Estimation of trajectory of protective efficacy in infectious disease prevention trials using recurrent event times.

In studies of infectious disease prevention, the level of protective efficacy of medicinal products such as vaccines and prophylactic drugs tends to vary over time. Many products require administration of multiple doses at scheduled times, as opposed to one-off or continual intervention. Accurate information on the trajectory of the level of protective efficacy over time facilitates informed clinical recommendations and implementation strategies, for example, with respect to the timing of administration of the doses. Based on concepts from pharmacokinetic and pharmacodynamic modeling, we propose a non-linear function for modeling the trajectory after each dose. The cumulative effect of multiple doses of the products is captured by an additive series of the function. The model has the advantages of parsimony and interpretability, while remaining flexible in capturing features of the trajectories. We incorporate this series into the Andersen-Gill model for analysis of recurrent event time data and compare it with alternative parametric and non-parametric functions. We use data on clinical malaria disease episodes from a trial of four doses of an anti-malarial drug combination for chemoprevention to illustrate, and evaluate the performance of the methods using simulation. The proposed method out-performed the alternatives in the analysis of real data in terms of Akaike and Bayesian Information Criterion. It also accurately captured the features of the protective efficacy trajectory such as the area under curve in simulations. The proposed method has strong potential to enhance the evaluation of disease prevention measures and improve their implementation strategies.

A sequential test for assessing the effectiveness of response strategies during an emerging epidemic.

In epidemiology, the fatality rate is an important indicator of disease severity and has been used to evaluate the effects of new treatments. During an emerging epidemic with limited resources, monitoring the changes in fatality rate can also provide signals on the evaluation of government policies and healthcare quality, which helps to guide public health decision. A statistical test is developed in this paper to detect changes in fatality rate over time during the course of an emerging infectious disease. A major advantage of the proposed test is that it only requires the regularly reported numbers of deaths and recoveries, which meets the actual need as detailed surveillance data are hard to collect during the course of an emerging epidemic especially the deadly infectious diseases with large magnitude. In addition, with the sequential testing procedure, the effective measures can be detected at the earliest possible time to provide guidance to policymakers for swift action. Simulation studies showed that the proposed test performs well and is sensitive in picking up changes in the fatality rate. The test is applied to the 2014-2016 Ebola outbreak in Sierra Leone for illustration.

Modelling non-linear patterns of time-varying intervention effects on recurrent events in infectious disease prevention studies.

Protective efficacy of vaccines and pharmaceutical products for prevention of infectious diseases usually vary over time. Information on the trajectory of the level of protection is valuable. We consider a parsimonious, non-linear and non-monotonic function for modelling time-varying intervention effects and compare it with several alternatives. The cumulative effects of multiple doses of intervention over time can be captured by an additive series of the function. We apply it to the Andersen-Gill model for analysis of recurrent time-to-event data. We re-analyze data from a trial of intermittent preventive treatment for malaria to illustrate and evaluate the method by simulation.

A novel method to monitor COVID-19 fatality rate in real-time, a key metric to guide public health policy.

An accurate estimator of the real-time fatality rate is warranted to monitor the progress of ongoing epidemics, hence facilitating the policy-making process. However, most of the existing estimators fail to capture the time-varying nature of the fatality rate and are often biased in practice. A simple real-time fatality rate estimator with adjustment for reporting delays is proposed in this paper using the fused lasso technique. This approach is easy to use and can be broadly applied to public health practice as only basic epidemiological data are required. A large-scale simulation study suggests that the proposed estimator is a reliable benchmark for formulating public health policies during an epidemic with high accuracy and sensitivity in capturing the changes in the fatality rate over time, while the other two commonly-used case fatality rate estimators may convey delayed or even misleading signals of the true situation. The application to the COVID-19 data in Germany between January 2020 and January 2022 demonstrates the importance of the social restrictions in the early phase of the pandemic when vaccines were not available, and the beneficial effects of vaccination in suppressing the fatality rate to a low level since August 2021 irrespective of the rebound in infections driven by the more infectious Delta and Omicron variants during the fourth wave.

