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Many of the dependent variables analyzed in the social sciences involve a time period of nonoccurrence prior to their occurrence. Demographers study death; but one cannot die without being born. Thus, one’s death is preceded by a time period after the person has been born during which time they do not die. Such a dependent variable is referred to as a time-to-event variable because there must be a time period of nonoccurrence before the event occurs. Such analyses have several names. The broadest ones are survival analysis or hazard analysis, owing to their early development in biostatistics and epidemiology, where researchers modeled the occurrence of death. The event of death was referred to as a hazard. Persons over a time interval not experiencing the hazard, that is, not dying, were referred to as surviving the hazard. There are two main types of survival models, continuous-time models and discrete-time methods. We direct most of our attention in this chapter to continuous-time models of survival analysis, and specifically to the Cox proportional hazard model. In the last section of the chapter, we focus on discrete-time survival models.
This study considers data from 5 waves of the English Longitudinal Study of Ageing (ELSA). We aim to study the impact of demographic and self-rated health variables including disability and diseases on the survival of the population aged 50+. The disability variables that we consider are mobility impairment, difficulties in performing Activities of Daily Living (ADL) and Instrumental Activities of Daily Living (IADL). One of the problems with the survey study is missing observations. This may happen due to different reasons, such as errors, nonresponse and temporary withdrawals. We address this problem by applying single and multiple imputation methods. We then fit a Generalized Linear model (GLM) and Generalized Linear Mixed model (GLMM) to our data and show that a GLMM performs better than a GLM in terms of information criteria. We also look at the predictability of our models in terms of the time-dependent receiver operating characteristic (ROC) and the area of ROC, i.e. AUC. We conclude that among the disability factors, IADL and among the diseases, cancer significantly affect the survival of the English population aged 50 and older.
In examining the effect of Chinese talent-attracting programs launched by the Chinese government, with few exceptions, studies have rarely assessed these programs empirically and pertinently. We intend to fill the gap by assessing an important central government program – the Youth Thousand Talents Program – in Chapter Five. We start with proposing a transnational migration matrix of the academics to clarify the dynamic mechanism of achieving an academic brain gain at the high end. The transnational migration matrix suggests that the academics with high ability have competitiveness in both overseas and domestic academic job markets and can especially enjoy a higher salary and academic reputation in the host (overseas) academic job market due to the more mature mechanism of academic evaluation relative to their home country. The results show that some scholars whose last employer’s academic ranking is among the world’s Top 100 have stronger willingness to return. Compared to scholars with an overseas tenure-track position, those with a tenure position or a permanent position tended to stay overseas, the rate of their staying abroad increased with ages.
In the UK, the incidence and prevalence of inflammatory bowel disease (IBD) is increasing in paediatric populations. Environmental factors including acute gastroenteritis episodes (AGE) may impact IBD development. Infant rotavirus vaccination has been shown to significantly reduce AGE. This study aims to explore the association between vaccination with live oral rotavirus vaccines and IBD development. A population-based cohort study was used, analysing primary care data from the Clinical Practice Research Datalink Aurum. Participants included children born in the UK from 2010 to 2015, followed from a minimum of 6 months old to a maximum of 7 years old. The primary outcome was IBD, and the primary exposure was rotavirus vaccination. Cox regression analysis with random intercepts for general practices was undertaken, with adjustment for potential confounding factors. In a cohort of 907,477 children, IBD was recorded for 96 participants with an incidence rate of 2.1 per 100,000 person-years at risk. The univariable analysis hazard ratio (HR) for rotavirus vaccination was 1.45 (95% confidence interval (CI) 0.93–2.28). Adjustment in the multivariable model attenuated the HR to 1.19 (95% CI 0.53–2.69). This study shows no statistically significant association between rotavirus vaccination and development of IBD. However, it provides further evidence for the safety of live rotavirus vaccination.
Using a corpus linguistic approach, this article aims to answer the question of which factors contribute to a better chance of survival for words in the early Middle English lexicon. Because of the cognitive benefits of rhyme that have been shown in modern studies, there is a particular interest in rhyming position as a potential factor; other factors include frequency, suffix and geographical spread. The data are analysed using survival analysis, random forests and conditional inference trees in R. The results show that geographical spread is the most important factor, usually in combination with particular suffixes. Rhyme is not generally a significant factor in the same vein, and its importance seems to be restricted to individual cases.
