Multidimensional penalized splines for survival models: illustration for net survival trend analyses

BACKGROUND

In descriptive epidemiology, there are strong similarities between incidence and survival analyses. Because of the success of multidimensional penalized splines (MPSs) in incidence analysis, we propose in this pedagogical paper to show that MPSs are also very suitable for survival or net survival studies.

METHODS

The use of MPSs is illustrated in cancer epidemiology in the context of survival trends studies that require specific statistical modelling. We focus on two examples (cervical and colon cancers) using survival data from the French cancer registries (cases 1990-2015). The dynamic of the excess mortality hazard according to time since diagnosis was modelled using an MPS of time since diagnosis, age at diagnosis and year of diagnosis. Multidimensional splines bring the flexibility necessary to capture any trend patterns while penalization ensures selecting only the complexities necessary to describe the data.

RESULTS

For cervical cancer, the dynamic of the excess mortality hazard changed with the year of diagnosis in opposite ways according to age: this led to a net survival that improved in young women and worsened in older women. For colon cancer, regardless of age, excess mortality decreases with the year of diagnosis but this only concerns mortality at the start of follow-up.

CONCLUSIONS

MPSs make it possible to describe the dynamic of the mortality hazard and how this dynamic changes with the year of diagnosis, or more generally with any covariates of interest: this gives essential epidemiological insights for interpreting results. We use the R package survPen to do this type of analysis.

Advancing proactive crash prediction: A discretized duration approach for predicting crashes and severity

Driven by advancements in data-driven methods, recent developments in proactive crash prediction models have primarily focused on implementing machine learning and artificial intelligence. However, from a causal perspective, statistical models are preferred for their ability to estimate effect sizes using variable coefficients and elasticity effects. Most statistical framework-based crash prediction models adopt a case-control approach, matching crashes to non-crash events. However, accurately defining the crash-to-non-crash ratio and incorporating crash severities pose challenges. Few studies have ventured beyond the case-control approach to develop proactive crash prediction models, such as the duration-based framework. This study extends the duration-based modeling framework to create a novel framework for predicting crashes and their severity. Addressing the increased computational complexity resulting from incorporating crash severities, we explore a tradeoff between model performance and estimation time. Results indicate that a 15 % sample drawn at the epoch level achieves a balanced approach, reducing data size while maintaining reasonable predictive accuracy. Furthermore, stability analysis of predictor variables across different samples reveals that variables such as Time of day (Early afternoon), Weather condition (Clear), Lighting condition (Daytime), Illumination (Illuminated), and Volume require larger samples for more accurate coefficient estimation. Conversely, Daytime (Early morning, Late morning, Late afternoon), Lighting condition (Dark lighted), Terrain (Flat), Land use (Commercial, Rural), Number of lanes, and Speed converge towards true estimates with small incremental increases in sample size. The validation reveals that the model performs better in highway segments experiencing more frequent crashes (segments where the duration between crashes is less than 100 h, or approximately 4 days).

Cuproptosis-related gene subtypes predict prognosis in patients with head and neck squamous cell carcinoma

BACKGROUND

Head and neck squamous cell carcinoma (HNSCC) is the sixth most common cancer worldwide. A novel form of copper-dependent and reactive oxygen species (ROS)-dependent cell death, cuproptosis, has been described in many cancers. The roles and potential mechanisms of cuproptosis-related genes (CRGs) are still unclear in HNSCC.

METHOD

We downloaded TCGA datasets of HNSCC genomic mutations and clinic data from The Cancer Genome Atlas. Based on the Cuproptosis-related differentially expressed genes in HNSCC, we constructed a prognostic signature.

RESULTS

Eight CRGs have been identified as associated with the prognosis of HNSCC. According to Kaplan-Meier analyses, HNSCC with a high Risk Score had a poor prognosis. Furthermore, the AUC of the Risk Score for the 1-, 3-, and 5- year overall survival was respectively, 0.70, 0.71, and 0.68. TCGA data revealed that T cell functions, such as HLA, cytolytic activity, inflammation regulation, co-inhibition, and co-stimulation, differed significantly between members of the low and high groups. The immune checkpoint genes PD-L1, PD-L1, and CTLA-4 were also expressed differently in the two risk groups.

CONCLUSIONS

A CRG signature was defined that is associated with the prognosis of patients with HNSCC.

Widely targeted quantitative lipidomics and prognostic model reveal plasma lipid predictors for nasopharyngeal carcinoma

BACKGROUND

Dysregulation of lipid metabolism is closely associated with cancer progression. The study aimed to establish a prognostic model to predict distant metastasis-free survival (DMFS) in patients with nasopharyngeal carcinoma (NPC), based on lipidomics.

METHODS

The plasma lipid profiles of 179 patients with locoregionally advanced NPC (LANPC) were measured and quantified using widely targeted quantitative lipidomics. Then, patients were randomly split into the training (125 patients, 69.8%) and validation (54 patients, 30.2%) sets. To identify distant metastasis-associated lipids, univariate Cox regression was applied to the training set (P < 0.05). A deep survival method called DeepSurv was employed to develop a proposed model based on significant lipid species (P < 0.01) and clinical biomarkers to predict DMFS. Concordance index and receiver operating curve analyses were performed to assess model effectiveness. The study also explored the potential role of lipid alterations in the prognosis of NPC.

RESULTS

Forty lipids were recognized as distant metastasis-associated (P < 0.05) by univariate Cox regression. The concordance indices of the proposed model were 0.764 (95% confidence interval (CI), 0.682-0.846) and 0.760 (95% CI, 0.649-0.871) in the training and validation sets, respectively. High-risk patients had poorer 5-year DMFS compared with low-risk patients (Hazard ratio, 26.18; 95% CI, 3.52-194.80; P < 0.0001). Moreover, the six lipids were significantly correlated with immunity- and inflammation-associated biomarkers and were mainly enriched in metabolic pathways.

CONCLUSIONS

Widely targeted quantitative lipidomics reveals plasma lipid predictors for LANPC, the prognostic model based on that demonstrated superior performance in predicting metastasis in LANPC patients.

Accurate prognostic prediction for patients with clear cell renal cell carcinoma using a ferroptosis-related long non-coding RNA risk model

INTRODUCTION

Ferroptosis is a recently discovered type of programmed cell death that plays a crucial role in tumor occurrence and progression. However, no prognostic model has been established yet for clear cell renal cell carcinoma (ccRCC) using ferroptosis-related long non-coding RNAs (lncRNAs).