Analysis of clustered interval-censored data using a class of semiparametric partly linear frailty transformation models.

A flexible class of semiparametric partly linear frailty transformation models is considered for analyzing clustered interval-censored data, which arise naturally in complex diseases and dental research. This class of models features two nonparametric components, resulting in a nonparametric baseline survival function and a potential nonlinear effect of a continuous covariate. The dependence among failure times within a cluster is induced by a shared, unobserved frailty term. A sieve maximum likelihood estimation method based on piecewise linear functions is proposed. The proposed estimators of the regression, dependence, and transformation parameters are shown to be strongly consistent and asymptotically normal, whereas the estimators of the two nonparametric functions are strongly consistent with optimal rates of convergence. An extensive simulation study is conducted to study the finite-sample performance of the proposed estimators. We provide an application to a dental study for illustration.

Inclusion of unexposed subjects improves the precision and power of self-controlled case series method.

The self-controlled case series is an important method in the studies of the safety of biopharmaceutical products. It uses the conditional Poisson model to make comparison within persons. In models without adjustment for age (or other time-varying covariates), cases who are never exposed to the product do not contribute any information to the estimation. We provide analytic proof and simulation results that the inclusion of unexposed cases in the conditional Poisson model with age adjustment reduces the asymptotic variance of the estimator of the exposure effect and increases power. We re-analysed a vaccine safety dataset to illustrate.

A sequential test to compare the real-time fatality rates of a disease among multiple groups with an application to COVID-19 data.

Infectious diseases, such as the ongoing COVID-19 pandemic, pose a significant threat to public health globally. Fatality rate serves as a key indicator for the effectiveness of potential treatments or interventions. With limited time and understanding of novel emerging epidemics, comparisons of the fatality rates in real-time among different groups, say, divided by treatment, age, or area, have an important role to play in informing public health strategies. We propose a statistical test for the null hypothesis of equal real-time fatality rates across multiple groups during an ongoing epidemic. An elegant property of the proposed test statistic is that it converges to a Brownian motion under the null hypothesis, which allows one to develop a sequential testing approach for rejecting the null hypothesis at the earliest possible time when statistical evidence accumulates. This property is particularly important as scientists and clinicians are competing with time to identify possible treatments or effective interventions to combat the emerging epidemic. The method is widely applicable as it only requires the cumulative number of confirmed cases, deaths, and recoveries. A large-scale simulation study shows that the finite-sample performance of the proposed test is highly satisfactory. The proposed test is applied to compare the difference in disease severity among Wuhan, Hubei province (exclude Wuhan) and mainland China (exclude Hubei) from February to March 2020. The result suggests that the disease severity is potentially associated with the health care resource availability during the early phase of the COVID-19 pandemic in mainland China.

The English and Chinese language versions of the Short Form 12-item Health Survey are equivalent.

BACKGROUND: The Short Form 12-item Health Survey (SF-12v2) was originally developed in English, but it is also available in Hong Kong (HK) Chinese. While both language versions had their measurement properties well assessed in their respective populations, their measurement invariance in scores has not been examined. Therefore, we aimed to assess their measurement invariance. METHODS: We conducted a cross-sectional study on individuals aged 18 years or older at a university campus. Those who were bilingual in English and Chinese were randomly assigned to self-complete either the standard English or the HK Chinese SF-12v2. Measurement invariance of the two components and eight scales of the SF-12v2 was concluded if the corresponding 90% confidence interval (CI) for the difference between the two language versions entirely fell within the minimal clinically important difference of ± 3 units. Multiple-group confirmatory factor analysis (CFA) was also performed. RESULTS: A total of 1013 participants completed the SF-12v2 (496 in English and 517 in HK Chinese), with a mean age of 22 years (Range 18-58), and 626 participants (62%) were female. There were no significant differences in demographics. Only the physical and mental components and the mental health (MH) scale had their 90% CIs (0.21 to 1.61, - 1.00 to 0.98, and - 0.86 to 2.84, respectively) completely fall within the ± 3 units. The multiple-group CFA showed partial strict invariance. CONCLUSIONS: The English and HK Chinese versions of the SF-12v2 can be used in studies with their two components and MH scores pooled in the analysis.

