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PubMed1999

A threshold causal model for clinical trials with departures from intended treatment.

Randomized clinical trials often are planned to study a specific intervention. However, the collection of data on treatment actually received often reveals variable levels of treatment exposure (or 'dose') across subjects, due to non-compliance or other reasons. This paper presents a new method, using such 'dose' data as well as control group responses, to assess a causal dose-response relationship. The specific model utilizes a threshold function and incorporates a random effect term to allow for heterogeneous treatment responses among subjects. Further modelling of the random effects allows for reduction of error variance and control for potential confounders. The threshold dose is estimated using a residual variance criterion based on a transformed model. Estimates of standard errors and confidence intervals are obtained using a bootstrap procedure. The method is applied to data from an AIDS clinical trial. A simulation study demonstrates the adequacy of the threshold estimates for particular sample sizes and error variances. The limitations of this essentially exploratory method, as well as some possible extensions, are discussed. Published in 1999 by John Wiley & Sons, Ltd. This article is a US Government Work and is in the public domain in the United States.

CD4 Lymphocyte Count↗

PubMed1999

On the application of integer-valued time series models for the analysis of disease incidence.

Statistical time series models are practical tools in public health surveillance. Their capacity to forecast future disease incidence values exemplifies their usefulness. Using these forecasts, one can develop strategies to trigger alerts to public health officials when irregular disease incidence values have occurred. Clearly, the better the forecasting performance of the model class used in the time series analysis, the more realistic are the alerts triggered. The time series analysis of disease incidence values has often entailed the Box and Jenkins model class. However, this class was designed to model real-valued variables whereas disease incidences are integer-valued variables. A new class of time series models, called integer-valued autoregressive models, has been developed and studied over the past decade. The objective of this paper is to introduce this new class of models to the application of time series analysis of infectious disease incidence, and to demonstrate its advantages over the class of real-valued Box and Jenkins models. The paper also presents a bootstrap method developed for the calculation of forecast interval limits.

Communicable Diseases↗

PubMed2000

A two-sample test with interval censored data via multiple imputation.

Interval censored data arise naturally in large scale panel studies where subjects can only be followed periodically and the event of interest can only be recorded as having occurred between two examination times. In this paper we consider the problem of comparing two interval-censored samples. We propose to impute exact failure times from interval-censored observations to obtain right censored data, then apply existing techniques, such as Harrington and Fleming's G(rho) tests to imputed right censored data. To appropriately account for variability, a multiple imputation algorithm based on the approximate Bayesian bootstrap (ABB) is discussed. Through simulation studies we find that it performs well. The advantage of our proposal is its simplicity to implement and adaptability to incorporate many existing two-sample comparison techniques for right censored data. The method is illustrated by reanalysing the Breast Cosmesis Study data set.

Algorithms↗

PubMed2000

Uncertainty of AIDS incubation time and its effects on back-calculation estimates.

Incubation time is the period from the onset of HIV infection to AIDS. The distribution of the incubation time is one of the main parameters of the back-calculation method for the estimation of incidence of HIV infection. Because of the long and variable incubation time, the assessment of its distribution is uncertain and this uncertainty spreads through the back-calculation method and affects the estimation of the precision of incidence of HIV infection. We propose a method to investigate the sensitivity of the estimates to variations of the incubation times, with particular regard to the covariate AGE in the modelling of the incubation period, making use of the parametric bootstrap. An application to the HIV epidemic in Italy is presented. The amplification of the uncertainty of the HIV incidence estimates resulting from the implementation of our proposed method tends to concentrate around the earlier periods of the epidemic, corresponding to the right tail of the incubation time distribution, which is very sensitive to small perturbations.

Acquired Immunodeficiency Syndrome↗

PubMed2000

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.

Adolescent↗

PubMedDate not supplied

Assessing the relative accuracies of two screening tests in the presence of verification bias.

Epidemiological studies of dementia often use two-stage designs because of the relatively low prevalence of the disease and the high cost of ascertaining a diagnosis. The first stage of a two-stage design assesses a large sample with a screening instrument. Then, the subjects are grouped according to their performance on the screening instrument, such as poor, intermediate and good performers. The second stage involves a more extensive diagnostic procedure, such as a clinical assessment, for a particular subset of the study sample selected from each of these groups. However, not all selected subjects have the clinical diagnosis because some subjects may refuse and others are unable to be clinically assessed. Thus, some subjects screened do not have a clinical diagnosis. Furthermore, whether a subject has a clinical diagnosis depends not only on the screening test result but also on other factors, and the sampling fractions for the diagnosis are unknown and have to be estimated. One of the goals in these studies is to assess the relative accuracies of two screening tests. Any analysis using only verified cases may result in verification bias. In this paper, we propose the use of two bootstrap methods to construct confidence intervals for the difference in the accuracies of two screening tests in the presence of verification bias. We illustrate the application of the proposed methods to a simulated data set from a real two-stage study of dementia that has motivated this research.

