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Selective congruence, namely a pairing of various biospheric cycles of certain frequencies with different environmental ones and further selectivity of phase behavior at the given frequency characterize an ultradian to infradian, prominently circadian transdisciplinary spectrum. Diseases documented among others to be influenced by the cosmos range from individuals' strokes to populations' crime and terrorism, conditions studied by chronomics as time structures (chronomes). Methods of investigation include the extended cosinor allowing for the added estimation of the period with a measure of uncertainty, as well as global and gliding spectral windows complemented by chronobiologic serial sections. These methods estimate, each of them with uncertainties, changes as a function of time in weather on earth and in space on the one hand and in human personal and broader affairs on the other. They further map features of these time structures that may change as a function of time in a logically consistent way. Associations of several biological time series with physical environmental variables are presented herein, as are methods used for their investigation and a statistical assessment of their congruence.

The relationship between state murder rates and the liberalization of conditions under which a citizen can obtain a permit to carry a concealed weapon (shall-issue laws) is controversial and important for policy. Many analyses have been done during the last decade, but regression to the mean has been ignored with the exception of two papers which concluded that it did not matter. We consider state murder rates for 1976–2001 and compare relative murder rate slopes (relative to the U.S. murder rate) for the five years following state adoption of shall-issue laws to the five years preceding for the 25 states becoming shall-issue in 1981–1996. We find strong evidence for regression to the mean. Using both a random and a fixed effects model, we compare analyses ignoring the regression effect via a paired t-test to those controlling for it by conditioning on the pre shall-issue slopes. We find that controlling for regression to the mean changes the sign of the estimated intervention effect on murder rate slopes...

Background Many clinical trials have multiple outcomes. Formal interim monitoring guidelines that take account of multiple outcomes can be useful to Data Monitoring Committees (DMC). Previous research has focused on marginal criteria that control the overall type I error for bivariate endpoints corresponding to efficacy and safety. Usually, an `or' decision rule is used, that is, the trial is stopped when either the safety or the efficacy endpoint crosses a boundary. Purpose In many trials there is not a clear difference between what is considered a safety and an efficacy endpoint. Likewise, in some studies there is interest in more than one disease outcome and while there may be a primary efficacy endpoint, interim monitoring might also involve a measure of overall health. For these situations, an `and' decision rule might be more appropriate; that is, the trial is stopped only when both endpoints cross a boundary. Formulation of this new decision rule at the design stage would encourage more discussion among trial investigators of monitoring guidelines and would result in improved guidelines for DMCs. Methods In this paper, we propose stopping guidelines for such trials with two major outcomes that control the overall type I error and stop early only if both endpoints indicate superiority for the same treatment. Trials with two treatments are considered and we develop sets of paired two-sided boundaries, permitting one endpoint to be primary and the other supportive, with or without pre-specifying which one is primary. Results The results show that the boundaries depend on the correlation between the two outcomes. The critical values increase as the correlation increases in most cases. For low to moderate correlation and before the last stage, critical values based on the O'Brien Fleming (or Pocock) error spending function that consider the correlation are lower than those which do not. Limitations Investigators might not want to stop a trial early with the small size of the critical values that result from this decision rule for some situations. For a trial in which the treatment effect for one outcome is large, while for the other it is small, the proposed decision rule has low power to accept this treatment for its superiority on both outcomes. Also, we do not provide a separate P-value for each outcome since type I error is not controlled for individual null hypotheses. Conclusions For trials involving two major health outcomes these stopping guidelines may be appropriate for DMCs when the trial investigators and sponsor recommend that early termination not be considered unless the findings are consistent for both outcomes. Clinical Trials 2007; 4: 140—153. http://ctj.sagepub.com

