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PubMed2004

Confidence intervals for the effect of a prognostic factor after selection of an 'optimal' cutpoint.

When investigating the effects of potential prognostic or risk factors that have been measured on a quantitative scale, values of these factors are often categorized into two groups. Sometimes an 'optimal' cutpoint is chosen that gives the best separation in terms of a two-sample test statistic. It is well known that this approach leads to a serious inflation of the type I error and to an overestimation of the effect of the prognostic or risk factor in absolute terms. In this paper, we illustrate that the resulting confidence intervals are similarly affected. We show that the application of a shrinkage procedure to correct for bias, together with bootstrap resampling for estimating the variance, yields confidence intervals for the effect of a potential prognostic or risk factor with the desired coverage.

Breast Neoplasms↗

PubMed2004

The 'Fishing License' method for analysing the time course of effects in repeated measurements.

Inference on the time of onset and the duration of a treatment effect is a challenging problem in biomedical research. These studies often generate repeated measurements from subjects in a treated group and a control group during the same time period. We propose a simple approach, called the 'Fishing License' method, to test for a treatment effect occurring during an unspecified time interval. The method is based on a statistic of the largest absolute value of the t statistic between two groups obtained by considering every possible time interval in the observed time period. A bootstrapped null distribution of the test statistic is used to determine the critical value. The method also provides estimates of onset and ending times, when the null hypothesis of no effect is rejected. Simulated and real experimental data sets were generated for assessing the performance of the method.

Air Pollutants↗

PubMed2004

13C-urea breath test for Helicobacter pylori in young children: cut-off point determination by finite mixture model.

The 13C-urea breath test (UBT) is currently regarded as one of the most important noninvasive diagnostic methods for detecting Helicobacter pylori (H. pylori) infection in adults and children. However, for infants and young children, the standard for UBT interpretation has not been validated, and its reliability has not been established for diagnosing H. pylori infection in this group. The primary outcome data from UBT consist of mixture data, which come from subjects whose H. pylori infection classifications are unconfirmed. In this paper, we propose the finite mixture distribution method to identify a reliable UBT cut-off value in a large baseline sample in which gastric biopsy is not available to confirm the H. pylori infection in younger children. Maximum likelihood estimators of the parameters in the mixture model were obtained using an expectation maximization (EM) algorithm. The standard deviation of the cut-off point was estimated by bootstrap methods. We applied the same analytical methods to the UBT results yielded from the follow up, as well as the overall UBT results in the longitudinal cohort data. The cut-off points from those UBT data sets are similar. The advantage of the finite mixture model is that it may be used to calculate sensitivity and specificity in the absence of other diagnostic tests.

Breath Tests↗

PubMed2004

The multiple-record systems estimator when registrations refer to different but overlapping populations.

In multiple-record systems estimation it is usually assumed that all registration relate to the same population. In this paper, we develop a method which can be used when the registrations relate to different populations, in the sense that they cover, for example, different time periods or regions. We show that under certain conditions ignoring that the registrations relate to different populations results in correct estimates of population size. The EM algorithm is presented as a method that can be used for more general problems. The parametric bootstrap is used to construct a confidence interval. The proposed method is then applied to a data set with five registrations of neural tube defects, that cover different time periods.

Algorithms↗

PubMed2004

Power and sample size determination when assessing the clinical relevance of trial results by 'responder analyses'.

A fundamental issue in regulatory decision making is the assessment of the benefit/risk profile of a compound. In order to do this, establishing the existence of a treatment effect by a significance test is not sufficient, but the clinical relevance of a potential benefit must also be taken into account. A number of regulatory guidelines propose that clinical relevance should be assessed by considering the rate of responders, i.e. the proportion of patients who are observed to achieve an apparently meaningful benefit. In this paper, we present methods for planning clinical trials that aim at demonstrating both statistical and clinical significance in superiority trials. Procedures based on analytical calculations are derived for normally distributed data and the case of a single endpoint as well as multiple primary outcomes. A bootstrap procedure is proposed that can be applied to non-normal data. Application is illustrated by a clinical trial in Alzheimer's disease.