METHODS

In the present study, lncRNA expression profiles, sex, age, TMN stage, and other clinical data of ccRCC samples were extracted from The Cancer Genome Atlas database. In addition, ferroptosis-related lncRNAs were identified using co-expression analysis, and the risk model was established using Cox regression and least absolute shrinkage and selection operator regression analyses. Log-rank test and Kaplan-Meier analysis were performed to evaluate the predictive accuracy of the risk model for the overall survival (OS) of patients with ccRCC. Moreover, the functional enrichment of ferroptosis-related lncRNAs was performed and visualized using Gene Ontology and Kyoto Encyclopedia of Genes and Genomes.

RESULTS

Eight prognostic ferroptosis-related lncRNAs were identified, such as LINC01615, AC026401.3, LINC00944, AL590094.1, DLGAP1-AS2, AC016773.1, AC147651.1, and AP000439.2, making up the ferroptosis-related lncRNA risk model. The risk model effectively divided patients with ccRCC into high- and low-risk groups, and their survival time was calculated. The high-risk group showed significantly shorter OS compared to the low-risk group. The nomogram to predict the survival rate of the patients revealed that the risk score was the most critical factor affecting OS in patients with ccRCC. The ferroptosis-related lncRNA risk model was an independent predictor of prognostic risk assessment in patients with ccRCC.

CONCLUSION

The ferroptosis-related lncRNAs risk model and genomic clinicopathological nomogram have the potential to accurately predict the prognosis of patients with ccRCC and could serve as potential therapeutic targets in the future.

Hazard and cumulative incidence of umbilical cord metabolic acidemia at birth in fetuses experiencing the second stage of labor and pathologic intrapartum fetal heart rate requiring expedited delivery

PURPOSE

The aim of the study was to determine the cause-specific hazard (CSH) and the cumulative incidence function (CIF) for umbilical cord metabolic acidemia at birth (MA; pH < 7.0 and/or BE [Formula: see text] - 12 mmol/L) at delivery in patients experiencing the 2nd stage of labor (2STG), stratified for both FIGO-2015 pathologic intrapartum cardiotocography requiring expedited delivery (CTG_RED) and duration of 2nd stage of labor.

METHODS

3459 pregnancies experiencing the 2nd stage of labor and delivering at the Division of Obstetrics and Prenatal Medicine, IRCCS Sant'Orsola-Malpighi Hospital, Bologna (Italy), were identified between 2018 and 2019. Survival analysis was used to assess CSH and CIF for MA, stratified for FIGO-2015 pathologic CTG and relevant covariates.

RESULTS

FIGO-2015 pathological CTG with expedited operative delivery or urgent cesarean section within 10 or 20 min from diagnosis, respectively occurred in 282/3459 (8.20%). The rate of MA at delivery was 3.32% (115/3459). The spline of CSH for MA showed a direct correlation with the duration of 2STG always presenting higher values and greater slope in the presence of pathologic CTG, with plateau between 60 and 120 min and rapid increase after 120 min. The CIF at 180 min in the 2STG was 2.67% for nonpathological and 10.63% for pathological CTG_RED. Nulliparity, pathological CTG, and meconium-stained amniotic fluid resulted significant predictors of MA in our multivariable model.

CONCLUSION

The risk for MA increases moderately across the 2STG with nonpathological CTG and quadruples with pathological CTG_RED. Adjustment for other predictors of MA including meconium-stained amniotic fluid and nulliparity reveals a significant hazard increase for MA associated with pathologic CTG_RED.

Ophthalmic artery Doppler for pre-eclampsia prediction at the first trimester: a Bayesian survival-time model

OBJECTIVE

To develop a Bayesian survival-time model for the prediction of pre-eclampsia (PE) at the first trimester using a combination of established biomarkers including maternal characteristics and history, mean arterial pressure (MAP), uterine artery Doppler pulsatility index (UtA-PI), and Placental Growth Factor (PlGF)) with an ophthalmic artery Doppler peak ratio (PR) analysis.

METHODS

The receiving operator curve (ROC) analysis was used to determine the area under the curve (AUC), detection rate (DR), and positive screening cut-off value of the model in predicting the occurrence of early-onset PE (< 34 weeks' gestation) and preterm PE (< 37 weeks' gestation).

RESULTS

Of the 946 eligible participants, 71 (7.49%) subjects were affected by PE. The incidences of early-onset and preterm PE were 1% and 2.2%, respectively. At a 10% false-positive rate, using the high-risk cut-off 1:49, with AUC 0.981 and 95%CI 0.965-0.998, this model had an 100% of DR in predicting early-onset PE. The DR of this model in predicting preterm PE is 71% when using 1:13 as the cut-off, with AUC 0.919 and 95%CI 0.875-0.963.

CONCLUSION

Combination ophthalmic artery Doppler PR with the previously established biomarkers could improve the accuracy of early and preterm PE prediction at the first trimester screening.

Joint modeling of longitudinal measures of pneumonia and time to convalescence among pneumonia patients: a comparison of separate and joint models

BACKGROUND

Globally, pneumonia is the leading cause of children under age five morbidity and mortality with 98% of deaths in developing countries.

OBJECTIVE

This study aimed to identify the determinants of longitudinal measures of pneumonia and time to convalescence or recovery of under five admitted pneumonia patients at Felege Hiwot Referral Hospital, Bahir Dar, Ethiopia.

METHODS

A prospective cohort study was conducted among a randomly selected sample of 101 pneumonia patients using simple random sampling who were on follow up from December 2019 to February 2020. A Linear mixed effect model were used for the longitudinal outcomes and joint model for modeling both longitudinal and time to event outcomes jointly respectively.

RESULTS

The significant values of shared parameters in the survival sub model shows that the use of joint modeling of multivariate longitudinal outcomes with the time to event outcome is the best model compared to separate models. The estimated values of the association parameters: - 0.297(p-value = 0.0021), - 0.121) (p-value = < 0.001) and 0.5452 (p-value = 0.006) indicates association of respiratory rate, pulse rate and oxygen saturation respectively with time to recovery. The significant values show that there is an evidence to say that there is a negative relationship between longitudinal measures of respiratory rate and pulse rate with time to recovery and there is positive relationship between longitudinal measures of oxygen saturation with time to recovery. Variables age, birth order, dangerous signs, severity and visit time were significant factors on the longitudinal measure of pulse rate. The significant factors related to longitudinal measures of oxygen saturation were birth order, severity and visit. From this we can conclude that birth order, severity and visit were significant variables that simultaneously affect the longitudinal measures of respiratory rate, pulse rate and oxygen saturation of patients at 5% level of significance.

CONCLUSION

Results of multivariate joint analysis shows that severity was significant variable that jointly affects the three longitudinal measures and time to recovery of pneumonia patients and we can conclude that patients with severe pneumonia have high values of respiratory rate and pulse rate as well as less amount of oxygen saturation and they need longer time to recover from the disease.