Black or African American↗

PubMed1999

Fieller's theorem and linkage disequilibrium mapping.

Linkage disequilibrium mapping exploits the fact that at genetic markers close enough to a disease locus on a particular chromosome, we expect to find an association between the disease and marker alleles. Furthermore, the magnitude of the association is expected to follow a unimodal curve when plotted against location, with the peak at the disease location. In practice, for real data, we usually see deviations from such a curve due to other influences such as evolutionary variability, mutation, and selection. Here we propose fitting a quadratic curve to data of this nature, estimating the location of the disease locus by the point at which the curve is maximum. A key feature of our method is the use of transformations of both location and disequilibrium, so that departures from a unimodal curve are incorporated by fitting the curve not to the original location and disequilibrium values but to the transformed values. In addition, we estimate the covariances between the disequilibrium values at linked loci using either a multinomial approximation or a bootstrap procedure. The location estimate from our method is the ratio of two quantities that, in large samples, are normally distributed, and so we use Fieller's theorem to obtain a confidence interval for the disease gene location. We successfully apply our method to data from several published studies in which the true disease gene location is known.

Alleles↗

PubMedDate not supplied

Adjusting for bias in C/E ratio estimates.

The estimator used to calculate incremental cost-effectiveness (C/E) ratios from sampled data is biased but consistent. While the bias may be negligible in studies with large sample sizes, it is potentially important in analyses based on small samples. When patient-level data on costs and effects are available, bootstrap simulation methods can be used to estimate the bias of a C/E ratio and adjust the point estimate accordingly.

Bias↗

PubMed1999

An estimate of the crosstalk matrix in four-dye fluorescence-based DNA sequencing.

Color separation is an essential step of the data processing in the four-dye fluorescence detection strategy used in automated DNA sequencing. In this paper, we propose a model to describe the crosstalk phenomenon, and show how the assumptions of the model are supported by experimental data. The crosstalk matrix is estimated via a reparameterization based on a mapping between the distribution of fluorescence intensities and that of dye concentrations. An iterative algorithm is designed to implement the estimation. To evaluate the color-correction quality of a crosstalk matrix, we propose a quantitative measure based on the distribution of the color-corrected data. We illustrate this method by applying it to a sequencing trace of slab gel electrophoresis obtained at the Human Genome Center at Lawrence Berkeley National Laboratory, and that of capillary electrophoresis provided by the Department of Chemistry at UC, Berkeley. The accuracy of this method is also assessed by the bootstrap method.

Algorithms↗

PubMed2000

Discriminating between homodimeric and monomeric proteins in the crystalline state.

Scores calculated from intermolecular contacts of proteins in the crystalline state are used to differentiate monomeric and homodimeric proteins, by classification into two categories separated by a cut-off score value. The generalized classification error is estimated by using bootstrap re-sampling on a nonredundant set of 172 water-soluble proteins whose prevalent quaternary state in solution is known to be either monomeric or homodimeric. A statistical potential, based on atom-pair frequencies across interfaces observed with homodimers, is found to yield an error rate of 12.5%. This indicates a small but significant improvement over the measure of solvent accessible surface area buried in the contact interface, which achieves an error rate of 15.4%. A further modification of the latter parameter relating the two most extensive contacts of the crystal results in an even lower error rate of 11.1%.

Crystallization↗

PubMed2001

Artificial neural networks: opening the black box.

