Capturing simple and complex time-dependent effects using flexible parametric survival models: A simulation study

Explanatory factors for the survival benefit among hip and knee arthroplasty patients with osteoarthritis

Objective

Studies have shown that osteoarthritis patients who underwent a primary total hip or knee arthroplasty (THA/TKA) experience better survival than the general population, yet there is limited evidence explaining this counter-intuitive difference. We investigated whether this better survival is also present in the Netherlands and to what extent it could be explained by a patient selection effect, whereby patients with more favorable health and socioeconomic status (SES) are more likely to receive THA/TKA.

Design

In this registry-based study, we compared the survival, health and SES of THA/TKA osteoarthritis patients to those of the general Dutch population. The patient cohort included 224,785 THA and 198,691 TKA patients who underwent an arthroplasty between 2010-2020. The proportions of the survival differences explained by better health (as measured by the EQ-5D) and SES (postcode-level) were estimated using spline-based survival models and Dutch lifetables.

Results

The eleven-year survival of THA and TKA patients were 8.7% and 8.1% better than the general population. Although health and SES predicted individual survival, they explained only ≈7% of the survival benefit.

Conclusions

Our study confirmed that Dutch osteoarthritis THA/TKA patients experience better survival than the general population, but raises important questions as to the explanation. A more favorable health status and/or SES did not explain most of the survival benefit. This may be partly due to limitations of the available measures of health and SES in our study, but also leaves other explanations (e.g. barriers to receive access to care, lifestyle changes) open for further research.

Mental illness and non-metastatic colorectal cancer treatment and survival, a nationwide study of almost 70,000 patients

BACKGROUND AND PURPOSE

The impact of mental illness on treatment and outcomes for patients with colorectal cancer (CRC) has not been investigated with potential confounders and mediators accounted for.

PATIENTS AND METHODS

Colorectal Cancer Database (CRCBaSe), a linked national registry database, was used to analyse stage I-III CRC patients diagnosed in Sweden between 2008 and 2021. The exposure of interest was a history of mental illness. Treatment outcomes were analysed with logistic regressions. Flexible parametric models were fitted for survival analysis. Analyses were adjusted for pre-specified confounders.

RESULTS

Patients with a history of severe mental illness presented with more advanced tumours and comorbidities. They were more likely to undergo emergency surgery (OR 1.56, 95% CI 1.32-1.84) and less likely to receive adjuvant treatment (OR 0.65, 95% CI 0.53-0.80) than patients with no history of mental illness. Five-year standardised overall survival (OS) was worse for those with a history of mild and severe mental illness, 64.6% (95%CI 63.9-65.3) and 61.8% (95%CI 59.7-63.8) compared to those without 69.3% (95%CI 68.9-69.7). Although time to recurrence was not significantly impacted, standardised survival after recurrence was worse for patients with a history of severe mental illness, with a 3-year survival after recurrence of 24% compared to 30% in those without a history of mental illness.

INTERPRETATION

Although the differences were smaller compared to previous studies, patients with a history of mental illnesses still do worse. The management of CRC patients with psychiatric comorbidities presents complex challenges necessitating personalised solutions.

Income disparities in loss in life expectancy after colon and rectal cancers: a Swedish register-based study

BACKGROUND

Differences in the prognosis after colorectal cancer (CRC) by socioeconomic position (SEP) have been reported previously; however, most studies focused on survival differences at a particular time since diagnosis. We quantified the lifetime impact of CRC and its variation by SEP, using individualised income to conceptualise SEP.

METHODS

Data included all adults with a first-time diagnosis of colon or rectal cancers in Sweden between 2008 and 2021. The analysis was done separately for colon and rectal cancers using flexible parametric models. For each cancer and income group, we estimated the life expectancy in the absence of cancer, the life expectancy in the presence of cancer and the loss in life expectancy (LLE).