Long-term exposure to low air pollutant concentrations and hospitalisation for respiratory diseases in older men: A prospective cohort study in Perth, Australia

Background

Acute exposure to ambient air pollution even at low concentrations has been associated with increased hospitalisation for respiratory diseases but the effects of long-term exposure are less certain. In this study, we investigated the associations between long-term exposures to PM_2.5, PM_2.5 absorbance and NO₂ and hospitalisation for asthma, chronic obstructive pulmonary disease and pneumonia in a cohort of older men living in Perth, Western Australia, a city where the levels of air pollutants are well below the world standards.

Materials and methods

The study population of 11,156 men with no prior hospitalisation for respiratory disease was drawn from the Health in Men Study (HIMS) cohort of men aged >65 years living in Perth, Western Australia between 1996-1999. PM_2.5, PM_2.5 absorbance (PM_2.5a) and NO₂ were measured across the Perth metropolitan area over three seasons in 2012. Land use regression (LUR) models were used to estimate annual concentrations of PM_2.5, PM_2.5 absorbance and NO₂ at the residential address of each participant from inception (1996) to 2015. Hospitalisation for respiratory disease between inception and 2015 was ascertained using the Western Australian Data Linkage System. The association between exposure to air pollution with hospitalisation for respiratory disease was examined using Cox regression analysis.

Results

No statistically significant associations were observed in the fully adjusted models. However, positive associations were observed with first hospitalisation for pneumonia (HR 1.08, 95% CI: 1.01–1.16) when adjusted for age, year of enrolment, smoking status, education, BMI and physical activity.

Conclusions

In this longitudinal study of older men we found no evidence of associations between increased long-term exposure to low-level air pollution with increased risk of hospitalisation for respiratory diseases in Perth, Australia. More studies on respiratory morbidity associated with exposure to low levels of air pollution are needed for more comprehensive understanding of the overall risk.

Prognosis of lasso-like penalized Cox models with tumor profiling improves prediction over clinical data alone and benefits from bi-dimensional pre-screening

BACKGROUND

Prediction of patient survival from tumor molecular '-omics' data is a key step toward personalized medicine. Cox models performed on RNA profiling datasets are popular for clinical outcome predictions. But these models are applied in the context of "high dimension", as the number p of covariates (gene expressions) greatly exceeds the number n of patients and e of events. Thus, pre-screening together with penalization methods are widely used for dimensional reduction.

METHODS

In the present paper, (i) we benchmark the performance of the lasso penalization and three variants (i.e., ridge, elastic net, adaptive elastic net) on 16 cancers from TCGA after pre-screening, (ii) we propose a bi-dimensional pre-screening procedure based on both gene variability and p-values from single variable Cox models to predict survival, and (iii) we compare our results with iterative sure independence screening (ISIS).

RESULTS

First, we show that integration of mRNA-seq data with clinical data improves predictions over clinical data alone. Second, our bi-dimensional pre-screening procedure can only improve, in moderation, the C-index and/or the integrated Brier score, while excluding irrelevant genes for prediction. We demonstrate that the different penalization methods reached comparable prediction performances, with slight differences among datasets. Finally, we provide advice in the case of multi-omics data integration.

CONCLUSIONS

Tumor profiles convey more prognostic information than clinical variables such as stage for many cancer subtypes. Lasso and Ridge penalizations perform similarly than Elastic Net penalizations for Cox models in high-dimension. Pre-screening of the top 200 genes in term of single variable Cox model p-values is a practical way to reduce dimension, which may be particularly useful when integrating multi-omics.

A new survival model based on ferroptosis-related genes (FRGS) for prognostic prediction in bladder cancer

BACKGROUND

Bladder cancer (BLCA) is a malignant urothelial carcinoma with a high mortality rate. Ferroptosis is a new type of programmed cell death and functions in suppressing tumor growth and progression. However, few studies focus on ferroptosis and BLCA.

MATERIALS AND METHODS

We explored the potential oncogenic roles of ferroptosis-related genes in BLCA based on multiple public datasets. We then used univariate and multivariate cox regression to build a new survival model based on ferroptosis-related genes to predict the survival of BLCA.

RESULTS

We found that 23 ferroptosis-related genes had a strong correlation with each other in BLCA. Eight ferroptosis-related genes, CDKN1A, HSPA5, NFE2L2, MT1G, FANCD2, CISD1, TFRC, NCOA4, had a significantly different expression and heat-map. HSPA5 and CISD1 have a statistically significant difference in OS and DFS. Besides, CISD1 had an ideal nomogram to predict the 1-3-5-year OS (C-index: 0.701, P < .001). Furthermore, HSPA5 and CISD1 had a lower DNA methylation rate than normal tissue and HSPA5 had a positive connection with TMB (P = .02). In addition, HSPA5 participated in the DNA replication and P53 signaling pathway, and CISD1 mediated the oxidative phosphorylation and positive regulation of the intrinsic apoptotic signaling pathway.

CONCLUSION

Ferroptosis-related genes had a strong correlation with BLCA, notably, HSPA5 and CISD1 may play a role in inducing ferroptosis to suppress bladder tumorigenesis and CISD1 can be a novel prognostic biomarker as well as an effective target for diagnosis and treatment in BLCA.

Open-source distributed learning validation for a larynx cancer survival model following radiotherapy

INTRODUCTION

Prediction models are useful to design personalised treatment. However, safe and effective implementation relies on external validation. Retrospective data are available in many institutions, but sharing between institutions can be challenging due to patient data sensitivity and governance or legal barriers. This study validates a larynx cancer survival model performed using distributed learning without any sensitive data leaving the institution.

METHODS

Open-source distributed learning software based on a stratified Cox proportional hazard model was developed and used to validate the Egelmeer et al. MAASTRO survival model across two hospitals in two countries. The validation optimised a single scaling parameter multiplied by the original predicted prognostic index. All analyses and figures were based on the distributed system, ensuring no information leakage from the individual centres. All applied software is provided as freeware to facilitate distributed learning in other institutions.

RESULTS

1745 patients received radiotherapy for larynx cancer in the two centres from Jan 2005 to Dec 2018. Limiting to a maximum of one missing value in the parameters of the survival model reduced the cohort to 1095 patients. The Harrell C-index was 0.74 (CI95%, 0.71-0.76) and 0.70 (0.66-0.75) for the two centres. However, the model needed a scaling update. In addition, it was found that survival predictions of patients undergoing hypofractionation were less precise.

CONCLUSION

Open-source distributed learning software was able to validate, and suggest a minor update to the original survival model without central access to patient sensitive information. Even without the update, the original MAASTRO survival model of Egelmeer et al. performed reasonably well, providing similar results in this validation as in its original validation.

