Competing risks and multivariate outcomes in epidemiological and clinical trial research.

Data analysis methods for the study of treatments or exposures in relation to a clinical outcome in the presence of competing risks have a long history, often with inference targets that are hypothetical, thereby requiring strong assumptions for identifiability with available data. Here data analysis methods are considered that are based on single and higher dimensional marginal hazard rates, quantities that are identifiable under standard independent censoring assumptions. These lead naturally to joint survival function estimators for outcomes of interest, including competing risk outcomes, and provide the basis for addressing a variety of data analysis questions. These methods will be illustrated using simulations and Women's Health Initiative cohort and clinical trial data sets, and additional research needs will be described.

The renin-angiotensin aldosterone system and osteoporosis: findings from the Women's Health Initiative.

New users of RAAS inhibitors, including ACE inhibitors and ARBs, have a small increased risk for fracture in the first 3 years of use, with a reduced risk of fracture with longer duration of use. INTRODUCTION: Pharmacological inhibitors of the renin-angiotensin aldosterone system (RAAS) are used to treat hypertension. However, the relationship of these medications to osteoporosis is inconsistent, and no study has included simultaneous measurements of both incident fractures and bone mineral density (BMD). METHODS: The association of RAAS inhibitor use (n = 131,793) with incident fractures in new users of these medications in women in the Women's Health Initiative over a minimum median follow-up of 6.5 years was assessed by Cox proportional hazard models. The association of incident fractures by a cumulative duration of use of these medications (< 3 years.) and (> 3 years.) was also estimated. Subgroup analysis of fracture risk by RAAS inhibitor use confined to women with hypertension was also performed (n = 33,820). The association of RAAS inhibitor use with changes in BMD of the hip was estimated by linear regression in 8940 women with dual energy X-ray absorptiometry measurements. RESULTS: There was no significant association between RAAS inhibitor use and all fractures in the final adjusted multivariable models including hip BMD (HR 0.86 (0.59, 1.24)). However, among users of RAAS inhibitors, including ACE inhibitors and angiotensin receptor blockers (ARBs), hazard ratios for all incident fracture sites in final multivariable models including hip BMD showed dramatic differences by duration of use, with short duration of use (3 years or less) associated with a marked increased risk for fracture (HR 3.28 (1.66, 6.48)) to (HR 6.23 (3.11, 12.46)) and use for more than 3 years associated with a reduced fracture risk (HR 0.40 (0.24, 0.68) to (HR 0.44 (0.20, 0.97)) . Findings were similar in the subgroup of women with a history of hypertension. There was no significant change in BMD of the hip by RAAS inhibitor use. CONCLUSIONS: In postmenopausal women, use of RAAS inhibitors, including ACE inhibitors and ARBs, is associated with an increased risk for fracture among new users of these medications in the first 3 years of use. However, long-term use (> 3 years) is associated with a reduced risk. Consideration for fracture risk may be part of the decision-making process for initiation of these medications for other disease states.

Higher Dimensional Clayton-Oakes Models for Multivariate Failure Time Data.

The Clayton-Oakes bivariate failure time model is extended to dimensions m > 2 in a manner that allows unspecified marginal survivor functions for all dimensions less than m. Special cases that allow unspecified marginal survivor functions of dimension q with q < m, while making some provisions for dependencies of dimension greater than q, are also described.

Reliable evidence from placebo-controlled, randomized, clinical trials for menopausal hormone therapy's influence on incidence and deaths from breast cancer.

In an invited editorial, Dr Shapiro proposes that vaginal bleeding leading to unblinding and subsequent detection bias explains the breast cancer increase seen with estrogen plus progestin in the Women's Health Initiative (WHI) clinical trial (1) . In the context of a uniform detection program of protocol-mandated annual mammography and breast examinations, such a proposal is medically implausible. Dr Shapiro suggests detection bias would identify a larger number of 'slowly growing tumors that would otherwise remain clinically silent'. The findings of more advanced cancers with increased deaths from breast cancer in the estrogen plus progestin group refute this conjecture. During early post-intervention phases of both WHI hormone therapy trials, when breast cancer detection bias is asserted by Dr Shapiro because participants had been informed of randomization assignment, breast cancer incidence rates were lower (rather than higher) than during intervention. Thus, Dr Shapiro's claims are directly refuted by findings from the WHI randomized clinical trials. Health-care providers should be aware that randomized clinical trial evidence supports estrogen plus progestin increasing breast cancer incidence and deaths from breast cancer. In contrast, among women with prior hysterectomy, randomized clinical trial evidence supports estrogen alone reducing breast cancer incidence and deaths from breast cancer.

