SAS macros for point and interval estimation of area under the receiver operating characteristic curve for non-proportional and proportional hazards Weibull models

Aims and objectives  For prediction of risk of cardiovascular end points using survival models the proportional hazards assumption is often not met. Thus, non-proportional hazards models are more appropriate for developing risk prediction equations in such situations. However, computer program for evaluating the prediction performance of such models has been rarely addressed. We therefore developed SAS macro programs for evaluating the discriminative ability of a non-proportional hazards Weibull model developed by Anderson (1991) and that of a proportional hazards Weibull model using the area under receiver operating characteristic (ROC) curve.

Method  Two SAS macro programs for non-proportional hazards Weibull model using Proc NLIN and Proc NLP respectively and model validation using area under ROC curve (with its confidence limits) were written with SAS IML language. A similar SAS macro for proportional hazards Weibull model was also written.

Results  The computer program was applied to data on coronary heart disease incidence for a Framingham population cohort. The five risk factors considered were current smoking, age, blood pressure, cholesterol and obesity. The predictive ability of the non-proportional hazard Weibull model was slightly higher than that of its proportional hazard counterpart. An advantage of SAS Proc NLP in terms of the example provided here is that it provides significance level for the parameter estimates whereas Proc NLIN does not.

Conclusion  The program is very useful for evaluating the predictive performance of non-proportional and proportional hazards Weibull models.

Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

Development of a log-quadratic model to describe microbial inactivation, illustrated by thermal inactivation of Clostridium botulinum

In the commercial food industry, demonstration of microbiological safety and thermal process equivalence often involves a mathematical framework that assumes log-linear inactivation kinetics and invokes concepts of decimal reduction time (DT), z values, and accumulated lethality. However, many microbes, particularly spores, exhibit inactivation kinetics that are not log linear. This has led to alternative modeling approaches, such as the biphasic and Weibull models, that relax strong log-linear assumptions. Using a statistical framework, we developed a novel log-quadratic model, which approximates the biphasic and Weibull models and provides additional physiological interpretability. As a statistical linear model, the log-quadratic model is relatively simple to fit and straightforwardly provides confidence intervals for its fitted values. It allows a DT-like value to be derived, even from data that exhibit obvious "tailing." We also showed how existing models of non-log-linear microbial inactivation, such as the Weibull model, can fit into a statistical linear model framework that dramatically simplifies their solution. We applied the log-quadratic model to thermal inactivation data for the spore-forming bacterium Clostridium botulinum and evaluated its merits compared with those of popular previously described approaches. The log-quadratic model was used as the basis of a secondary model that can capture the dependence of microbial inactivation kinetics on temperature. This model, in turn, was linked to models of spore inactivation of Sapru et al. and Rodriguez et al. that posit different physiological states for spores within a population. We believe that the log-quadratic model provides a useful framework in which to test vitalistic and mechanistic hypotheses of inactivation by thermal and other processes. Copyright © 2009, American Society for Microbiology. All Rights Reserved.

In vitro characterization of coevaporates containing chitosan for colonic drug delivery

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Chitosan/Carbomer-based tablets containing Metronidazole for potential treatment of periodontal diseases

Mucoadhesive tablets with different mixtures of chitosan and carbomer homopolymer type B were prepared in order to obtain new formulations containing metronidazole for periodontal disease treatment. All tablets were characterized by swelling and erosion studies, ex vivo mucoadhesion force and in vitro drug release. The drug released mechanism was described by Korsmeyer-Peppas and Weibull models. Tablets containing increased amounts of chitosan presented higher swelling ability and the drug release was prolonged in the simulated saliva fluid. The mechanisms for the drug release from tablets were complex, including diffusion, swelling and erosion simultaneously. This kind of delivery system is suitable for formulating metronidazole mucoadhesive systems, representing a good alternative for the local treatment of periodontal diseases.

Uncertainty About the Incubation Period of AIDS and its Impact on Backcalculation

We analyze three sets of doubly-censored cohort data on incubation times, estimating incubation distributions using semi-parametric methods and assessing the comparability of the estimates. Weibull models appear to be inappropriate for at least one of the cohorts, and the estimates for the different cohorts are substantially different. We use these estimates as inputs for backcalculation, using a nonparametric method based on maximum penalized likelihood. The different incubations all produce fits to the reported AIDS counts that are as good as the fit from a nonstationary incubation distribution that models treatment effects, but the estimated infection curves are very different. We also develop a method for estimating nonstationarity as part of the backcalculation procedure and find that such estimates also depend very heavily on the assumed incubation distribution. We conclude that incubation distributions are so uncertain that meaningful error bounds are difficult to place on backcalculated estimates and that backcalculation may be too unreliable to be used without being supplemented by other sources of information in HIV prevalence and incidence.

