Effects of treatment-induced mortality and tumor-induced mortality on tests for carcinogenicity in small samples

Statistical tests of carcinogenicity are shown to have varying degrees of robustness to the effects of mortality. Mortality induced by two different mechanisms is studied--mortality due to the tumor of interest, and mortality due to treatment independent of the tumor. The two most commonly used tests, the life-table test and the Cochran-Armitage linear trend test, are seen to be highly sensitive to increases in treatment lethality using small-sample simulations. Increases in tumor lethality are seen to affect the performance of commonly used prevalence tests such as logistic regression. A simple survival-adjusted quantal response test appears to be the most robust of all the procedures considered.     

Evaluation of Animal Carcinogenicity Studies: Cochran‐Armitage Trend Test vs. Multiple Contrast Tests

Typical animal carcinogenicity studies involve the comparison of several dose groups to a negative control. The uncorrected asymptotic Cochran‐Armitage trend test with equally spaced dose scores is the most frequently used test in such set‐ups. However, this test based on a weighted linear regression on proportions. It is well known that the Cochran‐Armitage test lacks in power for other shapes than the assumed linear one. Therefore, dichotomous multiple contrast tests are introduced. These build the maximum over several single contrasts, where each of them is chosen appropriately to cover a specific dose‐response shape. An extensive power study has been conducted to compare multiple contrast tests with the approaches used so far. Crucial results will be presented in this paper. Moreover, exact tests and continuity corrected versions are introduced and compared to the traditional uncorrected approaches regarding size and power behaviour. A trend test for any shape of the dose‐response relationship for either crude tumour rates or mortality‐ adjusted rates based on the simple Poly‐3 transformation is proposed for evaluation of carcinogenicity studies.     

Efficiency of age-adjusted tests in animal carcinogenicity experiments

Carcinogenicity experiments may be analysed by a simple comparison of the control and exposed groups with respect to the proportions of observed tumors amongst dead animals, when longevity is identical in control and exposed groups. This simple-proportions test is invalid when longevity varies between groups and age-adjusted methods such as the Hoel-Walburg or logrank test are needed. This paper stresses that there is an advantage to using age-adjusted tests, even when the simple-proportions test is valid. The argument is based on calculations of the asymptotic relative efficiency of the simple-proportions test with respect to both the Hoel-Walburg and the logrank tests.     

The influence of local environment on the aging and mortality ofAedes aegypti (L.): Case study in Fortaleza‐CE,Brazil

It is generally assumed that the daily probability of survival of mosquitoes is independent of age. To test this assumption we have conducted a three‐year experimental fieldwork study (2005–2007) at Fortaleza‐CE in Brazil, determining daily survival rates of the dengue vector Aedes aegypti (L.). Survival rates of adult Ae. aegypti may be age‐dependent and the statistical analysis is a sensitive approach for comparing patterns of mosquito survival. The mosquito survival data were better fit by a Weibull survival function than by the more traditionally used Gompertz or logistic survival functions. Gompertz, Weibull, or logistic survival functions often fit the survival, and the tails of the survival curves usually appear to fall between the values predicted by the three functions. We corroborate that the mortality of Ae. aegypti in semi‐natural conditions may no more be considered as a constant phenomenon during the life of adult mosquitoes but varies according to the age and environmental conditions under a tropical climate. This study estimates the variability in the survival rate of Ae. aegypti and environmental factors that are related to such variability. The statistical analysis shows that the fitting ability, concerning the hazard function, was in decreasing order: Seasonal Cox, the three‐parameter Gompertz, and the three‐parameter Weibull, that was similar to the three‐parameter logistic. The advantage of using the Cox model is that it is convenient for exploring the relationship between survival and several explanatory variables. The Cox model has the advantage of preserving the variable in its original quantitative form and of using a maximum of information. The survival analyses indicate that mosquito mortality is both age‐ and environment‐dependent.     

Male survival advantage on the Baja California peninsula

A consistent finding from contemporary Western societies is that women outlive men. However, what is unclear is whether sex differences in survival are constant across varying socio-ecological conditions. We test the universality of the female survival advantage with mortality data from a nineteenth century population in the Baja California peninsula of Mexico. When examined simply, we find evidence for a male-biased survival advantage. However, results from Cox regression clearly show the importance of age intervals for variable survival patterns by sex. Our key findings are that males: (i) experience significantly lower mortality risk than females during the ages 15–30 (RR = 0.69), (ii) are at a significantly increased risk of dying in the 61+ category (RR = 1.30) and (iii) do not experience significantly different mortality risk at any other age interval (0–14, 31–45, 46–60). We interpret our results to stem from differing intrinsic and extrinsic risk factors for sex-biased mortality across age intervals, highlighting the relevance of a lifecourse approach to the study of survival advantage. Ultimately, our results make clear the need to more broadly consider variability in mortality risk factors across time and place to allow for a clearer understanding of human survival differences.     

