On the Comparison of Umbrella Pattern Treatment Means with a Control Mean

This paper is concerned with comparing several increasing dose levels (treatments) with a zero dose control when the prior information about the umbrella pattern treatment means is available. The problem of testing whether there is at least one treatment which is better than the control is considered. Multiple test procedures are then proposed for deciding treatments (if any) which are better than the control. Some approximate criticial values of the proposed tests are reported. The results of a Monte Carlo power study are presented.     

Multiple Testing for Detecting Efficient Dose Steps

In the comparison of various dose levels it can often be assumed that the parameters to be tested follow an order restriction. Two closed multiple test procedures for detecting the highest dose level still providing a shift in the response distribution as compared to the adjacent lower dose level is proposed. One is based on one sided comparisons between neighbouring doses, the other uses Helmert-type contrast statistics. If a sequence of testing is fixed in advance the multiple test can be suitably modified. The power of the procedures is simulated under the assumption of normally distributed responses for various constellations of the dose means. It is compared with the power of a general Holm-type procedure discussed in BUDDE & BAUER (1989).     

Combining One‐sided and Two‐sided Confidence Interval Procedures for Successive Comparisons of Ordered Treatment Effects

Lee and Spurrier (1995) present one‐sided and two‐sided confidence interval procedures for making successive comparisons between ordered treatments. Their procedures have important applications for problems where the treatments can be assumed to satisfy a simple ordering, such as for a sequence of increasing dose‐levels of a drug. The two‐sided procedure provides both upper and lower bounds on the differences between successive treatments, whereas the one‐sided procedure only provides lower bounds on these differences. However, the one‐sided procedure allows sharper inferences regarding which treatments can be declared to be better than their previous ones. In this paper we apply the results obtained in Hayter , Miwa , and Liu (2000) to develop a new procedure which combines the good aspects of both the one‐sided and the two‐sided procedures. This new procedure maintains the inferential sensitivity of the one‐sided procedure while also providing both upper and lower bounds on the differences between successive treatments. Some new critical points are needed which are tabulated for the balanced case where the sample sizes are all equal. The application of the new procedure is illustrated with an example.     

More Powerful Likelihood Ratio Tests for Isotonic Binomial Proportions

Binomial group testing involves pooling individuals into groups and observing a binary response on each group. Results from the group tests can then be used to draw inference about population proportions. Its use as an experimental design has received much attention in recent years, especially in public‐health screening experiments and vector‐transfer designs in plant pathology. We investigate the benefits of group testing in situations wherein one desires to test whether or not probabilities are increasingly ordered across the levels of an observed qualitative covariate, i.e., across strata of a population or among treatment levels. We use a known likelihood ratio test for individual testing, but extend its use to group‐testing situations to show the increases in power conferred by using group testing when operating in this constrained parameter space. We apply our methods to data from an HIV study involving male subjects classified as intraveneous drug users.     

Assessing the amount of heterogeneity in random-effects meta-analysis

In a random-effects meta-analysis, a new confidence interval for the heterogeneity parameter is proposed. With this interval, the amount of heterogeneity in a meta-analysis can be assessed so that it can be judged whether the pooling of the estimates is meaningful. Through suitable corrections of the lower bound, based on the treatment effect measure of interest, the resulting interval yields satisfactory results with respect to the predefined confidence coefficient. Lower and upper bound of the interval can be used for one-sided hypothesis testing on the amount of the underlying between-trial variability.     

Estimation and confidence regions for multi-dimensional effective dose

The problem of finding confidence regions for multiple predictor variables corresponding to given expected values of a response variable has not been adequately resolved. Motivated by an example from a study on hyperbaric exposure using a logistic regression model, we develop a conceptual framework for the estimation of the multi-dimensional effective dose for binary outcomes. The k -dimensional effective dose can be determined by conditioning on k - 1 components and solving for the last component as a conditional univariate effective dose. We consider various approaches for calculating confidence regions for the multi-dimensional effective dose and compare them via a simulation study for a range of possible designs. We analyze data related to decompression sickness to illustrate our procedure. Our results provide a practical approach to finding confidence regions for predictor variables for a given response value.     

