Stable computational methods for additive binomial models with application to adjusted risk differences

Risk difference is an important measure of effect size in biostatistics, for both randomised and observational studies. The natural way to adjust risk differences for potential confounders is to use an additive binomial model, which is a binomial generalised linear model with an identity link function. However, implementations of the additive binomial model in commonly used statistical packages can fail to converge to the maximum likelihood estimate (MLE), necessitating the use of approximate methods involving misspecified or inflexible models. A novel computational method is proposed, which retains the additive binomial model but uses the multinomial–Poisson transformation to convert the problem into an equivalent additive Poisson fit. The method allows reliable computation of the MLE, as well as allowing for semi-parametric monotonic regression functions. The performance of the method is examined in simulations and it is used to analyse two datasets from clinical trials in acute myocardial infarction. Source code for implementing the method in R is provided as supplementary material (see Appendix A).Australian Research Counci

logbin: An R Package for Relative Risk Regression Using the Log-Binomial Model

Relative risk regression using a log-link binomial generalized linear model (GLM) is an important tool for the analysis of binary outcomes. However, Fisher scoring, which is the standard method for fitting GLMs in statistical software, may have difficulties in converging to the maximum likelihood estimate due to implicit parameter constraints. logbin is an R package that implements several algorithms for fitting relative risk regression models, allowing stable maximum likelihood estimation while ensuring the required parameter constraints are obeyed. We describe the logbin package and examine its stability and speed for different computational algorithms. We also describe how the package may be used to include flexible semi-parametric terms in relative risk regression models

Impact of metabolic syndrome and its components on cardiovascular disease event rates in 4900 patients with type 2 diabetes assigned to placebo in the field randomised trial

<p>Abstract</p> <p>Background</p> <p>Patients with the metabolic syndrome are more likely to develop type 2 diabetes and may have an increased risk of cardiovascular disease (CVD) events.We aimed to establish whether CVD event rates were influenced by the metabolic syndrome as defined by the World Health Organisation (WHO), the National Cholesterol Education Program (NCEP) Adult Treatment Panel III (ATP III) and the International Diabetes Federation (IDF) and to determine which component(s) of the metabolic syndrome (MS) conferred the highest cardiovascular risk in in 4900 patients with type 2 diabetes allocated to placebo in the Fenofibrate Intervention and Event Lowering in Diabetes (FIELD) trial.</p> <p>Research design and methods</p> <p>We determined the influence of MS variables, as defined by NCEP ATPIII, IDF and WHO, on CVD risk over 5 years, after adjustment for CVD, sex, HbA_1c, creatinine, and age, and interactions between the MS variables in a Cox proportional-hazards model.</p> <p>Results</p> <p>About 80% had hypertension, and about half had other features of the metabolic syndrome (IDF, ATPIII). There was no difference in the prevalence of metabolic syndrome variables between those with and without CVD at study entry. The WHO definition identified those at higher CVD risk across both sexes, all ages, and in those without prior CVD, while the ATPIII definition predicted risk only in those aged over 65 years and in men but not in women. Patients meeting the IDF definition did not have higher risk than those without IDF MS.</p> <p>CVD risk was strongly influenced by prior CVD, sex, age (particularly in women), baseline HbA1_c, renal dysfunction, hypertension, and dyslipidemia (low HDL-c, triglycerides > 1.7 mmol/L). The combination of low HDL-c and marked hypertriglyceridemia (> 2.3 mmol/L) increased CVD risk by 41%. Baseline systolic blood pressure increased risk by 16% per 10 mmHg in those with no prior CVD, but had no effect in those with CVD. In those without prior CVD, increasing numbers of metabolic syndrome variables (excluding waist) escalated risk.</p> <p>Conclusion</p> <p>Absence of the metabolic syndrome (by the WHO definition) identifies diabetes patients without prior CVD, who have a lower risk of future CVD events. Hypertension and dyslipidemia increase risk.</p