RESULTS

We found large income disparities in life expectancy after a cancer diagnosis, with larger differences among the youngest patients. Higher income resulted in more years lost following a cancer diagnosis. For example, 40-year-old females with colon cancer lost 17.64 years if in the highest-income group and 13.68 years if in the lowest-income group. Rectal cancer resulted in higher LLE compared with colon cancer. Males lost a larger proportion of their lives. All patients, including the oldest, lost more than 30% of their remaining life expectancy. Based on the number of colon and rectal cancer diagnoses in 2021, colon cancer results in almost double the number of years lost compared with rectal cancer (24 669 and 12 105 years, respectively).

CONCLUSION

While our results should be interpreted in line with what individualised income represents, they highlight the need to address inequalities.

Survival trends for patients diagnosed with cutaneous malignant melanoma in the Nordic countries 1990-2016: The NORDCAN survival studies

BACKGROUND

The survival in patients diagnosed with cutaneous malignant melanoma (CMM) has improved in the Nordic countries in the last decades. It is of interest to know if these improvements are observed in all ages and for both women and men.

METHODS

Patients diagnosed with CMM in the Nordic countries in 1990-2016 were identified in the NORDCAN database. Flexible parametric relative survival models were fitted, except for Iceland where a non-parametric Pohar-Perme approach was used. A range of survival metrics were estimated by sex, both age-standardised and age-specific.

RESULTS

The 5-year relative survival improved in all countries, in both women and men and across age. While the improvement was more pronounced in men, women still had a higher survival at the end of the study period. The survival was generally high, with age-standardised estimates of 5-year relative survival towards the end of the study period ranging from 85% in Icelandic men to 95% in Danish women. The age-standardised and reference-adjusted 5-year crude probability of death due to CMM ranged from 5% in Danish and Swedish women to 13% in Icelandic men.

CONCLUSION

Although survival following CMM was relatively high in the Nordic countries in 1990, continued improvements in survival were observed throughout the study period in both women and men and across age.

An illness-death multistate model to implement delta adjustment and reference-based imputation with time-to-event endpoints

With a treatment policy strategy, therapies are evaluated regardless of the disturbance caused by intercurrent events (ICEs). Implementing this estimand is challenging if subjects are not followed up after the ICE. This circumstance can be dealt with using delta adjustment (DA) or reference-based (RB) imputation. In the survival field, DA and RB imputation have been researched so far using multiple imputation (MI). Here, we present a fully analytical solution. We use the illness-death multistate model with the following transitions: (a) from the initial state to the event of interest, (b) from the initial state to the ICE, and (c) from the ICE to the event. We estimate the intensity function of transitions (a) and (b) using flexible parametric survival models. Transition (c) is assumed unobserved but identifiable using DA or RB imputation assumptions. Various rules have been considered: no ICE effect, DA under proportional hazards (PH) or additive hazards (AH), jump to reference (J2R), and (either PH or AH) copy increment from reference. We obtain the marginal survival curve of interest by calculating, via numerical integration, the probability of transitioning from the initial state to the event of interest regardless of having passed or not by the ICE state. We use the delta method to obtain standard errors (SEs). Finally, we quantify the performance of the proposed estimator through simulations and compare it against MI. Our analytical solution is more efficient than MI and avoids SE misestimation-a known phenomenon associated with Rubin's variance equation.

Inequalities in treatment among patients with colon and rectal cancer: a multistate survival model using data from England national cancer registry 2012-2016

BACKGROUND

Individual and tumour factors only explain part of observed inequalities in colorectal cancer survival in England. This study aims to investigate inequalities in treatment in patients with colorectal cancer.

METHODS

All patients diagnosed with colorectal cancer in England between 2012 and 2016 were followed up from the date of diagnosis (state 1), to treatment (state 2), death (state 3) or censored at 1 year after the diagnosis. A multistate approach with flexible parametric model was used to investigate the effect of income deprivation on the probability of remaining alive and treated in colorectal cancer.

RESULTS

Compared to the least deprived quintile, the most deprived with stage I-IV colorectal cancer had a lower probability of being alive and treated at all the time during follow-up, and a higher probability of being untreated and of dying. The probability differences (most vs. least deprived) of being alive and treated at 6 months ranged between -2.4% (95% CI: -4.3, -1.1) and -7.4% (-9.4, -5.3) for colon; between -2.0% (-3.5, -0.4) and -6.2% (-8.9, -3.5) for rectal cancer.

