latent class and survival mixture model identified 4 activity trajectory classes: always active (16.6%), fast declining (19.2%), stable moderate (32.3%), and always sedentary (31.9%). Obesity, coronary artery disease, chronic obstructive pulmonary disease, depressive symptoms, low self-efficacy, mobility disability, and low energy were associated with sedentary behavior and/or a fast decline in activity. Women in the fast declining and always sedentary classes had hazard ratios for death of 2.34 (95% confidence interval: 1.20, 4.59) and 3.34 (95% confidence interval: 1.72, 6.47), respectively, compared with the always active class; no mortality difference was found between the stable moderate and always active groups (hazard ratio = 1.24, 95% confidence interval: 0.63, 2.47). Our findings suggest that physical activity does not have to be vigorous to be beneficial and that the gain may be the greatest among women who reported the lowest levels of activity.

Admissible mixing distributions for a general class of mixture survival models with known asymptotics

Statistical analysis of data on the longest living humans leaves room for speculation whether the human force of mortality is actually leveling off. Based on this uncertainty, we study a mixture failure model, introduced by Finkelstein and Esaulova (2006) that generalizes, among others, the proportional hazards and accelerated failure time models. In this paper we first, extend the Abelian theorem of these authors to mixing distributions, whose densities are functions of regular variation. In addition, taking into account the asymptotic behavior of the mixture hazard rate prescribed by this Abelian theorem, we prove three Tauberian-type theorems that describe the class of admissible mixing distributions. We illustrate our findings with examples of popular mixing distributions that are used to model unobserved heterogeneity.