Activities of Daily Living↗

PubMed2004

Ordered multiple-class ROC analysis with continuous measurements.

Receiver operating characteristic (ROC) curves have been useful in two-group classification problems. In three- and multiple-class diagnostic problems, an ROC surface or hyper-surface can be constructed. The volume under these surfaces can be used for inference using bootstrap techniques or U-statistics theory. In this article, ROC surfaces and hyper-surfaces are defined and their behaviour and utility in multi-group classification problems is investigated. The formulation of the problem is equivalent to what has previously been proposed in the general multi-category classification problem but the definition of ROC surfaces here is less complex and addresses directly the narrower problem of ordered categories in the three-class and, by extension, the multi-class problem applied to continuous and ordinal data. Non-parametric manipulation of both continuous and discrete test data and comparison between two diagnostic tests applied to the same subjects are considered. A three-group classification example in the context of HIV neurological disease is presented and the results are discussed.

AIDS Dementia Complex↗

PubMed2005

Non-parametric estimation of the odds ratios for continuous exposures using generalized additive models with an unknown link function.

The generalized additive, model (GAM) is a powerful and widely used tool that allows researchers to fit, non-parametrically, the effect of continuous predictors on a transformation of the mean response variable. Such a transformation is given by a so-called link function, and in GAMs this link function is assumed to be known. Nevertheless, if an incorrect choice is made for the link, the resulting GAM is misspecified and the results obtained may be misleading. In this paper, we propose a modified version of the local scoring algorithm that allows for the non-parametric estimation of the link function, by using local linear kernel smoothers. To better understand the effect that each covariate produces on the outcome, results are expressed in terms of the non-parametric odds ratio (OR) curves. Bootstrap techniques were used to correct the bias in the OR estimation and to construct point-wise confidence intervals. A simulation study was carried out to assess the behaviour of the resulting estimates. The proposed methodology was illustrated using data from the AIDS Register of Galicia (NW Spain), with a view to assessing the effect of the CD4 lymphocyte count on the probability of being AIDS-diagnosed via Tuberculosis (TB). This application shows how the link's flexibility makes it possible to obtain OR curve estimates that are less sensitive to the presence of outliers and unusual values that are often present in the extremes of the covariate distributions.

AIDS-Related Opportunistic Infections↗

PubMed2005

Semi-parametric modelling for costs of health care technologies.

Cost data that arise in the evaluation of health care technologies usually exhibit highly skew, heavy-tailed and, possibly, multi-modal distributions. Distribution-free methods for analysing these data, such as the bootstrap, or those based on the asymptotic normality of sample means, may often lead to inefficient or misleading inferences. On the other hand, parametric models that fit the data (or a transformation of the data) equally well can produce very different answers. We consider a Bayesian approach, and model cost data with a distribution composed of a piecewise constant density up to an unknown endpoint, and a generalized Pareto distribution for the remaining tail.

Animals↗

PubMed2005

Ranking states' immunization coverage: an example from the National Immunization Survey.

The National Immunization Survey (NIS) provides state-level estimates of preschool immunization coverage. These coverages are frequently presented in ranked lists, and ranks are frequently over-interpreted. In this paper, we highlight the difficulty in interpreting ranked point estimates. To demonstrate the uncertainty of ranks, parametric bootstrap methods were used to derive 90 per cent confidence intervals for ranks of state vaccination coverage levels among preschool children. We graphically compared states to a reference state. If NIS data are used to rank states, one should consider presenting confidence intervals for rank and the results of comparisons of one state with another graphically.

Child, Preschool↗

PubMed2005

Efficient estimation of the risk of a disease by quantile-categories of a key predictor variable using generalized additive models.