CONCLUSION

Persistent inequalities in treatment were observed in patients with colorectal cancer at every stage, due to delayed access to treatment and premature death.

Modifiable lifestyle risk factors and survival after diagnosis with multiple myeloma

BACKGROUND

While remaining incurable, median overall survival for MM now exceeds 5 years. Yet few studies have investigated how modifiable lifestyle factors influence survival. We investigate whether adiposity, diet, alcohol, or smoking are associated with MM-related fatality.

RESEARCH DESIGN AND METHODS

We recruited 760 incident cases of MM via cancer registries in two Australian states during 2010-2016. Participants returned questionnaires on health and lifestyle. Follow-up ended in 2020. Flexible parametric survival models were used to estimate hazard ratios (HR) and 95% confidence intervals (CI) for lifestyle exposures and risk of all-cause and MM-specific fatality.

RESULTS

Higher pre-diagnosis Alternative Healthy Eating Index (AHEI) scores were associated with reduced MM-specific fatality (per 10-unit score, HR = 0.84, 95%CI = 0.70-0.99). Pre-diagnosis alcohol consumption was inversely associated with MM-specific fatality, compared with nondrinkers (0.1-20 g per day, HR = 0.59, 95%CI = 0.39-0.90; >20 g per day, HR = 0.67, 95%CI = 0.40-1.13). Tobacco smoking was associated with increased all-cause fatality compared with never smoking (former smokers: HR = 1.44, 95%CI = 1.10-1.88; current smokers: HR = 1.30, 95%CI = 0.80-2.10). There was no association between pre-enrollment body mass index (BMI) and MM-specific or all-cause fatality.

CONCLUSIONS

Our findings support established recommendations for healthy diets and against smoking. Higher quality diet, as measured by the AHEI, may improve survival post diagnosis with MM.

A proposal to analyze the progression of non-dialytic chronic kidney disease by surrogate endpoints: introducing parametric survival models

Introduction

Chronic kidney disease (CDK) progression studies increasingly use surrogate endpoints based on the estimated glomerular filtration rate. The clinical characteristics of these endpoints bring new challenges in comparing groups of patients, as traditional Cox models may lead to biased estimates mainly because they do not assume a hazard function.

Objective

This study proposes the use of parametric survival analysis models with the three most commonly used endpoints in nephrology based on a case study. Estimated glomerular filtration rate (eGFR) decay > 5 mL/year, eGFR decline > 30%, and change in CKD stage were evaluated.

Method

The case study is a 5-year retrospective cohort study that enrolled 778 patients in the predialysis stage. Exponential, Weibull, Gompertz, lognormal, and logistic models were compared, and proportional hazard and accelerated failure time (AFT) models were evaluated.

Results

The endpoints had quite different hazard functions, demonstrating the importance of choosing appropriate models for each. AFT models were more suitable for the clinical interpretation of the effects of covariates on these endpoints.

Conclusion

Surrogate endpoints have different hazard distributions over time, which is already recognized by nephrologists. More flexible analysis techniques that capture these relevant clinical characteristics in decision-making should be encouraged and disseminated in nephrology research.

Modelling multiple time-scales with flexible parametric survival models

BACKGROUND

There are situations when we need to model multiple time-scales in survival analysis. A usual approach in this setting would involve fitting Cox or Poisson models to a time-split dataset. However, this leads to large datasets and can be computationally intensive when model fitting, especially if interest lies in displaying how the estimated hazard rate or survival change along multiple time-scales continuously.

METHODS

We propose to use flexible parametric survival models on the log hazard scale as an alternative method when modelling data with multiple time-scales. By choosing one of the time-scales as reference, and rewriting other time-scales as a function of this reference time-scale, users can avoid time-splitting of the data.

