Regressive logistic and proportional hazards disease models for within-family analyses of measured genotypes, with application to a CYP17 polymorphism and breast cancer

Various statistical methods have been proposed to evaluate associations between measured genetic variants and disease, including some using family designs. For breast cancer and rare variants, we applied a modified segregation analysis method that uses the population cancer incidence and population-based case families in which a mutation is known to be segregating. Here we extend the method to a common polymorphism, and use a regressive logistic approach to model familial aggregation by conditioning each individual on their mother's breast cancer history. We considered three models: 1) class A regressive logistic model; 2) age-of-onset regressive logistic model; and 3) proportional hazards familial model. Maximum likelihood estimates were calculated using the software MENDEL. We applied these methods to data from the Australian Breast Cancer Family Study on the CYP17 5UTR TC MspA1 polymorphism measured for 1,447 case probands, 787 controls, and 213 relatives of case probands found to have the CC genotype. Breast cancer data for first- and second-degree relatives of case probands were used. The three methods gave consistent estimates. The best-fitting model involved a recessive inheritance, with homozygotes being at an increased risk of 47% (95% CI, 28-68%). The cumulative risk of the disease up to age 70 years was estimated to be 10% or 22% for a CYP17 homozygote whose mother was unaffected or affected, respectively. This analytical approach is well-suited to the data that arise from population-based case-control-family studies, in which cases, controls and relatives are studied, and genotype is measured for some but not all subjects.

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.

Laboratory and non-laboratory-based risk prevention models for secondary prevention of cardiovascular disease : the LIPID study

Aims : The aims of this study were to examine whether risk prediction models for recurrent cardiovascular disease (CVD) events have prognostic value, and to particularly examine the performance of those models based on non-laboratory data. We also aimed to construct a risk chart based on the risk factors that showed the strongest relationship with CVD.

Methods and results : Cox proportional hazards models were used to calculate a risk score for each recurrent event in a CVD patient who was enrolled in a very large randomized controlled clinical trial. Patients were then classified into groups according to quintiles of their risk score. These risk models were validated by calibration and discrimination analyses based on data from patients recruited in New Zealand for the same study. Non-laboratory-based risk factors, such as age, sex, body mass index, smoking status, angina grade, history of myocardial infarction, revascularization, stroke, diabetes or hypertension and treatment with pravastatin, were found to be significantly associated with the risk of developing a recurrent CVD event. Patients who were classified into the medium and high-risk groups had two-fold and four-fold the risk of developing a CVD event compared with those in the low-risk group, respectively. The risk prediction models also fitted New Zealand data well after recalibration.

Conclusion : A simpler non-laboratory-based risk prediction model performed equally as well as the more comprehensive laboratory-based risk prediction models. The risk chart based on the further simplified Score Model may provide a useful tool for clinical cardiologists to assess an individual patient's risk for recurrent CVD events.

Robust plug-in estimators in proportional scatter models

We address the problem of estimating the principal axes and their size in the case of several populations under the assumption of a proportional model. We propose robust estimators for the common principal axes and their size. The robust estimators are based on asymptotically normal and equivariant robust scatter estimators. The asymptotic distribution of the robust estimators including the proportionality constants are derived. © 2003 Elsevier B.V. All rights reserved.

Survival analysis of time-to-event data in respiratory health research studies

This article provides a review of techniques for the analysis of survival data arising from respiratory health studies. Popular techniques such as the Kaplan–Meier survival plot and the Cox proportional hazards model are presented and illustrated using data from a lung cancer study. Advanced issues are also discussed, including parametric proportional hazards models, accelerated failure time models, time-varying explanatory variables, simultaneous analysis of multiple types of outcome events and the restricted mean survival time, a novel measure of the effect of treatment.

Birthweight and childhood cancer : preliminary findings from the International Childhood Cancer Cohort Consortium (I4C)

BACKGROUND: Evidence relating childhood cancer to high birthweight is derived primarily from registry and case-control studies. We aimed to investigate this association, exploring the potential modifying roles of age at diagnosis and maternal anthropometrics, using prospectively collected data from the International Childhood Cancer Cohort Consortium.

METHODS: We pooled data on infant and parental characteristics and cancer incidence from six geographically and temporally diverse member cohorts [the Avon Longitudinal Study of Parents and Children (UK), the Collaborative Perinatal Project (USA), the Danish National Birth Cohort (Denmark), the Jerusalem Perinatal Study (Israel), the Norwegian Mother and Child Cohort Study (Norway), and the Tasmanian Infant Health Survey (Australia)]. Birthweight metrics included a continuous measure, deciles, and categories (≥4.0 vs. <4.0 kilogram). Childhood cancer (377 cases diagnosed prior to age 15 years) risk was analysed by type (all sites, leukaemia, acute lymphoblastic leukaemia, and non-leukaemia) and age at diagnosis. We estimated hazard ratios (HR) and 95% confidence intervals (CI) from Cox proportional hazards models stratified by cohort.