Survivor Curves for Leptospira autumnalis Akiyami A Based on Most-Probable-Number Values

The validity of survivor curves for Leptospira autumnalis Akiyami A based on most-probable-number values is supported by the following observations: (i) linear regression lines fell within most of the 95% confidence intervals; (ii) linear correlation coefficients (r) were consistently high (i.e., near -1); and (iii) statistical tests for goodness of fit usually accepted the linear model. These tests are consistent with an exponential death rate for the test organism in defined solutions. The influence of temperature and pH on survival was demonstrated by showing a statistically significant difference in survivor curve slopes.     

Estimating HIV Prevalence in Zimbabwe Using Population-Based Survey Data

Estimates of HIV prevalence computed using data obtained from sampling a subgroup of the national population may lack the representativeness of all the relevant domains of the population. These estimates are often computed on the assumption that HIV prevalence is uniform across all domains of the population. Use of appropriate statistical methods together with population-based survey data can enhance better estimation of national and subgroup level HIV prevalence and can provide improved explanations of the variation in HIV prevalence across different domains of the population. In this study we computed design-consistent estimates of HIV prevalence, and their respective 95% confidence intervals at both the national and subgroup levels. In addition, we provided a multivariable survey logistic regression model from a generalized linear modelling perspective for explaining the variation in HIV prevalence using demographic, socio-economic, socio-cultural and behavioural factors. Essentially, this study borrows from the proximate determinants conceptual framework which provides guiding principles upon which socio-economic and socio-cultural variables affect HIV prevalence through biological behavioural factors. We utilize the 2010–11 Zimbabwe Demographic and Health Survey (2010–11 ZDHS) data (which are population based) to estimate HIV prevalence in different categories of the population and for constructing the logistic regression model. It was established that HIV prevalence varies greatly with age, gender, marital status, place of residence, literacy level, belief on whether condom use can reduce the risk of contracting HIV and level of recent sexual activity whereas there was no marked variation in HIV prevalence with social status (measured using a wealth index), method of contraceptive and an individual’s level of education.     

Tests for Monotonic Trend from Case‐Control Data: Cochran‐Armitage‐Mantel Trend Test,Isotonic Regression and Single and Multiple Contrast Tests

Tests for a monotonic trend between an ordered categorical exposure and disease status are routinely carried out from case‐control data using the Mantel‐extension trend test or the asymptotically equivalent Cochran‐Armitage test. In this study, we considered two alternative tests based on isotonic regression, namely an order‐restricted likelihood ratio test and an isotonic modification of the Mantel‐extension test extending the recent proposal by Mancuso, Ahn and Chen (2001) to case‐control data. Furthermore, we considered three tests based on contrasts, namely a single contrast (SC) test based on Schaafsma's coefficients, the Dosemeci and Benichou (DB) test, a multiple contrast (MC) test based on the Helmert, reverse‐Helmert and linear contrasts and we derived their case‐control versions. Using simulations, we compared the statistical properties of these five alternative tests to those of the Mantel‐extension test under various patterns including no relationship, as well as monotonic and non‐monotonic relationships between exposure and disease status. In the case of no relationship, all tests had close to nominal type I error except in situations combining a very unbalanced exposure distribution and small sample size, where the asymptotic versions of the three tests based on contrasts were highly anticonservative. The use of bootstrap instead of asymptotic versions corrected this anticonservatism. For monotonic patterns, all tests had close powers. For non monotonic patterns, the DB‐test showed the most favourable results as it was the least powerful test. The two tests based on isotonic regression were the most powerful tests and the Mantel‐extension test, the SC‐ and MC‐tests had in‐between powers. The six tests were applied to data from a case‐control study investigating the relationship between alcohol consumption and risk of laryngeal cancer in Turkey. In situations with no evidence of a monotonic relationship between exposure and disease status, the three tests based on contrasts did not conclude in favour of a significant trend whereas all the other tests did. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adjusted regression trend test for a multicenter clinical trial