Suppose that one wishes to make inference to the risk of a disease by the population quartile-categories of a key continuous predictor variable. When one collects data on a prospective cohort, the standard method is simply to categorize the key predictor variable by the empirical quartiles. One may then include indicator variables for these empirical quartile-categories as predictors, along with other covariates, in a generalized linear model (GLM), with the observed health status of each subject as the response. The standard GLM method, however, is relatively inefficient, because it treats all observations that fall in the same quartile-category of the predictor variable identically, regardless of whether they lie in the centre or near the boundaries of that category. Alternatively, one may include the key predictor variable, along with other covariates, in a generalized additive model (GAM), again with the observed health status of each subject as the response. The alternative GAM method non-parametrically estimates the functional relationship between the key predictor variable and the response. One may then compute statistics of interest, such as proportions and odds ratios, from the fitted GAM equation using the empirical quartile-categories. Simulations show that both the GLM and GAM methods are nearly unbiased, but the latter method produces smaller variances and narrower bootstrap confidence intervals. An example from nutritional epidemiology illustrates the use of these methods.

Adult↗

PubMed2005

Assessing the effect of interventions in the context of mixture distributions with detection limits.

Many quantitative assay measurements of metabolites of environmental toxicants in clinical investigations are subject to left censoring due to values falling below assay detection limits. Moreover, when observations occur in both unexposed individuals and exposed individuals who reflect a mixture of two distributions due to differences in exposure, metabolism, response to intervention and other factors, the measurements of these biomarkers can be bimodally distributed with an extra spike below the limit of detection. Therefore, estimating the effect of interventions on these biomarkers becomes an important and challenging problem. In this article, we present maximum likelihood methods to estimate the effect of intervention in the context of mixture distributions when a large proportion of observations are below the limit of detection. The selection of the number of components of mixture distributions was carried out using both bootstrap-based and cross-validation-based information criterion. We illustrate our methods using data from a randomized clinical trial conducted in Qidong, People's Republic of China.

Anticarcinogenic Agents↗

PubMed2005

Methods for capture-recapture analysis when cases lack personal identifiers.

Methods for estimating the size of a closed population from a capture-recapture study require the availability of unique identifiers on each of two lists. These identifiers are used to identify the number of individuals appearing on both lists. When the number of individuals appearing on both lists cannot be determined with certainty from the data, matching between the lists is problematic. In this paper, we develop a weighted estimator to account for all possible matches between two lists. A bootstrap procedure is proposed for estimation. To illustrate the methods, we used two lists that recorded New York State (NYS) hospitalizations due to pertussis in 1996 to estimate the number of persons hospitalized for pertussis in NYS that year.

Algorithms↗

PubMed2005

A comparison of imputation methods in a longitudinal randomized clinical trial.

It is common for longitudinal clinical trials to face problems of item non-response, unit non-response, and drop-out. In this paper, we compare two alternative methods of handling multivariate incomplete data across a baseline assessment and three follow-up time points in a multi-centre randomized controlled trial of a disease management programme for late-life depression. One approach combines hot-deck (HD) multiple imputation using a predictive mean matching method for item non-response and the approximate Bayesian bootstrap for unit non-response. A second method is based on a multivariate normal (MVN) model using PROC MI in SAS software V8.2. These two methods are contrasted with a last observation carried forward (LOCF) technique and available-case (AC) analysis in a simulation study where replicate analyses are performed on subsets of the originally complete cases. Missing-data patterns were simulated to be consistent with missing-data patterns found in the originally incomplete cases, and observed complete data means were taken to be the targets of estimation. Not surprisingly, the LOCF and AC methods had poor coverage properties for many of the variables evaluated. Multiple imputation under the MVN model performed well for most variables but produced less than nominal coverage for variables with highly skewed distributions. The HD method consistently produced close to nominal coverage, with interval widths that were roughly 7 per cent larger on average than those produced from the MVN model.

Aged↗

PubMed2005

Extended information criterion (EIC) approach for linear mixed effects models under restricted maximum likelihood (REML) estimation.