Predictive performance for placental dysfunction related stillbirth of the competing risks model for small for gestational age fetuses

OBJECTIVES

First, to examine the predictive performance for placental dysfunction related stillbirths of the competing risks model for small for gestational age (SGA) fetuses based on a combination of maternal risk factors, estimated fetal weight (EFW) and uterine artery pulsatility index (UtA-PI); and second, to compare the performance of this model to that of stillbirth-specific model utilizing the same biomarkers and to the Royal College of Obstetricians and Gynecologists (RCOG) guideline for the investigation and management of the SGA fetus.

DESIGN

Prospective observational study.

SETTING

Two UK maternity hospitals.

POPULATION

131,514 women with singleton pregnancies attending for routine ultrasound examination at 19-24 weeks' gestation.

METHODS

The predictive performance for stillbirth achieved by three models was compared. Main outcome measure Placental dysfunction related stillbirth.

RESULTS

At 10% false positive rate, the competing risks model predicted 59%, 66% and 71% of placental dysfunction related stillbirths, at any gestation, at <37 weeks and at <32 weeks, respectively, which were similar to the respective figures of 62%, 70% and 73% for the stillbirth-specific model. At a screen positive rate of 21.8 %, as defined by the RCOG guideline, the competing risks model predicted 71%, 76% and 79% of placental dysfunction related stillbirths at any gestation, at <37 weeks and at <32 weeks, respectively, and the respective figures for the RCOG guideline were 40%, 44% and 42%.

CONCLUSION

The predictive performance for placental dysfunction related stillbirths by the competing risks model for SGA was similar to the stillbirth-specific model and superior to the RCOG guideline.

Adapted time-varying covariates Cox model for predicting future cirrhosis development performs well in a large hepatitis C cohort

Background

Patients with hepatitis C virus (HCV) frequently remain at risk for cirrhosis after sustained virologic response (SVR). Existing cirrhosis predictive models for HCV do not account for dynamic antiviral treatment status and are limited by fixed laboratory covariates and short follow up time. Advanced fibrosis assessment modalities, such as transient elastography, remain inaccessible in many settings. Improved cirrhosis predictive models are needed.

Methods

We developed a laboratory-based model to predict progression of liver disease after SVR. This prediction model used a time-varying covariates Cox model adapted to utilize longitudinal laboratory data and to account for antiretroviral treatment. Individuals were included if they had a history of detectable HCV RNA and at least 2 AST-to-platelet ratio index (APRI) scores available in the national Veterans Health Administration from 2000 to 2015, Observation time extended through January 2019. We excluded individuals with preexisting cirrhosis. Covariates included baseline patient characteristics and 16 time-varying laboratory predictors. SVR, defined as permanently undetectable HCV RNA after antiviral treatment, was modeled as a step function of time. Cirrhosis development was defined as two consecutive APRI scores > 2. We predicted cirrhosis development at 1-, 3-, and 5-years follow-up.

Results

In a national sample of HCV patients (n = 182,772) with a mean follow-up of 6.32 years, 42% (n = 76,854) achieved SVR before 2016 and 16.2% (n = 29,566) subsequently developed cirrhosis. The model demonstrated good discrimination for predicting cirrhosis across all combinations of laboratory data windows and cirrhosis prediction intervals. AUROCs ranged from 0.781 to 0.815, with moderate sensitivity 0.703–0.749 and specificity 0.723–0.767.

Conclusion

A novel adaptation of time-varying covariates Cox modeling technique using longitudinal laboratory values and dynamic antiviral treatment status accurately predicts cirrhosis development at 1-, 3-, and 5-years among patients with HCV, with and without SVR. It improves upon earlier cirrhosis predictive models and has many potential population-based applications, especially in settings without transient elastography available.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12911-021-01711-7.

Systematic analysis of the relationship between ovarian cancer prognosis and alternative splicing

Background

Ovarian cancer(OC) is the gynecological tumor with the highest mortality rate, effective biomarkers are of great significance in improving its prognosis. In recent years, there have been many studies on alternative splicing (AS) events, and the role of AS events in tumor has become a focus of attention.

Methods

Data were downloaded from the TCGA database and Univariate Cox regression analysis was performed to determine AS events associated with OC prognosis.Eight prognostic models of OC were constructed in R package, and the accuracy of the models were evaluated by the time-dependent receiver operating characteristic (ROC) curves.Eight types of survival curves were drawn to evaluate the differences between the high and low risk groups.Independent prognostic factors of OC were analyzed by single factor independent analysis and multi-factor independent prognostic analysis.Again, Univariate Cox regression analysis was used to analyze the relationship between splicing factors(SF) and AS events, and Gene Ontology(GO) and Kyoto Encyclopedia of Genes and Genomes(KEGG) enrichment analysis were performed on OS-related SFs to understand the pathways.

Results

Univariate Cox regression analysis showed that among the 15,278 genes, there were 31,286 overall survival (OS) related AS events, among which 1524 AS events were significantly correlated with OS. The area under the time-dependent receiver operating characteristic curve (AUC) of AT and ME were the largest and the RI was the smallest,which were 0.757 and 0.68 respectively. The constructed models have good value for the prognosis assessment of OC patients. Among the eight survival curves, AP was the most significant difference between the high and low risk groups, with a P value of 1.61e − 1.The results of single factor independent analysis and multi-factor independent prognostic analysis showed that risk score calculated by the model and age could be used as independent risk factors.According to univariate COX regression analysis,109 SFs were correlated with AS events and adjusted in two ways: positive and negative.

Conclusions

SFs and AS events can directly or indirectly affect the prognosis of OC patients. It is very important to find effective prognostic markers to improve the survival rate of OC.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13048-021-00866-1.

Exploring transition durations of rear-end collisions based on vehicle trajectory data: A survival modeling approach

The time-to-collision (TTC) index and its extended variants have been widely utilized to assess rear-end collision risks, but the characteristics of the time-series data have not been fully explored, especially for the transition from safe to risky conditions. This study proposes a novel approach in rear-end collision risk analysis based on the concept of transition durations. The vehicle trajectory data were extracted and the TTC index was used to identify risky and safe conditions. Three important transition durations are defined and their rationalities for evaluating rear-end collision risks are examined by developing random-parameters accelerated failure time (AFT) survival models. Furthermore, a typical case from real trajectory data is taken to discuss the limitations of using TTC and its variants, and the advantage of the proposed transition durations. The results of random-parameters AFT models reveal contributing factors affecting the length of three durations and demonstrate the rationality of transition durations in rear-end collision risks analysis. It is indicated that the proposed method outperforms TTC and its variants in evaluating rear-end collision risks, because it could not only provide the information of time point but also the variation of time-series data.

