Bayesian analysis of longitudinal Johne's disease diagnostic data without a gold standard test.

A Bayesian methodology was developed based on a latent change-point model to evaluate the performance of milk ELISA and fecal culture tests for longitudinal Johne's disease diagnostic data. The situation of no perfect reference test was considered; that is, no "gold standard." A change-point process with a Weibull survival hazard function was used to model the progression of the hidden disease status. The model adjusted for the fixed effects of covariate variables and random effects of subject on the diagnostic testing procedure. Markov chain Monte Carlo methods were used to compute the posterior estimates of the model parameters that provide the basis for inference concerning the accuracy of the diagnostic procedure. Based on the Bayesian approach, the posterior probability distribution of the change-point onset time can be obtained and used as a criterion for infection diagnosis. An application is presented to an analysis of ELISA and fecal culture test outcomes in the diagnostic testing of paratuberculosis (Johne's disease) for a Danish longitudinal study from January 2000 to March 2003. The posterior probability criterion based on the Bayesian model with 4 repeated observations has an area under the receiver operating characteristic curve (AUC) of 0.984, and is superior to the raw ELISA (AUC=0.911) and fecal culture (sensitivity=0.358, specificity=0.980) tests for Johne's disease diagnosis.

Estimating receiver operating characteristic curves with covariates when there is no perfect reference test for diagnosis of Johne's disease.

Paratuberculosis (Johne's disease) is a significant animal health problem. Evaluation of diagnostic tests for Johne's disease has been difficult due to lack of a gold standard test. In recent years, there has been interest in receiver operating characteristic (ROC) curve estimation without any gold standard test. Typically, either Bayesian or maximum likelihood methods are proposed. Although these methods overcome the lack of a gold standard test in ROC curve estimation, little work has been done to incorporate covariates in the analysis. In this paper, we propose a method for estimation of ROC curves based on statistical models to adjust for covariate effects when the true disease states of test animals are unknown. The covariates may be correlated with the disease process or with the diagnostic testing procedure, or both. We propose a 2-part Bayesian model: first, a logistic regression model for disease prevalence is used to fit the covariates; second, a linear model is used to fit the covariates to the distribution of test scores. We used Markov chain Monte Carlo methods to compute the posterior estimates of the sensitivities and specificities that provide the groundwork for inference concerning the diagnostic procedure's accuracy. We applied the methodology to milk ELISA scores from several dairy-cow herds for the diagnostic testing of paratuberculosis. We found that both milk yield and its interaction with age had significant effects on the disease process whereas only milk yield was significant on the testing procedure.

Selenium supplementation, baseline plasma selenium status and incidence of prostate cancer: an analysis of the complete treatment period of the Nutritional Prevention of Cancer Trial.

OBJECTIVE: To present the results (to January 1996, the end of blinded treatment) of the Nutritional Prevention of Cancer (NPC) Trial, a randomized trial of selenium (200 micro g daily) designed to test the hypothesis that selenium supplementation (SS) could reduce the risk of recurrent nonmelanoma skin cancer among 1312 residents of the Eastern USA. MATERIALS AND METHODS: Original secondary analyses of the NPC to 1993 showed striking inverse associations between SS and prostate cancer incidence. A subsequent report revealed that this effect was accentuated among men with the lowest baseline plasma selenium concentrations. The effects of treatment overall and within subgroups of baseline prostate-specific antigen (PSA) and plasma selenium concentrations were examined using incidence rate ratios and Cox proportional hazards models. RESULTS: SS continued to significantly reduce the overall incidence (relative risk and 95% confidence interval) of prostate cancer (0.51, 0.29-0.87). The protective effect of SS appeared to be confined to those with a baseline PSA level of

Discovering subpopulation structure with latent class mixed models.

The linear mixed model is a well-known method for incorporating heterogeneity (for example, subject-to-subject variation) into a statistical analysis for continuous responses. However heterogeneity cannot always be fully captured by the usual assumptions of normally distributed random effects. Latent class mixed models offer a way of incorporating additional heterogeneity which can be used to uncover distinct subpopulations, to incorporate correlated non-normally distributed outcomes and to classify individuals. The methodology is motivated with examples in health care studies and a detailed illustration is drawn from the Nutritional Prevention of Cancer trials. Latent class models are used with longitudinal data on prostate specific antigen (PSA) as well as incidence of prostate cancer. The models are extended to accommodate prostate cancer as a survival endpoint; this is compared to treating it as a binary endpoint. Four subpopulations are identified which differ both with regard to their PSA trajectories and their incidence rates of prostate cancer.