In clinical data analysis, the restricted maximum likelihood (REML) method has been commonly used for estimating variance components in the linear mixed effects model. Under the REML estimation, however, it is not straightforward to compare several linear mixed effects models with different mean and covariance structures. In particular, few approaches have been proposed for the comparison of linear mixed effects models with different mean structures under the REML estimation. We propose an approach using extended information criterion (EIC), which is a bootstrap-based extension of AIC, for comparing linear mixed effects models with different mean and covariance structures under the REML estimation. We present simulation studies and applications to two actual clinical data sets.

Biometry↗

PubMed2006

Effect measures in non-parametric regression with interactions between continuous exposures.

In many biomedical studies, interest is often attached to calculating effect measures in the presence of interactions between two continuous exposures. Traditional approaches based on parametric regression are limited by the degree of arbitrariness involved in transforming these exposures into categorical variables or imposing a parametric form on the regression function. In this paper, we present: (a) a flexible non-parametric method for estimating effect measures through generalized additive models including interactions; and (b) bootstrap techniques for (i) testing the significance of interaction terms, and (ii) constructing confidence intervals for effect measures. The validity of our methodology is supported by simulations, and illustrated using data from a study of possible risk factors for post-operative infection. This application revealed a hitherto unreported effect: for patients with high plasma glucose levels, increased risk is associated, not only with low, but also with high percentages of lymphocytes.

Algorithms↗

PubMed2006

Non-parametric assessment of non-inferiority with censored data.

We suggest non-parametric tests for showing non-inferiority of a new treatment compared to a standard therapy when data are censored. To this end the difference and the odds ratio curves of the entire survivor functions over a certain time period are considered. Two asymptotic approaches for solving these testing problems are investigated, which are based on bootstrap approximations. The performance of the test procedures is investigated in a simulation study, and some guidance on which test to use in specific situations is derived. The proposed methods are applied to a trial in which two thrombolytic agents for the treatment on acute myocardial infarction were compared, and to a study on irradiation therapies for advanced non-small-cell lung cancer. Non-inferiority over a large time period of the study can be shown in both cases.

Computer Simulation↗

PubMed2006

Efficient estimation of log-normal means with application to pharmacokinetic data.

In this paper, the problem of interest is efficient estimation of log-normal means. Several existing estimators are reviewed first, including the sample mean, the maximum likelihood estimator, the uniformly minimum variance unbiased estimator and a conditional minimal mean squared error estimator. A new estimator is then proposed, and we show that it improves over the existing estimators in terms of squared error risk. The improvement is more significant with small sample sizes and large coefficient of variations, which is common in clinical pharmacokinetic (PK) studies. In addition, the new estimator is very easy to implement, and provides us with a simple alternative to summarize PK data, which are usually modelled by log-normal distributions. We also propose a parametric bootstrap confidence interval for log-normal means around the new estimator and illustrate its nice coverage property with a simulation study. Our estimator is compared with the existing ones via theoretical calculations and applications to real PK studies.

Area Under Curve↗

PubMed2007

Appropriateness of some resampling-based inference procedures for assessing performance of prognostic classifiers derived from microarray data.

The goal of many gene-expression microarray profiling clinical studies is to develop a multivariate classifier to predict patient disease outcome from a gene-expression profile measured on some biological specimen from the patient. Often some preliminary validation of the predictive power of a profile-based classifier is carried out using the same data set that was used to derive the classifier. Techniques such as cross-validation or bootstrapping can be used in this setting to assess predictive power, and if applied correctly, can result in a less biased estimate of predictive accuracy of a classifier. However, some investigators have attempted to apply standard statistical inference procedures to assess the statistical significance of associations between true and cross-validated predicted outcomes. We demonstrate in this paper that naïve application of standard statistical inference procedures to these measures of association under null situations can result in greatly inflated testing type I error rates. Under alternatives of small to moderate associations, confidence interval coverage probabilities may be too low, although for very large associations coverage probabilities approach their intended values. Our results suggest that caution should be exercised in interpreting some of the claims of exceptional prognostic classifier performance that have been reported in prominent biomedical journals in the past few years.

Clinical Trials as Topic↗