Approximately 20% of young adults in the United States are obese, and most gain weight between young and middle adulthood. Few studies have examined the association between elevated BMI in early adulthood and mortality or examined such effects independent of changes in weight. We know of no studies in African American samples.
We used data from 13,941 African American and White adults who self-reported their weight at age 25 and had weight and height measured when they were 45-64 years of age (1987-89). Date of death was ascertained from 1987 to 2005. Hazard ratios and hazard differences for the effects of BMI at age 25 on all-cause mortality were determined using Cox proportional hazard and additive hazard models, respectively.
In the combined ethnic-gender groups, the hazard ratio associated with a 5 kg/m2 increment in BMI at age 25 was 1.28 (95% CI: 1.22, 1.35) and the hazard difference was 2.75 (2.01, 3.50) deaths/1,000 person-years. Associations were observed in all four ethnic-gender groups. Models including weight change from age 25 to age in 1987-89 resulted in null estimates for BMI in African American men, while associations were maintained or only mildly attenuated in other ethnic-gender groups.
Excess weight during young adulthood should be avoided as it contributes to increases in death rates that may be independent of changes in weight experienced in later life. Further study is needed to better understand these associations in African American men.
BMI; young adulthood; mortality; White Americans; African Americans; risk ratio; risk difference
In many biomedical studies, it is common that due to budget constraints, the primary covariate is only collected in a randomly selected subset from the full study cohort. Often, there is an inexpensive auxiliary covariate for the primary exposure variable that is readily available for all the cohort subjects. Valid statistical methods that make use of the auxiliary information to improve study efficiency need to be developed. To this end, we develop an estimated partial likelihood approach for correlated failure time data with auxiliary information. We assume a marginal hazard model with common baseline hazard function. The asymptotic properties for the proposed estimators are developed. The proof of the asymptotic results for the proposed estimators is nontrivial since the moments used in estimating equation are not martingale-based and the classical martingale theory is not sufficient. Instead, our proofs rely on modern empirical theory. The proposed estimator is evaluated through simulation studies and is shown to have increased efficiency compared to existing methods. The proposed methods are illustrated with a data set from the Framingham study.
Marginal hazard model; Correlated failure time; Validation set; Auxiliary covariate
Age, family history, and body mass index (BMI) influence the prevalence of hypertension, but very little is known about the interplay of these factors in Chinese populations. The authors examined this issue in Chinese adults (n = 4104) in the People’s Republic of China Study. In young adults (24–39 years), the prevalence of hypertension/1000 persons (95% confidence interval [CI]) at the referent BMI was greater among subjects with a parental history of hypertension (35; 15–54) compared with those without (7; 3–11). Among middle-aged (40–71 years) adults, the prevalence of hypertension was similar regardless of parental history; however, the effect of BMI was modified by parental history status. For example, at BMI = 25 kg/m2, the prevalence difference/1000 persons was 375 (95% CI = 245–506) and 97 (95% CI = 51–144) among subjects with and without a parental history, respectively. These large differences call for further investigation of the genetic and environmental factors that could be driving this interaction.
Asian; blood pressure; body mass index; Chinese; family history
In this article, we propose a class of semiparametric transformation rate models for recurrent event data subject to right-censoring and potentially stopped by a terminating event (e.g., death). These transformation models include both additive rates model and proportional rates model as special cases. Respecting the property that no recurrent events can occur after the terminating event, we model the conditional recurrent event rate given survival. Weighted estimating equations are constructed to estimate the regression coefficients and baseline rate function. In particular, the baseline rate function is approximated by wavelet function. Asymptotic properties of the proposed estimators are derived and a data-dependent criterion is proposed for selecting the most suitable transformation. Simulation studies show that the proposed estimators perform well for practical sample sizes. The proposed methods are used in two real-data examples: a randomized trial of rhDNase and a community trial of Vitamin A.
recurrent event data; transformation model; additive rates model; proportional rates model; terminating event; wavelet approximation
We propose an additive mixed effect model to analyze clustered failure time data. The proposed model assumes an additive structure and include a random effect as an additional component. Our model imitates the commonly used mixed effect models in repeated measurement analysis but under the context of hazards regression; our model can also be considered as a parallel development of the gamma-frailty model in additive model structures. We develop estimating equations for parameter estimation and propose a way of assessing the distribution of the latent random effect in the presence of large clusters. We establish the asymptotic properties of the proposed estimator. The small sample performance of our method is demonstrated via a large number of simulation studies. Finally, we apply the proposed model to analyze data from a diabetic study and a treatment trial for congestive heart failure.
