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PubMed2007

LongCriSP: a test for bump hunting in longitudinal data.

We propose an extension of the Harezlak and Heckman (J. Comput. Graph. Statist. 2001; 10(4): 713-729) test for detecting local extrema to the longitudinal data setting. We use penalized spline regression techniques (Statist. Sci. 1996; 11:89-102) to provide a computationally efficient method of testing for relatively large data sets. We estimate the p-values of our test, LongCriSP, with a smoothed bootstrap. Our simulation studies indicate that the test is generally conservative and has power exceeding 70 per cent at the alpha = 0.1 nominal level in most considered settings. Finally, we apply our testing procedure to the longitudinal measurements of body mass index of former prisoners of war in Vietnam and conclude that the mean population curve exhibits non-monotone behaviour.

Body Mass Index↗

PubMedDate not supplied

Statistical methods for estimating attributable risk from retrospective data.

This paper extends Levin's measure of attributable risk to adjust for confounding by aetiologic factors other than the exposure of interest. One can estimate this extended measure from case-control data provided either (i) from the control data one can estimate exposure prevalence within each stratum of the confounding factor; or (ii) one has additional information available concerning the confounder distribution and the stratum-specific disease rates. In both cases we give maximum likelihood estimates and their estimated asymptotic variances, and show them to be independent of the sampling design (matched vs. random). Computer simulations investigate the behaviour of these estimates and of three types of confidence intervals when sample size is small relative to the number of confounder strata. The simulations indicate that attributable risk estimates tend to be too low. The bias is not serious except when exposure prevalence is high among controls. In this case the estimates and their standard error estimates are also highly unstable. In general, the asymptotic standard error estimates performed quite well, even in small samples, and even when the true asymptotic standard error was too small. By contrast, the bootstrap estimate tended to be too large. None of the three confidence intervals proved superior in accuracy to the other two. Thus there appears no advantage in using the log-based interval suggested by Walter which is always longer than the simpler symmetric interval.

Adult↗

PubMed1989

Assessing diagnostic tests by a strictly proper scoring rule.

Evaluation of univariate quantitative diagnostic tests by strictly proper scoring rules is considered as an alternative to the traditional error rate measures. In principle, the posterior probability of disease as a function of the test value is estimated from training observations, and subsequently the score is assessed on a set of test samples. The same subjects may serve as training and test samples when the bootstrap procedure is applied for estimation of standard errors and correction of bias. The method is demonstrated using serum bile acids and bilirubin in patients with liver disease. The power for comparison of scores from two tests is compared with that from error rate measures for some typical situations.

Bile Acids and Salts↗

PubMed1989

Comparison of correlated correlations.

We consider a problem where kappa highly correlated variables are available, each being a candidate for predicting a dependent variable. Only one of the kappa variables can be chosen as a predictor and the question is whether there are significant differences in the quality of the predictors. We review several tests derived previously and propose a method based on the bootstrap. The motivating medical problem was to predict 24 hour proteinuria by protein-creatinine ratio measured at either 08:00, 12:00 or 16:00. The tests which we discuss are illustrated by this example and compared using a small Monte Carlo study.

Humans↗

PubMed1990

An application of the LFP survival model to smoking cessation data.

We use a limited failure population (LFP) model based on the Weibull distribution to model the times from initial abstinence to return to smoking for subjects enrolled in programmes to help them stop smoking. The model contains a third parameter that corresponds to the proportion of subjects who permanently abstain from smoking. The data are subject to both right and interval censoring. Furthermore, subjects receive treatment in groups, and individuals in the same group may provide correlated outcomes. Use of a maximum likelihood estimation procedure which assumes independent outcomes provides reasonable parameter estimates, but the corresponding standard errors tend to be too small, which results in tests with inflated type I error levels and confidence intervals that tend to be too narrow. We use a bootstrap procedure to obtain more reasonable values for the standard errors and to construct confidence intervals that more nearly achieve the stated coverage probabilities.

Confidence Intervals↗

PubMed1990

Model selection and the estimation of odds ratios in the presence of extraneous factors.