Studies using a series of increasing doses of a compound, including a zero dose control, are often conducted to study the effect of the compound on the response of interest. For a one-way design, Tukey et al. (1985, Biometrics 41, 295-301) suggested assessing trend by examining the slopes of regression lines under arithmetic, ordinal, and arithmetic-logarithmic dose scalings. They reported the smallest p-value for the three significance tests on the three slopes for safety assessments. Capizzi et al. (1992, Biometrical Journal 34, 275-289) suggested an adjusted trend test, which adjusts the p-value using a trivariate t-distribution, the joint distribution of the three slope estimators. In this paper, we propose an adjusted regression trend test suitable for two-way designs, particularly for multicenter clinical trials. In a step-down fashion, the proposed trend test can be applied to a multicenter clinical trial to compare each dose with the control. This sequential procedure is a closed testing procedure for a trend alternative. Therefore, it adjusts p-values and maintains experimentwise error rate. Simulation results show that the step-down trend test is overall more powerful than a step-down least significant difference test.     

Comparability of segmented line regression models

Segmented line regression models, which are composed of continuous linear phases, have been applied to describe changes in rate trend patterns. In this article, we propose a procedure to compare two segmented line regression functions, specifically to test (i) whether the two segmented line regression functions are identical or (ii) whether the two mean functions are parallel allowing different intercepts. A general form of the test statistic is described and then the permutation procedure is proposed to estimate the p-value of the test. The permutation test is compared to an approximate F-test in terms of the p-value estimation and the performance of the permutation test is studied via simulations. The tests are applied to compare female lung cancer mortality rates between two registry areas and also to compare female breast cancer mortality rates between two states.     

Analysis of Randomized Dose-Finding-Studies: Closure Test Modifications Based on Multiple Contrast Tests

The power of single contrast tests strongly depends on the a priori unknown shape of the dose response relationship. Two approaches can be used to overcome this major disadvantage: the likelihood ratio test for order restriction or multiple contrast tests. Within the closure principle, the shape for the different hyptheses varies. Therefore multiple contrast tests are used as trend tests. Based on a simulation study the power advantage of this approach in comparison with single contrast tests is demonstrated.     

Mortality among Canadian military personnel exposed to low-dose radiation.

We carried out a cohort study of mortality among 954 Canadian military personnel exposed to low-dose ionizing radiation during nuclear reactor clean-up operations at Chalk River Nuclear Laboratories, Chalk River, Ont., and during observation of atomic test blasts in the United States and Australia in the 1950s. Two controls matched for age, service, rank and trade were selected for each exposed subject. Mortality among the exposed and control groups was ascertained by means of record linkage with the Canadian Mortality Data Base. Survival analysis with life-table techniques did not reveal any difference in overall mortality between the exposed and control groups. Analysis of cause-specific mortality showed similar mortality patterns in the two groups; there was no elevation in the exposed group in the frequency of death from leukemia or thyroid cancer, the causes of death most often associated with radiation exposure. Analysis of survival by recorded gamma radiation dose also did not show any effect of radiation dose on mortality. The findings are in agreement with the current scientific literature on the risk of death from exposure to low-dose radiation.     

Description of growth by simple versus complex models for Baltic Sea spring spawning herring

The objective was to find a length–growth model to help differentiate between herring stocks (Clupea harengus l.) when their length–growth shows systematically different patterns. The most essential model restriction was that it should react robustly against variations in the underlying age range which varies not only over time but also between the different herring stocks. Because of the limited age range, significance tests as well as confidence intervals of the model parameters should allow a small sample restriction. Thus, parameter estimation should be of an analytical rather than asymptotic nature and the model should contain a minimum set of parameters. The article studies the comparative characteristics of a simple non‐asymptotic two‐parameter growth model (allometric length–growth function, abbreviated as ALG model) in contrast to higher parametric and more complex growth models (logistic and von‐Bertalanffy growth functions, abbreviated as LGF and VBG models). An advantage of the ALG model is that it can be easily linearized and the growth coefficients can be directly derived as regression parameters. The intrinsic ALG model linearity makes it easy to test restrictions (normality, homoscedasticity and serial uncorrelation of the error term) and to formulate analytic confidence intervals. The ALG model features were exemplified and validated by a 1995 Baltic spring spawning herring (BSSH) data set that included a 12‐year age range. The model performance was compared with that of the logistic and the von‐Bertalanffy length–growth curves for different age ranges and by means of various parameter estimation techniques. In all cases the ALG model performed better and all ALG model restrictions (no autocorrelation, homoscedasticity, and normality of the error term) were fulfilled. Furthermore, all findings seemed to indicate a pseudo‐asymptotic growth for BSSH. The proposed model was explicitly derived for of herring length‐growth; the results thus should not be generalized interspecifically without additional proof.     