Additive models; Clustered survival; Goodness of fit; Hazards rate; Moment methods; Random effects
Several researchers have reported that Chinese adults may have a greater chronic disease burden than Whites, especially at lower body mass index (BMI) levels.
To compare the incidence of lipid abnormalities in Chinese (n=5,303), White (n=10,752) and Black (n=3,408) middle-aged adults and the effect of BMI on these incidences.
Data were from the People’s Republic of China (PRC) and the Atherosclerosis Risk in Communities (ARIC) studies. In each ethnic group, we calculated the adjusted cumulative incidence for high total cholesterol (≥240 mg/dL), LDL-cholesterol (≥160 mg/dL), and triglycerides (≥200 mg/dL) and low HDL-cholesterol (≤40 in men and ≤50 mg/dL in women) adjusted for age, gender, education, field site, smoking and drinking status. Risk differences associated with BMI (referent=18.5–22.9 kg/m2) were calculated using weighted linear regression and slopes compared using the Wald test.
Chinese had lower incidence of abnormal total cholesterol, LDL-cholesterol and triglycerides than Whites in most BMI groups and had lower incidence of abnormal HDL-cholesterol and triglycerides than Blacks. Across the range of 18.5 to <30, BMI was more strongly associated with the incidence of having high total cholesterol in Chinese and Whites than in Blacks. Similar trends were seen for LDL-cholesterol and triglycerides, but were not always statistically significant. In contrast, BMI was more highly associated with incidence of low HDL-cholesterol in Whites than in Chinese or Blacks.
Although differences in the incidence of lipid abnormalities and the impact of BMI were identified, results varied by lipid type indicating no consistent ethnic/national pattern.
Obesity; Total cholesterol; LDL-cholesterol; HDL-cholesterol; Triglycerides; Ethnicity
Two-stage design has long been recognized to be a cost-effective way for conducting biomedical studies. In many trials, auxiliary covariate information may also be available, and it is of interest to exploit these auxiliary data to improve the efficiency of inferences. In this paper, we propose a 2-stage design with continuous outcome where the second-stage data is sampled with an “outcome-auxiliary-dependent sampling” (OADS) scheme. We propose an estimator which is the maximizer for an estimated likelihood function. We show that the proposed estimator is consistent and asymptotically normally distributed. The simulation study indicates that greater study efficiency gains can be achieved under the proposed 2-stage OADS design by utilizing the auxiliary covariate information when compared with other alternative sampling schemes. We illustrate the proposed method by analyzing a data set from an environmental epidemiologic study.
Auxiliary covariate; Kernel smoothing; Outcome-auxiliary-dependent sampling; 2-stage sampling design
The objective of this study was to compare cardiovascular disease (CVD) risk factor levels in adults with a history of weight loss to levels in adults who did not lose weight, after both groups subsequently experienced an approximate 1-year interval of weight maintenance. Extant data from the Aerobics Center Longitudinal Study (ACLS) were used to identify 5,151 adults who were weight maintainers (maintained weight within ±3.0% over two consecutive periods of ~1 year) or weight-loss maintainers (lost >3.0–<5.0% or ≥5.0% of body weight in the first interval and maintained that loss in the second interval). Mixed models regression was used to accommodate repeated measures and adjust for gender, age, smoking, cardiorespiratory fitness, decade of clinic visit, interval length, and BMI at the time of risk factor measurement. Coefficients from the model were used to calculate the adjusted risk factor levels in the three groups. Differences in total cholesterol (−3.8 mg/dl, 95% confidence interval: −5.5, −2.0), low-density lipoprotein (LDL) cholesterol (−3.0 mg/dl, confidence interval: −4.8, −1.1), triglycerides (−6.1 mg/dl, confidence interval: −10.6, −1.7) and diastolic blood pressure (−0.8 mg/dl, confidence interval: −1.4, −0.3) indicated that levels were slightly more favorable in the ≥5.0% weight-loss maintenance group than weight maintenance group. Levels were similar for glucose, high-density lipoprotein (HDL) cholesterol and systolic blood pressure. This work indicates that, when adjusted for covariates including current BMI, adults with a history of weight loss may have CVD risk factors to levels as good, or perhaps even better than, those observed in adults who maintain their weight.