RESULT

Through case-studies we demonstrate the usefulness of this method and provide examples of graphical representations of estimated hazard rates and survival proportions. The model gives nearly identical results to using a Poisson model, without requiring time-splitting.

CONCLUSION

Flexible parametric survival models are a powerful tool for modelling multiple time-scales. This method does not require splitting the data into small time-intervals, and therefore saves time, helps avoid technological limitations and reduces room for error.

A comparison of statistical methods to predict the residual lifetime risk

Lifetime risk measures the cumulative risk for developing a disease over one's lifespan. Modeling the lifetime risk must account for left truncation, the competing risk of death, and inference at a fixed age. In addition, statistical methods to predict the lifetime risk should account for covariate-outcome associations that change with age. In this paper, we review and compare statistical methods to predict the lifetime risk. We first consider a generalized linear model for the lifetime risk using pseudo-observations of the Aalen-Johansen estimator at a fixed age, allowing for left truncation. We also consider modeling the subdistribution hazard with Fine-Gray and Royston-Parmar flexible parametric models in left truncated data with time-covariate interactions, and using these models to predict lifetime risk. In simulation studies, we found the pseudo-observation approach had the least bias, particularly in settings with crossing or converging cumulative incidence curves. We illustrate our method by modeling the lifetime risk of atrial fibrillation in the Framingham Heart Study. We provide technical guidance to replicate all analyses in R.

Comparison of statistical methods for the analysis of recurrent adverse events in the presence of non-proportional hazards and unobserved heterogeneity: a simulation study

Background

In preventive drug trials such as intermittent preventive treatment for malaria prevention during pregnancy (IPTp), where there is repeated treatment administration, recurrence of adverse events (AEs) is expected. Challenges in modelling the risk of the AEs include accounting for time-to-AE and within-patient-correlation, beyond the conventional methods. The correlation comes from two sources; (a) individual patient unobserved heterogeneity (i.e. frailty) and (b) the dependence between AEs characterised by time-dependent treatment effects. Potential AE-dependence can be modelled via time-dependent treatment effects, event-specific baseline and event-specific random effect, while heterogeneity can be modelled via subject-specific random effect. Methods that can improve the estimation of both the unobserved heterogeneity and treatment effects can be useful in understanding the evolution of risk of AEs, especially in preventive trials where time-dependent treatment effect is expected.

Methods

Using both a simulation study and the Chloroquine for Malaria in Pregnancy (NCT01443130) trial data to demonstrate the application of the models, we investigated whether the lognormal shared frailty models with restricted cubic splines and non-proportional hazards (LSF-NPH) assumption can improve estimates for both frailty variance and treatment effect compared to the conventional inverse Gaussian shared frailty model with proportional hazard (ISF-PH), in the presence of time-dependent treatment effects and unobserved patient heterogeneity. We assessed the bias, precision gain and coverage probability of 95% confidence interval of the frailty variance estimates for the models under varying known unobserved heterogeneity, sample sizes and time-dependent effects.

Results

The ISF-PH model provided a better coverage probability of 95% confidence interval, less bias and less precise frailty variance estimates compared to the LSF-NPH models. The LSF-NPH models yielded unbiased hazard ratio estimates at the expense of imprecision and high mean square error compared to the ISF-PH model.

Conclusion

The choice of the shared frailty model for the recurrent AEs analysis should be driven by the study objective. Using the LSF-NPH models is appropriate if unbiased hazard ratio estimation is of primary interest in the presence of time-dependent treatment effects. However, ISF-PH model is appropriate if unbiased frailty variance estimation is of primary interest.