Background Most methods of sample size calculations for survival trials adjust the estimated outcome event rates for noncompliance based on the assumption that non-compliance is independent of the risk of the outcome event although there has been published evidence that noncompliers are often at a higher risk than compliers. More recent work has started to consider the situations of informative noncompliance and different risks for noncompliers. However, the possibility of a time-varying association between noncompliance and risk has been ignored. Our analysis indicated a strong time-varying relationship between noncompliance defined as permanent discontinuation of study treatments and risk of the outcome event in the CONVINCE trial. Purpose The purpose of this research is to develop methods for the log-rank sample size calculations for two-arm clinical trials that allow for the relationship between risk and noncompliance to vary over time and to study how sample size requirements vary with different patterns of the time relationship. Methods The method developed takes Lakatos’ Markov chain approach as a basis, modifying it to incorporate time dynamics, and emphasizing permanent discontinuation of study medication as the form of noncompliance to be considered. Results Results with our method show that sample size depends on the relative rates of noncompliance in the two arms, the hazard for the outcome event following non-compliance, whether it involves switching to the hazard of the opposite arm or is common to both arms, and whether noncompliance occurs early or late in the trial. These factors interact with each other in complex ways, precluding simple summaries. Limitations This research focuses on two-arm clinical trials with time to event as primary outcome measure. The method developed is not directly applicable to trials with more complicated designs and/or trials with other types of primary outcome. Conclusions The pattern of the relationship between noncompliance and risk can have a dramatic impact on the sample size and power calculations in survival studies. The method introduced provides a useful tool for investigators to explore the optimal sample size accounting for various dynamic associations between noncompliance and risk.

Group sequential tests are widely used for interim analyses in randomized clinical trials. These tests have been extended to bivariate outcomes, but calculation of boundary values is computationally intensive. In this paper, we compare 3 algorithms: (1) quasi-Monte Carlo; (2) Schervish's MULNOR; and (3) a bivariate version of Armitage's recursive formula proposed by Jennison and Turnbull, for calculating boundary values for the L-region bivariate design which takes account of the correlation between the outcomes. Up to 5 interim analyses (stages) and a range of values for the correlation between the two endpoints were considered. The three algorithms produced very similar boundary values, but the quasi-Monte Carlo approach was much faster than the other two. The quasi-Monte Carlo method is an attractive approach for studying higher dimensions-designs with more stages and designs with more than two outcomes. The increased speed of this algorithm may permit the development of more flexible monitoring guidelines for multiple endpoints for clinical trials.

Two independent groups recently published data comparing pulsatile luteinizing hormone (LH) release between depressed and control women. Despite similar populations and LH sampling frequency, they reached different conclusions: Meller et al. [Am. J. Psych. 154 (1997) 1454] found disruption of normal LH pulsatility in depressed women, whereas Young et al. [Arch. Gen. Psych. 57 (2000) 1157] did not. To resolve this discrepancy, the current study applies a single, well-established statistical method, spectral analysis, to the two data sets and concludes that both depressed populations display significantly altered LH pulsatile release.

Interest in the use of random effects in the survival analysis setting has been increasing. However, the computational complexity of such frailty models has limited their general use. Although fitting frailty models has traditionally been difficult, standard algorithms for fitting Cox semiparametric and parametric regression models can be readily extended to include penalized regression. We demonstrate that solutions for gamma shared frailty models can be obtained exactly via penalized estimation. Similarly, Gaussian frailty models are closely linked to penalized models. Fitting frailty models with penalized likelihoods can be made quite efficient by taking advantage of computational methods available for penalized models. We have implemented penalized regression for the coxph function of S-Plus and illustrate the algorithms with examples using the Cox model.

First vaccines are traditionally licensed after showing favourable results from phase III efficacy trials. Subsequent competing vaccines, however, have been licensed primarily on the basis of immunogenicity data rather than clinical efficacy. Focusing on pneumococcal vaccines where optical densities are measured and serum antibody concentrations are 'estimated' (from a statistical model) using an immunoglobulin (IgG) enzyme-linked immunosorbent assay (ELISA), the focus of this paper will centre on two highly related issues: the determination of an upper limit for quality control used in the assay methodology (let us call it the maximum tolerated limit or MTL) and the identification of vaccine responders. The goal is to show that these two issues are inter-related, so that investigators could reduce misclassification which would interfere with the eventual comparison of immunogenicity results.

