Risk projection for time-to-event outcome from population-based case-control studies leveraging summary statistics from the target population.

Risk stratification based on prediction models has become increasingly important in preventing and managing chronic diseases. However, due to cost- and time-limitations, not every population can have resources for collecting enough detailed individual-level information on a large number of people to develop risk prediction models. A more practical approach is to use prediction models developed from existing studies and calibrate them with relevant summary-level information of the target population. Many existing studies were conducted under the population-based case-control design. Gail et al. (J Natl Cancer Inst 81:1879-1886, 1989) proposed to combine the odds ratio estimates obtained from case-control data and the disease incidence rates from the target population to obtain the baseline hazard function, and thereby the pure risk for developing diseases. However, the approach requires the risk factor distribution of cases from the case-control studies be same as the target population, which, if violated, may yield biased risk estimation. In this article, we propose two novel weighted estimating equation approaches to calibrate the baseline risk by leveraging the summary information of (some) risk factors in addition to disease-free probabilities from the targeted population. We establish the consistency and asymptotic normality of the proposed estimators. Extensive simulation studies and an application to colorectal cancer studies demonstrate the proposed estimators perform well for bias reduction in finite samples.

Re-calibrating pure risk integrating individual data from two-phase studies with external summary statistics.

Accurate risk assessment is critical in clinical decision-making. It entails the projected risk based on a risk prediction model agreeing with the observed risk in the target cohort. However, the model often over- or under-estimates the risk. Building a new model for the target cohort would be ideal but costly. It is therefore of great interest to recalibrate an existing model for the target cohort. Existing methods have been proposed to recalibrate the model by leveraging the disease incidence rates from the target cohort. However, they assume the same covariate distribution across cohorts and when the assumption is violated, the recalibrated model can be substantially biased. Further, recalibration is also complicated by the two-phase sampling design that is commonly used for developing risk prediction models. In this paper, we develop a weighted estimating-equation approach accounting for the two-phase design and combine it with a weighted empirical likelihood that leverages the summary information on both disease incidence rates and covariates from the target cohort. We provide a resampling-based inference procedure. Our extensive simulation results show that using the summary information from the target population, the proposed recalibration method yields nearly unbiased risk estimates under a wide range of scenarios. An application to a colorectal cancer study also illustrates that the proposed method yields a well-calibrated model in the target cohort.

Risk-adjusted cUSUM control charts for shared frailty survival models with application to hip replacement outcomes: a study using the NJR dataset.

BACKGROUND: Continuous monitoring of surgical outcomes after joint replacement is needed to detect which brands' components have a higher than expected failure rate and are therefore no longer recommended to be used in surgical practice. We developed a monitoring method based on cumulative sum (CUSUM) chart specifically for this application. METHODS: Our method entails the use of the competing risks model with the Weibull and the Gompertz hazard functions adjusted for observed covariates to approximate the baseline time-to-revision and time-to-death distributions, respectively. The correlated shared frailty terms for competing risks, corresponding to the operating unit, are also included in the model. A bootstrap-based boundary adjustment is then required for risk-adjusted CUSUM charts to guarantee a given probability of the false alarm rates. We propose a method to evaluate the CUSUM scores and the adjusted boundary for a survival model with the shared frailty terms. We also introduce a unit performance quality score based on the posterior frailty distribution. This method is illustrated using the 2003-2012 hip replacement data from the UK National Joint Registry (NJR). RESULTS: We found that the best model included the shared frailty for revision but not for death. This means that the competing risks of revision and death are independent in NJR data. Our method was superior to the standard NJR methodology. For one of the two monitored components, it produced alarms four years before the increased failure rate came to the attention of the UK regulatory authorities. The hazard ratios of revision across the units varied from 0.38 to 2.28. CONCLUSIONS: An earlier detection of failure signal by our method in comparison to the standard method used by the NJR may be explained by proper risk-adjustment and the ability to accommodate time-dependent hazards. The continuous monitoring of hip replacement outcomes should include risk adjustment at both the individual and unit level.

Comparison of under-five mortality for 2000, 2005 and 2011 surveys in Ethiopia.

BACKGROUND: Though the socio-economic situation of the Ethiopian household is improving along with the decrease in under-five child mortality. But, under-five mortality is still one of the major problems. Identification of the risk factors change over time which mismatches with the diminishing rate of under-five mortality is important to address the problems. METHODS: The survey data used for this research was taken from three different Ethiopian Demographic and Health Surveys (2000, 2005 and 2011). This data was used to identify the effect of time varying under-five mortality risk factors. The Cox proportional hazard model was adapted for the analysis. RESULTS: The effect of respondent's current age, age at first birth and educational level on the under-five mortality rate significantly diminishes in the recent surveys. On the other hand, the effect of the number of births in the last 5 years increases more in 2011 than in the earlier two surveys. Similarly, number of household members in the house and the number of under-five children in the house demonstrated a difference through years. Regarding total children ever born, child death is more for the year 2000 followed by 2005 and 2011. CONCLUSION: Based on the study, our findings confirmed that under-five mortality is a serious problem in the country. The analysis displayed that the hazard of under-five mortality has a decreasing pattern in years. The result for regions showed that there was an increase in years for some of the regions. This research work gives necessary information to device improved teaching for family planning and children health care to change the child mortality circumstance in the country. Our study suggests that the impact of demographic characteristics and socio-economic factors on child mortality should account for their integral changes over time.

Comparison of different parametric proportional hazards models for interval-censored data: a simulation study.

Interval censoring occurs frequently in clinical trials, but is often simplified to a right censoring problem because statistical methods in this area are under developed. It is recognized that analyzing interval censored data as right-censored data can lead to biased results. Although statistical methods have been developed to estimate survival function and to test hypothesis, estimating hazard ratio (HR) in a proportional hazards (PH) model for interval censored data remains as a challenge. Semi-parametric PH model was developed but difficult to implement, and thus rarely used in practice. Parametric PH method can be easily implemented but received little attention in practice because the impact of mis-specifying baseline hazard function on HR estimate was not well understood. We examined the performance of parametric PH models, using 3 baseline hazard functions: exponential, Weibull, and a 10-piece exponential function, under different underlying data distributions and censoring schema, through an extensive simulation study. Data were generated from 6 different models representing a range of possible scenarios in clinical trials. The simulation study revealed that mis-specifying baseline hazard function had little impact on the HR estimates. Robust estimate of HR with little bias and small mean square errors (MSE) were obtained using a PH model with a Weibull or 10-piece exponential function approximating baseline hazard function. Bigger bias and MSE were observed when using an exponential function to approximate a complex baseline hazard function. Examples are included. Based on these findings, we advocate the use of parametric PH models for the analysis of interval censored data.