Determinants of CD4 cell count decline after treatment interruption

Patients who had started HAART (Highly Active Anti-Retroviral Treatment) under previous aggressive DHHS guidelines (1997) underwent a life-long continuous HAART that was associated with many short term as well as long term complications. Many interventions attempted to reduce those complications including intermittent treatment also called pulse therapy. Many studies were done to study the determinants of rate of fall in CD4 count after interruption as this data would help guide treatment interruptions. The data set used here was a part of a cohort study taking place at the Johns Hopkins AIDS service since January 1984, in which the data were collected both prospectively and retrospectively. The patients in this data set consisted of 47 patients receiving via pulse therapy with the aim of reducing the long-term complications. ^ The aim of this project was to study the impact of virologic and immunologic factors on the rate of CD4 loss after treatment interruption. The exposure variables under investigation included CD4 cell count and viral load at treatment initiation. The rates of change of CD4 cell count after treatment interruption was estimated from observed data using advanced longitudinal data analysis methods (i.e., linear mixed model). Using random effects accounted for repeated measures of CD4 per person after treatment interruption. The regression coefficient estimates from the model was then used to produce subject specific rates of CD4 change accounting for group trends in change. The exposure variables of interest were age, race, and gender, CD4 cell counts and HIV RNA levels at HAART initiation. ^ The rate of fall of CD4 count did not depend on CD4 cell count or viral load at initiation of treatment. Thus these factors may not be used to determine who can have a chance of successful treatment interruption. CD4 and viral load were again studied by t-tests and ANOVA test after grouping based on medians and quartiles to see any difference in means of rate of CD4 fall after interruption. There was no significant difference between the groups suggesting that there was no association between rate of fall of CD4 after treatment interruption and above mentioned exposure variables. ^

HPV vaccine coverage in Texas counties: An application of multilevel, small area estimation

Health departments, research institutions, policy-makers, and healthcare providers are often interested in knowing the health status of their clients/constituents. Without the resources, financially or administratively, to go out into the community and conduct health assessments directly, these entities frequently rely on data from population-based surveys to supply the information they need. Unfortunately, these surveys are ill-equipped for the job due to sample size and privacy concerns. Small area estimation (SAE) techniques have excellent potential in such circumstances, but have been underutilized in public health due to lack of awareness and confidence in applying its methods. The goal of this research is to make model-based SAE accessible to a broad readership using clear, example-based learning. Specifically, we applied the principles of multilevel, unit-level SAE to describe the geographic distribution of HPV vaccine coverage among females aged 11-26 in Texas.^ Multilevel (3 level: individual, county, public health region) random-intercept logit models of HPV vaccination (receipt of ≥ 1 dose Gardasil® ) were fit to data from the 2008 Behavioral Risk Factor Surveillance System (outcome and level 1 covariates) and a number of secondary sources (group-level covariates). Sampling weights were scaled (level 1) or constructed (levels 2 & 3), and incorporated at every level. Using the regression coefficients (and standard errors) from the final models, I simulated 10,000 datasets for each regression coefficient from the normal distribution and applied them to the logit model to estimate HPV vaccine coverage in each county and respective demographic subgroup. For simplicity, I only provide coverage estimates (and 95% confidence intervals) for counties.^ County-level coverage among females aged 11-17 varied from 6.8-29.0%. For females aged 18-26, coverage varied from 1.9%-23.8%. Aggregated to the state level, these values translate to indirect state estimates of 15.5% and 11.4%, respectively; both of which fall within the confidence intervals for the direct estimates of HPV vaccine coverage in Texas (Females 11-17: 17.7%, 95% CI: 13.6, 21.9; Females 18-26: 12.0%, 95% CI: 6.2, 17.7).^ Small area estimation has great potential for informing policy, program development and evaluation, and the provision of health services. Harnessing the flexibility of multilevel, unit-level SAE to estimate HPV vaccine coverage among females aged 11-26 in Texas counties, I have provided (1) practical guidance on how to conceptualize and conduct modelbased SAE, (2) a robust framework that can be applied to other health outcomes or geographic levels of aggregation, and (3) HPV vaccine coverage data that may inform the development of health education programs, the provision of health services, the planning of additional research studies, and the creation of local health policies.^

