Stepwise Procedures under Unknown Variances for Toxicological Evaluation

Toxicological study is of practical importance in modern drug development. Proper statistical methodologies for toxicological evaluation of new developed drugs are undoubtedly necessary. In toxicological studies, it is practically desirable for a method to not declare the safety of a developed drug at a higher dosage prior to the declaration of the safety at lower dosages. Hsu and Berger 's stepwise confidence interval method was recently proposed for this purpose. Unfortunately, their procedure necessitates the homogeneity of variances among dosages, which is seldom satisfied in practice. In this article, via the application of the Stein 's two‐stage sampling method, we propose a stepwise confidence interval procedure for the same task without the homoscedasticity restriction. In addition, our procedure is shown to control its family‐wise type I error rate at the pre‐chosen nominal level. A simulation study will be conducted to compare our method, Hsu and Berger 's stepwise confidence interval method, and a single stage stepwise testing procedure based on Welch 's approximation. Our procedure is empirically shown to outperform Hsu and Berger 's procedure under heteroscedasticity and perform similarly with Welch 's procedure. An example will be used to illustrate our method.     

A Revisit on Comparing the Asymptotic Interval Estimators of Odds Ratio in a Single 2 × 2 Table

It is well known that Cornfield 's confidence interval of the odds ratio with the continuity correction can mimic the performance of the exact method. Furthermore, because the calculation procedure of using the former is much simpler than that of using the latter, Cornfield 's confidence interval with the continuity correction is highly recommended by many publications. However, all these papers that draw this conclusion are on the basis of examining the coverage probability exclusively. The efficiency of the resulting confidence intervals is completely ignored. This paper calculates and compares the coverage probability and the average length for Woolf s logit interval estimator, Gart 's logit interval estimator of adding 0.50, Cornfield 's interval estimator with the continuity correction, and Cornfield 's interval estimator without the continuity correction in a variety of situations. This paper notes that Cornfield 's interval estimator with the continuity correction is too conservative, while Cornfield 's method without the continuity correction can improve efficiency without sacrificing the accuracy of the coverage probability. This paper further notes that when the sample size is small (say, 20 or 30 per group) and the probability of exposure in the control group is small (say, 0.10) or large (say, 0.90), using Cornfield 's method without the continuity correction is likely preferable to all the other estimators considered here. When the sample size is large (say, 100 per group) or when the probability of exposure in the control group is moderate (say, 0.50), Gart 's logit interval estimator is probably the best.     

Confidence Intervals for Microbial Density Using Serial Dilutions with MPN Estimates

An alteration to Woodward's methods is recommended for deriving a 1 — α confidence interval for microbial density using serial dilutions with most-probable-number (MPN) estimates. Outcomes of the serial dilution test are ordered by their MPNs. A lower limit for the confidence interval corresponding to an outcome y is the density for which y and all higher ordered outcomes have total probability α/2. An upper limit is derived in the analogous way. An alteration increases the lowest lower limits and decreases the highest upper limits. For comparison, a method that is optimal in the sense of null hypothesis rejection is described. This method ranks outcomes dependent upon the microbial density in question, using proportional first derivatives of the probabilities. These and currently used methods are compared. The recommended method is shown to be more desirable in certain respects, although resulting in slightly wider confidence intervals than De Man's (1983) method.     

Confidence Intervals for the Risk Ratio in Cohort Studies under Inverse Sampling

Three simple interval estimates for the risk ratio in inverse sampling are considered. The first two interval estimates are derived on the basis of Fieller's Theorem and the delta method with the logarithmic transformation, respectively. The third interval estimate is derived on the basis of an F-test statistic proposed by BENNETT (1981) for testing equal probabilities of a disease between two comparison groups when the disease is rare. To evaluate the performance of these three methods, a Monte Carlo simulation is used to compare the actual coverage probability with the nominal confidence level for each method and to estimate the expected length of the corresponding confidence interval in a variety of situations. On the basis of the results found in the simulation, we have concluded that the method with the logarithmic transformation is either equivalent to or better than the other two methods for all situations considered here.     

An Exact Confidence Interval for the Ratio of Two Related Proportions

I propose an exact confidence interval for the ratio of two proportions when the proportions are not independent. One application is to estimate the population prevalence using a screening test with perfect specificity but imperfect sensitivity. The population prevalence is the ratio of the observed prevalence divided by the test's sensitivity. I describe a method to calculate exact confidence intervals for this problem and compare these results with approximate confidence intervals given previously.     