Estimation of the primary, secondary and composite effects of malaria vaccines using data on multiple clinical malaria episodes.

BACKGROUND: An effective malaria vaccine affects the risk of malaria directly, through the vaccine-induced immune response (the primary effect), and indirectly, as a consequence of reduced exposure to malaria infection and disease, leading to slower acquisition of natural immunity (the secondary effect). The beneficial primary effect may be offset by a negative secondary effect, resulting in a smaller or nil composite effect. Reports of malaria vaccine trials usually present only the composite effect. We aimed to demonstrate how the primary and secondary effects can also be estimated from trial data. METHODS: We propose an enhancement to the conditional frailty model for the estimation of primary effect using data on disease episodes. We use the Andersen-Gill model to estimate the composite effect. We consider taking the ratio of the hazard ratios to estimate the secondary effect. We used directed acyclic graphs and data from a randomized trial of the RTS,S/AS02 malaria vaccine to illustrate the problems and solutions. Time-varying effects were estimated by partitioning the follow-up into four time periods. RESULTS: The primary effect estimates from our proposed model were consistently stronger than the conditional frailty model in the existing literature. The primary effect of the vaccine was consistently stronger than the composite effect across all time periods. Both the primary and composite effects were stronger in the first three months, with hazard ratios (95% confidence interval) 0.62 (0.49-0.79) and 0.68 (0.54-0.84), respectively; the hazard ratios weakened over time. The secondary effect appeared mild, with hazard ratio 1.09 (1.02-1.16) in the first three months. CONCLUSIONS: The proposed analytic strategy facilitates a more comprehensive interpretation of trial data on multiple disease episodes. The RTS,S/AS02 vaccine had modest primary and secondary effects that waned over time, but the composite effect in preventing clinical malaria remained positive up to the end of the study. CLINICAL TRIALS REGISTRATION: ClinicalTrials.gov NCT00197041.

Survival analysis with change-points in covariate effects.

We apply a maximal likelihood ratio test for the presence of multiple change-points in the covariate effects based on the Cox regression model. The covariate effect is assumed to change smoothly at one or more unknown change-points. The number of change-points is inferred by a sequential approach. Confidence intervals for the regression and change-point parameters are constructed by a bootstrap method based on Bernstein polynomials conditionally on the number of change-points. The methods are assessed by simulations and are applied to two datasets.

Statistical inference in matched case-control studies of recurrent events.

BACKGROUND: The concurrent sampling design was developed for case-control studies of recurrent events. It involves matching for time. Standard conditional logistic-regression (CLR) analysis ignores the dependence among recurrent events. Existing methods for clustered observations for CLR do not fit the complex data structure arising from the concurrent sampling design. METHODS: We propose to break the matches, apply unconditional logistic regression with adjustment for time in quintiles and residual time within each quintile, and use a robust standard error for observations clustered within persons. We conducted extensive simulation to evaluate this approach and compared it with methods based on CLR. We analysed data from a study of childhood pneumonia to illustrate the methods. RESULTS: The proposed method and CLR methods gave very similar point estimates of association and showed little bias. The proposed method produced confidence intervals that achieved the target level of coverage probability, whereas the CLR methods did not, except when disease incidence was low. CONCLUSIONS: The proposed method is suitable for the analysis of case-control studies with recurrent events.

Bias control in the analysis of case-control studies with incidence density sampling.