Effects of fenofibrate on renal function in patients with type 2 diabetes mellitus: the Fenofibrate Intervention and Event Lowering in Diabetes (FIELD) Study

Abstract Aims/hypothesis Fenofibrate caused an acute, sustained plasma creatinine increase in the Fenofibrate Intervention and Event Lowering in Diabetes (FIELD) and Action to Control Cardiovascular Risk in Diabetes (ACCORD) studies. We assessed fenofibrate’s renal effects in a FIELD washout sub-study. Methods Type 2 diabetic patients (n=9795) aged 50 to 75 years were randomly assigned to fenofibrate (n=4895) or placebo (n=4900) for 5 years, after 6 weeks fenofibrate run-in. Albuminuria (urinary albumin:creatinine ratio) measured at baseline, year 2 and close-out) and estimated GFR, measured 4 to 6 monthly according to the Modification of Diet in Renal Disease study, were pre-specified endpoints. Plasma creatinine was re-measured 8 weeks after treatment cessation at close-out (washout sub-study, n=661). Analysis was by intention-to-treat. Results During fenofibrate run-in, plasma creatinine increased by 10.0 µmol/l (p<0.001), but quickly reversed on placebo assignment. It remained higher on fenofibrate than on placebo, but the chronic rise was slower (1.62 µmol/l vs 1.89 µmol/l annually, p=0.01), with less estimated GFR loss (1.19 vs 2.03 ml min−1 1.73 m−2 annually, p<0.001). After washout, estimated GFR had fallen less from baseline on fenofibrate (1.9 ml min−1 1.73 m−2, p=0.065) than on placebo (6.9 ml min−1 1.73 m−2, p<0.001), sparing 5.0 ml min−1 1.73 m−2 (95% CI 2.3-7.7, p<0.001). Greater preservation of estimated GFR with fenofibrate was observed during greater reduction over the active run-in period (pre-randomisation) of triacylglycerol (n=186 vs 170) and baseline hypertriacylglycerolaemia (n=89 vs 80) alone, or combined with low HDL-cholesterol (n=71 vs 60). Fenofibrate reduced urine albumin concentrations and hence albumin:creatinine ratio by 24% vs 12% (p<0.001; mean difference 14% [95% CI 9-18]; p<0.001), with 14% less progression and 18% more albuminuria regression (p<0.001) than in participants on placebo. End-stage renal event frequency was similar (n=21 vs 26, p=0.48). Conclusions/interpretation Fenofibrate reduced albuminuria and slowed estimated GFR loss over 5 years, despite initially and reversibly increasing plasma creatinine. Fenofibrate may delay albuminuria and GFR impairment in type 2 diabetes patients. Confirmatory studies are merited. Trial registration: ISRCTN64783481 Funding: The study was funded by grants from Laboratoires Fournier, Dijon, France (now part of Solvay and Abbott Pharmaceuticals) and the NHMRC of Australia.Laboratoires Fournier, Dijon, France (now part of Solvay and Abbott Pharmaceuticals

Effects of fenofibrate on renal function in patients with type 2 diabetes mellitus: the Fenofibrate Intervention and Event Lowering in Diabetes (FIELD) Study