Empirical nonparametric bootstrap strategies in quantitative trait loci mapping: conditioning on the genetic model.

Several nonparametric bootstrap methods are tested to obtain better confidence intervals for the quantitative trait loci (QTL) positions, i.e., with minimal width and unbiased coverage probability. Two selective resampling schemes are proposed as a means of conditioning the bootstrap on the number of genetic factors in our model inferred from the original data. The selection is based on criteria related to the estimated number of genetic factors, and only the retained bootstrapped samples will contribute a value to the empirically estimated distribution of the QTL position estimate. These schemes are compared with a nonselective scheme across a range of simple configurations of one QTL on a one-chromosome genome. In particular, the effect of the chromosome length and the relative position of the QTL are examined for a given experimental power, which determines the confidence interval size. With the test protocol used, it appears that the selective resampling schemes are either unbiased or least biased when the QTL is situated near the middle of the chromosome. When the QTL is closer to one end, the likelihood curve of its position along the chromosome becomes truncated, and the nonselective scheme then performs better inasmuch as the percentage of estimated confidence intervals that actually contain the real QTL''s position is closer to expectation. The nonselective method, however, produces larger confidence intervals. Hence, we advocate use of the selective methods, regardless of the QTL position along the chromosome (to reduce confidence interval sizes), but we leave the problem open as to how the method should be altered to take into account the bias of the original estimate of the QTL''s position.     

Generalized Confidence Intervals for Ratios of Regression Coefficients with Applications to Bioassays

The problem of constructing a confidence interval for the ratio of two regression coefficients is addressed in the context of multiple regression. The concept of a Generalized Confidence Interval is used, and the resulting confidence interval is shown to perform well in terms of coverage probability. The proposed methodology always results in an interval, unlike the confidence region generated from Fieller's theorem. The procedure can easily be implemented for parallel‐line assays, slope‐ratio assays, and quantal assays under a probit model. Furthermore, this approach can also be extended to compute confidence intervals based on data from multiple bioassays. The results are illustrated using several examples.     

Notes on interval estimation of the gamma correlation under stratified random sampling

We have developed four asymptotic interval estimators in closed forms for the gamma correlation under stratified random sampling, including the confidence interval based on the most commonly used weighted‐least‐squares (WLS) approach (CIWLS), the confidence interval calculated from the Mantel‐Haenszel (MH) type estimator with the Fisher‐type transformation (CIMHT), the confidence interval using the fundamental idea of Fieller's Theorem (CIFT) and the confidence interval derived from a monotonic function of the WLS estimator of Agresti's α with the logarithmic transformation (MWLSLR). To evaluate the finite‐sample performance of these four interval estimators and note the possible loss of accuracy in application of both Wald's confidence interval and MWLSLR using pooled data without accounting for stratification, we employ Monte Carlo simulation. We use the data taken from a general social survey studying the association between the income level and job satisfaction with strata formed by genders in black Americans published elsewhere to illustrate the practical use of these interval estimators.     

Confidence Intervals of the Simple Difference between the Proportions of a Primary Infection and a Secondary Infection,Given the Primary Infection

This paper discusses interval estimation of the simple difference (SD) between the proportions of the primary infection and the secondary infection, given the primary infection, by developing three asymptotic interval estimators using Wald's test statistic, the likelihood‐ratio test, and the basic principle of Fieller's theorem. This paper further evaluates and compares the performance of these interval estimators with respect to the coverage probability and the expected length of the resulting confidence intervals. This paper finds that the asymptotic confidence interval using the likelihood ratio test consistently performs well in all situations considered here. When the underlying SD is within 0.10 and the total number of subjects is not large (say, 50), this paper further finds that the interval estimators using Fieller's theorem would be preferable to the estimator using the Wald's test statistic if the primary infection probability were moderate (say, 0.30), but the latter is preferable to the former if this probability were large (say, 0.80). When the total number of subjects is large (say, ≥200), all the three interval estimators perform well in almost all situations considered in this paper. In these cases, for simplicity, we may apply either of the two interval estimators using Wald's test statistic or Fieller's theorem without losing much accuracy and efficiency as compared with the interval estimator using the asymptotic likelihood ratio test.     

Measurement of activity of urea resistant neutrophil alkaline phosphatase as an antenatal screening test for Down's syndrome.