Prognostic importance of anaemia in HIV type-1-infected patients starting antiretroviral therapy: collaborative analysis of prospective cohort studies

BACKGROUND: In HIV type-1-infected patients starting highly active antiretroviral therapy (HAART), the prognostic value of haemoglobin when starting HAART, and of changes in haemoglobin levels, are not well defined. METHODS: We combined data from 10 prospective studies of 12,100 previously untreated individuals (25% women). A total of 4,222 patients (35%) were anaemic: 131 patients (1.1%) had severe (<8.0 g/dl), 1,120 (9%) had moderate (male 8.0-<11.0 g/dl and female 8.0- < 10.0 g/dl) and 2,971 (25%) had mild (male 11.0- < 13.0 g/ dl and female 10.0- < 12.0 g/dl) anaemia. We separately analysed progression to AIDS or death from baseline and from 6 months using Weibull models, adjusting for CD4+ T-cell count, age, sex and other variables. RESULTS: During 48,420 person-years of follow-up 1,448 patients developed at least one AIDS event and 857 patients died. Anaemia at baseline was independently associated with higher mortality: the adjusted hazard ratio (95% confidence interval) for mild anaemia was 1.42 (1.17-1.73), for moderate anaemia 2.56 (2.07-3.18) and for severe anaemia 5.26 (3.55-7.81). Corresponding figures for progression to AIDS were 1.60 (1.37-1.86), 2.00 (1.66-2.40) and 2.24 (1.46-3.42). At 6 months the prevalence of anaemia declined to 26%. Baseline anaemia continued to predict mortality (and to a lesser extent progression to AIDS) in patients with normal haemoglobin or mild anaemia at 6 months. CONCLUSIONS: Anaemia at the start of HAART is an important factor for short- and long-term prognosis, including in patients whose haemoglobin levels improved or normalized during the first 6 months of HAART.

Prognosis of HIV-associated non-Hodgkin lymphoma in patients starting combination antiretroviral therapy

OBJECTIVE: We examined survival and prognostic factors of patients who developed HIV-associated non-Hodgkin lymphoma (NHL) in the era of combination antiretroviral therapy (cART). DESIGN AND SETTING: Multicohort collaboration of 33 European cohorts. METHODS: We included all cART-naive patients enrolled in cohorts participating in the Collaboration of Observational HIV Epidemiological Research Europe (COHERE) who were aged 16 years or older, started cART at some point after 1 January 1998 and developed NHL after 1 January 1998. Patients had to have a CD4 cell count after 1 January 1998 and one at diagnosis of the NHL. Survival and prognostic factors were estimated using Weibull models, with random effects accounting for heterogeneity between cohorts. RESULTS: Of 67 659 patients who were followed up during 304 940 person-years, 1176 patients were diagnosed with NHL. Eight hundred and forty-seven patients (72%) from 22 cohorts met inclusion criteria. Survival at 1 year was 66% [95% confidence interval (CI) 63-70%] for systemic NHL (n = 763) and 54% (95% CI: 43-65%) for primary brain lymphoma (n = 84). Risk factors for death included low nadir CD4 cell counts and a history of injection drug use. Patients developing NHL on cART had an increased risk of death compared with patients who were cART naive at diagnosis. CONCLUSION: In the era of cART two-thirds of patients diagnosed with HIV-related systemic NHL survive for longer than 1 year after diagnosis. Survival is poorer in patients diagnosed with primary brain lymphoma. More advanced immunodeficiency is the dominant prognostic factor for mortality in patients with HIV-related NHL.

Switching to second-line antiretroviral therapy in resource-limited settings: comparison of programmes with and without viral load monitoring

BACKGROUND: In high-income countries, viral load is routinely measured to detect failure of antiretroviral therapy (ART) and guide switching to second-line ART. Viral load monitoring is not generally available in resource-limited settings. We examined switching from nonnucleoside reverse transcriptase inhibitor (NNRTI)-based first-line regimens to protease inhibitor-based regimens in Africa, South America and Asia. DESIGN AND METHODS: Multicohort study of 17 ART programmes. All sites monitored CD4 cell count and had access to second-line ART and 10 sites monitored viral load. We compared times to switching, CD4 cell counts at switching and obtained adjusted hazard ratios for switching (aHRs) with 95% confidence intervals (CIs) from random-effects Weibull models. RESULTS: A total of 20 113 patients, including 6369 (31.7%) patients from 10 programmes with access to viral load monitoring, were analysed; 576 patients (2.9%) switched. Low CD4 cell counts at ART initiation were associated with switching in all programmes. Median time to switching was 16.3 months [interquartile range (IQR) 10.1-26.6] in programmes with viral load monitoring and 21.8 months (IQR 14.0-21.8) in programmes without viral load monitoring (P < 0.001). Median CD4 cell counts at switching were 161 cells/microl (IQR 77-265) in programmes with viral load monitoring and 102 cells/microl (44-181) in programmes without viral load monitoring (P < 0.001). Switching was more common in programmes with viral load monitoring during months 7-18 after starting ART (aHR 1.38; 95% CI 0.97-1.98), similar during months 19-30 (aHR 0.97; 95% CI 0.58-1.60) and less common during months 31-42 (aHR 0.29; 95% CI 0.11-0.79). CONCLUSION: In resource-limited settings, switching to second-line regimens tends to occur earlier and at higher CD4 cell counts in ART programmes with viral load monitoring compared with programmes without viral load monitoring.