An analysis of cancer prevention by selenium.

The nutritional functions of selenium (Se) are recognized as being due to a number of Se-containing proteins. It is not clear, however, whether any of these function in the anti-tumorigenic effects of Se most of which have been demonstrated for Se exposures greater than those required for selenoprotein expression. Indeed, other anti-tumorigenic mechanisms have been demonstrated for certain Se-metabolites. The Nutritional Prevention of Cancer Trial found supplemental Se (200 microg/day, as Se-enriched yeast) to be associated with significant reductions in cancer risks in subjects with pre-treatment plasma Se concentrations below ca. 120 ng/ml (1.5 nmoles/ml), which level would appear to require food-Se intakes of ca. 1.5 microg/kg body weight/day. However, the putative anti-carcinogenic Se-metabolite(s) should be more relevant than total plasma Se as a supplementation target for cancer prevention. These may be components of the non-protein-bound fraction of Se in plasma, which constitutes 2-4% of total plasma Se.

A latent class mixed model for analysing biomarker trajectories with irregularly scheduled observations.

This paper considers a latent class model to uncover subpopulation structure for both biomarker trajectories and the probability of disease outcome in highly unbalanced longitudinal data. A specific pattern of trajectories can be viewed as a latent class in a finite mixture where membership in latent classes is modelled with a polychotomous logistic regression. The biomarker trajectories within a latent class are described by a linear mixed model with possibly time-dependent covariates and the probabilities of disease outcome are estimated via a class specific model. Thus the method characterizes biomarker trajectory patterns to unveil the relationship between trajectories and outcomes of disease. The coefficients for the model are estimated via a generalized EM (GEM) algorithm, a natural tool to use when latent classes and random coefficients are present. Standard errors of the coefficients are calculated using a parametric bootstrap. The model fitting procedure is illustrated with data from the Nutritional Prevention of Cancer trials; we use prostate specific antigen (PSA) as the biomarker for prostate cancer and the goal is to examine trajectories of PSA serial readings in individual subjects in connection with incidence of prostate cancer.

Statistical models for longitudinal biomarkers of disease onset.

We consider the analysis of serial biomarkers to screen and monitor individuals in a given population for onset of a specific disease of interest. The biomarker readings are subject to error. We survey some of the existing literature and concentrate on two recently proposed models. The first is a fully Bayesian hierarchical structure for a mixed effects segmented regression model. Posterior estimates of the changepoint (onset time) distribution are obtained by Gibbs sampling. The second is a hidden changepoint model in which the onset time distribution is estimated by maximum likelihood using the EM algorithm. Both methods lead to a dynamic index that represents a strength of evidence that onset has occurred by the current time in an individual subject. The methods are applied to some large data sets concerning prostate specific antigen (PSA) as a serial marker for prostate cancer. Rules based on the indices are compared to standard diagnostic criteria through the use of ROC curves adapted for longitudinal data.

Decreased incidence of prostate cancer with selenium supplementation: results of a double-blind cancer prevention trial.

OBJECTIVE: To test if supplemental dietary selenium is associated with changes in the incidence of prostate cancer. PATIENTS AND METHOD: A total of 974 men with a history of either a basal cell or squamous cell carcinoma were randomized to either a daily supplement of 200 microg of selenium or a placebo. Patients were treated for a mean of 4.5 years and followed for a mean of 6.5 years. RESULTS: Selenium treatment was associated with a significant (63%) reduction in the secondary endpoint of prostate cancer incidence during 1983-93. There were 13 prostate cancer cases in the selenium-treated group and 35 cases in the placebo group (relative risk, RR=0.37, P=0.002). Restricting the analysis to the 843 patients with initially normal levels of prostate-specific antigen (< or = 4 ng/mL), only four cases were diagnosed in the selenium-treated group and 16 cases were diagnosed in the placebo group after a 2 year treatment lag, (RR=0.26 P=0.009). There were significant health benefits also for the other secondary endpoints of total cancer mortality, and the incidence of total, lung and colorectal cancer. There was no significant change in incidence for the primary endpoints of basal and squamous cell carcinoma of the skin. In light of these results, the 'blinded' phase of this trial was stopped early. CONCLUSIONS: Although selenium shows no protective effects against the primary endpoint of squamous and basal cell carcinomas of the skin, the selenium-treated group had substantial reductions in the incidence of prostate cancer, and total cancer incidence and mortality that demand further evaluation in well-controlled prevention trials.