Simultaneous confidence regions for closed tests,including Holm‐, Hochberg‐, and Hommel‐related procedures

The derivation of simultaneous confidence regions for some multiple‐testing procedures (MTPs) of practical interest has remained an unsolved problem. This is the case, for example, for Hochberg's step‐up MTP and Hommel's more powerful MTP that is neither a step‐up nor a step‐down procedure. It is shown in this article how the direct approach used previously by the author to construct confidence regions for certain closed‐testing procedures (CTPs) can be extended to a rather general setup. The general results are then applied to a situation with one‐sided inferences and CTPs belonging to a class studied by Wei Liu. This class consists of CTPs based on ordered marginal p‐values. It includes Holm's, Hochberg's, and Hommel's MTPs. A property of the confidence regions derived for these three MTPs is that no confidence assertions sharper than rejection assertions can be made unless all null hypotheses are rejected. Briefly, this is related to the fact that these MTPs are quite powerful. The class of CTPs considered includes, however, also MTPs related to Holm's, Hochberg's, and Hommel's MTPs that are less powerful but are such that confidence assertions sharper than rejection assertions are possible even if not all null hypotheses are rejected. One may thus choose and prespecify such an MTP, though this is at the cost of less rejection power.     

Bayesian inference for disease prevalence using negative binomial group testing

Group testing, also known as pooled testing, and inverse sampling are both widely used methods of data collection when the goal is to estimate a small proportion. Taking a Bayesian approach, we consider the new problem of estimating disease prevalence from group testing when inverse (negative binomial) sampling is used. Using different distributions to incorporate prior knowledge of disease incidence and different loss functions, we derive closed form expressions for posterior distributions and resulting point and credible interval estimators. We then evaluate our new estimators, on Bayesian and classical grounds, and apply our methods to a West Nile Virus data set.     

Feasibility of setting up generic alert levels for maximum skin dose in fluoroscopically guided procedures

PurposeThe feasibility of setting-up generic, hospital-independent dose alert levels to initiate vigilance on possible skin injuries in interventional procedures was studied for three high-dose procedures (chemoembolization (TACE) of the liver, neuro-embolization (NE) and percutaneous coronary intervention (PCI)) in 9 European countries.MethodsGafchromic® films and thermoluminescent dosimeters (TLD) were used to determine the Maximum Skin Dose (MSD). Correlation of the online dose indicators (fluoroscopy time, kerma- or dose-area product (KAP or DAP) and cumulative air kerma at interventional reference point (K_a,r)) with MSD was evaluated and used to establish the alert levels corresponding to a MSD of 2 Gy and 5 Gy. The uncertainties of alert levels in terms of DAP and K_a,r, and uncertainty of MSD were calculated.ResultsAbout 20–30% of all MSD values exceeded 2 Gy while only 2–6% exceeded 5 Gy. The correlations suggest that both DAP and K_a,r can be used as a dose indicator for alert levels (Pearson correlation coefficient p mostly >0.8), while fluoroscopy time is not suitable (p mostly <0.6). Generic alert levels based on DAP (Gy cm²) were suggested for MSD of both 2 Gy and 5 Gy (for 5 Gy: TACE 750, PCI 250 and NE 400). The suggested levels are close to the lowest values published in several other studies. The uncertainty of the MSD was estimated to be around 10–15% and of hospital-specific skin dose alert levels about 20–30% (with coverage factor k = 1).ConclusionsThe generic alert levels are feasible for some cases but should be used with caution, only as the first approximation, while hospital-specific alert levels are preferred as the final approach.     

A Simple Testing Procedure “Control versus k Treatments” for One-sided Ordered Alternatives,with Application in Toxicology

A simple testing procedure “control versus k treatments” for one-sided ordered alternatives for univariate, continuous variables is given. With a simulation study both the first kind risk a and the power behaviour under several distributions, expected value profiles, sample sizes and a levels are shown.     