Artificial neural networks now are used in many fields. They have become well established as viable, multipurpose, robust computational methodologies with solid theoretic support and with strong potential to be effective in any discipline, especially medicine. For example, neural networks can extract new medical information from raw data, build computer models that are useful for medical decision-making, and aid in the distribution of medical expertise. Because many important neural network applications currently are emerging, the authors have prepared this article to bring a clearer understanding of these biologically inspired computing paradigms to anyone interested in exploring their use in medicine. They discuss the historical development of neural networks and provide the basic operational mathematics for the popular multilayered perceptron. The authors also describe good training, validation, and testing techniques, and discuss measurements of performance and reliability, including the use of bootstrap methods to obtain confidence intervals. Because it is possible to predict outcomes for individual patients with a neural network, the authors discuss the paradigm shift that is taking place from previous "bin-model" approaches, in which patient outcome and management is assumed from the statistical groups in which the patient fits. The authors explain that with neural networks it is possible to mediate predictions for individual patients with prevalence and misclassification cost considerations using receiver operating characteristic methodology. The authors illustrate their findings with examples that include prostate carcinoma detection, coronary heart disease risk prediction, and medication dosing. The authors identify and discuss obstacles to success, including the need for expanded databases and the need to establish multidisciplinary teams. The authors believe that these obstacles can be overcome and that neural networks have a very important role in future medical decision support and the patient management systems employed in routine medical practice.

Decision Theory↗

PubMed2000

Nucleolus organizer regions (AgNORs) and total tumor mass are independent prognostic parameters for treatment-free period in chronic lymphocytic leukemia.

The aim of our study was to evaluate whether the nucleolus organizer regions (AgNOR) of circulating lymphocytes in chronic lymphocytic leukemia (CLL) could predict the duration of the stable phase (treatment-free period) of this disease. Age, sex, peripheral lymphoctes, hemoglobin, platelet count, Binet's stage, total tumor mass (TTM) and AgNOR pattern at diagnosis were assessed in 57 patients and compared with the time from diagnosis until patients fulfilled the criteria to start chemotherapy. In univariate Cox regression, Binet's stage, hemoglobin, number of peripheral lymphocytes, TTM and the percentage of lymphocytes containing one AgNOR cluster (circulating proliferative fraction) had predictive value. In the multivariate Cox model, only TTM and the percentage of cells with one AgNOR cluster were independent factors predicting the duration of the stable phase. Repetition of these analyses in 500 data sets created by bootstrap resampling confirmed the results. Summing up the percentage of lymphocytes with an AgNOR cluster and the TTM value, a simple prognostic index could be created to give information about the duration of the stable phase in CLL.

Cell Division↗

PubMed2000

On the inclusion of prevalent cases in HIV/AIDS natural history studies through a marker-based estimate of time since seroconversion.

In most cohort studies of HIV infection and AIDS, seroprevalent cases provide a substantial amount of information. Inclusion of these people in natural history studies requires a fairly unbiased method to estimate their seroconversion distribution. When a cohort-based estimate is not feasible, an alternative is to estimate individual seroconversion distributions, based on marker values at entry. In this paper, a non-parametric marker-based estimation method is developed. The method is applied to data from the Amsterdam cohort study on homosexual men. For seroprevalent cases who entered the study between October 1984 and April 1985, individual seroconversion distributions are estimated based on their first measured CD4 count. In subsequent survival analyses, dates of seroconversion are estimated via conditional mean imputation. Inclusion of these seroprevalent cases greatly improves the quality of the data. Age at seroconversion is a significant cofactor for disease progression, a result not found when analysis is restricted to those who seroconvert. To incorporate the uncertainty in the imputed date of seroconversion, a bootstrap procedure is developed for the computation of p-values and confidence intervals. In our analyses, standard procedures, which ignore the uncertainty in the imputed date of seroconversion, perform almost as well.

Acquired Immunodeficiency Syndrome↗

PubMed2000

Summarizing the predictive power of a generalized linear model.

This paper studies summary measures of the predictive power of a generalized linear model, paying special attention to a generalization of the multiple correlation coefficient from ordinary linear regression. The population value is the correlation between the response and its conditional expectation given the predictors, and the sample value is the correlation between the observed response and the model predicted value. We compare four estimators of the measure in terms of bias, mean squared error and behaviour in the presence of overparameterization. The sample estimator and a jack-knife estimator usually behave adequately, but a cross-validation estimator has a large negative bias with large mean squared error. One can use bootstrap methods to construct confidence intervals for the population value of the correlation measure and to estimate the degree to which a model selection procedure may provide an overly optimistic measure of the actual predictive power.

Bias↗

PubMedDate not supplied

Methodological issues in the development of the Canadian Cancer Incidence Atlas.