OBJECTIVE--To investigate the value of measuring maternal urea resistant neutrophil alkaline phosphatase activity as an antenatal screening test for Down''s syndrome. DESIGN--Case-control study of blood samples collected at nine to 27 weeks of pregnancy. SETTING--Antenatal clinics in London and Oxford. PATIENTS--72 Women whose fetuses had been diagnosed by amniocentesis or chorionic villus sampling as having Down''s syndrome and 156 women whose fetuses did not have the syndrome. Only singleton pregnancies were studied. MAIN OUTCOME MEASURE--Activity of urea resistant neutrophil alkaline phosphatase measured cytochemically. RESULTS--The median enzyme activity in the index patients was 1.65 times the expected median for the controls at the same duration of pregnancy (p less than 0.0001; 95% confidence interval 1.56 to 1.74). A cut off value that identified the 5% of control patients with the highest activities yielded a rate of detection of Down''s syndrome of 79% (95% confidence interval 70 to 89%). CONCLUSION--Activity of urea resistant neutrophil alkaline phosphatase is an effective maternal blood marker for Down''s syndrome. Its use in antenatal screening could lead to a substantial improvement in the detection of this disorder. Before introducing the test into routine medical practice it will have to be automated so that it can be used on a large scale and is less subjective.     

Direct and indirect estimation of the sex ratio of mutation frequencies in hemophilia A.

Carrier detection tests were carried out in 119 families with hemophilia A by using the data obtained with current DNA techniques (e.g., RFLP analysis and direct identification of mutations), conventional carrier detection tests (e.g., factor VIII:C and von Willebrand factor antigen), and pedigree information. On the basis of this data, we estimated the sex ratio of mutation frequencies with three completely different methods and compared the results. Since the classical indirect method derived from Haldane is substantially influenced by reproductive fitness (f), the sex ratio of mutation frequencies was estimated for both f = .3 and f = .5, resulting in a male:female mutation ratio of 5.37 (95% confidence interval 2.16-13.02) and 3.26 (95% confidence interval 0.97-8.73), respectively. According to the equilibrium-independent indirect method formulated by Rosendaal et al., the male:female ratio was estimated to be 3.4 (95% confidence interval 1.18-8.81). Since current DNA techniques provide information on the grandparental origin of the patient''s X chromosome, we were twice able to estimate directly the male:female mutation ratio as 15:1, by using the quotients of mutation origin (maternal grandfather/maternal grandmother and maternal grandfather/patient''s mother, respectively). Application of the Fisher test shows that the male mutation rate is higher than the female rate (P = 8.55 x 10(-7). Since all three completely different approaches unequivocally showed a higher male than female mutation frequency, this should be considered to be an established fact in calculating the risk in hemophilia A families.     

SPECIES LIMITS IN THE LONG-BILLED PIPITS OF THE SOUTHERN AFROTROPICS

Clancey, P. A. 1985. Species limits in the long-billed pipits of the southern Afrotropics. Ostrich 56:157-169.

It has long been appreciated by systematists that the present polytypic species of Longbilled Pipit Anthus similis of the Afrotropics is composite, the populations inhabiting deciduous Miombo (Brachystegia) woodland south of the equator being specifically distinct from those of drier, more open and often mountainous terrain, to the south and northeast. Resolution of the complex requires the recognition of three species: the Longbilled Pipit Anthus similis Jerdon, the Wood Pipit A. nyassae Neumann and Jackson's Pipit A. latistriatus Jackson in which a new subspecies is proposed. The African Richard's Pipit A. cinna-momeus Rüppell is marginally involved. The current complicated mosaic of sympatric polytypic species of the Miombo woodlands biome extending from western Zaïre and Angola, to southern Tanzania, Moçambique and Zimbabwe results from a situation in which specifically discrete descendants of a primary colonization are sympatric with populations of a lineage resulting from a second colonization. The ancestral stocks are considered to be of Eurasian origin. They have become modified in Africa since the Pleistocene by the interaction of climatic and vegetational oscillations, dieback, subspeciation and adaptive convergence. The Mountain Pipit A. hoeschi of the southeastern highland massif of Africa is seen as a remotely detached isolate stemming from the same ancestral stock as the contemporary Jackson's Pipit A. latistriatus. A revised systematic arrangement of the taxa involved in this enquiry is proposed.     