Benchmark dose calculation from epidemiological data

A threshold for dose-dependent toxicity is crucial for standards setting but may not be possible to specify from empirical studies. Crump (1984) instead proposed calculating the lower statistical confidence bound of the benchmark dose, which he defined as the dose that causes a small excess risk. This concept has several advantages and has been adopted by regulatory agencies for establishing safe exposure limits for toxic substances such as mercury. We have examined the validity of this method as applied to an epidemiological study of continuous response data associated with mercury exposure. For models that are linear in the parameters, we derived an approximative expression for the lower confidence bound of the benchmark dose. We find that the benchmark calculations are highly dependent on the choice of the dose-effect function and the definition of the benchmark dose. We therefore recommend that several sets of biologically relevant default settings be used to illustrate the effect on the benchmark results and to stimulate research that will guide an a priori choice of proper default settings.     

Confidence bands for low-dose risk estimation with quantal response data

We study the use of simultaneous confidence bands for low-dose risk estimation with quantal response data, and derive methods for estimating simultaneous upper confidence limits on predicted extra risk under a multistage model. By inverting the upper bands on extra risk, we obtain simultaneous lower bounds on the benchmark dose (BMD). Monte Carlo evaluations explore characteristics of the simultaneous limits under this setting, and a suite of actual data sets are used to compare existing methods for placing lower limits on the BMD.     

Combining multiple comparisons and modeling techniques in dose-response studies

The analysis of data from dose-response studies has long been divided according to two major strategies: multiple comparison procedures and model-based approaches. Model-based approaches assume a functional relationship between the response and the dose, taken as a quantitative factor, according to a prespecified parametric model. The fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose-response model. Multiple comparison procedures regard the dose as a qualitative factor and make very few, if any, assumptions about the underlying dose-response model. The primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect. One approach is to evaluate the significance of contrasts between different dose levels, while preserving the family-wise error rate. Such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation. We describe a unified strategy to the analysis of data from dose-response studies which combines multiple comparison and modeling techniques. We assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose-response curve, while preserving the family-wise error rate. The selected model is then used to provide inference on adequate doses.     

Maximally efficient two-stage screening

In DNA library screening, blood testing, and monoclonal antibody generation, significant savings in the number of assays can be realized by employing group sampling. Practical considerations often limit the number of stages of group testing that can be performed. We address situations in which only two stages of testing are used. We define efficiency to be the expected number of positives isolated per assay performed and assume gold-standard tests with unit sensitivity and specificity. Although practical tests never are golden, polymerase chain reaction (PCR) methods provide procedures for screening recombinant libraries that are strongly selective yet retain high sensitivity even when samples are pooled. Also, results for gold-standard tests serve as bounds on the performance of practical testing procedures. First we derive formulas for the efficiency of certain extensions of the popular rows-and-columns technique. Then we derive an upper bound on the efficiency of any two-stage strategy that lies well below the classical upper bound for situations with no constraint on the number of stages. This establishes that a restriction to only two stages necessitates performing many more assays than efficient multistage procedures need. Next, we specialize the bound to cases in which each item belonging only to pools that tested positive in stage 1 must be tested individually in stage 2. The specialized bound for such positive procedures is tight because we show that an appropriate multidimensional extension of the rows-and-columns technique achieves it. We also show that two-stage positive procedures in which the stage-1 groups are selected at random perform suboptimally, thereby establishing that efficient tests must be structured carefully.     

Simultaneous confidence sets for several effective doses

Construction of simultaneous confidence sets for several effective doses currently relies on inverting the Scheffé type simultaneous confidence band, which is known to be conservative. We develop novel methodology to make the simultaneous coverage closer to its nominal level, for both two‐sided and one‐sided simultaneous confidence sets. Our approach is shown to be considerably less conservative than the current method, and is illustrated with an example on modeling the effect of smoking status and serum triglyceride level on the probability of the recurrence of a myocardial infarction.     

Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests

The confirmatory analysis of pre-specified multiple hypotheses has become common in pivotal clinical trials. In the recent past multiple test procedures have been developed that reflect the relative importance of different study objectives, such as fixed sequence, fallback, and gatekeeping procedures. In addition, graphical approaches have been proposed that facilitate the visualization and communication of Bonferroni-based closed test procedures for common multiple test problems, such as comparing several treatments with a control, assessing the benefit of a new drug for more than one endpoint, combined non-inferiority and superiority testing, or testing a treatment at different dose levels in an overall and a subpopulation. In this paper, we focus on extended graphical approaches by dissociating the underlying weighting strategy from the employed test procedure. This allows one to first derive suitable weighting strategies that reflect the given study objectives and subsequently apply appropriate test procedures, such as weighted Bonferroni tests, weighted parametric tests accounting for the correlation between the test statistics, or weighted Simes tests. We illustrate the extended graphical approaches with several examples. In addition, we describe briefly the gMCP package in R, which implements some of the methods described in this paper.     