The Treatment of Mild Hypertension Trial was a randomized, double-blind clinical trial conducted from 1986 to 1992 comparing the efficacy of six antihypertensive treatment regimens in 902 participants with stage I hypertension. To satisfy a secondary objective of the study, follow-up information on mortality and cardiovascular morbidity was collected. For this objective the aim was to ascertain the vital and cardiovascular event status as of the last day of the trial. This was accomplished by inviting each participant to attend a closeout visit shortly after the closeout date. In addition to serving as verification of vital status, this visit allowed data collection on nonfatal events that occurred between the last clinic visit and the closeout date. During this visit the patient was unblinded to study medication and given a medical summary of their participation during the trial, as well as a bottle of open-label medication. The advantages of a closeout visit are discussed along with a call for studies to provide clearer definitions of lost to follow-up and censoring times used in life-table analyses, especially when the primary event includes both fatal and nonfatal events. Control Clin Trials 2001;22:56–61

The Controlled ONset Verapamil INvestigation of Cardiovascular Endpoints (CONVINCE) Trial is a randomized, prospective, double-blind, parallel-group, two-arm, actively controlled, multicenter, international 5-year clinical trial involving 15,000 patients. CONVINCE will compare the incidence of fatal or nonfatal myocardial infarction (MI), fatal or nonfatal stroke, or cardiovascular-disease-related death in two antihypertensive treatment regimens. One treatment arm begins with controlled onset-extended release (COER)-verapamil, which has its major antihypertensive effect 6-12 hours after administration. The other arm (standard of care (SOC)) begins with either hydrochlorothiazide (HCTZ) or atenolol, one of which is preselected by the investigator for an individual patient prior to randomization. Secondary objectives include comparisons of the regimens for each of the components of the primary endpoint (separately), death or hospitalization related to cardiovascular disease, efficacy in lowering blood pressure to goal, primary events occurring between 6 am and noon, all-cause mortality, withdrawals from blinded therapy, cancer, and hospitalizations due to bleeding. Patients may be enrolled if they are hypertensive and at least 55 years of age and have an established second risk factor for cardiovascular disease. Initial medications include COER-verapamil (180 mg/d), HCTZ (12.5 mg/d), or atenolol (50 mg/d). Initial doses are doubled if blood pressure (BP) does not reach goal (systolic BP140 mm and diastolic BP90 mm Hg). If BP is not controlled by the higher dose of the initial medication, HCTZ is added to COER-verapamil, or the SOC choice not initially selected is added in the SOC arm. An ACE-inhibitor is recommended (although nearly any open-label medication is allowed) as the third step for patients whose BP is not adequately controlled or who have a contraindication to one of the two SOC medications. Patients take two sets of tablets daily, one in the morning and one in the evening. Although most patients switch from an established antihypertensive medication to randomized treatment, untreated patients with stages I-III hypertension (SBP between 140 and 190 or DBP between 90 and 110 mm Hg) are eligible. Outcomes are monitored by an independent Data and Safety Monitoring Board. Enrollment began during the third quarter of 1996, and follow-up is to be completed in the third quarter of 2002.

Background The kinetics of colorectal epithelial cell proliferation is altered in patients at increased risk for colon cancer. Calcium administration ameliorates such proliferative changes in rodents. Findings in preliminary clinical trials have suggested similar effects in humans. Purpose A randomized, double-blind, placebo-controlled, clinical trial was designed to determine whether calcium supplementation will reduce the colorectal epithelial cell proliferation rate and normalize the distribution of proliferating cells within colorectal crypts (i.e., shift the zone of proliferation from the entire crypt to the lower 60% of the crypt, which is thought to be the normal proliferative zone of the crypt) in patients with sporadic adenomas. Methods Sporadic adenoma patients (n = 193) were treated with placebo (n = 66), 1.0 g calcium (n = 64), or 2.0 g calcium (n = 63) daily for 6 months. Rectal mucosa biopsy specimens were obtained at base line and at 1-, 2-, and 6-month follow-up. Cell proliferation was measured by detection of S-phase-associated proliferating cell nuclear antigen by immunohistochemical methods. The cell proliferation rate, called labeling index (LI), was calculated as the proportion of labeled cells in the crypts. The deviation of the proliferative zone from the normal location in the lower 60% of the crypt was calculated as the proportion of labeled cells in the upper 40% of the crypt, called distributional index (phi h). The effects of calcium treatment on the LI and phi h were expressed as relative effects--(calcium follow-up/calcium base line)/(placebo follow-up/placebo base line). Calculations and inference testing of the relative effects were accomplished using a repeated-measures mixed model on log-transformed LI and phi h values. All statistical tests were two-sided. Results Scorable biopsy specimens were obtained on 170 patients at base line, 164 at 1 month, 161 at 2 months, and 163 at 6 months. The difference in the change in the LI between the combined calcium groups and the placebo group was insignificant, with a relative effect of calcium versus placebo of 0.97 (P = .87). However, for the phi h, the relative effect of calcium versus placebo was 0.50 (P = .05) in the combined calcium groups, 0.56 (P = .16) in the 1.0-g calcium group, and 0.44 (P = .05) in the 2.0-g calcium group. Conclusions Calcium supplementation normalizes the distribution of proliferating cells without affecting the proliferation rate in the colorectal mucosa of sporadic adenoma patients. Implications These results support further study of whether alterations in colon cell proliferative kinetics represent true intermediate steps in colon carcinogenesis that can be used to investigate the etiology and prevention of, and whether a higher calcium consumption can reduce the risk of, colon cancer.