Clinical characteristics and risk factors for mortality in COVID-19 inpatients in Birjand, Iran: a single-center retrospective study

Background

The coronavirus disease 2019(COVID-19) has affected mortality worldwide. The Cox proportional hazard (CPH) model is becoming more popular in time-to-event data analysis. This study aimed to evaluate the clinical characteristics in COVID-19 inpatients including (survivor and non-survivor); thus helping clinicians give the right treatment and assess prognosis and guide the treatment.

Methods

This single-center study was conducted at Hospital for COVID-19 patients in Birjand. Inpatients with confirmed COVID-19 were included. Patients were classified as the discharged or survivor group and the death or non-survivor group based on their outcome (improvement or death). Clinical, epidemiological characteristics, as well as laboratory parameters, were extracted from electronic medical records. Independent sample T test and the Chi-square test or Fisher’s exact test were used to evaluate the association of interested variables. The CPH model was used for survival analysis in the COVID-19 death patients. Significant level was set as 0.05 in all analyses.

Results

The results showed that the mortality rate was about (17.4%). So that, 62(17%) patients had died due to COVID-19, and 298 (83.6%) patients had recovered and discharged. Clinical parameters and comorbidities such as oxygen saturation, lymphocyte and platelet counts, hemoglobin levels, C-reactive protein, and liver and kidney function, were statistically significant between both studied groups. The results of the CPH model showed that comorbidities, hypertension, lymphocyte counts, platelet count, and C-reactive protein level, may increase the risk of death due to the COVID-19 as risk factors in inpatients cases.

Conclusions

Patients with, lower lymphocyte counts in hemogram, platelet count and serum albumin, and high C-reactive protein level, and also patients with comorbidities may have more risk for death. So, it should be given more attention to risk management in the progression of COVID-19 disease.

Prediction of transient ischemic attack and minor stroke in people with type 2 diabetes mellitus

AIMS

People with type 2 diabetes (T2DM) have an increased risk of transient ischemic attack and minor stroke (TIA) which are frequently followed by an ischemic stroke. We aimed to develop a predictive model for incident TIA in people with T2DM.

METHODS

We pooled data from two longitudinal cohort studies, Atherosclerosis Risk in Communities (ARIC) and the Cardiovascular Health Study (CHS), using a two-stage approach. First, we used a random effects model to interpolate risk factors of individuals between follow-up exams. Second, we used forward selection to develop a proportional hazards model for time to incident TIA. We internally validated our model using 10-fold cross-validation.

RESULTS

Among 3575 participants with T2DM, mean (SD) age was 60 (10) years and body mass index was 30 (6) kg/m2. Sixty-nine incident TIAs occurred during 38,364 person-years of follow-up. The multivariable model included age at diagnosis of diabetes (hazard ratio 1.13 (95% confidence interval: 1.05,1.21) per year), systolic blood pressure (1.25 (1.04,1.49) per 10 mmHg), a quadratic function of diastolic blood pressure, and history of congestive heart failure (2.08 (1.26, 3.42)). The median cross-validated Harrell's C-index was 0.80.

CONCLUSION

Blood pressure and heart failure are risk factors for the earliest stages of cerebrovascular disease.

Bile acid indices as biomarkers for liver diseases II: The bile acid score survival prognostic model

BACKGROUND

Cholestatic liver diseases are characterized by an accumulation of toxic bile acids (BA) in the liver, blood and other tissues which lead to progressive liver injury and poor prognosis in patients.

AIM

To discover and validate prognostic biomarkers of cholestatic liver diseases based on the urinary BA profile.

METHODS

We analyzed urine samples by liquid chromatography-tandem mass spectrometry and investigated the use of the urinary BA profile to develop survival models that can predict the prognosis of hepatobiliary diseases. The urinary BA profile, a set of non-BA parameters, and the adverse events of liver transplant and/or death were monitored in 257 patients with cholestatic liver diseases for up to 7 years. The BA profile was characterized by calculating BA indices, which quantify the composition, metabolism, hydrophilicity, formation of secondary BA, and toxicity of the BA profile. We have developed and validated the bile-acid score (BAS) model (a survival model based on BA indices) to predict the prognosis of cholestatic liver diseases.

RESULTS

We have developed and validated a survival model based on BA (the BAS model) indices to predict the prognosis of cholestatic liver diseases. Our results demonstrate that the BAS model is more accurate and results in higher true-positive and true-negative prediction of death compared to both non-BAS and model for end-stage liver disease (MELD) models. Both 5- and 3-year survival probabilities markedly decreased as a function of BAS. Moreover, patients with high BAS had a 4-fold higher rate of death and lived for an average of 11 mo shorter than subjects with low BAS. The increased risk of death with high vs low BAS was also 2-4-fold higher and the shortening of lifespan was 6-7-mo lower compared to MELD or non-BAS. Similarly, we have shown the use of BAS to predict the survival of patients with and without liver transplant (LT). Therefore, BAS could be used to define the most seriously ill patients, who need earlier intervention such as LT. This will help provide guidance for timely care for liver patients.

CONCLUSION

The BAS model is more accurate than MELD and non-BAS models in predicting the prognosis of cholestatic liver diseases.

Genetic analysis of resistance in Mekong striped catfish (Pangasianodon hypophthalmus) to bacillary necrosis caused by Edwardsiella ictaluri

The aim of this study was to analyse four cohabitation challenge-test experiments with Mekong striped catfish (Pangasianodon hypophthalmus) against the bacterium Edwardsiella ictaluri. The data were genetically analysed per experiment by three models: 1) a cross-sectional linear model; 2) a cross-sectional threshold model; and 3) a linear survival model, at both 50% mortality (for models 1 and 2) and at the end of the test (for all three models). In two of the experiments (3 and 4) that were carried out in two replicated tanks, the predicted family effects (sum of sire, dam and common environmental effects) in each tank were correlated with the family survival in the other replicated tank (cross-validation). The heritability estimates of resistance to E. ictaluri infection were ≤ 0.012 with the survival model, and up to 0.135 - 0.220 (50% survival) and 0.085 and 0.174 (endpoint survival) for the cross-sectional linear and threshold models, respectively. The challenge test should aim for an endpoint survival that ceases naturally at 50%. Then, genetic analysis should be carried out for survival at the endpoint (reflecting susceptibility) with a simple cross-sectional linear model.

Estimation of treatment effects and model diagnostics with two-way time-varying treatment switching: an application to a head and neck study

Treatment switching frequently occurs in clinical trials due to ethical reasons. Intent-to-treat analysis without adjusting for switching yields biased and inefficient estimates of the treatment effects. In this paper, we propose a class of semiparametric semi-competing risks transition survival models to accommodate two-way time-varying switching. Theoretical properties of the proposed method are examined. An efficient expectation-maximization algorithm is derived to obtain maximum likelihood estimates and model diagnostic tools. Existing software is used to implement the algorithm. Simulation studies are conducted to demonstrate the validity of the model. The proposed method is further applied to data from a clinical trial with patients having recurrent or metastatic squamous-cell carcinoma of head and neck.