RESULTS: A linear relationship was noted for each kilogram increment in birthweight adjusted for gender and gestational age for all cancers [HR = 1.26; 95% CI 1.02, 1.54]. Similar trends were observed for leukaemia. There were no significant interactions with maternal pre-pregnancy overweight or pregnancy weight gain. Birthweight ≥4.0 kg was associated with non-leukaemia cancer among children diagnosed at age ≥3 years [HR = 1.62; 95% CI 1.06, 2.46], but not at younger ages [HR = 0.7; 95% CI 0.45, 1.24, P for difference = 0.02].

CONCLUSION: Childhood cancer incidence rises with increasing birthweight. In older children, cancers other than leukaemia are particularly related to high birthweight. Maternal adiposity, currently widespread, was not demonstrated to substantially modify these associations. Common factors underlying foetal growth and carcinogenesis need to be further explored.

The metabolic syndrome and cancer: is the metabolic syndrome useful for predicting cancer risk above and beyond its individual components?

AIMS: The metabolic syndrome (MetS) is a risk factor for cancer. However, it is not known if the MetS confers a greater cancer risk than the sum of its individual components, which components drive the association, or if the MetS predicts future cancer risk. MATERIALS AND METHODS: We linked 20,648 participants from the Australian and New Zealand Diabetes and Cancer Collaboration with complete data on the MetS to national cancer registries and used Cox proportional hazards models to estimate associations of the MetS, the number of positive MetS components, and each of the five MetS components separately with the risk for overall, colorectal, prostate and breast cancer. Hazard ratios (HR) and 95% confidence intervals (95%CI) are reported. We assessed predictive ability of the MetS using Harrell's c-statistic. RESULTS: The MetS was inversely associated with prostate cancer (HR 0.85; 95% CI 0.72-0.99). We found no evidence of an association between the MetS overall, colorectal and breast cancers. For those with five positive MetS components the HR was 1.12 (1.02-1.48) and 2.07 (1.26-3.39) for overall, and colorectal cancer, respectively, compared with those with zero positive MetS components. Greater waist circumference (WC) (1.38; 1.13-1.70) and elevated blood pressure (1.29; 1.01-1.64) were associated with colorectal cancer. Elevated WC and triglycerides were (inversely) associated with prostate cancer. MetS models were only poor to moderate discriminators for all cancer outcomes. CONCLUSIONS: We show that the MetS is (inversely) associated with prostate cancer, but is not associated with overall, colorectal or breast cancer. Although, persons with five positive components of the MetS are at a 1.2 and 2.1 increased risk for overall and colorectal cancer, respectively, and these associations appear to be driven, largely, by elevated WC and BP. We also demonstrate that the MetS is only a moderate discriminator of cancer risk.

Comparison of anthropometric measures as predictors of cancer incidence: a pooled collaborative analysis of 11 Australian cohorts

Obesity is a risk factor for cancer. However, it is not known if general adiposity, as measured by body mass index (BMI) or central adiposity [e.g., waist circumference (WC)] have stronger associations with cancer, or which anthropometric measure best predicts cancer risk. We included 79,458 men and women from the Australian and New Zealand Diabetes and Cancer Collaboration with complete data on anthropometry [BMI, WC, Hip Circumference (HC), WHR, waist to height ratio (WtHR), A Body Shape Index (ABSI)], linked to the Australian Cancer Database. Cox proportional hazards models assessed the association between each anthropometric marker, per standard deviation and the risk of overall, colorectal, post-menopausal (PM) breast, prostate and obesity-related cancers. We assessed the discriminative ability of models using Harrell's c-statistic. All anthropometric markers were associated with overall, colorectal and obesity-related cancers. BMI, WC and HC were associated with PM breast cancer and no significant associations were seen for prostate cancer. Strongest associations were observed for WC across all outcomes, excluding PM breast cancer for which HC was strongest. WC had greater discrimination compared to BMI for overall and colorectal cancer in men and women with c-statistics ranging from 0.70 to 0.71. We show all anthropometric measures are associated with the overall, colorectal, PM breast and obesity-related cancer in men and women, but not prostate cancer. WC discriminated marginally better than BMI. However, all anthropometric measures were similarly moderately predictive of cancer risk. We do not recommend one anthropometric marker over another for assessing an individuals' risk of cancer.