Precision Intervals for Estimates of the Difference in Success Rates for Binary Random Variables Based on the Permutation Principle

Fisher's exact test is a very commonly applied test in clinical trials with a binary outcome variable (e.g. success/failure). However confidence statements about the difference of success rates are usually based on the normal approximation. This may sometimes lead to the confusing statement that the test is statistically significant at a prespecified level while the corresponding confidence interval includes the zero difference and vice versa. Here, we construct precision intervals for the difference of success rates from two independent samples based on the permutation principle which are in perfect agreement with the discrete (permutation) test and compare it to examples from the literature. APL programs are provided.     

Confidence Intervals for Population Allele Frequencies: The General Case of Sampling from a Finite Diploid Population of Any Size

The estimation of population allele frequencies using sample data forms a central component of studies in population genetics. These estimates can be used to test hypotheses on the evolutionary processes governing changes in genetic variation among populations. However, existing studies frequently do not account for sampling uncertainty in these estimates, thus compromising their utility. Incorporation of this uncertainty has been hindered by the lack of a method for constructing confidence intervals containing the population allele frequencies, for the general case of sampling from a finite diploid population of any size. In this study, we address this important knowledge gap by presenting a rigorous mathematical method to construct such confidence intervals. For a range of scenarios, the method is used to demonstrate that for a particular allele, in order to obtain accurate estimates within 0.05 of the population allele frequency with high probability (%), a sample size of is often required. This analysis is augmented by an application of the method to empirical sample allele frequency data for two populations of the checkerspot butterfly (Melitaea cinxia L.), occupying meadows in Finland. For each population, the method is used to derive % confidence intervals for the population frequencies of three alleles. These intervals are then used to construct two joint % confidence regions, one for the set of three frequencies for each population. These regions are then used to derive a % confidence interval for Jost''s D, a measure of genetic differentiation between the two populations. Overall, the results demonstrate the practical utility of the method with respect to informing sampling design and accounting for sampling uncertainty in studies of population genetics, important for scientific hypothesis-testing and also for risk-based natural resource management.     

Sample size determination for confidence intervals on the population mean and on the difference between two population means

Sample size determination is usually based on the premise that a hypothesis test is to be used. A confidence interval can sometimes serve better than a hypothesis test. In this paper a method is presented for sample size determination based on the premise that a confidence interval for a simple mean, or for the difference between two means, with normally distributed data is to be used. For this purpose, a concept of power relevant to confidence intervals is given. Some useful tables giving required sample size using this method are also presented.     

An Empirical Method for Establishing Positional Confidence Intervals Tailored for Composite Interval Mapping of QTL

Background

Improved genetic resolution and availability of sequenced genomes have made positional cloning of moderate-effect QTL realistic in several systems, emphasizing the need for precise and accurate derivation of positional confidence intervals (CIs) for QTL. Support interval (SI) methods based on the shape of the QTL likelihood curve have proven adequate for standard interval mapping, but have not been shown to be appropriate for use with composite interval mapping (CIM), which is one of the most commonly used QTL mapping methods.

Results

Based on a non-parametric confidence interval (NPCI) method designed for use with the Haley-Knott regression method for mapping QTL, a CIM-specific method (CIM-NPCI) was developed to appropriately account for the selection of background markers during analysis of bootstrap-resampled data sets. Coverage probabilities and interval widths resulting from use of the NPCI, SI, and CIM-NPCI methods were compared in a series of simulations analyzed via CIM, wherein four genetic effects were simulated in chromosomal regions with distinct marker densities while heritability was fixed at 0.6 for a population of 200 isolines. CIM-NPCIs consistently capture the simulated QTL across these conditions while slightly narrower SIs and NPCIs fail at unacceptably high rates, especially in genomic regions where marker density is high, which is increasingly common for real studies. The effects of a known CIM bias toward locating QTL peaks at markers were also investigated for each marker density case. Evaluation of sub-simulations that varied according to the positions of simulated effects relative to the nearest markers showed that the CIM-NPCI method overcomes this bias, offering an explanation for the improved coverage probabilities when marker densities are high.

Conclusions

Extensive simulation studies herein demonstrate that the QTL confidence interval methods typically used to positionally evaluate CIM results can be dramatically improved by accounting for the procedural complexity of CIM via an empirical approach, CIM-NPCI. Confidence intervals are a critical measure of QTL utility, but have received inadequate treatment due to a perception that QTL mapping is not sufficiently precise for procedural improvements to matter. Technological advances will continue to challenge this assumption, creating even more need for the current improvement to be refined.     

Incidence of leukaemia in young people in the vicinity of Hinkley Point nuclear power station, 1959-86.