A cohort study of body fatness and coronary mortality in middle -aged men

Data from the Chicago Western Electric Study were used to investigate whether central fat distribution, as estimated by the ratio of subscapular-to-triceps skinfold, was associated with 25-year risk of death from coronary heart disease in a cohort of 1,945 middle-aged employed men. Subscapular-triceps skinfold ratio was found positively and significantly associated with risk of coronary death after adjustment for age and body mass index. The age-adjusted proportional hazards regression coefficient was 0.2078 with 95% confidence interval of 0.0087 to 0.4069. A difference of 1.1 in the subscapular-triceps skinfold ratio (the difference between the mean of the fifth quintile and of the first and second quintiles combined) was associated with a relative risk of 1.31 with 95% confidence interval of 1.06 to 1.62. The coefficient was decreased to 0.1961 (95% confidence interval of ($-$0.0028 to 0.3950) after adjustment for diastolic blood pressure, serum cholesterol and cigarette smoking as well as age and body mass index. At least some of the effect of central fat on coronary risk is probably mediated by blood pressure and serum lipids, but whether all of the effect can be accounted for blood pressure and serum lipids is uncertain.^ This study supports the concept that central fat distribution is a risk factor for 25-year risk of coronary death in middle-aged men. ^

Logistic regression with incompletely observed binary

Logistic regression is one of the most important tools in the analysis of epidemiological and clinical data. Such data often contain missing values for one or more variables. Common practice is to eliminate all individuals for whom any information is missing. This deletion approach does not make efficient use of available information and often introduces bias.^ Two methods were developed to estimate logistic regression coefficients for mixed dichotomous and continuous covariates including partially observed binary covariates. The data were assumed missing at random (MAR). One method (PD) used predictive distribution as weight to calculate the average of the logistic regressions performing on all possible values of missing observations, and the second method (RS) used a variant of resampling technique. Additional seven methods were compared with these two approaches in a simulation study. They are: (1) Analysis based on only the complete cases, (2) Substituting the mean of the observed values for the missing value, (3) An imputation technique based on the proportions of observed data, (4) Regressing the partially observed covariates on the remaining continuous covariates, (5) Regressing the partially observed covariates on the remaining continuous covariates conditional on response variable, (6) Regressing the partially observed covariates on the remaining continuous covariates and response variable, and (7) EM algorithm. Both proposed methods showed smaller standard errors (s.e.) for the coefficient involving the partially observed covariate and for the other coefficients as well. However, both methods, especially PD, are computationally demanding; thus for analysis of large data sets with partially observed covariates, further refinement of these approaches is needed. ^

The number and timing of time -dependent covariate measurements for the Cox regression model

The problem of analyzing data with updated measurements in the time-dependent proportional hazards model arises frequently in practice. One available option is to reduce the number of intervals (or updated measurements) to be included in the Cox regression model. We empirically investigated the bias of the estimator of the time-dependent covariate while varying the effect of failure rate, sample size, true values of the parameters and the number of intervals. We also evaluated how often a time-dependent covariate needs to be collected and assessed the effect of sample size and failure rate on the power of testing a time-dependent effect.^ A time-dependent proportional hazards model with two binary covariates was considered. The time axis was partitioned into k intervals. The baseline hazard was assumed to be 1 so that the failure times were exponentially distributed in the ith interval. A type II censoring model was adopted to characterize the failure rate. The factors of interest were sample size (500, 1000), type II censoring with failure rates of 0.05, 0.10, and 0.20, and three values for each of the non-time-dependent and time-dependent covariates (1/4,1/2,3/4).^ The mean of the bias of the estimator of the coefficient of the time-dependent covariate decreased as sample size and number of intervals increased whereas the mean of the bias increased as failure rate and true values of the covariates increased. The mean of the bias of the estimator of the coefficient was smallest when all of the updated measurements were used in the model compared with two models that used selected measurements of the time-dependent covariate. For the model that included all the measurements, the coverage rates of the estimator of the coefficient of the time-dependent covariate was in most cases 90% or more except when the failure rate was high (0.20). The power associated with testing a time-dependent effect was highest when all of the measurements of the time-dependent covariate were used. An example from the Systolic Hypertension in the Elderly Program Cooperative Research Group is presented. ^