Abstract Aims/hypothesis Fenofibrate caused an acute, sustained plasma creatinine increase in the Fenofibrate Intervention and Event Lowering in Diabetes (FIELD) and Action to Control Cardiovascular Risk in Diabetes (ACCORD) studies. We assessed fenofibrate’s renal effects in a FIELD washout sub-study. Methods Type 2 diabetic patients (n=9795) aged 50 to 75 years were randomly assigned to fenofibrate (n=4895) or placebo (n=4900) for 5 years, after 6 weeks fenofibrate run-in. Albuminuria (urinary albumin:creatinine ratio) measured at baseline, year 2 and close-out) and estimated GFR, measured 4 to 6 monthly according to the Modification of Diet in Renal Disease study, were pre-specified endpoints. Plasma creatinine was re-measured 8 weeks after treatment cessation at close-out (washout sub-study, n=661). Analysis was by intention-to-treat. Results During fenofibrate run-in, plasma creatinine increased by 10.0 µmol/l (p<0.001), but quickly reversed on placebo assignment. It remained higher on fenofibrate than on placebo, but the chronic rise was slower (1.62 µmol/l vs 1.89 µmol/l annually, p=0.01), with less estimated GFR loss (1.19 vs 2.03 ml min−1 1.73 m−2 annually, p<0.001). After washout, estimated GFR had fallen less from baseline on fenofibrate (1.9 ml min−1 1.73 m−2, p=0.065) than on placebo (6.9 ml min−1 1.73 m−2, p<0.001), sparing 5.0 ml min−1 1.73 m−2 (95% CI 2.3-7.7, p<0.001). Greater preservation of estimated GFR with fenofibrate was observed during greater reduction over the active run-in period (pre-randomisation) of triacylglycerol (n=186 vs 170) and baseline hypertriacylglycerolaemia (n=89 vs 80) alone, or combined with low HDL-cholesterol (n=71 vs 60). Fenofibrate reduced urine albumin concentrations and hence albumin:creatinine ratio by 24% vs 12% (p<0.001; mean difference 14% [95% CI 9-18]; p<0.001), with 14% less progression and 18% more albuminuria regression (p<0.001) than in participants on placebo. End-stage renal event frequency was similar (n=21 vs 26, p=0.48). Conclusions/interpretation Fenofibrate reduced albuminuria and slowed estimated GFR loss over 5 years, despite initially and reversibly increasing plasma creatinine. Fenofibrate may delay albuminuria and GFR impairment in type 2 diabetes patients. Confirmatory studies are merited. Trial registration: ISRCTN64783481 Funding: The study was funded by grants from Laboratoires Fournier, Dijon, France (now part of Solvay and Abbott Pharmaceuticals) and the NHMRC of Australia.Laboratoires Fournier, Dijon, France (now part of Solvay and Abbott Pharmaceuticals

Opposite associations between alanine aminotransferase and γ-glutamyl transferase levels and all-cause mortality in type 2 diabetes: analysis of the Fenofibrate Intervention and Event Lowering in Diabetes (FIELD) study

Aims Reported associations between liver enzymes and mortality may not hold true in type 2 diabetes, owing to a high prevalence of non-alcoholic fatty liver disease, which has been linked to cardiovascular disease and mortality in its own right. Our study aimed to determine whether alanine aminotransferase (ALT) or γ-glutamyl transferase (GGT) levels predict mortality in type 2 diabetes, and to examine possible mechanisms. Methods Data from the Fenofibrate Intervention and Event Lowering in Diabetes (FIELD) study were analysed to examine the relationship between liver enzymes and all-cause and cause-specific mortality over 5 years. Results Over 5 years, 679 (6.9%) individuals died. After adjustment, for every standard deviation increase in ALT (13.2U/L), the HR for death on study was 0.85 (95% CI 0.78-0.93), p70 U/L, compared with GGT ≤70 U/L, had HR 1.82 (1.48−2.24), p70 U/L was associated with higher risks of death due to cardiovascular disease, cancer and non-cancer/non-cardiovascular causes. The relationship for ALT persisted after adjustment for indirect measures of frailty but was attenuated by elevated hsCRP. Conclusions As in the general population, ALT has a negative, and GGT a positive, correlation with mortality in type 2 diabetes when ALT is less than two times the upper limit of normal. The relationship 4 for ALT appears specific for death due to cardiovascular disease. Links of low ALT with frailty, as a potential mechanism for relationships seen, were neither supported nor conclusively refuted by our analysis and other factors are also likely to be important in those with type 2 diabetes

Semi-parametric regression models for risk differences, rate differences and relative risks