This paper deals with model selection and the estimation of odds ratios from cross-classified frequencies in the presence of extraneous factors. The odds ratio is estimated in different ways dependent on whether the extraneous factor is modelled as an effect modifier, a confounder, or neither. Routinely this choice is based on statistical tests of null hypotheses. By contrast, we propose selection of the model which is estimated to maximize the accuracy of the estimator of the odds ratio, on average. We demonstrate how a non-parametric bootstrap method can be used to carry out the selection, and illustrate the methodology using an example on use of oral contraceptives and myocardial infarction.

Adult↗

PubMed1991

A statistical method for assessing a threshold in epidemiological studies.

I describe a method for estimating and testing a threshold value in epidemiological studies. A threshold effect indicates an association between a risk factor and a defined outcome above the threshold value but none below it. An important field of application is occupational medicine where, for a lot of chemical compounds and other agents which are non-carcinogenic health hazards, so-called threshold limit values or TLVs are specified. The method is presented within the framework of the logistic regression model, which is widely used in the analysis of the relationship between some explanatory variables and a dependent dichotomous outcome. In most available programs for this and also for other models the concept of a threshold is disregarded. The method for assessing a threshold consists of an estimation procedure using the maximum-likelihood technique and a test procedure based on the likelihood-ratio statistic R, following under the null hypothesis (no threshold) a quasi one-sided chi 2 distribution with one degree of freedom. This use of this distribution is supported by a simulation study. The method is applied to data from an epidemiological study of the relationship between occupational dust exposure and chronic bronchitic reactions. The results are confirmed by bootstrap resampling.

Bronchitis↗

PubMed1991

Detection of outlying data in bioavailability/bioequivalence studies.

This paper considers the problem of detecting outlying data in bioavailability/bioequivalence studies. We define outlying subjects as those whose responses in bioavailability to all formulations differ from the rest of the subjects. We also define an outlying observation as the response in bioavailability of a subject to a particular formulation which is grossly different from the average bioavailability of that formulation calculated from all subjects. We propose two test procedures. The first, based on two-sample Hotelling T2, is to detect possible outlying subjects. The second, based on residuals from formulation means, is to identify possible outlying observations within subjects. Both procedures take into account the covariance structure of the responses to formulations, dependence of test statistics, and multiplicity of test procedures. We apply the Monte Carlo or bootstrap simulation to evaluate the sampling distributions of test statistics. An example from a 3-way crossover bioequivalence study illustrates the two procedures.

Biological Availability↗

PubMed1991

The unseen sample in cohort studies: estimation of its size and effect. Multicenter AIDS Cohort Study.

Recruitment of disease-free subjects into cohort studies and measurement of their time from exposure/infection to disease selectively excludes individuals (the unseen sample) who had earlier exposure and who have shorter times to disease. The unseen and observed samples may differ in other characteristics in addition to incubation period and exposure/infection time. For data with known truncation times, we develop non-parametric maximum likelihood estimates of the size, exposure/infection dates and distribution of incubation time in the unseen sample. We provide procedures to estimate and compensate for the biasing effects due to exclusion of the unseen sample in descriptive and survival analysis. We give consistency properties of these estimates and assess variability using bootstrap methods. One can use imputation to derive the above estimates from data with unknown truncation times that have been estimated parametrically. Application is made to an AIDS cohort study of over 5000 homosexual men. Important estimates obtained from this application are the annual seroconversion rates from 1978 to 1983, not otherwise obtainable in this study population.

Acquired Immunodeficiency Syndrome↗

PubMed1992

Analysis of aberrations in public health surveillance data: estimating variances on correlated samples.

The detection of unusual patterns in health data presents an important challenge to health workers interested in early identification of epidemics or important risk factors. A useful procedure for detection of aberrations is the ratio of a current report to some historic baseline. This work addresses the problem of finding the variance of such a ratio when the surveillance reports are correlated. Results show that, when estimating this variance or the variance of the sample mean from a series of observations with an estimated correlation structure, bootstrap and jackknife estimates may be overly optimistic. The delta method or a classical method may be more useful when such model dependence is inappropriate.