Reduction of cancer mortality and incidence by selenium supplementation.

PATIENTS AND METHOD: In order to test the hypothesis that a dietary supplement of selenium (Se) may reduce cancer risk, 1312 patients with histories of basa/squamous cell carcinomas of the skin were assigned in random, double-blind fashion to daily oral supplements of either Se-enriched yeast (200 micrograms Se/day), or a low-Se yeast placebo. Patients were recruited in 1983 to 1990 and were followed with regular dermatologic examinations through, 1993 for a total of 8269 person-years of observation. Skin cancer diagnoses were confirmed histologically and plasma Se concentration was determined at 6 to 12 months intervals. All deaths and patient-reported illnesses were confirmed and documented by consultation with the patient medical care providers. RESULTS: Results showed that Se-supplementation did not significantly affect the incidences of recurrent basal/squamous cell carcinomas of the skin. However, Se-treatment was associated with reductions in total cancer mortality and in the incidences of lung, colorectal, prostate and total cancers. These effects were consistent over time and between study clinics. CONCLUSION: The results strongly suggest benefits of Se-supplementation for this cohort of patients and support the hypothesis that supplemental Se can reduce risks to at least some types of cancer.

Reduction of cancer risk with an oral supplement of selenium.

The hypothesis that a dietary supplement of selenium (Se) may reduce cancer risk was tested experimentally in humans. Patients with histories of basal/squamous cell carcinomas of the skin were assigned randomly in double-blind fashion to daily oral supplements of either Se-enriched yeast (200 micrograms Se/day), or a low-Se yeast placebo. A total of 1312 patients recruited in 1983-1990 were followed with regular dermatologic examinations through 1993 for a total of 8269 person-years of observation. Skin cancer diagnoses were confirmed histologically. Plasma Se concentration was determined at 6-12 months intervals. All deaths and patient-reported illnesses were recorded; reported cancers were confirmed and documented by consultation with the patient medical care providers. The results indicate that Se did not significantly affect the primary endpoints: incidences of recurrent basal/squamous cell carcinomas of the skin. However, Se-treatment was associated with reductions in several secondary endpoints: total mortality, mortality from all cancers combined, as well as the incidence of all cancers combined, lung cancer, colorectal cancer and prostate cancer. The consistencies of these associations over time, between study clinics and for the leading cancer sites strongly suggests benefits of Se-supplementation for this cohort of patients, supporting the hypothesis that supplemental Se can reduce cancer risk. Although Se did not shown protective effects against non-melanoma skin cancers, the suggested reductions in risks to other frequent cancers demand further evaluation in well controlled clinical intervention trials.

Regression models for recurrent event data: parametric random effects models with measurement error.

Statistical methodology is presented for the statistical analysis of non-linear measurement error models. Our approach is to provide adjustments for the usual maximum likelihood estimators, their standard errors and associated significance tests in order to account for the presence of measurement error in some of the covariates. We illustrate the technique with a mixed effects Poisson regression model for recurrent event data applied to a randomized clinical trial for the prevention of skin tumours.

Effects of selenium supplementation for cancer prevention in patients with carcinoma of the skin. A randomized controlled trial. Nutritional Prevention of Cancer Study Group.