Thesis by publication.Bibliography: pages 251-266.1. Introduction -- 2. Background -- 3. Additive binomial regression -- 4. Semi-parametric regression -- 5. Additive negative binomial regression -- 6. Discussion.Two fundamental biostatistical measures are the risk and the rate of event occurrence, representing the probability of an event and the expected number of events during a fixed time period. Regression models can be used to relate an individual's characteristics to the risk or rate of an event, such as the occurrence of disease or death. This allows identification of high-risk individuals and can reveal ways in which risk may be reduced.Generalised linear models (GLMs) for binary and count data are an important statistical tool for risk and rate modelling, and semi-parametric extensions provide additional flexibility. However, some key GLMs of interest have parameter constraints implied by the risk and rate models, and standard model-fitting algorithms can be numerically unstable. This is particularly true for GLMs that allow estimation of risk differences, rate differences and relative risks.In this thesis by publication new variants of the Expectation-Maximisation (EM) algorithm are developed in order to provide reliable and flexible methods for fitting such models to binary and count data. This begins with the development of a method for additional binomial GLMs, which allows for reliable adjustment of risk differences. An extension of this and other EM-type algorithms for binomial and Poisson GLMs is then provided, which allows for flexible semi-parametric regression based on spline models. As well as risk differences, these models allow reliable estimation of rate differences and relative risks. A method for additive regression under a negative binomial model is also developed, which can be used to estimate rate differences when the observed counts show more variation than is expected under a Poisson model. These methods all ensure that the fitted models respect the required parameter constraints, and their stability allows us to reliably use resampling methods that require many auxiliary analyses, such as the bootstrap.The utility of these approaches is demonstrated by applying them to various clinical datasets. The methods described in this thesis have all been implemented in open-source packages for the R computing environment and have been made available online.Mode of access: World wide web1 online resource (xviii, 266 pages

Simulated data used in "The importance of censoring in competing risks analysis of the subdistribution hazard"

The simulated data used for analysis in "The importance of censoring in competing risks analysis of the subdistribution hazard". Simulated using the method described in Additional file 1. Warning: Large file. Contains 1000 datasets of 300 observations each, for each of 105 parameter combinations (31,500,000 rows). Some programs (e.g. Excel) will not be able to open it in full. csv file with columns: p.comp: risk of the competing event in exposure group A for this scenario [0 to 0.30 in increments of 0.05] lnb.cens: log(hazard ratio) for loss to follow-up in old versus young individuals for this scenario [0 to 1 in increments of 0.25] lnb.evt: log(subdistribution hazard ratio) for the event of interest in exposure group B vs group A for this scenario [0, 0.5, 1] sim: ID of the simulated dataset for this scenario [1-1000] exposure: exposure group (0 = A, 1 = B) of this individual age: age group (0 = young, 1 = old) of this individual time: time-to-event or censoring for this individual evtcode: event type (0 = censoring, 1 = event of interest, 2 = competing event) censcode: type of censoring (1 = end-of-study, 2 = loss to follow-up

Flexible regression models for rate differences, risk differences and relative risks

Generalized additive models (GAMs) based on the binomial and Poisson distributions can be used to provide flexible semi-parametric modelling of binary and count outcomes. When used with the canonical link function, these GAMs provide semi-parametrically adjusted odds ratios and rate ratios. For adjustment of other effect measures, including rate differences, risk differences and relative risks, non-canonical link functions must be used together with a constrained parameter space. However, the algorithms used to fit these models typically rely on a form of the iteratively reweighted least squares algorithm, which can be numerically unstable when a constrained non-canonical model is used. We describe an application of a combinatorial EM algorithm to fit identity link Poisson, identity link binomial and log link binomial GAMs in order to estimate semi-parametrically adjusted rate differences, risk differences and relative risks. Using smooth regression functions based on B-splines, the method provides stable convergence to the maximum likelihood estimates, and it ensures that the estimates always remain within the parameter space. It is also straightforward to apply a monotonicity constraint to the smooth regression functions. We illustrate the method using data from a clinical trial in heart attack patients.18 page(s