This article presents exploratory data analytic methodology for visualizing and summarizing data that can be represented as individual-specific curves. We propose a simplified form of functional data analysis. A nonparametric scatterplot smooth is applied to each individual's data, followed by a principal components analysis of the smoothed data. We then display the individual smooth curves in an array organized by principal component scores. The display suggests interpretable summary measures. The methodology is applied to the measurement of proliferative activity, a biomarker for colon cancer risk. We use the summary measures in the analysis of a pilot study clinical trial.

Several models of a population survival curve composed of two piecewise exponential distributions are developed. In one formulation the hazard rate changes at a point that is an unobservable random variable that varies between individuals. The population hazard function may decrease with age even when all individuals' hazards are increasing. In a second formulation, the population hazard function is modeled directly. Several models are fit to the survival history of a cohort of 5751 highly inbred male Drosophila melanogaster and the British coal mining disaster data.

SUMMARY Nonproportional hazards can often be expressed by extending the Cox model to include time varying coefficients; e.g., for a single covariate, the hazard function for subject i is modelled as exp { fl(t)Zi(t)}. A common example is a treatment effect that decreases with time. We show that the function /3(t) can be directly visualized by smoothing an appropriate residual plot. Also, many tests of proportional hazards, including those of Cox (1972), Gill & Schumacher (1987), Harrell (1986), Lin (1991), Moreau, O'Quigley & Mesbah (1985), Nagelkerke, Oosting & Hart (1984), O'Quigley & Pessione (1989), Schoenfeld (1980) and Wei (1984) are related to time-weighted score tests of the proportional hazards hypothesis, and can be visualized as a weighted least-squares line fitted to the residual plot.

BACKGROUND Colonic epithelial cell proliferation is increased in patients at high risk for colon cancer. Calcium administration has ameliorated the proliferative changes in rodents, and findings in small, uncontrolled clinical trials have suggested similar effects in humans. PURPOSE This preliminary, double-blind, randomized clinical trial was designed 1) to investigate whether supplemental calcium will reduce colonic epithelial cell proliferation in patients with sporadic adenomas who consume a high-fat, Western-style diet; 2) to determine the sample size (number of scorable crypts per person) needed to achieve adequate statistical power; and 3) to evaluate the feasibility of full-scale clinical trials. METHODS Twenty-one sporadic adenoma patients were treated daily with placebo or 1200 mg of supplemental calcium. To determine colonic epithelial cell proliferation, we used tritiated thymidine labeling of colon crypt epithelial cells in rectal biopsy specimens and calculated the percentage of labeled cells (labeling index [LI]). Two pathology technician "readers" independently scored each specimen, and inter-reader reliability was determined. Subjects remained on their usual diet during the study, and intake of calories, calcium, total fat, and vitamin D did not differ substantially among them. We calculated curves for statistical power to determine the number of scorable crypts needed per person for detection of a statistically significant difference (P < .05) of 1.0% in mean LI. RESULTS The pooled baseline LI was 4.7%. In the calcium-treated group, the LI increased 0.6% (proportional increase, 12.8%); in the placebo-treated group, it decreased 0.5% (proportional decrease, 10.6%). The difference between change in the mean LI from baseline to 8 weeks' follow-up in the placebo group versus the calcium group was not statistically significant. The intraclass correlation coefficient for inter-reader reliability for the baseline LI was .66. Analyses indicated scoring eight crypts sufficient for estimates of the LI adequate for between-group comparisons, a level achieved in 81% of biopsy specimens. CONCLUSIONS Calcium carbonate supplements delivering 1200 mg elemental calcium daily may not decrease colonic epithelial cell proliferation over an 8-week period in sporadic adenoma patients. In future trials measuring the LI, consideration should be given to ensuring adequate numbers of scorable crypts and to the impact of inadequate biopsy procedures, labeling failure, reader reliability, and participant withdrawal. Our findings support the feasibility of a full-scale clinical trial to further study the relationships among dietary calcium, colonic epithelial cell proliferation, and colorectal cancer.