The Canadian Cancer Incidence Atlas is among recent national atlases using incidence rather than mortality data. Methods used to assess the significance and spatial correlation of the age-standardized rates (ASIRs) for the 290 census divisions are described. The expected number of cases by area was used to determine cancer sites with sufficient cases to be mapped. ASIR significance was assessed using a simulation based on a Poisson distribution. The consistency of the observed case distributions with the Poisson distribution was examined. The bootstrap confidence interval (CI) for the ASIR developed by Swift was used in the atlas. Spatial correlation was assessed with Moran's I/I(max) and the significance determined by a simulation in order to allow for area population variation. Data quality indicators typically used for cancer registries were presented, supplemented by a registry questionnaire.

Atlases as Topic↗

PubMed2000

Smooth estimation of the survival function for interval censored data.

Interval censored data arise naturally in large-scale panel studies where subjects can only be followed periodically and the event of interest can only be observed in some time intervals. To estimate the survival function the non-parametric maximum likelihood estimator (NPMLE) is commonly used, which is a step function having some large jumps. However, in many applications the underlying survival function can be reasonably assumed to be smooth, and then the NPMLE does not efficiently use this information. Two smooth estimators have been f the NPMLE; another is the logspline density model. However, to our knowledge there is no finite sample study yet to assess their performance in the literature. In this paper we first show by simulation that both smooth estimators improve over the NPMLE for smooth survival functions. We then apply these estimators to compare two survival curves. The test statistics based on the maximum difference between two survival functions (Kolmogorov-Smirnov test) and on the integrated weighted difference of two survival functions (IWDB test) are investigated via the bootstrap. From our simulation studies the IWDB test seems particularly promising for some stochastically ordered survival functions that do not satisfy the proportional hazards model. The methods are illustrated by reanalysing the Breast Cosmesis Study data set.

Breast↗

PubMed2000

Analysis of a cluster randomized trial with binary outcome data using a multi-level model.

The use of multi-level logistic regression models was explored for the analysis of data from a cluster randomized trial investigating whether a training programme for general practitioners' reception staff could improve women's attendance at breast screening. Twenty-six general practices were randomized with women nested within them, requiring a two-level model which allowed for between-practice variability. Comparisons were made with fixed effect (FE) and random effects (RE) cluster summary statistic methods, ordinary logistic regression and a marginal model based on generalized estimating equations with robust variance estimates. An FE summary statistic method and ordinary logistic regression considerably understated the variance of the intervention effect, thus overstating its statistical significance. The marginal model produced a higher statistical significance for the intervention effect compared to that obtained from the RE summary statistic method and the multi-level model. Because there was only a moderate number of practices and these had unbalanced cluster sizes, reliable asymptotic properties for the robust standard errors used in the marginal model may not have been achieved. While the RE summary statistic method cannot handle multiple covariates easily, marginal and multi-level models can do so. In contrast to multi-level models however, marginal models do not provide direct estimates of variance components, but treat these as nuisance parameters. Estimates of the variance components were of particular interest in this example. Additionally, parametric bootstrap methods within the multi-level model framework provide confidence intervals for these variance components, as well as a confidence interval for the effect of intervention which allows for the imprecision in the estimated variance components. The assumption of normality of the random effects can be checked, and the models extended to investigate multiple sources of variability.

Breast Neoplasms↗

PubMed2000

Definition of individual bioequivalence: occasion-to-occasion versus mean switchability.

Two moment-based scaled definitions of individual bioequivalence are discussed. Based on a mixed effects linear model, their evaluations respectively lead to an unweighted (theta(11)) and a parametric (theta(15)) metric. The two metrics are estimated with respect to study design and two estimation methods. Results show that the two IBE metrics perform equivalently in the fully replicated design. In the semi-replicated design, the definition of theta(11) may not be valid while the evaluation of theta(15) results in a reduction of the weights in the mean difference and switchability components of the metric. Percentage rejection rates in the latter design indicate that theta(11) is more conservative than theta(15). This is because there is an increase of about 15 per cent in the producer risk in theta(11) relative to theta(15) compared to a 7 per cent increase in the consumer risk in theta(15) relative to theta(11). A further disadvantage of the design is that there is a 33 per cent loss in the subject-by-treatment variance efficiency which is reflected in a similar amount of decreased sensitivity to departures from perfect bioequivalence even when more subjects are used to equalize the number of exposure occasions in the two designs. It is concluded that a mean switchability criterion may be more appropriate from an interpretability perspective, the bootstrap resampling method used to evaluate individual bioequivalence based on theta(11) may need to be bias-corrected and that the semi-replicated design should be used cautiously.

Humans↗