BACKGROUND: Previous simulation studies of the case-control study design using incidence density sampling, which required individual matching for time, showed biased estimates of association from conditional logistic regression (CLR) analysis; however, the reason for this is unknown. Separately, in the analysis of case-control studies using the exclusive sampling design, it has been shown that unconditional logistic regression (ULR) with adjustment for an individually matched binary factor can give unbiased estimates. The validity of this analytic approach in incidence density sampling needs evaluation. METHODS: In extensive simulations using incidence density sampling, we evaluated various analytic methods: CLR with and without a bias-reduction method, ULR with adjustment for time in quintiles (and residual time within quintiles) and ULR with adjustment for matched sets and bias reduction. We re-analysed a case-control study of Haemophilus influenzae type B vaccine using these methods. RESULTS: We found that the bias in the CLR analysis from previous studies was due to sparse data bias. It can be controlled by the bias-reduction method for CLR or by increasing the number of cases and/or controls. ULR with adjustment for time in quintiles usually gave results highly comparable to CLR, despite breaking the matches. Further adjustment for residual time trends was needed in the case of time-varying effects. ULR with adjustment for matched sets tended to perform poorly despite bias reduction. CONCLUSIONS: Studies using incidence density sampling may be analysed by either ULR with adjustment for time or CLR, possibly with bias reduction.

Longitudinal measurement invariance and explanatory IRT models for adolescents' oral health-related quality of life.

BACKGROUND: Longitudinal invariance is a perquisite for a valid comparison of oral health-related quality of life (OHRQoL) scores over time. Item response theory (IRT) models can assess measurement invariance and allow better estimation of the associations between predictors and latent construct. By extending IRT models, this study aimed to investigate the longitudinal invariance of the two 8-item short forms of the Child Perception Questionnaire (CPQ11-14) regression short form (RSF:8) and item-impact short form (ISF:8) and identify factors associated with adolescents' OHRQoL and its change. METHODS: All students from S1 and S2 (equivalent to US grades 6 and 7) who were born in April 1997 and May 1997 (at age 12) from 45 randomly selected secondary schools were invited to participate in this study and followed up after 3 years. Data on the CPQ11-14 RSF:8 and CPQ11-14 ISF:8, demographics, oral health behavior and status were collected. Explanatory graded response models were fitted to both short forms of the CPQ11-14 data for assessing longitudinal invariance and factors associated with OHRQoL. The Bayesian estimation method - Monte Carlo Markov Chain (MCMC) with Gibbs sampling was adopted for parameter estimation and the credible intervals were used for inference. RESULTS: Data from 649 children at age 12 at baseline and 415 children at age 15 at follow up were analyzed. For the 12 years old children, healthier oral health behavior, better gum status, families with both parents employed and parents' education level were found to be associated with better OHRQoL. Four items among the 2 short forms lacked longitudinal invariance. With statistical adjustment of longitudinal invariance, OHRQoL were found improved in general over the 3 years but no predictor was associated with OHRQoL in follow-up. For those with decreased family income, their OHRQoL had worsened over 3 years. CONCLUSIONS: IRT explanatory analysis enables a more valid identification of the factors associated with OHRQoL and its changes over time. It provides important information to oral healthcare researchers and policymakers.

Estimation of age effect with change-points on survival of cancer patients.

There is a global trend that the average onset age of many human complex diseases is decreasing, and the age of cancer patients becomes more spread out. The age effect on survival is nonlinear in practice and may have one or more important change-points at which the trend of the effect can be very different before and after these threshold ages. Identification of these change-points allows clinical researchers to understand the biologic basis for the complex relation between age and prognosis for optimal prognostic decision. This paper considers estimation of the potentially nonlinear age effect for general partly linear survival models to ensure a valid statistical inference on the treatment effect. A simple and efficient sieve maximum likelihood estimation method that can be implemented easily using standard statistical software is proposed. A data-driven adaptive algorithm to determine the optimal location and the number of knots for the identification of the change-points is suggested. Simulation studies are performed to study the performance of the proposed method. For illustration purpose, the method is applied to a breast cancer data set from the public domain to investigate the effect of onset age on the disease-free survival of the patients. The results revealed that the risk is highest among young patients and young postmenopausal patients, probably because of a change in hormonal environment during a certain phase of menopause.