Socioeconomic sequelae of drug abuse in a Swedish national cohort

BACKGROUND

Drug abuse is frequently associated with negative sequelae such as reduced socioeconomic functioning. The extent to which these associations are attributable to a causal role of the disorder versus confounding factors that increase risk for both drug abuse and negative socioeconomic outcomes is unclear.

METHODS

Drug abuse cases were identified using Swedish national medical, pharmacy, and criminal registers. Applying Cox proportional hazard models, we tested the association between drug abuse and four outcomes: early retirement, social assistance, unemployment, and income at age 50. We used co-relative models to determine whether familial confounding factors accounted for observed associations.

RESULTS

In models adjusted for birth year, education, and early onset externalizing behavior, drug abuse was strongly associated with early retirement (hazard ratios [HR] = 5.13-6.28), social assistance (HR = 6.74-7.89), and income at age 50 (beta = -0.19 to -0.12); it was more modestly associated with unemployment (HR = 1.05-1.20). For social assistance and income (both sexes), and early retirement (women only), a model in which the association was partly attributable to familial factors fit the data well; residual associations support a partially causal role of drug abuse. For unemployment and early retirement among men, there was little evidence of familial confounding.

CONCLUSIONS

The negative socioeconomic sequelae of drug abuse are likely due in part to familial confounding factors in conjunction with a causal relationship and/or unmeasured non-familial confounders. Relative contributions from distinct mechanisms differed across socioeconomic outcomes, which could have implications for understanding the potential impact of prevention and intervention efforts.

All-cause mortality and long-term exposure to low level air pollution in the '45 and up study' cohort, Sydney, Australia, 2006-2015

BACKGROUND

Epidemiological studies show that long-term exposure to ambient air pollution reduces life expectancy. Most studies have been in environments with relatively high concentrations such as North America, Europe and Asia. Associations at the lower end of the concentration-response function are not well defined.

OBJECTIVES

We assessed associations between all-cause mortality and exposure to annual average particulate matter <2.5 μm (PM_2.5) and nitrogen dioxide (NO₂) in Sydney, Australia, where concentrations are relatively low.

METHODS

The '45 and Up Study' comprises a prospective longitudinal cohort from the state of New South Wales, Australia with 266,969 participants linked to death registry data. We analyzed data for the participants who resided in Sydney at baseline questionnaire (n = 75,268). Exposures to long-term pollution were estimated using annual averages from a chemical transport model (PM_2.5), and a satellite-based land-use regression model (NO₂). Socio-demographic information was extracted from the baseline questionnaire. Cox proportional hazard models were applied to estimate associations, while adjusting for covariates.

RESULTS

In our cohort mean annual PM_2.5 was 4.5 μg/m³ and mean NO₂ was 17.8 μg/m³. The mortality rate was 4.4% over the 7 years of follow up. Models that adjusted for individual-level and area-level risk factors resulted in a detrimental non statistically significant hazard ratio (HR) of 1.05 (95% CI: 0.98-1.12) per 1 μg/m³ increase in PM_2.5, and 1.03 (95% CI: 0.98-1.07) per 5 μg/m³ increase in NO₂.

CONCLUSIONS

We found evidence that low-level air pollution exposure was associated with increased risk of mortality in this cohort of adults aged 45 years and over, even at the relatively low concentrations seen in Sydney. However, a clear determination of the association with mortality is difficult because the results were sensitive to some covariates. Our findings are supportive of emerging evidence that exposure to low levels of air pollution reduces life expectancy.

Recent Developments in Health Economic Modelling of Cancer Therapies

Arguably, the most common structure currently adopted for oncology modelling is the three-state partitioned survival model with the following states: stable disease, post-progression and dead. This design can, therefore, be adopted to capture the progressive nature of cancer. This chapter outlines the three-state model approach as well as introducing several other key aspects of economic modelling in oncology.

Cost-effectiveness of nivolumab in patients with advanced renal cell carcinoma treated in the United States

Background

We evaluated the cost-effectiveness of nivolumab versus everolimus in patients with advanced renal cell carcinoma (RCC) from a US payer perspective.

Methods

A partitioned survival model consisting of three health states, progression-free survival (PFS), progressive disease, and death, was developed to evaluate the cost-effectiveness of intravenous nivolumab versus oral everolimus over a lifetime. The proportion of patients in each state was calculated based on parametric distributions fitted to PFS and overall survival (OS) data from CheckMate 025 (N = 821), a large randomized phase 3 trial of nivolumab versus everolimus for advanced RCC. Health state utility data were derived from CheckMate 025 EQ-5D data. Scenario analyses and deterministic and probabilistic sensitivity analyses assessed the impact of uncertainty in model inputs on outcomes.

Results

Over a 25-year lifetime horizon, treatment with nivolumab resulted in a gain of 0.64 quality-adjusted life-years (QALYs) versus everolimus. Nivolumab had greater total costs versus everolimus ($US197,089 vs. $US163,902), mainly due to higher acquisition costs. The incremental cost-utility ratio (ICUR), a measure of incremental costs divided by incremental QALYs, was $US51,714 per QALY gained for nivolumab versus everolimus, and an incremental cost-effectiveness ratio was $US44,576 per life-year gained for nivolumab versus everolimus. In sensitivity analyses, average body weight had the greatest impact on the ICUR for nivolumab versus everolimus (base case $US51,714; range $US8863-$US94,566). At a $US150,000 willingness-to-pay (WTP) threshold, nivolumab had a 91.7% probability of being cost-effective versus everolimus.

Conclusions

In the United States, at a WTP threshold of $US150,000 per QALY, nivolumab was found to be cost-effective. Key drivers of cost-effectiveness were survival inputs for OS and the average weight of patients; the latter directly affects nivolumab drug acquisition cost.

Can stress biomarkers predict preterm birth in women with threatened preterm labor?

BACKGROUND

Preterm birth is a major paediatric challenge difficult to prevent and with major adverse outcomes. Prenatal stress plays an important role on preterm birth; however, there are few stress-related models to predict preterm birth in women with Threatened Preterm Labor (TPL).

OBJECTIVE

The aim of this work is to study the influence of stress biomarkers on time until birth in TPL women.

METHODS

Eligible participants were pregnant women between 24 and 31 gestational weeks admitted to the hospital with TPL diagnosis (n=166). Stress-related biomarkers (α-amylase and cortisol) were determined in saliva samples after TPL diagnosis. Participants were followed-up until labor. A parametric survival model was constructed based on α-amylase, cortisol), TPL gestational week, age, parity, and multiple pregnancy. The model was adjusted using a logistic distribution and it was implemented as a nomogram to predict the labor probability at 7- and 14-day term.