Trial registration

ClinicalTrials.gov; NCT01443130

Comparison of the performances of survival analysis regression models for analysis of conception modes and risk of type-1 diabetes among 1985-2015 Swedish birth cohort

The goal is to examine the risk of conception mode-type-1 diabetes using different survival analysis modelling approaches and examine if there are differentials in the risk of type-1 diabetes between children from fresh and frozen-thawed embryo transfers. We aimed to compare the performances and fitness of different survival analysis regression models with the Cox proportional hazard (CPH) model used in an earlier study. The effect of conception modes and other prognostic factors on type-1 diabetes among children conceived either spontaneously or by assisted reproductive technology (ART) and its sub-groups was modelled in the earlier study. We used the information on all singleton children from the Swedish Medical Birth Register hosted by the Swedish National Board of Health and Welfare, 1985 to 2015. The main explanatory variable was the mode of conception. We applied the CPH, parametric and flexible parametric survival regression (FPSR) models to the data at 5% significance level. Loglikelihood, Akaike and Bayesian information criteria were used to assess model fit. Among the 3,138,540 singletons, 47,938 (1.5%) were conceived through ART (11,211 frozen-thawed transfer and 36,727 fresh embryo transfer). In total, 18,118 (0.58%) of the children had type-1 diabetes, higher among (0.58%) those conceived spontaneously than the ART-conceived (0.42%). The median (Interquartile range (IQR)) age at onset of type-1 diabetes among spontaneously conceived children was 10 (14-6) years, 8(5-12) for ART, 6 (4-10) years for frozen-thawed embryo transfer and 9 (5-12) years for fresh embryo transfer. The estimates from the CPH, FPSR and parametric PH models are similar. There was no significant difference in the risk of type-1 diabetes among ART- and spontaneously conceived children; FPSR: (adjusted Hazard Ratio (aHR) = 1.070; 95% Confidence Interval (CI):0.929-1.232, p = 0.346) vs CPH: (aHR = 1.068; 95%CI: 0.927-1.230, p = 0.361). A sub-analysis showed that the adjusted hazard of type-1 diabetes was 37% (aHR = 1.368; 95%CI: 1.013-1.847, p = 0.041) higher among children from frozen-thawed embryo transfer than among children from spontaneous conception. The hazard of type-1 diabetes was higher among children whose mothers do not smoke (aHR = 1.296; 95%CI:1.240-1.354, p<0.001) and of diabetic mothers (aHR = 6.419; 95%CI:5.852-7.041, p<0.001) and fathers (aHR = 8.808; 95%CI:8.221-9.437, p<0.001). The estimates from the CPH, parametric models and the FPSR model were close. This is an indication that the models performed similarly and any of them can be used to model the data. We couldn't establish that ART increases the risk of type-1 diabetes except when it is subdivided into its two subtypes. There is evidence of a greater risk of type-1 diabetes when conception is through frozen-thawed transfer.

Direct modelling of age standardized marginal relative survival through incorporation of time-dependent weights

BACKGROUND

When quantifying the probability of survival in cancer patients using cancer registration data, it is common to estimate marginal relative survival, which under assumptions can be interpreted as marginal net survival. Net survival is a hypothetical construct giving the probability of being alive if it was only possible to die of the cancer under study, enabling comparisons between populations with differential mortality rates due to causes other the cancer under study. Marginal relative survival can be estimated non-parametrically (Pohar Perme estimator) or in a modeling framework. In a modeling framework, even when just interested in marginal relative survival it is necessary to model covariates that affect the expected mortality rates (e.g. age, sex and calendar year). The marginal relative survival function is then obtained through regression standardization. Given that these covariates will generally have non-proportional effects, the model can become complex before other exposure variables are even considered.

METHODS

We propose a flexible parametric model incorporating restricted cubic splines that directly estimates marginal relative survival and thus removes the need to model covariates that affect the expected mortality rates. In order to do this the likelihood needs to incorporate the marginal expected mortality rates at each event time taking account of informative censoring. In addition time-dependent weights are incorporated into the likelihood. An approximation is proposed through splitting the time scale into intervals, which enables the marginal relative survival model to be fitted using standard software. Additional weights can be incorporated when standardizing to an external reference population.

RESULTS

The methods are illustrated using national cancer registry data. In addition, a simulation study is performed to compare different estimators; a non-parametric approach, regression-standardization and the new marginal relative model. The simulations study shows the new approach is unbiased and has good relative precision compared to the non-parametric estimator.

CONCLUSION

The approach enables estimation of standardized marginal relative survival without the need to model covariates that affect expected mortality rates and thus reduces the chance of model misspecification.