In stratified case-cohort designs, samplings of case-cohort samples are conducted via a stratified random sampling based on covariate information available on the entire cohort members. In this paper, we extended the work of Kang & Cai (2009) to a generalized stratified case-cohort study design for failure time data with multiple disease outcomes. Under this study design, we developed weighted estimating procedures for model parameters in marginal multiplicative intensity models and for the cumulative baseline hazard function. The asymptotic properties of the estimators are studied using martingales, modern empirical process theory, and results for finite population sampling.
marginal hazards model; multivariate failure times; stratified case-cohort design; survival analysis; weighted estimating equations
The associations between adiposity and metabolic risk factors have been suggested to vary across ethnicities. Studies in Caucasians have shown that after adjusting for waist circumference and body mass index (BMI), a larger hip circumference may be protective for metabolic risk factors. To our knowledge, these associations have never been examined in a Chinese population.
Baseline (1987–1988) and follow-up (1993–1994) data were from the People's Republic of China Study (n = 1,144 men, n = 1,776 women). Logistic models were stratified by sex and adjusted for age, smoking, center, and education. Incidence differences (ID) comparing the sex specific 85th percentile to the 15th percentile of hip circumference were computed for elevated blood pressure, blood glucose and triglycerides, low high-density lipoprotein cholesterol (HDL-C), and multiple metabolic abnormalities (three or more of the aforementioned).
In models adjusted for waist circumference and BMI, the ID [95% confidence interval (CI)] per 1,000 persons associated with a 12-cm larger hip were −132 (−237, −26) for low HDL-C; −85 (−138, −31) for elevated triglycerides; and −49 (−83, −4) for multiple metabolic abnormalities. In males, a larger hip circumference was not associated with a reduction of incident risk factors, although the ID tended to be negative.
In Chinese women, greater mass in the lower trunk region was inversely associated with incident high triglycerides, low HDL-C, and multiple metabolic abnormalities when adjusted for general and central adiposity. This association was not detected in men. Additional research is needed to better understand the mechanisms by which fat at different depots results in differential risk.
Background. The aim of the study is to determine how the food store environment modifies the effects of an intervention on diet among low-income women. Study Design. A 16-week face-to-face behavioral weight loss intervention was delivered among low income midlife women.
Methods. The retail food environment for all women was characterized by (1) the number and type of food stores within census tracts; (2) availability of healthy foods in stores where participants shop; (3) an aggregate score of self-reported availability of healthy foods in neighborhood and food stores. Statistical Analyses. Multivariable linear regression was used to model the food store environment as an effect modifier between the intervention effect of fruit and vegetable serving change. Results. Among intervention participants with a low perception of availability of healthy foods in stores, the intervention effect on fruit and vegetable serving change was greater [1.89, 95% CI (0.48, 3.31)] compared to controls. Among intervention participants residing in neighborhoods with few super markets, the intervention effect on fruit and vegetable serving change was greater [1.62, 95% CI (1.27, 1.96)] compared to controls. Conclusion. Results point to how the food store environment may modify the success of an intervention on diet change among low-income women.
Few studies have examined the impact of weight history. Extant data from the Atherosclerosis Risk in Communities Study were used to compare risk factors for normal-weight (body mass index: 18.5–24.9 kg/m2) adults with a history of weight loss (n = 775) with those for persons with a history of weight maintenance (n = 5,164). In this 1987–1998 US study, the authors also compared risk factors for preobese (body mass index: 25.0–29.9 kg/m2) adults with a history of weight gain (n = 1,296) versus weight maintenance (n = 6,721). They used mixed-models regression to adjust for ethnicity, gender, age, education, field center, smoking, alcohol consumption, follow-up time, and follow-up body mass index. Compared with adults with a history of weight maintenance, adults with a 3-year history of weight loss had more favorable total and low density lipoprotein cholesterol levels and similar glucose, high density lipoprotein cholesterol, and triglyceride levels. In contrast, preobese adults with a 3-year history of weight gain had equivalent glucose and lipid levels at follow-up compared with adults with a history of weight maintenance. These findings suggest that, in addition to current weight, weight history may impact glucose and lipid levels.