This study examines the influence of founding conditions and decisions on new companies' performance, analysing how both environmental context and organisational dynamics interact to determine their success. It distinguishes between two different success indicators: survival and profitable growth. An empirical study conducted using a sample of 3,722 new agri-food companies in two different periods, one of economic stability and the other of recession, showed that founding conditions had long-lasting effects on post-entry performance. The economic context acted as a moderator of the relationship between individual factors and success. Adverse environmental conditions were also a determinant of success, making surviving firms more competitive and resilient. The results reflect the survival of the fitter principle by showing that early profitability reduced the risk of failure and made firms more likely to become profitable in the medium term. Internationalisation strategies developed organisational capabilities that created an imprint for adaptability and growth.
From 1 January 2022 to 4 September 2022, a total of 53 996 mpox cases were confirmed globally. Cases are predominantly concentrated in Europe and the Americas, while other regions are also continuously observing imported cases. This study aimed to estimate the potential global risk of mpox importation and consider hypothetical scenarios of travel restrictions by varying passenger volumes (PVs) via airline travel network. PV data for the airline network, and the time of first confirmed mpox case for a total of 1680 airports in 176 countries (and territories) were extracted from publicly available data sources. A survival analysis technique in which the hazard function was a function of effective distance was utilised to estimate the importation risk. The arrival time ranged from 9 to 48 days since the first case was identified in the UK on 6 May 2022. The estimated risk of importation showed that regardless of the geographic region, most locations will have an intensified importation risk by 31 December 2022. Travel restrictions scenarios had a minor impact on the global airline importation risk against mpox, highlighting the importance to enhance local capacities for the identification of mpox and to be prepared to carry out contact tracing and isolation.
Survival analysis studies the time-to-event for various subjects. In the biological and medical sciences, interest can focus on patient time to death due to various (competing) causes. In engineering reliability, one may study the time to component failure due to analogous factors or stimuli. Cure rate models serve a particular interest because, with advancements in associated disciplines, subjects can be viewed as “cured meaning that they do not show any recurrence of a disease (in biomedical studies) or subsequent manufacturing error (in engineering) following a treatment. This chapter generalizes two classical cure-rate models via the development of a COM–Poisson cure rate model. The chapter first describes the COM–Poisson cure rate model framework and general notation, and then details the model framework assuming right and interval censoring, respectively. The chapter then describes the broader destructive COM–Poisson cure rate model which allows for the number of competing risks to diminish via damage or eradication. Finally, the chapter details the various lifetime distributions considered in the literature to date for COM–Poisson-based cure rate modeling.
The hazard ratio (HR) is a commonly used summary statistic when comparing time to event (TTE) data between trial arms, but assumes the presence of proportional hazards (PH). Non-proportional hazards (NPH) are increasingly common in NICE technology appraisals (TAs) due to an abundance of novel cancer treatments, which have differing mechanisms of action compared with traditional chemotherapies. The goal of this study is to understand how pharmaceutical companies, evidence review groups (ERGs) and appraisal committees (ACs) test for PH and report clinical effectiveness in the context of NPH.
A thematic analysis of NICE TAs concerning novel cancer treatments published between 1 January 2020 and 31 December 2021 was undertaken. Data on PH testing and clinical effectiveness reporting for overall survival (OS) and progression-free survival (PFS) were obtained from company submissions, ERG reports, and final appraisal determinations (FADs).
NPH were present for OS or PFS in 28/40 appraisals, with log-cumulative hazard plots the most common testing methodology (40/40), supplemented by Schoenfeld residuals (20/40) and/or other statistical methods (6/40). In the context of NPH, the HR was ubiquitously reported by companies, inconsistently critiqued by ERGs (10/28), and commonly reported in FADs (23/28).