RESULTS

The time until labor was associated with cortisol (p=0.001), gestational week at TPL diagnosis (p=0.004), and age (p=0.02). Importantly, high cortisol levels at TPL diagnosis were predictive of latency to labor. Validation of the model yielded an optimum corrected AUC value of 0.63.

CONCLUSIONS

High cortisol levels at TPL diagnosis may have an important role in the preterm birth prediction. Our statistical model implemented as a nomogram provided accurate predictions of individual prognosis of pregnant women.

Bayesian regression model for recurrent event data with event-varying covariate effects and event effect

In the course of hypertension, cardiovascular disease events (e.g., stroke, heart failure) occur frequently and recurrently. The scientific interest in such study may lie in the estimation of treatment effect while accounting for the correlation among event times. The correlation among recurrent event times come from two sources: subject-specific heterogeneity (e.g., varied lifestyles, genetic variations, and other unmeasurable effects) and event dependence (i.e., event incidences may change the risk of future recurrent events). Moreover, event incidences may change the disease progression so that there may exist event-varying covariate effects (the covariate effects may change after each event) and event effect (the effect of prior events on the future events). In this article, we propose a Bayesian regression model that not only accommodates correlation among recurrent events from both sources, but also explicitly characterizes the event-varying covariate effects and event effect. This model is especially useful in quantifying how the incidences of events change the effects of covariates and risk of future events. We compare the proposed model with several commonly used recurrent event models and apply our model to the motivating lipid-lowering trial (LLT) component of the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT) (ALLHAT-LLT).

Establishment of an Adjusted Prognosis Analysis Model for Initially Diagnosed Non-Small-Cell Lung Cancer With Brain Metastases From Sun Yat-Sen University Cancer Center

BACKGROUND

The current published prognosis models for brain metastases (BMs) from cancer have not addressed the issue of either newly diagnosed non-small-cell lung cancer (NSCLC) with BMs or the lung cancer genotype. We sought to build an adjusted prognosis analysis (APA) model, a new prognosis model specifically for NSCLC patients with BMs at the initial diagnosis using adjusted prognosis analysis (APA).

PATIENTS AND METHODS

The model was derived using data from 1158 consecutive patients, with 837 in the derivation cohort and 321 in the validation cohort. The patients had initially received a diagnosis of BMs from NSCLC at Sun Yat-Sen University Cancer Center from 1994 to 2015. The prognostic factors analyzed included patient characteristics, disease characteristics, and treatments. The APA model was built according to the numerical score derived from the hazard ratio of each independent prognostic variable. The predictive accuracy of the APA model was determined using a concordance index and was compared with current prognosis models. The results were validated using bootstrap resampling and a validation cohort.

RESULTS

We established 2 prognostic models (APA 1 and 2) for the whole group of patients and for those with known epidermal growth factor receptor (EGFR) genotype, respectively. Six factors were independently associated with survival time: Karnofsky performance status, age, smoking history (replaced by EGFR mutation in APA 2), local treatment of intracranial metastases, EGFR-tyrosine kinase inhibitor treatment, and chemotherapy. Patients in the derivation cohort were stratified into low- (score, 0-2), moderate- (score, 3-5), and high-risk (score 6-7) groups according to the median survival time (16.6, 10.3, and 5.2 months, respectively; P < .001). The results were further confirmed in the validation cohort.

CONCLUSION

Compared with recursive partition analysis and graded prognostic assessment, APA seems to be more suitable for initially diagnosed NSCLC with BMs.

Temporal trends in the retention of BVD+ calves and associated animal and herd-level risk factors during the compulsory eradication programme in Ireland

The national BVD eradication programme in Ireland started on a voluntary basis in 2012, becoming compulsory in 2013. The programme relies on accurate identification and prompt removal of BVD+ calves. However, a minority of herd owners have chosen to retain BVD+ animals (defined as still being alive more than seven weeks after the date of the initial test), typically with a view to fattening them to obtain some salvage value. During each year of the programme, additional measures have been introduced and implemented to encourage prompt removal of BVD+ animals. The objective of this study was to describe temporal trends in the retention of BVD+ calves and associated animal and herd-level risk factors during the first three years of the compulsory eradication programme in Ireland. The study population included all BVD+ calves born in Ireland in 2013-2015. A parametric survival model was developed to model the time from the initial BVD test until the animal was slaughtered/died on farm or until 31 December 2015 (whichever was earlier). A total of 29,504 BVD+ animals, from 13,917 herds, were included in the study. The proportion of BVD+ animals that were removed from the herd within 7 weeks of the initial test date increased from 43.7% in 2013 to 70.3% in 2015. BVD+ animals born in 2015 had a much lower survival time (median=33days) compared to the 2013 birth cohort (median=62days), with a year on year reduction in survival of BVD+ calves. In the initial parametric survival models, all interactions with herd type were significant. Therefore, separate models were developed for beef and dairy herds. Overall the results of the survival models were similar, with birth year, BVD+ status, herd size, county of birth and birth month consistently identified as risk factors independent of herd type (beef or dairy) or the numbers of BVD+ animals (single or multiple) in the herd. In addition, the presence of a registered mobile telephone number was identified as a risk factor in all models except for dairy herds with a single BVD+, while the sex of the BVD+ calf was only identified as a risk factor in this model. Significant progress has been made in addressing the issue of retention of BVD+ calves, however, there is a need for further improvement. A number of risk factors associated with retention have been identified suggesting areas where future efforts can be addressed.

Trend of determinants of birth interval dynamics in Bangladesh

BACKGROUND

The distribution of birth intervals can be used to draw attention to important characteristics of dynamics of fertility process. The main objective of this paper is to examine the effects of socioeconomic, demographic and proximate determinants on the length of birth intervals of women of Bangladesh and also to see whether the effects are changed over the years.

METHODS

Birth intervals can be considered as correlated time-to-event data because two or more birth intervals could correspond to a single mother. Moreover, women from the same neighborhood usually share certain unobserved characteristics, which may also lead to correlated time-to-event data (birth interval). A parametric random effect (frailty) model is used to analyze correlated birth interval data obtained from three Bangladesh Demographic and Health Surveys (BDHS 2004, 2007, and 2011).

RESULTS

The results show that alongside different socioeconomic, demographic determinants, unobserved community and mother effects have considerable impact on birth interval in Bangladesh. However, the effects of different factors on birth interval changes in a small scale over the duration of 2004-2011.

CONCLUSIONS

Efficient policy is a priority for promoting longer birth spacing and achieving a decline in fertility.

Criteria-specific long-term survival prediction model for hepatocellular carcinoma patients after liver transplantation

AIM: To establish a model to predict long-term survival of hepatocellular carcinoma (HCC) patients after liver transplantation (MHCAT).