Fracture prediction from repeat BMD measurements in clinical practice

Summary: We investigated whether repeat BMD measurements in clinical populations are useful for fracture risk assessment. We report that repeat BMD measurements are a robust predictor of fracture in clinical populations; this is not affected by preceding BMD change or recent osteoporosis therapy. Introduction: In clinical practice, many patients selectively undergo repeat bone mineral density (BMD) measurements. We investigated whether repeat BMD measurements in clinical populations are useful for fracture risk assessment and whether this is affected by preceding change in BMD or recent osteoporosis therapy. Methods: We identified women and men aged ≥50 years who had a BMD measurement during 1990–2009 from a large clinical BMD database for Manitoba, Canada (n = 50,215). Patient subgroups aged ≥50 years at baseline with repeat BMD measures were identified. Data were linked to an administrative data repository, from which osteoporosis therapy, fracture outcomes, and covariates were extracted. Using Cox proportional hazards models, we assessed covariate-adjusted risk for major osteoporotic fracture (MOF) and hip fracture according to BMD (total hip, lumbar spine, femoral neck) at different time points. Results: Prevalence of osteoporosis therapy increased from 18 % at baseline to 55 % by the fourth measurement. Total hip BMD was predictive of MOF at each time point. In the patient subgroup with two repeat BMD measurements (n = 13,481), MOF prediction with the first and second measurements was similar: adjusted-hazard ratio (HR) per SD 1.45 (95 % CI 1.34–1.56) vs. 1.64 (95 % CI 1.48–1.81), respectively. No differences were seen when the second measurement results were stratified by preceding change in BMD or osteoporosis therapy (both p-interactions >0.2). Similar results were seen for hip fracture prediction and when spine and femoral neck BMD were analyzed. Conclusion: Repeat BMD measurements are a robust predictor of fracture in clinical populations; this is not affected by preceding BMD change or recent osteoporosis therapy.

The effect of modifiable risk factors on geographic mortality differentials: a modelling study

BACKGROUND: Australian mortality rates are higher in regional and remote areas than in major cities. The degree to which this is driven by variation in modifiable risk factors is unknown. METHODS: We applied a risk prediction equation incorporating smoking, cholesterol and blood pressure to a national, population based survey to project all-causes mortality risk by geographic region. We then modelled life expectancies at different levels of mortality risk by geographic region using a risk percentiles model. Finally we set high values of each risk factor to a target level and modelled the subsequent shift in the population to lower levels of mortality risk and longer life expectancy. RESULTS: Survival is poorer in both Inner Regional and Outer Regional/Remote areas compared to Major Cities for men and women at both high and low levels of predicted mortality risk. For men smoking, high cholesterol and high systolic blood pressure were each associated with the mortality difference between Major Cities and Outer Regional/Remote areas--accounting for 21.4%, 20.3% and 7.7% of the difference respectively. For women smoking and high cholesterol accounted for 29.4% and 24.0% of the difference respectively but high blood pressure did not contribute to the observed mortality differences. The three risk factors taken together accounted for 45.4% (men) and 35.6% (women) of the mortality difference. The contribution of risk factors to the corresponding differences for inner regional areas was smaller, with only high cholesterol and smoking contributing to the difference in men-- accounting for 8.8% and 6.3% respectively-- and only smoking contributing to the difference in women--accounting for 12.3%. CONCLUSIONS: These results suggest that health intervention programs aimed at smoking, blood pressure and total cholesterol could have a substantial impact on mortality inequities for Outer Regional/Remote areas.

Hypertension, antihypertensive treatment and cancer incidence and mortality : a pooled collaborative analysis of 12 Australian and New Zealand cohorts

BACKGROUND: Observational studies examining associations between hypertension and cancer are inconsistent. We explored the association of hypertension, graded hypertension and antihypertensive treatment with cancer incidence and mortality. METHOD: Eighty-six thousand five hundred and ninety-three participants from the Australian and New Zealand Diabetes and Cancer Collaboration were linked to the National Death Index and Australian Cancer Database. Cox proportional hazards models estimated hazard ratios and 95% confidence intervals (95% CI) for the association of treated and untreated hypertension with cancer incidence and mortality. RESULTS: Over a median follow-up of 15.1 years, 12 070 incident and 4350 fatal cancers were identified. Untreated and treated hypertension, compared with normotension, were associated with an increased risk for cancer incidence [hazard ratio 1.06, 95% CI (1.00-1.11) and 1.09 (1.02-1.16) respectively], and cancer mortality (1.07, 0.98-1.18) and (1.15, 1.03-1.28), respectively. When compared with untreated hypertension, treated hypertension did not have a significantly greater risk for cancer incidence (1.03, 0.97-1.10) or mortality (1.07, 0.97-1.19). A significant dose-response relationship was observed between graded hypertension and cancer incidence and mortality; Ptrend = 0.053 and Ptrend = 0.001, respectively. When stratified by treatment status, these relationships remained significant in untreated, but not in treated, hypertension. CONCLUSION: Hypertension, both treated and untreated, is associated with a modest increased risk for cancer incidence and mortality. Similar risks in treated and untreated hypertension suggest that the increased cancer risk is not explained by the use of antihypertensive treatment.