Semiparametric estimation of time-varying intervention effects using recurrent event data.

We consider the estimation of the optimal interval between doses for interventions such as malaria chemoprevention and vaccine booster doses that are applied intermittently in infectious disease control. A flexible exponential-like function to model the time-varying intervention effect in the framework of Andersen-Gill model for recurrent event time data is considered. The partial likelihood estimation approach is adopted, and a large scale simulation study is carried out to evaluate the performance of the proposed method. A simple guideline for the choice of the optimal interval between successive doses is proposed. The methodology is illustrated with the analysis of data from a malaria chemoprevention trial. Copyright © 2017 John Wiley & Sons, Ltd.

Sample size determination for fold-increase endpoints defined by paired interval-censored data.

Medical studies often define binary end-points by comparing the ratio of a pair of measurements at baseline and end-of-study to a clinically meaningful cut-off. For example, vaccine trials may define a response as at least a four-fold increase in antibody titers from baseline to end-of-study. Accordingly, sample size is determined based on comparisons of proportions. Since the pair of measurements is quantitative, modeling the bivariate cumulative distribution function to estimate the proportion gives more precise results than using dichotomization of data. This is known as the distributional approach to the analysis of proportions. However, this can be complicated by interval-censoring. For example, due to the nature of some laboratory measurement methods, antibody titers are interval-censored. We derive a sample size formula based on the distributional approach for paired interval-censored data. We compare the sample size requirement in detecting an intervention effect using the distributional approach to a conventional approach of dichotomization. Some practical guidance on applying the sample size formula is given.

Evaluation of psychometric properties and differential item functioning of 8-item Child Perceptions Questionnaires using item response theory.

BACKGROUND: Four-factor structure of the two 8-item short forms of Child Perceptions Questionnaire CPQ11-14 (RSF:8 and ISF:8) has been confirmed. However, the sum scores are typically reported in practice as a proxy of Oral health-related Quality of Life (OHRQoL), which implied a unidimensional structure. This study first assessed the unidimensionality of 8-item short forms of CPQ11-14. Item response theory (IRT) was employed to offer an alternative and complementary approach of validation and to overcome the limitations of classical test theory assumptions. METHODS: A random sample of 649 12-year-old school children in Hong Kong was analyzed. Unidimensionality of the scale was tested by confirmatory factor analysis (CFA), principle component analysis (PCA) and local dependency (LD) statistic. Graded response model was fitted to the data. Contribution of each item to the scale was assessed by item information function (IIF). Reliability of the scale was assessed by test information function (TIF). Differential item functioning (DIF) across gender was identified by Wald test and expected score functions. RESULTS: Both CPQ11-14 RSF:8 and ISF:8 did not deviate much from the unidimensionality assumption. Results from CFA indicated acceptable fit of the one-factor model. PCA indicated that the first principle component explained >30 % of the total variation with high factor loadings for both RSF:8 and ISF:8. Almost all LD statistic <10 indicated the absence of local dependency. Flat and low IIFs were observed in the oral symptoms items suggesting little contribution of information to the scale and item removal caused little practical impact. Comparing the TIFs, RSF:8 showed slightly better information than ISF:8. In addition to oral symptoms items, the item "Concerned with what other people think" demonstrated a uniform DIF (p < 0.001). The expected score functions were not much different between boys and girls. CONCLUSIONS: Items related to oral symptoms were not informative to OHRQoL and deletion of these items is suggested. The impact of DIF across gender on the overall score was minimal. CPQ11-14 RSF:8 performed slightly better than ISF:8 in measurement precision. The 6-item short forms suggested by IRT validation should be further investigated to ensure their robustness, responsiveness and discriminative performance.