glucose; lipoproteins; HDL cholesterol; lipoproteins; LDL cholesterol; obesity; triglycerides; weight gain; weight loss
The objective of this study was to examine the effect of weight history on blood pressure. Extant data from the Atherosclerosis Risk in Communities (ARIC) study were used to compare blood pressure in women (n = 5,675) and men (n = 4,893) with different 3-year weight histories, but similar current BMI. We used mixed models regression adjusted for ethnicity, age, education, field center, smoking, alcohol consumption, antihypertensive medications, interval length, and BMI at follow-up. We also examined associations between 3-year weight history and blood pressure within weight status categories (normal weight (≥ 18.5 to <25.0 kg/m2), overweight (≥ 25.0 to <30.0 kg/m2), and obese (≥ 30.0 kg/m2)). We found weight history affected both systolic and diastolic blood pressures. Compared to men at the same BMI who had maintained their weight, men who had experienced a 10% weight gain over the previous 3 years had systolic and diastolic blood pressures that were 2.6 and 1.9 mm Hg higher, respectively (P < 0.001 for both). Associations in women were in the same direction, but smaller at 0.9 and 0.6 mm Hg (P < 0.001). With the exception of diastolic blood pressure in normal weight women, we found no significant interactions between weight change and current weight status. In conclusion, some of the variation in blood pressure among individuals at the same BMI may be due to weight change history. Effects of 3-year weight change history appear to be stronger and more consistent in men than in women, and generally similar regardless of current weight status.
Few studies have focused on the impact of weight maintenance on cardiovascular disease risk factors or addressed whether changes differ by baseline weight status and medication usage. The authors examined these issues using 9 years of follow-up data on 3,235 men and women from the Atherosclerosis Risk in Communities (ARIC) Study who were aged 45–64 years at baseline (1987–1989). In participants not using medications, glucose (3.0 mg/dl, 95% confidence interval (CI): 2.4, 3.5) and triglycerides (10.1 mg/dl, 95% CI: 8.3, 11.9) increased, while total cholesterol (−9.6 mg/dl, 95% CI: −10.6, −8.6), low density lipoprotein cholesterol (−9.9 mg/dl, 95% CI: −10.9, −9.0), and high density lipoprotein cholesterol (−1.7 mg/dl, 95% CI: −2.1, −1.3) decreased. Systolic blood pressure (7.9 mmHg, 95% CI: 7.3, 8.4) increased, but diastolic blood pressure (−1.1 mmHg, 95% CI: −1.4, −0.7) declined. Normal weight (body mass index: 18.5–<25.0 kg/m2) participants had smaller increases in glucose compared with obese (body mass index: ≥30.0 kg/m2) participants. In contrast, the authors found less favorable changes in total, low density lipoprotein, and high density lipoprotein cholesterol, triglycerides, and diastolic blood pressure among normal weight compared with obese participants who maintained their weight. These patterns were similar across weight status groups regardless of medication usage.
blood pressure; cholesterol; HDL; cholesterol; LDL; glucose; obesity; triglycerides; weight gain; weight loss
Efficacious strategies for the primary prevention of coronary heart disease (CHD) are underused, and, when used, have low adherence. Existing efforts to improve use and adherence to these efficacious strategies have been so intensive that they are impractical for clinical practice.
We conducted a randomized trial of a CHD prevention intervention (including a computerized decision aid and automated tailored adherence messages) at one university general internal medicine practice. After obtaining informed consent and collecting baseline data, we randomized patients (men and women age 40-79 with no prior history of cardiovascular disease) to either the intervention or usual care. We then saw them for two additional study visits over 3 months. For intervention participants, we administered the decision aid at the primary study visit (1 week after baseline visit) and then mailed 3 tailored adherence reminders at 2, 4, and 6 weeks. We assessed our outcomes (including the predicted likelihood of angina, myocardial infarction, and CHD death over 10 years (CHD risk) and self-reported adherence) between groups at 3 month follow-up. Data collection occurred from June 2007 through December 2009. All study procedures were IRB approved.
We randomized 160 eligible patients (81 intervention; 79 control) and followed 96% to study conclusion. Mean predicted CHD risk at baseline was 11.3%. The intervention increased self-reported adherence to chosen risk reducing strategies by 25 percentage points (95% CI 8% to 42%), with the biggest effect for aspirin. It also changed predicted CHD risk by -1.1% (95% CI -0.16% to -2%), with a larger effect in a pre-specified subgroup of high risk patients.
A computerized intervention that involves patients in CHD decision making and supports adherence to effective prevention strategies can improve adherence and reduce predicted CHD risk.
Clinical trials registration number
Traditionally, weight management behavioral research has focused on individual-level influences, with little attention given to interpersonal factors that relate to the family behavioral context.
This research examines the association between baseline family functioning scores and weight loss success in a sample of African Americans and Whites enrolled in a 20-week weight loss program with a weight loss goal of ≥4 kg.