Analysis of Variance↗

PubMed1992

Estimating HIV prevalence and projecting AIDS incidence in the United States: a model that accounts for therapy and changes in the surveillance definition of AIDS.

The AIDS incubation distribution is changing in calendar time because of treatment and changes in the surveillance definition of AIDS. To obtain reliable estimates of HIV prevalence and projections of AIDS incidence in the 1990s using the method of backcalculation, we constructed an appropriate incubation distribution for each calendar date of infection. We parameterized the impact of treatment on the incubation distribution by specifying the relative hazard for AIDS in treated versus untreated people as a function of duration of HIV infection. To account for trends in the incubation distribution, we modelled the prevalence of treatment, the distribution of treatment onset times, and the impact of the revision of the AIDS surveillance definition in 1987. We selected and evaluated backcalculation models based on consistency with external information. We defined a 'plausible range' of estimates that took into account uncertainty about the natural incubation distribution and treatment efficacy, as well as bootstrap assessment of stochastic error. Using these methods, we projected that national United States AIDS incidence will plateau during 1991-1994 at over 50,000 cases per year. Projections exhibited substantial systematic uncertainty, and we calculated a plausible range for AIDS incidence in 1994 of 42,300 to 70,700 cases. An estimated 628,000 to 988,000 cumulative HIV infections occurred as of 1 January 1991. After accounting for AIDS mortality, we estimated that 484,000 to 844,000 people were living with HIV infection on 1 January 1991. Favourable trends in HIV incidence appeared in gay men and intravenous drug users. Plausible ranges for our estimates overlapped with those from a 'stage model' approach to incorporating treatment effects in backcalculations. Our approach, however, tended to yield smaller estimates of epidemic size, mainly because the parameters used with the stage model implied that more treatment was in use and that treatment was more effective than in our model.

Acquired Immunodeficiency Syndrome↗

PubMed1993

On population and individual bioequivalence.

In a traditional assessment of the bioequivalence of two formulations of a drug one compares the average bioavailability from the two formulations. Anderson and Hauck argued that in some situations it is not sufficient to demonstrate average bioequivalence, and they proposed a method for the assessment of what they called individual bioequivalence, which essentially is the comparison of the individual responses to the two drug formulations within subjects. In this paper we propose a unified strategy for the assessment of bioequivalence that encompasses new approaches to the assessment of both population bioequivalence, which is the comparison of the marginal or population distributions of bioavailabilities, and individual bioequivalence, which is the comparison of the conditional or within-subject distributions of bioavailabilities. The general idea is to use a comparison of the reference formulation to itself as the basis for the comparison of the test with the reference formulation. The new approaches overcome the main weakness of the current methods for the assessment of bioequivalence by considering the variability of bioavailabilities in addition to their means. The current methods for the assessment of bioequivalence, namely the conventional assessment of average bioequivalence and the proposal by Anderson and Hauck for the assessment of individual bioequivalence, emerge as special cases. One can evaluate the new bioequivalence criteria statistically by use of bootstrap confidence intervals.

Acetaminophen↗

PubMed1993

Further results on the non-parametric linear regression model in survival analysis.

This paper gives further developments of a non-parametric linear regression model in survival analysis. Three subjects are studied. First, martingale residuals, originally developed for the Cox model, are introduced for our linear model. Their theory is developed and they are shown to be useful for judging goodness of fit. The second focus of the paper is on the use of bootstrap replications to judge which features of the cumulative regression plots are likely to reflect real phenomena and not merely random variation. In particular, this is applied to judging whether the effect of a covariate disappears over time, a problem for which no formal test exists. The third subject is density type, or kernel, estimation of the regression functions themselves. This might give more direct information than the cumulative plots. The approaches are illustrated by data from a clinical trial of carcinoma of the oropharynx, and by survival times of grafts in renal patients.

Computer Simulation↗

PubMed1993

Mixture models and disease mapping.