OBJECTIVE: To determine whether a nutritional supplement of selenium will decrease the incidence of cancer. DESIGN: A multicenter, double-blind, randomized, placebo-controlled cancer prevention trial. SETTING: Seven dermatology clinics in the eastern United States. PATIENTS: A total of 1312 patients (mean age, 63 years; range, 18-80 years) with a history of basal cell or squamous cell carcinomas of the skin were randomized from 1983 through 1991. Patients were treated for a mean (SD) of 4.5 (2.8) years and had a total follow-up of 6.4 (2.0) years. INTERVENTIONS: Oral administration of 200 microg of selenium per day or placebo. MAIN OUTCOME MEASURES: The primary end points for the trial were the incidences of basal and squamous cell carcinomas of the skin. The secondary end points, established in 1990, were all-cause mortality and total cancer mortality, total cancer incidence, and the incidences of lung, prostate, and colorectal cancers. RESULTS: After a total follow-up of 8271 person-years, selenium treatment did not significantly affect the incidence of basal cell or squamous cell skin cancer. There were 377 new cases of basal cell skin cancer among patients in the selenium group and 350 cases among the control group (relative risk [RR], 1.10; 95% confidence interval [CI], 0.95-1.28), and 218 new squamous cell skin cancers in the selenium group and 190 cases among the controls (RR, 1.14; 95% CI, 0.93-1.39). Analysis of secondary end points revealed that, compared with controls, patients treated with selenium had a nonsignificant reduction in all-cause mortality (108 deaths in the selenium group and 129 deaths in the control group [RR; 0.83; 95% CI, 0.63-1.08]) and significant reductions in total cancer mortality (29 deaths in the selenium treatment group and 57 deaths in controls [RR, 0.50; 95% CI, 0.31-0.80]), total cancer incidence (77 cancers in the selenium group and 119 in controls [RR, 0.63; 95% CI, 0.47-0.85]), and incidences of lung, colorectal, and prostate cancers. Primarily because of the apparent reductions in total cancer mortality and total cancer incidence in the selenium group, the blinded phase of the trial was stopped early. No cases of selenium toxicity occurred. CONCLUSIONS: Selenium treatment did not protect against development of basal or squamous cell carcinomas of the skin. However, results from secondary end-point analyses support the hypothesis that supplemental selenium may reduce the incidence of, and mortality from, carcinomas of several sites. These effects of selenium require confirmation in an independent trial of appropriate design before new public health recommendations regarding selenium supplementation can be made

A computer program for sample size and power calculations in the design of multi-arm and factorial clinical trials with survival time endpoints.

This paper presents a computer program for use in the design of long-term clinical trials with multiple treatment arms in which the primary outcome variables are censored survival times. The treatment arms may be structured as a one-way or multi-way factorial design. It is assumed that patients are entered and randomized to a treatment arm during an accrual period. The patients are then followed for a fixed period during which there may be dropouts. Various distributional assumptions can be used to model the survival times. These include an option in which there is an effect of treatment duly after a lag or delay time. The program then computes the power of various statistical tests of hypotheses concerning treatment differences, interactions and trends. The power computations are "exact" in that they use the Monte Carlo method to obtain Type I and II error probabilities. However the program also outputs the normal approximations for comparison, although they are typically not accurate in these situations. Fisher's LSD method is used to adjust for the multiple comparisons. By comparing the power for various sets of design parameters, such as sample size, numbers of factor levels, patient accrual rate, and length of follow-up, an appropriate design can be constructed. Two examples are provided. The first is a simple one-way layout with multiple treatment arms; the second a two-way factorial design for a proposed large scale cancer chemoprevention trial.

Detection and assessment of clusters of disease: an application to nuclear power plant facilities and childhood leukaemia in Sweden.

We review some recent statistical methods for examining geographic patterns of disease incidence for the presence of clusters. General methods search for clusters throughout the study area and then assess the statistical significance of any clusters detected. Focused methods check for elevated incidence rates close to prespecified locations of putative sources of hazard. We apply the methods to leukaemia incidence data for children aged 0-15 years in Sweden (1980-1990), particularly in reference to locations of nuclear power facilities. Unlike some other studies, notably in the United Kingdom, we do not find any significant clusters.

A computer program for the statistical analysis of repeated event data using a mixed effects regression model.

This paper presents a computer program for fitting mixed effects regression models to repeated events data. The method has been described by Abu-Libdeh, Turnbull and Clark (Biometrics 46 (1990) 1017-1034). Such data can occur in longitudinal studies where subjects experience repeated events over time. The program allows the stepwise construction of a series of regression models which can be used to examine and test the influence of the various measured covariates upon the event rates. Two examples are provided. The first is a simple example involving the incidence of mammary tumors in rats. The second involves a very large complex data set from a clinical trial for the prevention of recurrent skin tumors.