Baseline surveys measuring six family functioning constructs were completed by 291 participants in a trial of weight loss maintenance. Analysis was limited to 217 participants in households with at least one other family member, and providing final weight measurements. We evaluated associations of family functioning, family composition, and demographic variables with weight loss success defined as losing ≥5% of initial body weight. Baseline predictors of weight loss success were determined using logistic regression analysis.
Participants were on average 61 years of age with BMI of 34 kg/m2; 57% were female and 75% self-identified as African American. Sixty-two percent lost at least 5% of initial body weight. In bivariate analysis, weight loss success was associated with higher income and education (p<0.01 and p=0.05, respectively), ethnicity (p<0.01), and the presence of a spouse (p=0.01). After adjusting for socio-demographic covariates in a multivariable model, the odds of weight loss success were independently influenced by a significant interaction between ethnicity and family cohesion (p<0.01).
These findings suggest that family context factors influence weight loss behaviors.
Weight loss; Family functioning; African American; Family cohesion; Behavioral intervention
The effect of endodontic involvement on tooth loss has not been quantified, so the present study aimed to assess this relationship after controlling for other relevant risk factors for tooth loss.
We analyzed data from 791 participants (18,798 teeth) in the Veterans Affairs Dental Longitudinal Study. Potential tooth- and person-level covariates were fitted into marginal proportional hazards models, including both apical radiolucencies (AR) and root canal therapy (RCT) status as time-dependent variables. Survival curves were plotted for teeth according to their AR and RCT status.
Both current AR and RCT status were associated with increased risk of tooth loss (p< 0.01), after controlling for baseline levels of periodontal disease, caries, tooth type, number of proximal contacts, number of teeth, age, education, and smoking history. Root canal filled (RCF) teeth seemed to have better survival than non-RCF teeth among teeth with AR, but worse survival than non-RCF teeth among teeth without AR.
Endodontic involvement was associated with tooth loss, controlling for other potential risk factors. Additional prospective studies are needed to provide better evidence as to the impact of endodontic involvement on tooth loss.
Apical radiolucency; endodontics; epidemiology; root canal therapy; survival analysis; tooth loss
Recurrent events are frequently encountered in biomedical studies. Evaluating the covariates effects on the marginal recurrent event rate is of practical interest. There are mainly two types of rate models for the recurrent event data: the multiplicative rates model and the additive rates model. We consider a more flexible additive–multiplicative rates model for analysis of recurrent event data, wherein some covariate effects are additive while others are multiplicative. We formulate estimating equations for estimating the regression parameters. The estimators for these regression parameters are shown to be consistent and asymptotically normally distributed under appropriate regularity conditions. Moreover, the estimator of the baseline mean function is proposed and its large sample properties are investigated. We also conduct simulation studies to evaluate the finite sample behavior of the proposed estimators. A medical study of patients with cystic fibrosis suffered from recurrent pulmonary exacerbations is provided for illustration of the proposed method.
Recurrent events; Rate regression; Additive–multiplicative rates model; Counting process; Empirical process
Insulin resistance (IR) has been associated with cardiovascular diseases (CVD). Heart rate variability (HRV), an index of cardiac autonomic modulation (CAM), is also associated with CVD mortality and CVD morbidity. Currently, there are limited data about the impairment of IR on the circadian pattern of CAM. Therefore, we conducted this investigation to exam the association between IR and the circadian oscillations of CAM in a community-dwelling middle-aged sample.
Homeostasis models of IR (HOMA-IR), insulin, and glucose were used to assess IR. CAM was measured by HRV analysis from a 24-hour electrocardiogram. Two stage modeling was used in the analysis. In stage one, for each individual we fit a cosine periodic model based on the 48 segments of HRV data. We obtained three individual-level cosine parameters that quantity the circadian pattern: mean (M), measures the overall average of a HRV index; amplitude (Â), measures the amplitude of the oscillation of a HRV index; and acrophase time (θ), measures the timing of the highest oscillation. At the second stage, we used a random-effects-meta-analysis to summarize the effects of IR variables on the three circadian parameters of HRV indices obtained in stage one of the analysis.
In persons without type diabetes, the multivariate adjusted β (SE) of log HOMA-IR and M variable for HRV were -0.251 (0.093), -0.245 (0.078), -0.19 (0.06), -4.89 (1.76), -3.35 (1.31), and 2.14 (0.995), for log HF, log LF, log VLF, SDNN, RMSSD and HR, respectively (all P < 0.05). None of the IR variables were significantly associated with Â or θ of the HRV indices. However, in eight type 2 diabetics, the magnitude of effect due to higher HOMA-IR on M, Â, and θ are much larger.