Self-Consistent Nonparametric Maximum Likelihood Estimator of the Bivariate Survivor Function.

As usually formulated the nonparametric likelihood for the bivariate survivor function is over-parameterized, resulting in uniqueness problems for the corresponding nonparametric maximum likelihood estimator. Here the estimation problem is redefined to include parameters for marginal hazard rates, and for double failure hazard rates only at informative uncensored failure time grid points where there is pertinent empirical information. Double failure hazard rates at other grid points in the risk region are specified rather than estimated. With this approach the nonparametric maximum likelihood estimator is unique, and can be calculated using a two-step procedure. The first step involves setting aside all doubly censored observations that are interior to the risk region. The nonparametric maximum likelihood estimator from the remaining data turns out to be the Dabrowska (1988) estimator. The omitted doubly censored observations are included in the procedure in the second stage using self-consistency, resulting in a non-iterative nonpara-metric maximum likelihood estimator for the bivariate survivor function. Simulation evaluation and asymptotic distributional results are provided. Moderate sample size efficiency for the survivor function nonparametric maximum likelihood estimator is similar to that for the Dabrowska estimator as applied to the entire dataset, while some useful efficiency improvement arises for corresponding distribution function estimator, presumably due to the avoidance of negative mass assignments.

Health risks and benefits from calcium and vitamin D supplementation: Women's Health Initiative clinical trial and cohort study.

SUMMARY: The Women's Health Initiative (WHI) double-blind, placebo-controlled clinical trial randomly assigned 36,282 postmenopausal women in the U.S. to 1,000 mg elemental calcium carbonate plus 400 IU of vitamin D(3) daily or placebo, with average intervention period of 7.0 years. The trial was designed to test whether calcium plus vitamin D supplementation in a population in which the use of these supplements was widespread would reduce hip fracture, and secondarily, total fracture and colorectal cancer. INTRODUCTION: This study further examines the health benefits and risks of calcium and vitamin D supplementation using WHI data, with emphasis on fractures, cardiovascular disease, cancer, and total mortality. METHODS: WHI calcium and vitamin D randomized clinical trial (CT) data through the end of the intervention period were further analyzed with emphasis on treatment effects in relation to duration of supplementation, and these data were contrasted and combined with corresponding data from the WHI prospective observational study (OS). RESULTS: Among women not taking personal calcium or vitamin D supplements at baseline, the hazard ratio [HR] for hip fracture occurrence in the CT following 5 or more years of calcium and vitamin D supplementation versus placebo was 0.62 (95 % confidence interval (CI), 0.38-1.00). In combined analyses of CT and OS data, the corresponding HR was 0.65 (95 % CI, 0.44-0.98). Supplementation effects were not apparent on the risks of myocardial infarction, coronary heart disease, total heart disease, stroke, overall cardiovascular disease, colorectal cancer, or total mortality, while evidence for a reduction in breast cancer risk and total invasive cancer risk among calcium plus vitamin D users was only suggestive. CONCLUSION: Though based primarily on a subset analysis, long-term use of calcium and vitamin D appears to confer a reduction that may be substantial in the risk of hip fracture among postmenopausal women. Other health benefits and risks of supplementation at doses considered, including an elevation in urinary tract stone formation, appear to be modest and approximately balanced.

Indirect calorimetry protocol development for measuring resting metabolic rate as a component of total energy expenditure in free-living postmenopausal women.