An alternative way to implement the Akaike Information Criterion (AIC) is proposed for the evaluation of staging systems for colorectal cancer.

A normative sample of 880 children was contrasted with a sample of 216 sexually abused children on the Child Sexual Behavior Inventory (CSBI), a 35-item behavior checklist assessing sexual behavior in children 2-12 years old. The CSBI total score differed significantly between the 2 groups after controlling for age, sex, maternal education, and family income, with sexually abused children showing a greater frequency of sexual behaviors than did the normative sample. Test-retest reliability, interitem correlations, cross-validation, and correlations with abuse characteristics were also reported

Objective To examine regional differences in the Controlled ONset Verapamil INvestigation of Cardiovascular Endpoints (CONVINCE) trial. Design Double-blind, randomized, international clinical trial. Setting Six hundred and sixty-one clinical centers in 15 countries. Patients Hypertensive volunteers (n = 16,602) with > or =1 additional cardiovascular risk factor, grouped into four regions: USA (n = 8144), Canada (n = 3405), Western Europe (Spain, UK, Italy, Sweden, Germany; n = 2048) or 'other' (Bulgaria, Israel, Mexico, Czech Republic, Hungary, Poland, Slovakia, Brazil; n = 2879); subgroupings included country and state/province within the USA and Canada. Interventions Randomized to COER-verapamil or the investigator's choice of either atenolol or hydrochlorothiazide, titrated and additional drugs added as required. Main outcome measures Baseline characteristics; blood pressure control, medication adherence and lost-to-follow-up at 2 years; and composite primary endpoint (stroke, myocardial infarction, cardiovascular death) by regional groupings. Results Regional differences were found at baseline for age, gender, blood pressure, percentage receiving antihypertensive drug therapy, initial choice of atenolol or hydrochlorothiazide, and risk factor profile. Blood pressure control rates increased markedly during follow-up in all regions, but varied significantly by region. Blood pressure control, medication adherence and lost-to-follow-up rates were poorest in the USA. After adjustment for baseline differences, the primary-event rate for each region was significantly lower than for the USA. Although baseline factors, blood pressure control and event rates varied by region, treatment differences did not. Conclusion Despite differences in baseline and follow-up measures across geographical regions, the absence of treatment differences by region suggests that the overall findings of CONVINCE are robust.

A method is proposed for the evaluation of in vitro experiments for combination chemotherapy, a new and growing area of cancer research. We first describe and review a popular graphical device called an isobologram. We then propose a statistical framework, a simple experimental design, and a statistical test for use with this widely accepted methodology. The test we propose is a score test based on the linear logistic regression model.

PURPOSE To evaluate sampling strategies used to estimate survival after uveal malignant melanoma that exclude some patients who would be censored from the analysis. METHODS Simulation was performed on a population-based data set of 133 patients who had an eye enucleated because of uveal melanoma. One thousand bootstrap samples of 80 patients were drawn, without replacement, according to three sampling strategies: a random draw (conventional strategy), a draw limited to patients who died of the tumor or survived at least 10 years without metastasis ("late-censoring" strategy), and a draw modified so that 40 patients died of melanoma and others survived at least 10 years without metastasis ("fifty-fifty" strategy). The bias in the Kaplan-Meier analysis and Cox proportional hazards regression was quantified. RESULTS The late-censoring strategy decreased the proportion of censored patients from 53% to 42%, whereas the fifty-fifty strategy assigned 50% of patients to this group. The former strategy overestimated mortality, the excess being 5.2% and 3.7% at 10 and 20 years, respectively. The latter strategy underestimated mortality, the bias being 1.6% and 4.6% at 10 and 20 years, respectively. The bias differed according to categories of explanatory variables so that the log-rank test statistic was inflated a median of 1.08 times (range, 0.73-1.87) and 1.14 times (range, 0.87-1.84), and the Wald chi(2) statistic of the Cox regression was inflated a median of 1.18 times (range, 0.79-2.13) and 1.16 times (range, 0.71-2.02), respectively, when the late-censoring and fifty-fifty strategies were applied. CONCLUSIONS Sampling strategies that exclude on purpose a proportion of patients who would be censored produce biased statistics, because they violate assumptions of survival analysis. Only random sampling from an underlying population produces unbiased survival estimates.