Predicting tree death for Fagus sylvatica and Abies alba using permanent plot data

Question: How well can mortality probabilities of deciduous trees(Fagus sylvatica) and conifers (Abies alba) be predicted using permanent plot data that describe growth patterns, tree species, tree size and site conditions? Location: Fagus forests in the montane belt of the Jura folds (Switzerland). Method: Permanent plot data were used to develop and validate logistic regression models predicting survival probabilities of individual trees. Backward model selection led to a reduced model containing the growth‐related variable ‘relative basal area increment’ (growth‐dependent mortality) and variables not directly reflecting growth such as species, size and site (growth‐independent mortality). Results: The growth‐mortality relationship was the same for both species (growth‐dependent mortality). However, species, site and tree size also influenced mortality probabilities (growth‐independent mortality). The predicted survival probabilities of the final model were well calibrated, and the model showed an excellent discriminatory power (area under the receiver operating characteristic curve = 0.896). Conclusion: Mortality probabilities of Fagus sylvatica and Abies alba can be predicted with high discriminatory power using a well calibrated logistic regression model. Extending this case study to a larger number of tree species and sites could provide species‐ and site‐specific tree mortality models that allow for more realistic projections of forest succession.     

On Exact Unconditional Test for Linear Trend in Dose‐Response Studies

The one‐degree‐of‐freedom Cochran‐Armitage (C‐A) test statistic for linear trend has been widely applied in various dose‐response studies (e.g., anti‐ulcer medications and short‐term antibiotics, animal carcinogenicity bioassays and occupational toxicant studies). This approximate statistic relies, however, on asymptotic theory that is reliable only when the sample sizes are reasonably large and well balanced across dose levels. For small, sparse, or skewed data, the asymptotic theory is suspect and exact conditional method (based on the C‐A statistic) seems to provide a dependable alternative. Unfortunately, the exact conditional method is only practical for the linear logistic model from which the sufficient statistics for the regression coefficients can be obtained explicitly. In this article, a simple and efficient recursive polynomial multiplication algorithm for exact unconditional test (based on the C‐A statistic) for detecting a linear trend in proportions is derived. The method is applicable for all choices of the model with monotone trend including logistic, probit, arcsine, extreme value and one hit. We also show that this algorithm can be easily extended to exact unconditional power calculation for studies with up to a moderately large sample size. A real example is given to illustrate the applicability of the proposed method.     

Age-adjusted exact trend tests in the event of rare occurrences

Preclinical animal carcinogenicity studies are usually concerned with testing the statistical significance of a dose-response relationship. When the response consists of a rare event such as the development of a certain type of tumor, exact statistical methods are often employed. The exact randomization trend test based on the multivariate hypergeometric distribution is less powerful in the presence of treatment-related risks other than the specified response. Particularly, the loss of power becomes more pronounced when competing risks cause progressively higher mortality rates with increasing dose, which is usual in practice. An age-adjusted form of the randomization test is proposed to adjust for this effect. Permutational distribution for Peto's cause-of-death (COD) test is also explored and compared with its asymptotic counterpart by simulation. The use of COD information has been a controversial issue due to the subjectivity in the pathologists' determinations as well as for economic reasons. The proposed age-adjusted exact test does not require COD, and it is shown to compare favorably to the COD tests via an extensive Monte Carlo simulation. Applications of the methods to two real data sets are included.     

Multifraction radiation response of mouse lung

The response of mouse lung to repeated doses of 60Co gamma-rays of as low as 115 cGy per fraction was measured using death from pneumonitis between 80 and 120 days after irradiation as the endpoint. A fractionation interval of 3 h was maintained for most regimens but in the longer experiments some 12 h intervals were introduced for logistic reasons. The longest overall duration (for a 43 fraction regimen) was 8 days. The total doses required to produce 50 per cent mortality increased continuously as dose/fraction was decreased, even from 160 to 115 cGy per fraction. Of clinical relevance, the steepness of the isoeffect curve over the dose range 115-500 cGy indicates that the lung shows greater sparing from dose fractionation than is characteristic of more rapidly-responding normal tissues, resembling, in this respect, other more slowly-responding tissues such as spinal cord. The plot of the reciprocal of the LD50 values as a function of dose per fraction was non-linear, suggesting that a linear quadratic dose response model may not be appropriate or that repair of cellular injury in lung is not complete in 3 h, or both.     