Elevated IR, among non-diabetics significantly impairs the overall mean levels of CAM. However, the Â or θ of CAM were not significantly affected by IR, suggesting that the circadian mechanisms of CAM are not impaired. However, among persons with type 2 diabetes, a group clinically has more severe form of IR, the adverse effects of increased IR on all three HRV circadian parameters are much larger.
As biological studies become more expensive to conduct, statistical methods that take advantage of existing auxiliary information about an expensive exposure variable are desirable in practice. Such methods should improve the study efficiency and increase the statistical power for a given number of assays. In this paper, we consider an inference procedure for multivariate failure time with auxiliary covariate information. We propose an estimated pseudo-partial likelihood estimator under the marginal hazard model framework and develop the asymptotic properties for the proposed estimator. We conduct simulation studies to evaluate the performance of the proposed method in practical situations and demonstrate the proposed method with a data set from the Studies of Left Ventricular Dysfunction (SOLVD,1991).
Auxiliary covariate; Marginal hazard model; Multivariate data; Pseudo-partial likelihood; Validation sample
In a case–cohort design, covariates are assembled only for a subcohort that is randomly selected from the entire cohort and any additional cases outside the subcohort. This design is appealing for large cohort studies of rare disease, especially when the exposures of interest are expensive to ascertain for all the subjects. We propose statistical methods for analyzing the case–cohort data with a semiparametric accelerated failure time model that interprets the covariates effects as to accelerate or decelerate the time to failure. Asymptotic properties of the proposed estimators are developed. The finite sample properties of case–cohort estimator and its relative efficiency to full cohort estimator are assessed via simulation studies. A real example from a study of cardiovascular disease is provided to illustrate the estimating procedure.
Accelerated failure time model; Case-cohort design; Stratified simple random sampling; Survival data
Multivariate failure time data arise frequently in survival analysis. A commonly used technique is the working independence estimator for marginal hazard models. Two natural questions are how to improve the efficiency of the working independence estimator and how to identify the situations under which such an estimator has high statistical efficiency. In this paper, three weighted estimators are proposed based on three different optimal criteria in terms of the asymptotic covariance of weighted estimators. Simplified close-form solutions are found, which always outperform the working independence estimator. We also prove that the working independence estimator has high statistical efficiency, when asymptotic covariance of derivatives of partial log-likelihood functions is nearly exchangeable or diagonal. Simulations are conducted to compare the performance of the weighted estimator and working independence estimator. A data set from Busselton population health surveys is analyzed using the proposed estimators.
Marginal hazard model; pseudo-partial likelihood; working independence estimator; optimal weight
Recurrent events data are frequently encountered and could be stopped by a terminal event in clinical trials. It is of interest to assess the treatment efficacy simultaneously with respect to both the recurrent events and the terminal event in many applications. In this paper we propose joint covariate-adjusted score test statistics based on joint models of recurrent events and a terminal event. No assumptions on the functional form of the covariates are needed. Simulation results show that the proposed tests can improve the efficiency over tests based on covariate unadjusted model. The proposed tests are applied to the SOLVD data for illustration.
Frailty; Proportional hazards; Proportional rates; Recurrent events data; Semiparametric model
In many biomedical studies with recurrent events, some markers can only be measured when events happen. For example, medical cost attributed to hospitalization can only incur when patients are hospitalized. Such marker data are contingent on recurrent events. In this paper, we present a proportional means model for modelling the markers using the observed covariates contingent on the recurrent event. We also model the recurrent event via a marginal rate model. Estimating equations are constructed to derive the point estimators for the parameters in the proposed models. The estimators are shown to be asymptotically normal. Simulation studies are conducted to examine the finite-sample properties of the proposed estimators and the proposed method is applied to a data set from the Vitamin A Community Trial.
Recurrent event; Recurrent marker; Joint models; Rate function; Estimating equation
We propose a class of additive transformation risk models for clustered failure time data. Our models are motivated by the usual additive risk model for independent failure times incorporating a frailty with mean one and constant variability which is a natural generalization of the additive risk model from univariate failure time to multivariate failure time. An estimating equation approach based on the marginal hazards function is proposed. Under the assumption that cluster sizes are completely random, we show the resulting estimators of the regression coefficients are consistent and asymptotically normal. We also provide goodness-of-fit test statistics for choosing the transformation. Simulation studies and real data analysis are conducted to examine the finite-sample performance of our estimators.
Additive model; Estimating equation; Goodness-of-fit; Robustness; Transformation