Pulse detection algorithms and spectral analysis are the two most common methods for analysing pulsatile hormone data. We compared a popular high quality pulse detection algorithm (CLUSTER) to spectral analysis on a data set comparing luteinizing hormone data in depressed and control women. For these data, periodogram analysis methods, in particular Fisher's periodicity test, were superior in distinguishing the groups. Extending the pulse detection method to include measures of intra-individual variability improved its discriminatory performance. The two methods complement each other.

Although high vegetable intakes have been associated with a lower risk of colorectal cancer, this relation is less well established for the precursor lesions, adenomatous polyps. With a case-control design involving adenomatous polyp cases (n = 564), colonoscopy-negative controls who were polyp free at colonoscopy (n = 682), and community controls (n = 535), this 1991-1994 Minnesota Cancer Prevention Research Unit study investigated the relation between fruit and vegetable consumption and first incident adenomatous polyps. Dietary intake was assessed using a food frequency questionnaire. For women, adenoma risk was approximately halved in the highest versus lowest quintile of juice consumption (cases vs. colonoscopy-negative controls: odds ratio (OR) = 0.50, 95% confidence interval (CI): 0.27, 0.92; cases vs. community controls: OR = 0.56, 95% CI: 0.30, 1.06). The association was stronger for adenomas with moderate or severe dysplasia compared with mild dysplasia. Juice was not associated with adenoma risk in men. The results for fruits, vegetables, total fruits and vegetables, green leafy vegetables, and several botanically and phytochemically defined subgroups generally were not statistically significant. Because elevated vegetable consumption has been associated with a lower risk of colorectal cancer, vegetables may have a stronger role in preventing the progression of adenomas to carcinomas rather than in preventing the initial appearance of adenomas.

Abstract —Blood pressure (BP) control rates around the world are suboptimal. Part 2 of the National Health and Nutrition Educational Survey (NHANES) III indicates that only 27.4% of hypertensive Americans aged 18 to 74 years have a BP of

OBJECTIVE To test the effect of daily supplemental calcium on serum total and high-density lipoprotein cholesterol (HDL-C) levels and blood pressure in adults. DESIGN Randomized, double-blind, placebo-controlled clinical trial; adjunct study to a trial of calcium and colon cell proliferation in patients with sporadic adenoma. SETTING Outpatient clinic. PATIENTS A total of 193 men and women, aged 30 to 74 years. INTERVENTION Treatment with 1.0 and 2.0 g/d of elemental calcium vs placebo over a 4-month period for cholesterol determinations and 6 months for blood pressure. MAIN OUTCOME MEASURES Serum total cholesterol and HDL-C levels, systolic and diastolic blood pressure. RESULTS Because there were no apparent differences in responses between the 1.0-g and 2.0-g calcium groups, their data were combined and compared with those of the placebo group. Among all participants, the mean total cholesterol level dropped 0.07 mmol/L (2.9 mg/dL) (1.3%) (P = .43) more, and the mean HDL-C level dropped 0.01 mmol/L (0.4 mg/dL) (1.1%) (P = .71) less in the calcium group than in the placebo group. Among participants without a history of hypercholesterolemia, the mean total cholesterol level dropped 0.18 mmol/L (6.8 mg/dL) (3.3%) (P = .10) and the HDL-C level dropped 0.02 mmol/L (0.6 mg/dL) (1.5%) (P = .61) more in the calcium group than in the placebo group. Among all participants, there was no apparent change in blood pressure until 6 months, when the mean systolic blood pressure dropped 0.8 mm Hg (0.6%) (P = .85) and the mean diastolic blood pressure dropped 0.4 mm Hg (0.5%) (P = .80) more in the calcium group than in the placebo group. CONCLUSIONS There were no substantial or statistically significant effects of calcium supplementation on total cholesterol or HDL-C levels or on blood pressure. There was a suggestion (not statistically significant) of a 0.07 to 0.18 mmol/L (3-7 mg/dL) or 2% to 4% drop in the total cholesterol level, a finding similar to that reported in other studies, which indicates the need for further study.