Overall asthma control achieved with budesonide/formoterol maintenance and reliever therapy for patients on different treatment steps

Background

Adjusting medication for uncontrolled asthma involves selecting one of several options from the same or a higher treatment step outlined in asthma guidelines. We examined the relative benefit of introducing budesonide/formoterol (BUD/FORM) maintenance and reliever therapy (Symbicort SMART^® Turbuhaler^®) in patients previously prescribed treatments from Global Initiative for Asthma (GINA) Steps 2, 3 or 4.

Methods

This is a post hoc analysis of the results of five large clinical trials (>12000 patients) comparing BUD/FORM maintenance and reliever therapy with other treatments categorised by treatment step at study entry. Both current clinical asthma control during the last week of treatment and exacerbations during the study were examined.

Results

At each GINA treatment step, the proportion of patients achieving target levels of current clinical control were similar or higher with BUD/FORM maintenance and reliever therapy compared with the same or a higher fixed maintenance dose of inhaled corticosteroid/long-acting β₂-agonist (ICS/LABA) (plus short-acting β₂-agonist [SABA] as reliever), and rates of exacerbations were lower at all treatment steps in BUD/FORM maintenance and reliever therapy versus same maintenance dose ICS/LABA (P < 0.01) and at treatment Step 4 versus higher maintenance dose ICS/LABA (P < 0.001). BUD/FORM maintenance and reliever therapy also achieved significantly higher rates of current clinical control and significantly lower exacerbation rates at most treatment steps compared with a higher maintenance dose ICS + SABA (Steps 2-4 for control and Steps 3 and 4 for exacerbations). With all treatments, the proportion of patients achieving current clinical control was lower with increasing treatment steps.

Conclusions

BUD/FORM maintenance and reliever therapy may be a preferable option for patients on Steps 2 to 4 of asthma guidelines requiring a more effective treatment and, compared with other fixed dose alternatives, is most effective in the higher treatment steps.     

Is a larger refuge always better? Dispersal and dose in pesticide resistance evolution

The evolution of resistance against pesticides is an important problem of modern agriculture. The high‐dose/refuge strategy, which divides the landscape into treated and nontreated (refuge) patches, has proven effective at delaying resistance evolution. However, theoretical understanding is still incomplete, especially for combinations of limited dispersal and partially recessive resistance. We reformulate a two‐patch model based on the Comins model and derive a simple quadratic approximation to analyze the effects of limited dispersal, refuge size, and dominance for high efficacy treatments on the rate of evolution. When a small but substantial number of heterozygotes can survive in the treated patch, a larger refuge always reduces the rate of resistance evolution. However, when dominance is small enough, the evolutionary dynamics in the refuge population, which is indirectly driven by migrants from the treated patch, mainly describes the resistance evolution in the landscape. In this case, for small refuges, increasing the refuge size will increase the rate of resistance evolution. Our analysis distils major driving forces from the model, and can provide a framework for understanding directional selection in source‐sink environments.     

Risk assessment for quantitative responses using a mixture model

A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment than others. A mixture model has traditionally been proposed to describe the distribution of responses in treatment groups for such experiments. Using a mixture dose-response model, we derive an upper confidence limit on additional risk, defined as the excess risk over the background risk due to an added dose. Our focus will be on experiments with continuous responses for which risk is the probability of an adverse effect defined as an event that is extremely rare in controls. The asymptotic distribution of the likelihood ratio statistic is used to obtain the upper confidence limit on additional risk. The method can also be used to derive a benchmark dose corresponding to a specified level of increased risk. The EM algorithm is utilized to find the maximum likelihood estimates of model parameters and an extension of the algorithm is proposed to derive the estimates when the model is subject to a specified level of added risk. An example is used to demonstrate the results, and it is shown that by using the mixture model a more accurate measure of added risk is obtained.