The effects of scale on tests for disease clustering.

Surveillance of a large geographic region for 'clusters' of adverse health events, particularly cancers, often involves searching for raised incidence in the vicinity of prespecified putative sources of hazard. For reasons of practicality or of confidentiality, incidence and population data are usually only available aggregated over subregions or 'cells'. The performance of statistical procedures designed to detect the presence of clusters can be highly sensitive to the level of aggregation, that is to the choice of partition of the region into the cells. We investigate this sensitivity in the cases of three recently proposed procedures, namely those of Besag and Newell, Stone, and Waller et al. For illustration, we use leukaemia incidence data for 1978-82 in a region of upstate New York, with inactive hazardous waste sites containing trichloroethylene acting as suspected sources.

Group sequential tests for bivariate response: interim analyses of clinical trials with both efficacy and safety endpoints.

We describe group sequential tests for a bivariate response. The tests are defined in terms of the two response components jointly, rather than through a single summary statistic. Such methods are appropriate when the two responses concern different aspects of a treatment; for example, one might wish to show that a new treatment is both as effective and as safe as the current standard. We present a formulation of the bivariate testing problem, introduce group sequential tests that satisfy Type I error conditions, and show how to find the sample size guaranteeing a specified power. We describe how properties of group sequential tests for bivariate normal observations can be computed by numerical integration.

Sequential equivalence testing and repeated confidence intervals, with applications to normal and binary responses.

We propose group sequential tests of the equivalence of two treatments based on ideas related to repeated confidence intervals. These tests adapt readily to unpredictable group sizes, to the possibility of continuing even though a boundary has been crossed, and to nonnormal observations. In comparing two binomial distributions, the required sample size depends strongly on the average success probability and an adaptive choice of group size is needed to produce an efficient test meeting specified error probability constraints. A special case is the experiment where interim analyses are performed, not for the purpose of early termination but simply to adjust the sample size so that nominal error rates will be guaranteed, despite the presence of a nuisance parameter.

Plasma selenium concentration predicts the prevalence of colorectal adenomatous polyps.

The objective of this cross-sectional study was to determine whether plasma selenium concentration predicts the prevalence of adenomatous polyps of the colon and rectum. The source population for the study was 101 patients undergoing sequential colonoscopies at the Veterans Affairs Medical Center, Tucson, AZ. The study population was then limited to the 48 patients (all male) undergoing their initial colonoscopy who did not have a diagnosis of colorectal cancer. For each of these patients, a prediagnostic fasting plasma selenium concentration was determined. The data from this study suggest that fasting plasma selenium concentrations may be an important risk factor for colorectal adenomas. Patients with fasting plasma selenium concentrations below the median (< 128 mcg/liter) were significantly more likely to have one or more adenomatous polyps (prevalence odds ratio 4.2) and more adenomatous polyps (3.5 times) per patient. There was also a suggestion of a more proximal distribution of adenomatous polyps in the patients with a lower level of selenium. These associations were not confounded by age or smoking. The results of this study are consistent with the experimental animal studies, geographic mortality studies, and prospective cohort studies of selenium and colorectal cancer.

Optimal checking procedures for monitoring laboratory analyses.

Many clinical, environmental, and epidemiologic studies rely heavily upon biochemical data, and the quality of these data is of paramount importance to the validity of study conclusions. Traditionally, far more attention has been given to the analysis of study data than has been given to monitoring the quality of the data. In this paper we draw an analogy between monitoring a laboratory system and an industrial production process and discuss the limitations of industrial quality control plans when applied in a laboratory setting. We derive methods for computing optimal checking schedules for laboratory analyses. These schedules formalize traditional laboratory practices of periodic checking and provide guidelines for the frequency and placement of checks within a finite batch of analyses. When laboratory system failure can be reasonably approximated by an exponential or geometric distribution, optimal checking schedules are relatively easy to compute. For more complex failure distributions, we present a dynamic programming approach. We describe an application to the measurement of selenium status in plasma samples using an electrothermal atomic absorption spectrophotometry procedure.