This chapter gives an introduction to the simplest concept: estimating the survival curve when there are no covariates. Although simple, it forms a platform for understanding the more complex material that follows. We do it twice, once informally (although making use of counting process ideas) in Section 1, and then a second time with the connections to counting processes and martingales much more complete. Sections 2 and 3 first give an overview of the necessary theory and then apply it to the informal results of Section 1, both validating and extending them. Section 4 discusses the extension to tied data. The reader might want to focus on Section 1 on the first reading, perhaps supplemented with the results (but not derivations) of Sections 3 and 4.

The Cox proportional hazards model [36] has become by a wide margin the most used procedure for modeling the relationship of covariates to a survival or other censored outcome.

A common clinical study design follows patients over time, recording end-point events as they occur for each individual. In a cancer clinical trial with death as the endpoint, there can be at most one event per patient. In other cases, multiple events are possible — for example, studies of recurrent infections in bone marrow transplantation recipients. The study goal is to model the event rate as a function of covariates measured at baseline. In a clinical trial, these would typically include the treatment group, measures of disease severity, patient age, and other sociodemographic variables. The proportional hazards regression model is a popular tool.

Measurements of proliferative activity in colonic epithelial cells are being used as surrogate endpoints in clinical trials for colon cancer prevention. Proliferative index data exemplify an important type of clinical trial endpoint. The outcome variable is a proportion in which the denominator is an ancillary statistic and in which measurement error and technician judgement are important sources of variability. The paper proposes a statistical model for a repeated measures clinical trial with this type of endpoint, in the context of proliferative activity data. The model is a two-stage random effects linear model in the log scale. In addition to fixed effects covariates, it explicitly incorporates two major sources of variability: the number of epithelial cells counted and the reader effect. Although the resulting likelihood is complicated, one can fit an approximate likelihood with minimal loss of efficiency using standard packages. We apply the model to a pilot randomized clinical trial.

The natural history of primary sclerosing cholangitis was studied in 426 patients from five medical centers. The median follow-up time was 3.0 years (range, 0.01-16.6 years); 100 patients had died by the time of last follow-up. Survival analysis (Cox proportional-hazards regression) was used to identify the variables most useful in predicting survival of patients with primary sclerosing cholangitis. Serum bilirubin concentration, histological stage on liver biopsy, age, and the presence of splenomegaly were independent predictors of a high risk of dying. A mathematical model to predict survival of patients with primary sclerosing cholangitis (based on referral values of those predictors) was statistically validated using two methods. Confidence intervals for predicting patient-specific survival probabilities are also presented. This model to predict survival could be used to stratify participants in therapeutic trials, counsel patients and their families, decide on candidacy for and timing of liver transplantation, and provide mathematical controls for evaluating the efficacy of therapies for primary sclerosing cholangitis, including transplantation.