An objective measure of energy intake is needed in epidemiologic studies to evaluate random and systematic error associated with dietary self-report tools. Total energy expenditure in weight-stable humans is accepted as a measure of energy intake, but doubly labeled water remains cost prohibitive for large studies. Our purpose was to develop a practical indirect calorimetry (IC) protocol for estimating resting metabolic rate (RMR) in free-living, postmenopausal women. We conducted duplicate IC measures 1 wk apart using a canopy system on 102 women ages 50-79 y from the Seattle area. We compared RMR for 0-5, 5-10, 5-15, 5-20, 5-25, 5-30, and 0- to 30-min IC segments and segments meeting stability criteria. The mean RMR for the first 5 min was significantly higher than other time segments (P = 0.001). Correlation coefficients between duplicate measures were high (r = 0.90). Use of defined stability criteria produced RMR measures that were 10-30 kcal (42-126 kJ) higher than the 5- to 10-min RMR measures and 40-60% of subjects did not achieve these stability criteria. For protocols including IC to assess RMR as a component of total energy expenditure in free-living, postmenopausal women, a single 10-min canopy study, excluding the first 5 min of data, produces reliable results with minimal subject burden.

Methodologic challenges in chronic disease population research.

Some recent important, and controversial, chronic disease population research settings are reviewed. These include studies of hormone replacement therapy and coronary heart disease; studies of dietary fat in relation to breast cancer; and studies of beta-carotene supplementation and lung cancer. In each case methodologic developments having a strong biostatistical component are identified as key to future progress. Some comments are also made on the need for an expanded disease prevention intervention development enterprise, and on the role that microarray genetic and genomic data may play in such development.

Incorporating age at onset information into the transmission/disequilibrium test.

In this paper, we proposed two approaches for incorporating the age at onset into the transmission/disequilibrium test (TDT). Trios (affected offspring and their parents) were extracted from the first four replicate data sets of the general population type. Focusing on chromosome 6 where MG6 and MG7 reside, we compared the usual TDT with the newly proposed tests in terms of gene localization.

Results of testing for anti-GM1 antibodies.

We used an ELISA technique to measure IgG and IgM antibodies to the ganglioside GM1, with the results expressed in arbitrary units. We tested 1007 sera from patients with peripheral neuropathy or muscle weakness. For IgG and IgM antibodies, the distribution of results differed significantly from a normal distribution. In the patient group, 81 of 1007 sera had elevated levels of IgG antibodies (> 10 units). Of these, 11 patients had very high levels (> 50 units). These 11 patients had diagnoses of GBS (4), motor neurone disease (3) or non-specific idiopathic neuropathy (4). For IgM antibodies, 115 of 1007 sera were positive (> 20 units). Of these, 18 patients had very high levels (> 50 units). These 18 patients had diagnoses of Guillain-Barré syndrome or Miller Fisher syndrome (4), multifocal motor neuropathy (4), motor neurone disease (2), non-specific neuropathy (2). We conclude that anti-GM1 antibodies in high titre are uncommon. Patients with multifocal motor neuropathy have high levels of antibody. However, patients with other disorders may also have high levels, so that anti-GM1 antibody levels alone are not a specific test for multifocal motor neuropathy. We found that antibodies to GM1 were present in the sera of patients with chronic idiopathic neuropathy, leading us to suggest that these antibodies may sometimes arise as a secondary response to disease.

Dependence estimation over a finite bivariate failure time region.

This article concerns nonparametric estimation of association between bivariate failure times. In the presence of independent right censoring, the support for failure time variates may be restricted and measures of dependence over a finite failure time region may be of particular interest. To this end, the reciprocal cross ratio function, weighted by the bivariate failure time density, is proposed as a summary measure of dependence over a failure time region. This 'relative risk' estimator is shown to be consistent and asymptotically normally distributed, with consistent bootstrap variance estimator. A finite-region version of Kendall's tau, which is suitable for censored failure time data, is also proposed, and corresponding asymptotic distribution theory is noted. The accuracy of these asymptotic approximations is studied in simulations and an illustration is provided.

Future possibilities in the prevention of breast cancer: fat and fiber and breast cancer research.

The potential for a reduction in dietary fat or for an increase in dietary fiber to reduce breast cancer risk has been debated for some years. It is argued here that available research data, even though extensive, leave open hypotheses ranging from little or no potential to major public health potential for breast cancer prevention by means of these dietary maneuvers. Some elements of a research strategy for testing these and other dietary breast cancer prevention hypotheses are described.