Ultra high pressure homogenization (UHPH) inactivation of Bacillus amyloliquefaciens spores in phosphate buffered saline (PBS) and milk

Ultra high pressure homogenization (UHPH) opens up new areas for dynamic high pressure assisted thermal sterilization of liquids. Bacillus amyloliquefaciens spores are resistant to high isostatic pressure and temperature and were suggested as potential surrogate for high pressure thermal sterilization validation. B. amyloliquefaciens spores suspended in PBS buffer (0.01 M, pH 7.0), low fat milk (1.5%, pH 6.7), and whole milk (3.5%, pH 6.7) at initial concentration of similar to 10(6) CFU/mL were subjected to UHPH treatments at 200, 300, and 350 MPa with an inlet temperature at similar to 80 degrees C. Thermal inactivation kinetics of B. amyloliquefaciens spores in PBS and milk were assessed with thin wall glass capillaries and modeled using first-order and Weibull models. The residence time during UHPH treatments was estimated to determine the contribution of temperature to spore inactivation by UHPH. No sublethal injury was detected after UHPH treatments using sodium chloride as selective component in the nutrient agar medium. The inactivation profiles of spores in PBS buffer and milk were compared and fat provided no clear protective effect for spores against treatments. Treatment at 200 MPa with valve temperatures lower than 125 degrees C caused no reduction of spores. A reduction of 3.5 log(10)CFU/mL of B. amyloliquefaciens spores was achieved by treatment at 350 MPa with a valve temperature higher than 150 degrees C. The modeled thermal inactivation and observed inactivation during UHPH treatments suggest that temperature could be the main lethal effect driving inactivation.

Economic design of (X)over-bar and R charts under Weibull shock models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Joint conomic design of (x)over-bar and R charts under Weibull shock models

This paper deals with the joint economic design of (x) over bar and R charts when the occurrence times of assignable causes follow Weibull distributions with increasing failure rates. The variable quality characteristic is assumed to be normally distributed and the process is subject to two independent assignable causes (such as tool wear-out, overheating, or vibration). One cause changes the process mean and the other changes the process variance. However, the occurrence of one kind of assignable cause does not preclude the occurrence of the other. A cost model is developed and a non-uniform sampling interval scheme is adopted. A two-step search procedure is employed to determine the optimum design parameters. Finally, a sensitivity analysis of the model is conducted, and the cost savings associated with the use of non-uniform sampling intervals instead of constant sampling intervals are evaluated.

Joint conomic design of x̄ and R charts under Weibull shock models

This paper deals with the joint economic design of x̄ and R charts when the occurrence times of assignable causes follow Weibull distributions with increasing failure rates. The variable quality characteristic is assumed to be normally distributed and the process is subject to two independent assignable causes (such as tool wear-out, overheating, or vibration). One cause changes the process mean and the other changes the process variance. However, the occurrence of one kind of assignable cause does not preclude the occurrence of the other. A cost model is developed and a non-uniform sampling interval scheme is adopted. A two-step search procedure is employed to determine the optimum design parameters. Finally, a sensitivity analysis of the model is conducted, and the cost savings associated with the use of non-uniform sampling intervals instead of constant sampling intervals are evaluated.

Weibull and generalised exponential overdispersion models with an application to ozone air pollution

We consider the problem of estimating the mean and variance of the time between occurrences of an event of interest (inter-occurrences times) where some forms of dependence between two consecutive time intervals are allowed. Two basic density functions are taken into account. They are the Weibull and the generalised exponential density functions. In order to capture the dependence between two consecutive inter-occurrences times, we assume that either the shape and/or the scale parameters of the two density functions are given by auto-regressive models. The expressions for the mean and variance of the inter-occurrences times are presented. The models are applied to the ozone data from two regions of Mexico City. The estimation of the parameters is performed using a Bayesian point of view via Markov chain Monte Carlo (MCMC) methods.

Distinguishing forced versus discretionary replacements in new product diffusion models

In many product categories of durable goods such as TV, PC, and DVD player, the largest component of sales is generated by consumers replacing existing units. Aggregate sales models proposed by diffusion of innovation researchers for the replacement component of sales have incorporated several different replacement distributions such as Rayleigh, Weibull, Truncated Normal and Gamma. Although these alternative replacement distributions have been tested using both time series sales data and individual-level actuarial “life-tables” of replacement ages, there is no census on which distributions are more appropriate to model replacement behaviour. In the current study we are motivated to develop a new “modified gamma” distribution by two reasons. First we recognise that replacements have two fundamentally different drivers – those forced by failure and early, discretionary replacements. The replacement distribution for each of these drivers is expected to be quite different. Second, we observed a poor fit of other distributions to out empirical data. We conducted a survey of 8,077 households to empirically examine models of replacement sales for six electronic consumer durables – TVs, VCRs, DVD players, digital cameras, personal and notebook computers. This data allows us to construct individual-level “life-tables” for replacement ages. We demonstrate the new modified gamma model fits the empirical data better than existing models for all six products using both a primary and a hold-out sample.