There is inconsistency in PH testing methodology used in TAs. ERGs are inconsistent in critiquing use of the HR in the context of NPH, and even when critiqued it remains a commonly reported outcome measure in FADs. Other measures of clinical effectiveness should be considered, along with guidance on clinical effectiveness reporting when NPH are present.
Obsessive-compulsive disorder (OCD) and schizophrenia are often reported as co-morbid conditions. However, the evidence of an association between OCD and the risk of schizophrenia is limited. This study investigated the risk of schizophrenia in patients newly diagnosed with OCD using a nationally representative sample cohort in South Korea.
Data were obtained from the 2002–2013 Korean National Health Insurance Service-National Sample Cohort of the National Health Insurance Service. Using propensity score matching, 2509 patients with OCD and a control group of 7527 patients were included in the analysis. Chi-squared tests were used to investigate and compare the general characteristics of the study population. The risk of schizophrenia was analysed using the Cox proportional hazard model.
The incidence rate was 45.79/10 000 person-year for patients with OCD and 4.19/10 000 person-year for patients without OCD. Patients with OCD had a higher risk of schizophrenia compared to the control group after adjusting for covariates (hazard ratio = 10.46, 95% confidence interval = 6.07–18.00).
This study identified an association between the diagnosis of OCD and the risk of schizophrenia in a South Korean national representative cohort. Further research using a prospective design to clarify the causality of OCD in schizophrenia in a controlled environment should be conducted to validate these findings.
Suicide risk is complex and nuanced, and how place impacts suicide risk when considered alongside detailed individual risk factors remains uncertain. We aimed to examine suicide risk in Denmark with both individual and neighbourhood level risk factors.
We used Danish register-based data to identify individuals born in Denmark from 1972, with full parental information and psychiatric diagnosis history. We fitted a two-level survival model to estimate individual and neighbourhood determinants on suicide risk.
We identified 1723 cases of suicide in Denmark during the follow-up period from 1982 to 2015. Suicide risk was explained mainly by individual determinants. Parental comorbidities, particularly maternal schizophrenia [incidence rate ratio (IRR): 2.29, 95% CI 1.56–3.16] and paternal death (2.29, 95% CI 1.31–3.72) partly explained suicide risk when adjusted for all other determinants. The general contextual effect of suicide risk across neighbourhoods showed a median incidence rate ratio (MRR) of 1.13 (1.01–1.28), which was further reduced with full adjustment. Suicide risk increased in neighbourhoods with a higher proportion of manual workers (IRR: 1.08; 1.03–1.14), and decreased with a higher population density (IRR: 0.89; 0.83–0.96).
Suicide risk varies mainly between individuals, with parental comorbidities having the largest effect on suicide risk. Suicide risk was less impacted by neighbourhood, though, albeit to a lesser extent than individual determinants, some characteristics were associated with suicide risk. Suicide prevention policies might consider targeting interventions towards individuals more vulnerable due to particular parental comorbidities, whilst taking into account that some neighbourhood characteristics might exacerbate this risk further.
Medical statistics as it applies to money, in particular insured sums, is the topic of this chapter which covers the history of annuities and life insurance. The way that this topic has been adapted by medical statistics, in particular as a result of a landmark paper in 1972 by David Cox, is addressed.
Time-dependent Cox proportional hazards regression is a popular statistical method used in kidney disease research to evaluate associations between biomarkers collected serially over time with progression to kidney failure. Typically, biomarkers of interest are considered time-dependent covariates being updated at each new measurement using last observation carried forward (LOCF). Recently, joint modeling has emerged as a flexible alternative for multivariate longitudinal and time-to-event data. This study describes and demonstrates multivariate joint modeling using as an example the association of serial biomarkers (plasma oxalate [POX] and urinary oxalate [UOX]) and kidney function among patients with primary hyperoxaluria in the Rare Kidney Stone Consortium Registry.
Time-to-kidney failure was regressed on serially measured biomarkers in two ways: time-dependent LOCF Cox proportional hazards regression and multivariate joint models.