On non-parametric maximum likelihood estimation of the bivariate survivor function.

The likelihood function for the bivariate survivor function F, under independent censorship, is maximized to obtain a non-parametric maximum likelihood estimator &Fcirc;. &Fcirc; may or may not be unique depending on the configuration of singly- and doubly-censored pairs. The likelihood function can be maximized by placing all mass on the grid formed by the uncensored failure times, or half lines beyond the failure time grid, or in the upper right quadrant beyond the grid. By accumulating the mass along lines (or regions) where the likelihood is flat, one obtains a partially maximized likelihood as a function of parameters that can be uniquely estimated. The score equations corresponding to these point mass parameters are derived, using a Lagrange multiplier technique to ensure unit total mass, and a modified Newton procedure is used to calculate the parameter estimates in some limited simulation studies. Some considerations for the further development of non-parametric bivariate survivor function estimators are briefly described.

Study of diet, biomarkers and cancer risk in the United States, China and Costa Rica.

One striking paradox in epidemiologic research is the strong association between diet and cancer in ecologic studies compared with the weaker associations reported in many within-country case-control and cohort studies. However, most ecologic studies have relied on indirect measures of dietary intake, such as food disappearance data. The objectives of our study were to assess the feasibility of collecting dietary and biomarker data from individuals living in countries having markedly different dietary patterns and cultures and to examine the magnitude of the between-country variation in their measurement. Adults surveyed in Shanghai (China), Costa Rica and King County (Washington, USA) completed a 24-hr dietary recall, a cancer risk factor survey, and provided a blood sample. We analyzed a subset of the blood specimens for vitamins C, E, carotenoids and phospholipid fatty acids. We observed substantial differences in nutrient intakes and in mean plasma concentrations of dietary biomarkers across the study populations. For example, King County participants had the highest daily intake of vitamin C (mean 78.3 +/- 12.2 mg compared with 42.6 +/- 38.3 mg in Shanghai and 34.8 +/- 43.8 mg in Costa Rica). The mean plasma vitamin C level in King County was also the highest of the 3 study sites: 927.9 +/- 43.9 microg/dl in King County, 585.7 +/- 35.9 microg/dl in Shanghai and 461.1 +/- 33.1 microg/dl in Costa Rica. Plasma trans fatty acids (a biomarker of a diet high in hydrogenated fats) were highest in King County and lowest in Shanghai.

Estimation of the correlation between nutrient intake measures under restricted sampling.

Food frequency questionnaires (FFQs) are commonly used to assess dietary intake in epidemiologic research. To evaluate the FFQ reliability, the commonly used approach is to estimate the correlation coefficient between the data given in FFQ and those in food records (for example, 4-day food records [4DFR]) for nutrients of interest. However, in a dietary intervention study, a criterion for eligibility may be to select participants who have baseline FFQ-measured dietary intake of percent energy from fat above a prespecified quantity. Other instruments, such as the 4DFR, may be subsequently administrated only to eligible participants. Under these circumstances, analysis without adjusting for the restricted population will usually lead to biased estimation of correlation coefficients and other parameters of interest. In this paper, we apply likelihood-based and multiple imputation (MI) methods to accommodate such incomplete data obtained as a result of the study design. A simulation study is conducted to examine finite sample performance of various estimators. We note that both the MI estimate and the maximum likelihood (ML) estimate based on a bivariate-normal model are not sensitive to departures from this normality assumption. This led us to investigate robustness properties of the ML estimator analytically. We present some data analyses from a dietary assessment study from the Women's Health Initiative to illustrate the methods.

Individually randomized intervention trials for disease prevention and control.