METHODS: Two hundred and twenty-three patients with HCC were followed for at least six years to identify independent risk factors for long-term survival after liver transplantation (LT). The criteria for HCC liver transplantation included the Milan, University of California San Francisco, Hangzhou and Shanghai Fudan criteria. The Cox regression model was used to build MHCAT specifying these criteria. A survival analysis was carried out for patients with high or low risk.

RESULTS: The one-, three- and five-year cumulative survival of HCC patients after LT was 78.9%, 53.2% and 46.4%, respectively. Of the HCC patients, the proportion meeting the Hangzhou and Fudan criteria was significantly higher than the proportion meeting the Milan criteria (64.6% vs 39.5%, 52.0% vs 39.5%, P < 0.05). Moreover, the proportion meeting the Hangzhou criteria was also significantly higher than the proportion meeting other criteria (P < 0.01). Pre-operative alfa-fetoprotein level, intraoperative blood loss and retransplantation were common significant predictors of long-term survival in HCC patients with reference to the Milan, University of California San Francisco and Fudan criteria, whereas in MHCAT based on the Hangzhou criteria, total bilirubin, intraoperative blood loss and retransplantation were independent predictors. The c-statistic for MHCAT was 0.773-0.824, with no statistical difference among these four criteria. According to the MHCAT scoring system, patients with low risk showed a higher five-year survival than those with high risk (P < 0.001).

CONCLUSION: MHCAT can effectively predict long-term survival for HCC patients, but needs to be verified by multi-center retrospective or randomized controlled trials.

Development of status epilepticus, sustained calcium elevations and neuronal injury in a rat survival model of lethal paraoxon intoxication

Paraoxon (POX) is an active metabolite of organophosphate (OP) pesticide parathion that has been weaponized and used against civilian populations. Exposure to POX produces high mortality. OP poisoning is often associated with chronic neurological disorders. In this study, we optimize a rat survival model of lethal POX exposures in order to mimic both acute and long-term effects of POX intoxication. Male Sprague-Dawley rats injected with POX (4mg/kg, ice-cold PBS, s.c.) produced a rapid cholinergic crisis that evolved into status epilepticus (SE) and death within 6-8min. The EEG profile for POX induced SE was characterized and showed clinical and electrographic seizures with 7-10Hz spike activity. Treatment of 100% lethal POX intoxication with an optimized three drug regimen (atropine, 2mg/kg, i.p., 2-PAM, 25mg/kg, i.m. and diazepam, 5mg/kg, i.p.) promptly stopped SE and reduced acute mortality to 12% and chronic mortality to 18%. This model is ideally suited to test effective countermeasures against lethal POX exposure. Animals that survived the POX SE manifested prolonged elevations in hippocampal [Ca(2+)]i (Ca(2+) plateau) and significant multifocal neuronal injury. POX SE induced Ca(2+) plateau had its origin in Ca(2+) release from intracellular Ca(2+) stores since inhibition of ryanodine/IP3 receptor lowered elevated Ca(2+) levels post SE. POX SE induced neuronal injury and alterations in Ca(2+) dynamics may underlie some of the long term morbidity associated with OP toxicity.

Comparison of bovine tuberculosis recurrence in Irish herds between 1998 and 2008

During the last several decades in Ireland, there has been substantial scientific progress in our understanding and related policy changes in the bovine tuberculosis (bTB) eradication programme. A range of performance measurements are routinely available, each highlighting a steadily improving situation in Ireland. However, recent research has highlighted an on-going problem of residual infection, contributing to recurrent breakdowns. In light of this general improvement, but also cognisant of residual infection, a critical evaluation of changes in effectiveness of managing recurrence is particularly valuable. Therefore, the objective of the study was to compare the herd-level risk of recurrence of bTB in Ireland between 1998 and 2008. A retrospective cohort study was carried out, using a Cox proportional-hazards model, to compare the risk of restriction recurrence in herds derestricted during 1998 and 2008. These herds were observed for up to 3 years from the end of the 'index restriction'. At the univariable level, 46.4% and 34.8% of study herds derestricted in 1998 and 2008, respectively, had a subsequent breakdown during the study period (χ(2)=70.6, P<0.001). In the multivariable analysis, there has been a significant reduction in bTB recurrence in Ireland, with 2008-derestricted herds being 0.74 times (95% confidence interval: 0.68-0.81) as likely to be restricted during the subsequent study period compared with 1998-derestricted herds. In the final Cox model, the rate of a future breakdown increased with increasing herd size, increasing number of standard reactors in the index restriction, increasing percentage of newly restricted herds within the District Electoral Division (DED) and if the herd had a previous bTB episode in the previous 5 years. The risk varied across herd type. The results from the current study provide further reassurance of an improved national situation, both in terms of limiting the establishment of new infection (bTB incidence) and in effectively clearing infection once detected (recurrence following derestriction). Recurrence of bTB requires effective implementation of multiple control strategies, focusing on identifying and removing residually infected cattle, and limiting environmental sources of infection, which in Ireland primarily relates to badgers.

A Parametric Survival Model When a Covariate is Subject to Left-Censoring

PROBLEM STATEMENT

Modeling survival data with a set of covariates usually assumes that the values of the covariates are fully observed. However, in a variety of applications, some values of a covariate may be left-censored due to inadequate instrument sensitivity to quantify the biospecimen. When data are left-censored, the true values are missing but are known to be smaller than the detection limit. The most commonly used ad-hoc method to deal with nondetect values is to substitute the nondetect values by the detection limit. Such ad-hoc analysis of survival data with an explanatory variable subject to left-censoring may provide biased and inefficient estimators of hazard ratios and survivor functions.

METHOD

We consider a parametric proportional hazards model to analyze time-to-event data. We propose a likelihood method for the estimation and inference of model parameters. In this likelihood approach, instead of replacing the nondetect values by the detection limit, we adopt a numerical integration technique to evaluate the observed data likelihood in the presence of a left-censored covariate. Monte Carlo simulations were used to demonstrate various properties of the proposed regression estimators including the consistency and efficiency.

RESULTS

The simulation study shows that the proposed likelihood approach provides approximately unbiased estimators of the model parameters. The proposed method also provides estimators that are more efficient than those obtained under the ad-hoc method. Also, unlike the ad-hoc estimators, the coverage probabilities of the proposed estimators are at their nominal level. Analysis of a large cohort study, genetic and inflammatory marker of sepsis study, shows discernibly different results based on the proposed method.

CONCLUSION

Naive use of detection limit in a parametric survival model may provide biased and inefficient estimators of hazard ratios and survivor functions. The proposed likelihood approach provides approximately unbiased and efficient estimators of hazard ratios and survivor functions.