In time-dependent LOCF Cox regression, higher POX was associated with increased risk of kidney failure (HR = 2.20 per doubling, 95% CI = [1.38-3.51], p < 0.001) whereas UOX was not (HR = 1.08 per doubling, [0.66–1.77], p = 0.77). In multivariate joint models, estimates suggest higher UOX may be associated with lower risk of kidney failure (HR = 0.42 per doubling [0.15–1.04], p = 0.066), though not statistically significant, since impaired urinary excretion of oxalate may reflect worsening kidney function.
Multivariate joint modeling is more flexible than LOCF and may better reflect biological plausibility since biomarkers are not steady-state values between measurements. While LOCF is preferred to naïve methods not accounting for changes in biomarkers over time, results may not accurately reflect flexible relationships that can be captured with multivariate joint modeling.
Bacterial antibiotic resistance (AMR) is a significant threat to public health, with the sentinel ‘ESKAPEE’ pathogens, being of particular concern. A cohort study spanning 5.5 years (2016–2021) was conducted at a provincial general hospital in Crete, Greece, to describe the epidemiology of ESKAPEE-associated bacteraemia regarding levels of AMR and their impact on patient outcomes. In total, 239 bloodstream isolates were examined from 226 patients (0.7% of 32 996 admissions) with a median age of 75 years, 28% of whom had severe comorbidity and 46% with prior stay in ICU. Multidrug resistance (MDR) was lowest for Pseudomonas aeruginosa (30%) and Escherichia coli (33%), and highest among Acinetobacter baumannii (97%); the latter included 8 (22%) with extensive drug-resistance (XDR), half of which were resistant to all antibiotics tested. MDR bacteraemia was more likely to be healthcare-associated than community-onset (RR 1.67, 95% CI 1.04–2.65). Inpatient mortality was 22%, 35% and 63% for non-MDR, MDR and XDR episodes, respectively (P = 0.004). Competing risks survival analysis revealed increasing mortality linked to longer hospitalisation with increasing AMR levels, as well as differential pathogen-specific effects. A. baumannii bacteraemia was the most fatal (14-day death hazard ratio 3.39, 95% CI 1.74–6.63). Differences in microbiology, AMR profile and associated mortality compared to national and international data emphasise the importance of similar investigations of local epidemiology.
Wine investment returns can come from overall market trends or price increases with age. Because of the short wine price histories available, market and maturation effects are difficult to separate. Consequently, researchers often obtain dramatically different estimates of investment returns. We find that data sample bias may be the hidden cause of the disparate estimates. In wine auction data, the sample bias refers to a shift in the distribution of which wines are traded as a function of their age. Such sample bias in panel data sampled across many different wine labels can distort the estimation of price increases versus age and consequently impact the estimation of market trends. This analysis shows that segmenting the analysis such that the data panels contain wine labels with similar trading characteristics can lead to a more stable estimation.
The analysis here looks at data from Bordeaux, Italy, Australia, and California. An Age-Period-Cohort (APC) analysis is applied to data panels from each region. Then the data in each region is segmented by a measure of popularity in order to reduce sampling bias. Data thus segmented is then re-analyzed to demonstrate the difference in estimating price appreciation lifecycles and market trends.
The survival cox analysis is becoming more popular in time-to-event data analysis. When there are unobserved /unmeasured individual factors, then the results of this model may not be dependable. Hence, this study aimed to determine the factors associated with Covid-19 patients’ survival time with considering frailty factor.
This study was conducted at 1 of the hospitals in Iran, so that hospitalized patients with COVID-19 were included. Epidemiological, clinical, laboratory, and outcome data on admission were extracted from electronic medical records. Gamma-frailty Cox model was used to identify the effects of the risk factors.
A total of 360 patients with COVID-19 enrolled in the study. The median age was 74 years (IQR 61 – 83), 903 (57·7%) were men, and 661 (42·3%) were women; the mortality rate was 17%. The Cox frailty model showed that there is at least a latent factor in the model (P = 0.005). Age and platelet count were negatively associated with the length of stay, while red blood cell count was positively associated with the length of stay of patients.
The Cox frailty model indicates that in addition to age, the frailty factor is a useful predictor of survival in Covid-19 patients.