Temporal improvements noted in life expectancy of patients with colorectal cancer; a Dutch population-based study

OBJECTIVE

Specific survival estimates are needed for the increasing number of colorectal cancer (CRC) survivors. The aim of this population-based study was to determine conditional loss in expectation of life (LEL) due to CRC.

STUDY DESIGN AND SETTING

All surgically treated patients with CRC registered in the Netherlands Cancer Registry with stage I-III between 1990-2016, were included (N = 203,216). Estimates of conditional LEL were predicted using flexible parametric models and the total life years lost due to cancer were estimated.

RESULTS

LEL decreased with older age and patients with rectal cancer or higher disease stage had highest LEL. In 2010, LEL for sixty-year old male and female patients was 2 vs. 2, 4 vs. 4, and 7 vs. 8 years for colon cancer, and 2 vs. 2, 4 vs. 5 and 7 vs. 8 years for rectal cancer, respectively. Conditional LEL in patients with CRC decreased during follow-up. Patients with combined stage I-III colon and rectal cancer in 2010 lost an estimated 18,628 and 11,336 life years.

CONCLUSION

This study quantified the impact of CRC on patient's life expectancy, both on individual and population level and demonstrated temporal improvements in CRC survival. These results provide meaningful information that can be used during follow-up.

Estimating restricted mean survival time and expected life-years lost in the presence of competing risks within flexible parametric survival models

Background

Royston-Parmar flexible parametric survival models (FPMs) can be fitted on either the cause-specific hazards or cumulative incidence scale in the presence of competing risks. An advantage of modelling within this framework for competing risks data is the ease at which alternative predictions to the (cause-specific or subdistribution) hazard ratio can be obtained. Restricted mean survival time (RMST), or restricted mean failure time (RMFT) on the mortality scale, is one such measure. This has an attractive interpretation, especially when the proportionality assumption is violated. Compared to similar measures, fewer assumptions are required and it does not require extrapolation. Furthermore, one can easily obtain the expected number of life-years lost, or gained, due to a particular cause of death, which is a further useful prognostic measure as introduced by Andersen.

Methods

In the presence of competing risks, prediction of RMFT and the expected life-years lost due to a cause of death are presented using Royston-Parmar FPMs. These can be predicted for a specific covariate pattern to facilitate interpretation in observational studies at the individual level, or at the population-level using standardisation to obtain marginal measures. Predictions are illustrated using English colorectal data and are obtained using the Stata post-estimation command, standsurv.

Results

Reporting such measures facilitate interpretation of a competing risks analysis, particularly when the proportional hazards assumption is not appropriate. Standardisation provides a useful way to obtain marginal estimates to make absolute comparisons between two covariate groups. Predictions can be made at various time-points and presented visually for each cause of death to better understand the overall impact of different covariate groups.

Conclusions

We describe estimation of RMFT, and expected life-years lost partitioned by each competing cause of death after fitting a single FPM on either the log-cumulative subdistribution, or cause-specific hazards scale. These can be used to facilitate interpretation of a competing risks analysis when the proportionality assumption is in doubt.

Performance evaluation of survival regression models in analysing Swedish dental implant complication data with frailty

The use of inappropriate methods for estimating the effects of covariates in survival data with frailty leads to erroneous conclusions in medical research. This study evaluated the performance of 13 survival regression models in assessing the factors associated with the timing of complications in implant-supported dental restorations in a Swedish cohort. Data were obtained from randomly selected cohort (n = 596) of Swedish patients provided with dental restorations supported in 2003. Patients were evaluated over 9 years of implant loss, peri-implantitis or technical complications. Best Model was identified using goodness, AIC and BIC. The loglikelihood, the AIC and BIC were consistently lower in flexible parametric model with frailty (df = 2) than other models. Adjusted hazard of implant complications was 45% (adjusted Hazard Ratio (aHR) = 1.449; 95% Confidence Interval (CI): 1.153-1.821, p = 0.001) higher among patients with periodontitis. While controlling for other variables, the hazard of implant complications was about 5 times (aHR = 4.641; 95% CI: 2.911-7.401, p<0.001) and 2 times (aHR = 2.338; 95% CI: 1.553-3.519, p<0.001) higher among patients with full- and partial-jaw restorations than those with single crowns. Flexible parametric survival model with frailty are the most suitable for modelling implant complications among the studied patients.