The incidence of leukaemia and non-Hodgkin''s lymphoma in young people (aged under 25) living in a predefined area around the nuclear power station at Hinkley Point, Somerset, was examined for the period 1959-86 by using cancer registry data. During the period since Hinley Point began operations--that is, 1964-86--there were 19 cases in the area compared with 10.4 expected from national rates, giving a standardised registration ratio of 1.82 (95% confidence interval 1.10 to 2.85). The incidence in the rest of Somerset was also high, however (standardised registration ratio 1.18; 95% confidence interval 0.98 to 1.41), and the high rate around Hinkley Point may simply have been reflecting the high local incidence (ratio of the two standardised registration ratio''s 1.54; 95% confidence interval 0.90 to 2.52). Analysis of predetermined five year periods showed that the excess cases in the Hinkley Point area were concentrated in the 10 years 1964-73 after commissioning of the station, at a time when rates in the rest of Somerset were close to the national average. In particular the nine cases occurring in the five years 1969-73 were about four times the number expected from national rates (standardised registration ratio 3.96; 95% confidence interval 1.81 to 7.52). Rates in the Hinkley Point area after 1973 were fairly low, especially as compared with the rest of Somerset. In the five years 1959-63 (that is, before Hinkley Point was commissioned) rates throughout Somerset (including the Hinkley Point area) were higher than the national rate. These findings should be interpreted with caution, and further studies are required to test the plausibility of theories relating to radiation and viruses.     

Overestimates of survival after HAART: implications for global scale-up efforts

Background

Monitoring the effectiveness of global antiretroviral therapy scale-up efforts in resource-limited settings is a global health priority, but is complicated by high rates of losses to follow-up after treatment initiation. Determining definitive outcomes of these lost patients, and the effects of losses to follow-up on estimates of survival and risk factors for death after HAART, are key to monitoring the effectiveness of global HAART scale-up efforts.

Methodology/Principal Findings

A cohort study comparing clinical outcomes and risk factors for death after HAART initiation as reported before and after tracing of patients lost to follow-up was conducted in Botswana''s National Antiretroviral Therapy Program. 410 HIV-infected adults consecutively presenting for HAART were evaluated. The main outcome measures were death or loss to follow-up within the first year after HAART initiation. Of 68 patients initially categorized as lost, over half (58.8%) were confirmed dead after tracing. Patient tracing resulted in reporting of significantly lower survival rates when death was used as the outcome and losses to follow-up were censored [1-year Kaplan Meier survival estimate 0.92 (95% confidence interval, 0.88–0.94 before tracing and 0.83 (95% confidence interval, 0.79–0.86) after tracing, log rank P<0.001]. In addition, a significantly increased risk of death after HAART among men [adjusted hazard ratio 1.74 (95% confidence interval, 1.05–2.87)] would have been missed had patients not been traced [adjusted hazard ratio 1.41 (95% confidence interval, 0.65–3.05)].

Conclusions/Significance

Due to high rates of death among patients lost to follow-up after HAART, survival rates may be inaccurate and important risk factors for death may be missed if patients are not actively traced. Patient tracing and uniform reporting of outcomes after HAART are needed to enable accurate monitoring of global HAART scale-up efforts.     

Drought-induced increase in tree mortality and corresponding decrease in the carbon sink capacity of Canada's boreal forests from 1970 to 2020

Canada's boreal forests, which occupy approximately 30% of boreal forests worldwide, play an important role in the global carbon budget. However, there is little quantitative information available regarding the spatiotemporal changes in the drought-induced tree mortality of Canada's boreal forests overall and their associated impacts on biomass carbon dynamics. Here, we develop spatiotemporally explicit estimates of drought-induced tree mortality and corresponding biomass carbon sink capacity changes in Canada's boreal forests from 1970 to 2020. We show that the average annual tree mortality rate is approximately 2.7%. Approximately 43% of Canada's boreal forests have experienced significantly increasing tree mortality trends (71% of which are located in the western region of the country), and these trends have accelerated since 2002. This increase in tree mortality has resulted in significant biomass carbon losses at an approximate rate of 1.51 ± 0.29 MgC ha⁻¹ year⁻¹ (95% confidence interval) with an approximate total loss of 0.46 ± 0.09 PgC year⁻¹ (95% confidence interval). Under the drought condition increases predicted for this century, the capacity of Canada's boreal forests to act as a carbon sink will be further reduced, potentially leading to a significant positive climate feedback effect.     

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.