The analysis and recognition of disease clustering in space and its representation on a map is one of the oldest problems in epidemiology. Some traditional methods of constructing such a map are presented. An alternative approach using mixture models to identify population heterogeneity and map construction within an empirical Bayes framework is described. For hepatitis B data from Berlin in 1989, a map is presented and the different methods are evaluated using a parametric bootstrap approach.

Bayes Theorem↗

PubMed1993

The relative importance of prognostic factors in studies of survival.

The relative importance of prognostic factors in regression can be measured either by standardized regression coefficients or by percentages of explained variation in a dependent variable. One advantage of using explained variation is the direct comparability of qualitative prognostic factors with others, or of groups of prognostic factors. The description of relative importance can be accomplished within marginal or partial effects analyses. It is demonstrated that it is possible not only to provide a descriptive ranking of prognostic factors according to their statistically determined importance, but also to make inferences concerning their relative importance, employing bootstrap techniques and procedures for multiple comparisons. The methods presented, which are new in the context of Cox regression, are exemplified by analyses of studies of lung cancer and breast cancer.

Adult↗

PubMedDate not supplied

Modelling transitional and joint marginal distributions in repeated categorical data.

When a repeated measures endpoint classifies people into several categories, marginal and transitional models provide two distinct approaches for data analysis. Marginal models estimate the probabilities of being in different categories over time. Transitional models estimate the probability of changing between any two given states during follow-up visits. This paper develops transitional and marginal models and applies them to a clinical trial of treatments of opiate addiction. The primary outcome was the presence or absence of opiates in a thrice weekly urine test, administered for 17 weeks. Subjects frequently miss visits, however, and in effect respond in one of three ways to a visit: missing, opiates present or opiates absent. Thus we have three possible states. Our transitional model conditions on the current state and models the transition from state k to one of the other (0, ..., K-1) states using a mutinomial logit model. This model generalizes previous work of Muenz and Rubinstein. Significant covariates in this model are predictive of state changes. Our marginal model views the state at each time point, rather than the transitions, as the primary response. Here we model the probability of being in state k with a multinomial logit model. Correlation within individuals over visits can be handled by applying the approach of Zeger and Liang or the bootstrap. Significant covariates in this model can include more 'global' summaries of a person such as extent of previous opiate use. Both marginal and transitional models are needed to provide a complete description of an individual's behaviour over time since global summaries might not affect transitions. Of particular substantive interest is how the opiate treatments affect both the marginal and transition probabilities.

Buprenorphine↗

PubMedDate not supplied

Testing for differences in changes in the presence of censoring: parametric and non-parametric methods.

Some commonly used parametric and non-parametric methods for analysing repeated measures with incomplete observations are briefly reviewed. The performances of these methods in the presence of completely random, as well as informative censoring are compared in simulated experiments generated under the linear random effects model with parameter values derived from realistic examples. The effects of some moderate model deviations are also compared. The results indicate that in the presence of informative censoring, the usual parametric and nonparametric methods derived under the assumption of random censoring could either suffer severe loss of power or provide false positive results. The conditional linear model for informative censoring when used in conjunction with the bootstrap variance estimation procedure performed well under both random and informative censoring mechanisms. The non-parametric procedure obtained by ranking the individual summary statistics, although not as efficient as the conditional linear model with robust variance, also performed relatively well in most situations. Therefore, in situations in which informative censoring is likely to occur it is important to select the proper method of analysis to test for the informativeness of censoring and to account for its effects.

Bias↗

PubMed1994

Smoothing grouped bivariate data to obtain the incubation period distribution of AIDS.

We use a penalized likelihood approach to obtain a smooth estimate of a bivariate distribution from grouped data where each observation consists of a region in a plane. The purpose of the analysis is to estimate the incubation period distribution of AIDS from the Multicenter AIDS Cohort Study, a prevalent cohort of homosexual men. In this article we illustrate the usefulness of the penalized likelihood approach. We also discuss the use of a cross-validation and a Bayesian scheme to choose the smoothing parameters and bootstrap samples to assess uncertainty.

AIDS Serodiagnosis↗