Discovery and validation of a personalized risk predictor for incident tuberculosis in low transmission settings

The risk of tuberculosis (TB) is variable among individuals with latent Mycobacterium tuberculosis infection (LTBI), but validated estimates of personalized risk are lacking. In pooled data from 18 systematically identified cohort studies from 20 countries, including 80,468 individuals tested for LTBI, 5-year cumulative incident TB risk among people with untreated LTBI was 15.6% (95% confidence interval (CI), 8.0-29.2%) among child contacts, 4.8% (95% CI, 3.0-7.7%) among adult contacts, 5.0% (95% CI, 1.6-14.5%) among migrants and 4.8% (95% CI, 1.5-14.3%) among immunocompromised groups. We confirmed highly variable estimates within risk groups, necessitating an individualized approach to risk stratification. Therefore, we developed a personalized risk predictor for incident TB (PERISKOPE-TB) that combines a quantitative measure of T cell sensitization and clinical covariates. Internal-external cross-validation of the model demonstrated a random effects meta-analysis C-statistic of 0.88 (95% CI, 0.82-0.93) for incident TB. In decision curve analysis, the model demonstrated clinical utility for targeting preventative treatment, compared to treating all, or no, people with LTBI. We challenge the current crude approach to TB risk estimation among people with LTBI in favor of our evidence-based and patient-centered method, in settings aiming for pre-elimination worldwide.

Bayesian frailty modeling of correlated survival data with application to under-five mortality

Background

There is high rate of under-five mortality in West Africa with little effort made to study determinants that significantly increase or decrease its risk across the West African sub-region. This is important since it will help in the design of effective intervention programs for each country or the entire region. The overall objective of this research evaluates the determinants of under-five mortality prior to the end of the 2015 Millennium Development Goals, to guide West African countries implement strategies that will aid them achieve the Sustainable Development Goal 3 by 2030.

Method

This study used the Demographic and Health Survey (DHS) data from twelve (12) out of the eighteen West African countries; Ghana, Benin, Cote d’ Ivoire, Guinea, Liberia, Mali, Niger, Nigeria, Sierra Leone, Burkina Faso, Gambia and Togo. Data were extracted from the children and women of reproductive age files as provided in the DHS report. The response or outcome variable of interest is under-five mortality rate. A Bayesian exponential, Weibull and Gompertz regression models via a gamma shared frailty model were used for the analysis. The deviance information criteria and Bayes factors were used to discriminate between models. These analyses were carried out using Stata version 15 software.

Results

The study recorded 101 (95% CI: 98.6–103.5) deaths per 1000 live births occurring among the twelve countries. Burkina Faso (124.4), Cote D’lvoire (110.1), Guinea (116.4), Nigeria (120.6) and Niger (118.3) recorded the highest child under-5 mortality rate. Gambia (48.1), Ghana (60.1) and Benin (70.4) recorded the least unde-5 mortality rate per 1000 livebirths. Multiple birth children were about two times more likely to die compared to singleton birth, in all except Gambia, Nigeria and Sierra Leone. We observed significantly higher hazard rates for male compared to female children in the combined data analysis (HR: 1.14, 95% CI: [1.10–1.18]). The country specific analysis in Benin, Cote D’lvoire, Guinea, Liberia, Mali and Nigeria showed higher under-5 mortality hazard rates among male children compared to female children whilst Niger was the only country to report significantly lower hazard rate of males compared to females.

Conclusion

There is still quite a substantial amount of work to be done in order to meet the Sustainable Development Goal 3 in 2030 in West Africa. There exist variant differences among some of the countries with respect to mortality rates and determinants which require different interventions and policy decisions.