Age of onset of obesity and risk of type 2 diabetes

OBJECTIVE: To compare a simple measure - age of onset of obesity - to an obese-years construct (a product of duration and magnitude of obesity) as risk factors for type 2 diabetes.

METHOD: Participants from the Framingham Heart Study who were not obese and did not have diabetes at baseline were included (n=4,320). The Akaike Information Criterion (AIC) was computed to compare four Cox proportional hazards models with incident diabetes as the outcome and: (i) obese-years; (ii) age of onset of obesity; (iii) body mass index (BMI); and (iv) age of onset of obesity plus magnitude of BMI combined, as exposures.

RESULTS: AIC indicated that the model with obese-years provided a more effective explanation of incidence of type 2 diabetes compared to the remaining three models. Models including age of onset of obesity plus BMI were not appreciably different from the model with BMI alone, except in those aged ≥60.

CONCLUSIONS: While obese-years was the optimal obesity construct to explain risk of type 2 diabetes, age of onset may be a useful, practical addition to current BMI in the elderly.

IMPLICATIONS: Where computation of obese-years is not possible or impractical, age of onset of obesity combined with BMI may provide a useful alternative.

Modelling grouped survival times in toxicological studies using generalized additive models

A method for combining a proportional-hazards survival time model with a bioassay model where the log-hazard function is modelled as a linear or smoothing spline function of log-concentration combined with a smoothing spline function of time is described. The combined model is fitted to mortality numbers, resulting from survival times that are grouped due to a common set of observation times, using Generalized Additive Models (GAMs). The GAM fits mortalities as conditional binomials using an approximation to the log of the integral of the hazard function and is implemented using freely-available, general software for fitting GAMs. Extensions of the GAM are described to allow random effects to be fitted and to allow for time-varying concentrations by replacing time with a calibrated cumulative exposure variable with calibration parameter estimated using profile likelihood. The models are demonstrated using data from a studies of a marine and a, previously published, freshwater taxa. The marine study involved two replicate bioassays of the effect of zinc exposure on survival of an Antarctic amphipod, Orchomenella pinguides. The other example modelled survival of the daphnid, Daphnia magna, exposed to potassium dichromate and was fitted by both the GAM and the process-based DEBtox model. The GAM fitted with a cubic regression spline in time gave a 61 % improvement in fit to the daphnid data compared to DEBtox due to a non-monotonic hazard function. A simulation study using each of these hazard functions as operating models demonstrated that the GAM is overall more accurate in recovering lethal concentration values across the range of forms of the underlying hazard function compared to DEBtox and standard multiple endpoint probit analyses.

Does an evidence-based sedation protocol improve practice and patient outcomes in critical care?

Learning Objective 1: compare protocol-directed sedation management with traditional non-protocol-directed practice in mechanically ventilated patients in an Australian critical care.

Learning Objective 2: explain the contrasting international research findings on sedation protocol implementation.
Minimization of sedation in critical care patients has recently received widespread support. Professional organizations internationally have published sedation management guidelines for critically ill patients to improve the use of research in practice, decrease practice variability and shorten mechanical ventilation duration. Innovations in practice have included the introduction of decision making protocols, daily sedation interruptions and new drugs and monitoring technologies. The aim of this study was to compare protocol-directed sedation management with traditional non-protocol-directed practice in mechanically ventilated patients in an Australian critical care setting.

A randomized, controlled trial design was used to study 312 mechanically ventilated adult patients in a general critical care unit at an Australian metropolitan teaching hospital. Patients were randomly assigned to receive protocol directed sedation management developed from evidence based guidelines (n=153) or usual clinical practice (n=159).

The median (95% CI) duration of ventilation was 58 hrs (44–78 hrs) for patients in the non-protocol group and 79 hrs (56–93) for those patients in the protocol group (p=0.20). Results were not significant for length of stay in critical care or hospital, the frequency of tracheostomies, and unplanned extubations. A Cox proportional hazards model estimated that protocol directed sedation management was associated with a 22% decrease (95% CI: 40% decrease to 2% increase, p=0.07) in the occurrence of successful weaning from mechanical ventilation.

Few randomized controlled trials have evaluated the effectiveness of protocol-directed sedation outside of North America. This study highlights the lack of transferability between different settings and different models of care. Qualified, high intensity nursing in the Australian critical care setting facilitates rapid, responsive decisions for sedation management and an increased success rate for weaning from mechanical ventilation.