P-394 Key Words: Blood Pressure Control, Clinical Trials, Multivariate Analyses

Hypertensive patients are often given a calcium antagonist to reduce cardiovascular disease risk, but the benefit compared with other drug classes is controversial.To determine whether initial therapy with controlled-onset extended-release (COER) verapamil is equivalent to a physician's choice of atenolol or hydrochlorothiazide in preventing cardiovascular disease.Double-blind, randomized clinical trial conducted at 661 centers in 15 countries. A total of 16 602 participants diagnosed as having hypertension and who had 1 or more additional risk factors for cardiovascular disease were enrolled between September 1996 and December 1998 and followed up until December 31, 2000. After a mean of 3 years of follow-up, the sponsor closed the study before unblinding the results.Initially, 8241 participants received 180 mg of COER verapamil and 8361 received either 50 mg of atenolol or 12.5 mg of hydrochlorothiazide. Other drugs (eg, diuretic, beta-blocker, or an angiotensin-converting enzyme inhibitor) could be added in specified sequence if needed.First occurrence of stroke, myocardial infarction, or cardiovascular disease-related death.Systolic and diastolic blood pressure were reduced by 13.6 mm Hg and 7.8 mm Hg for participants assigned to the COER verapamil group and by 13.5 and 7.1 mm Hg for partcipants assigned to the atenolol or hydrochlorothiazide group. There were 364 primary cardiovascular disease-related events that occurred in the COER verapamil group vs 365 in atenolol or hydrochlorothiazide group (hazard ratio [HR], 1.02; 95% confidence interval [CI], 0.88-1.18; P =.77). For fatal or nonfatal stroke, the HR was 1.15 (95% CI, 0.90-1.48); for fatal or nonfatal myocardial infarction, 0.82 (95% CI, 0.65-1.03); and for cardiovascular disease-related death, 1.09 (95% CI, 0.87-1.37). The HR was 1.05 (95% CI, 0.95-1.16) for any prespecified cardiovascular disease-related event and 1.08 (95% CI, 0.93-1.26) for all-cause mortality. Nonstroke hemorrhage was more common with participants in the COER-verapamil group (n = 118) compared with the atenolol or hydrochlorothiazide group (n = 79) (HR, 1.54 [95% CI, 1.16-2.04]; P =.003). More cardiovascular disease-related events occurred between 6 AM and noon in both the COER verapamil (99/277) and atenolol or hydrochlorothiazide (88/274) groups; HR, 1.15 (95% CI, 0.86-1.53).The CONVINCE trial did not demonstrate equivalence of a COER verapamil-based antihypertensive regimen compared with a regimen beginning with a diuretic or beta-blocker. When considered in the context of other trials of calcium antagonists, these data indicate that the effectiveness of calcium-channel therapy in reducing cardiovascular disease is similar but not better than diuretic or beta-blocker treatment.

We show how plots based on the residuals from a proportional hazards model may be used to reveal the correct functional form for covariates in the model. A smoothed plot of the martingale residues was suggested for this purpose by Therneau, Grambsch, and Fleming (1990, Biometrika 77, 147-160); however, its consistency required that the covariates be independent. They also noted that the plot could be biased for large covariate effects. We introduce two refinements which overcome these difficulties. The first is based on a ratio of scatter plot smooths, where the numerator is the smooth of the observed count plotted against the covariate, and the denominator is a smooth of the expected count. This is related to the Arjas goodness-of-fit plot (1988, Journal of the American Statistical Association 83, 204-212). The second technique smooths the martingale residuals divided by the expected count, using expected count as a weight. This latter approach is related to a GLM partial residual plot, as well as to the iterative methods of Hastie and Tibshirani (1990, Biometrics 46, 1005-1016) and Gentleman and Crowley (1991, Biometrics 47, 1283-1296). Applications to survival data sets are given.

SUMMARY An application of the method of rank correlation is proposed for testing independence between a censored survival time and an ordinal covariate. The test statistic counts the number of concordances minus the number of discordances at each time with event(s) and adds across times; it is expressible as a score statistic within the proportional hazards framework. The proposed test includes, as a special case, a generalization of Jonckheere's test against ordered alternatives and as applied to the analysis of categorical data, it can be seen as a generalization of the Mantel-Haenszel procedure.

A large-scale, community-based survey was done to assess the frequency of a wide variety of sexual behaviors in normal preadolescent children and to measure the relationship of these behaviors to age, gender, and socioeconomic and family variables. A sample of 880 2-through 12-year-old children screened to exclude those with a history of sexual abuse were rated by their mothers using several questionnaire measures. The frequency of different behaviors varied widely, with more aggressive sexual behaviors and behaviors imitative of adults being rare. Older children (both boys and girls) were less sexual than younger children. Sexuality was found to be related to the level of general behavior problems, as measured by the Achenbach Internalizing and Externalizing T scores and to a measure of family nudity. It was not related to socioeconomic variables.

A sequential sampling scheme in which observations are taken until the observed Fisher information exceeds a target value is considered for a restricted class of parametric families. It is proved that the theorems for fixed sample size asymptotic likelihood inference conditional on ancillary statistics are directly applicable to the sequential sampling scheme for location families. The fixed sample-size approximate ancillary statistic for two-dimensional curved exponential families is shown to be ancillary in the sequential sampling scheme. Evidence from Monte Carlo simulations suggests the applicability of the fixed sample size conditional likelihood inference theorems to these families as well. The distribution of the sequential sample size is shown to be asymptotically normal.