It is argued that randomized, controlled trials should fulfil a critical role in the identification of practical approaches to the prevention and control of chronic diseases. Because of the great public health potential of chemopreventive and behavioural approaches to chronic disease prevention there is need for a major interdisciplinary scientific effort aimed at intervention development. Because of the cost and duration of controlled trials to evaluate specific interventions there is a need for well-conducted feasibility, pilot and intermediate outcome trials, to inform and to justify corresponding full-scale trials having clinical disease outcomes. Compared to therapeutic trials, prevention trials need to have a greater emphasis on overall benefit versus risk assessment. Such trials need to be large enough, and of sufficient duration, to yield powerful tests of key hypotheses, and informative benefit versus risk summary statements. These requirements have a range of implications for intervention trial design, conduct, monitoring and reporting, which are reviewed and discussed. The clinical trial component of the ongoing Women's Health Initiative provides illustration throughout this discussion.

Nontreatment and aggressive narcotic therapy among hospitalized pancreatic cancer patients.

OBJECTIVES: Strong feelings about patient autonomy as expressed in living wills, polls, and legislative referenda have been challenging the medical establishment to increase nontreatment, defined as foregoing a life-prolonging treatment, and even to provide treatments having life-shortening potential to selected patients. Because there are little data about the actual practice of these procedures, including aggressive narcotic therapy as defined herein, we studied the terminal management of 417 pancreatic cancer patients. DESIGN AND PARTICIPANTS: The medical records of 417 residents of King County, Washington, who died of pancreatic cancer in the time periods 1959-1962, 1969-1972, and 1985-1990, were reviewed to study the frequency of, and risk factors for, end-of-life nontreatment decisions and aggressive narcotic therapy decisions, defined here as the decision to administer treatment doses of narcotics or major sedatives to already comatose patients within 4 hours of death. RESULTS: Antibiotics were not provided to 71% of the 70 febrile patients (two readings >38.33-38.83 degrees C or one reading of 38.88 degrees C), intravenous fluid was not provided to 43% of 294 dehydrated patients (oral intake <500 mL/24 hours), transfusions were not provided to 39% of 57 severely anemic patients (hematocrit <20%), and laparotomy was not performed for 86% of 36 patients with abdominal emergencies (obstruction, bleeding, dehiscence). Also, 46% of the 118 patients who were comatose for at least 24 hours before death received aggressive narcotic therapy, as defined above. A total of 335 of the 417 patients had documentation of at least one of the above life-threatening conditions or were comatose for at least 24 hours before death, and 289 (86%) of these patients experienced nontreatment of one or more of these conditions or received aggressive narcotic therapy. Nontreatment decisions for febrile, dehydrated, or anemic patients tended to be more frequent if the patient was comatose (P=.004, .010, and .065, respectively), if there was a nontreatment statement in the medical record (P=.009, .035, and .001, respectively), or if the patient was described as terminal (P=.262, .029, and .002, respectively). Aggressive narcotic therapy in comatose patients was more common among patients who had regular visitors (P=.002), who had pre-coma pain (P=.006), who had nontreatment statements in their charts (P=.031), whose in-charge physician was an oncologist (P < .001), who were treated in a community nonprofit hospital compared with a Catholic hospital (P=.007), or who were treated in recent years (P=.011). CONCLUSION: Both nontreatment and aggressive narcotic therapy forms of medical management have been occurring commonly in terminal pancreatic cancer patients in King County, Washington, during the past 3 decades, the latter with greater frequency in recent years.

On the accommodation of disease rate correlations in aggregate data studies of disease risk factors.

Prentice and Sheppard (1995, Biometrika 82, 113-125) proposed a method for estimating relative risks associated with poorly measured exposures using disease rates from multiple populations and exposure and confounding factor data from sample surveys of persons in each population. The method involved an assumption of independence of disease rates across populations, conditional on exposures and confounding factors. Here, this assumption is relaxed by allowing dependencies among the disease rates within a partition of the populations, perhaps defined on the basis of geographic proximity or cultural similarity. Such dependencies could, for example, derive from unmeasured risk factors that are shared among neighboring populations. Dependencies within an element of the partition are modeled by allowing a common correlation between the disease rates of contiguous populations and by inducing correlations between the rates for noncontiguous populations using a multivariate lognormal assumption. Estimating equations are proposed for relative risk parameter estimation, and robustness and efficiency properties are assessed through simulations. The relaxed estimation procedure is shown to yield useful efficiency gains when moderate or strong disease rate dependencies are present, especially when disease rate variances are large relative to binomial variance.