Previous studies have found that stressful life events (SLEs) are associated with an increased risk of adult depression. However, many studies are observational in nature and limited by methodological issues, such as potential confounding by genetic factors. Genetically informative research, such as the co-twin control design, can strengthen causal inference in observational studies. Discrete-time survival analysis has several benefits and multilevel survival analysis can incorporate frailty terms (random effects) to estimate the components of the biometric model. In the current study, we investigated associations between SLEs and depression risk in a population-based twin sample (N = 2299).
A co-twin control design was used to investigate the influence of the occurrence of SLEs on depression risk. The co-twin control design involves comparing patterns of associations in the full sample and within dizygotic (DZ) and monozygotic twins (MZ). Associations were modelled using discrete-time survival analysis with biometric frailty terms. Data from two time points were used in the analyses. Mean age at Wave 1 was 28 years and mean age at Wave 2 was 38 years.
SLE occurrence was associated with increased depression risk. Co-twin control analyses indicated that this association was at least in part due to the causal influence of SLE exposure on depression risk for event occurrence across all SLEs and for violent SLEs. A minor proportion of the total genetic risk of depression reflected genetic effects related to SLEs.
The results support previous research in implicating SLEs as important risk factors with probable causal influence on depression risk.
Natural infection with the influenza virus is believed to generate cross-protective immunity across both types and subtypes. However, less is known about the persistence of this immunity and thus the susceptibility of individuals to repeat infection. We used 13 years (2005–2017) of surveillance data from Queensland, Australia, to describe the incidence and distribution of repeat influenza infections. Consecutive infections that occurred within 14 days of prior infection were considered a mixed infection; those that occurred more than 14 days later were considered separate (repeat) infections. Kaplan-Meier plots were used to investigate the probability of reinfection over time and the Prentice, Williams and Peterson extension of the Cox proportional hazards model was used to assess the association of age and gender with reinfection. Among the 188 392 notifications received during 2005–2017, 6165 were consecutively notified for the same individual (3.3% of notifications), and 2958 were mixed infections (1.6%). Overall, the probability of reinfection was low: the cumulative incidence was <1% after one year, 4.6% after five years, and 9.6% after ten years. The majority of consecutive infections were the result of two type A infections (43%) and were most common among females (adjusted hazard ratio (aHR): 1.15, 95% confidence interval (CI) 1.09–1.21), children aged less than 5 years (relative to adults aged 18–64 years aHR: 1.58, 95% CI 1.47–1.70) and older adults aged at least 65 years (aHR: 1.35; 95% CI 1.24–1.47). Our study suggests consecutive infections are possible but rare. These findings have implications for our understanding of population immunity to influenza.
Quantitative social scientists use survival analysis to understand the forces that determine the duration of events. This Element provides a guideline to new techniques and models in survival analysis, particularly in three areas: non-proportional covariate effects, competing risks, and multi-state models. It also revisits models for repeated events. The Element promotes multi-state models as a unified framework for survival analysis and highlights the role of general transition probabilities as key quantities of interest that complement traditional hazard analysis. These quantities focus on the long term probabilities that units will occupy particular states conditional on their current state, and they are central in the design and implementation of policy interventions.
Considering that coronavirus disease 2019 (COVID-19) is an emerging disease and results in very different outcomes, from complete recovery to death, it is important to determine the factors affecting the survival of patients. Given the lack of knowledge about effective factors and the existence of differences in the outcome of individuals with similar values of the observed covariates, this study aimed to investigate the factors affecting the survival of patients with COVID-19 by the parametric survival model with the frailty approach.
The data of 139 patients with COVID-19 hospitalized in Imam Reza Hospital in Tabriz were analyzed by the Gompertz survival model with gamma frailty effect. At first, variables with P < 0.1 in univariable analysis were included in the multivariable analysis, and then the stepwise method was used for variable selection.
Diabetes mellitus was significantly related to the survival of hospitalized patients (P = 0.021). The rest of the investigated variables were not significant. The frailty effect was significant (P = 0.019).
In the investigated sample of patients with COVID-19, diabetes was an important variable related to patient survival. Also, the significant frailty effect indicates the existence of unobserved heterogeneity that causes individuals with a similar value of the observed covariates to have different survival distributions.