Assessing the goodness of fit of logistic regression models in large samples: A modification of the Hosmer-Lemeshow test

Evaluating the goodness of fit of logistic regression models is crucial to ensure the accuracy of the estimated probabilities. Unfortunately, such evaluation is problematic in large samples. Because the power of traditional goodness of fit tests increases with the sample size, practically irrelevant discrepancies between estimated and true probabilities are increasingly likely to cause the rejection of the hypothesis of perfect fit in larger and larger samples. This phenomenon has been widely documented for popular goodness of fit tests, such as the Hosmer-Lemeshow test. To address this limitation, we propose a modification of the Hosmer-Lemeshow approach. By standardizing the noncentrality parameter that characterizes the alternative distribution of the Hosmer-Lemeshow statistic, we introduce a parameter that measures the goodness of fit of a model but does not depend on the sample size. We provide the methodology to estimate this parameter and construct confidence intervals for it. Finally, we propose a formal statistical test to rigorously assess whether the fit of a model, albeit not perfect, is acceptable for practical purposes. The proposed method is compared in a simulation study with a competing modification of the Hosmer-Lemeshow test, based on repeated subsampling. We provide a step-by-step illustration of our method using a model for postneonatal mortality developed in a large cohort of more than 300 000 observations.     

Identifying genetic marker sets associated with phenotypes via an efficient adaptive score test

In recent years, genome-wide association studies (GWAS) and gene-expression profiling have generated a large number of valuable datasets for assessing how genetic variations are related to disease outcomes. With such datasets, it is often of interest to assess the overall effect of a set of genetic markers, assembled based on biological knowledge. Genetic marker-set analyses have been advocated as more reliable and powerful approaches compared with the traditional marginal approaches (Curtis and others, 2005. Pathways to the analysis of microarray data. TRENDS in Biotechnology 23, 429-435; Efroni and others, 2007. Identification of key processes underlying cancer phenotypes using biologic pathway analysis. PLoS One 2, 425). Procedures for testing the overall effect of a marker-set have been actively studied in recent years. For example, score tests derived under an Empirical Bayes (EB) framework (Liu and others, 2007. Semiparametric regression of multidimensional genetic pathway data: least-squares kernel machines and linear mixed models. Biometrics 63, 1079-1088; Liu and others, 2008. Estimation and testing for the effect of a genetic pathway on a disease outcome using logistic kernel machine regression via logistic mixed models. BMC bioinformatics 9, 292-2; Wu and others, 2010. Powerful SNP-set analysis for case-control genome-wide association studies. American Journal of Human Genetics 86, 929) have been proposed as powerful alternatives to the standard Rao score test (Rao, 1948. Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Mathematical Proceedings of the Cambridge Philosophical Society, 44, 50-57). The advantages of these EB-based tests are most apparent when the markers are correlated, due to the reduction in the degrees of freedom. In this paper, we propose an adaptive score test which up- or down-weights the contributions from each member of the marker-set based on the Z-scores of their effects. Such an adaptive procedure gains power over the existing procedures when the signal is sparse and the correlation among the markers is weak. By combining evidence from both the EB-based score test and the adaptive test, we further construct an omnibus test that attains good power in most settings. The null distributions of the proposed test statistics can be approximated well either via simple perturbation procedures or via distributional approximations. Through extensive simulation studies, we demonstrate that the proposed procedures perform well in finite samples. We apply the tests to a breast cancer genetic study to assess the overall effect of the FGFR2 gene on breast cancer risk.     

Is Gestational Hypertension Protective against Perinatal Mortality in Twin Pregnancies?

Background

Pregnancy-induced or gestational hypertension is a common pregnancy complication. Paradoxically, gestational hypertension has been associated with a protective effect against perinatal mortality in twin pregnancies in analytic models (logistic regression) without accounting for survival time. Whether this effect is real remains uncertain. This study aimed to validate the impact of gestational hypertension on perinatal mortality in twin pregnancies using a survival analysis approach.

Methods

This was a retrospective cohort study of 278,821 twin pregnancies, using the U.S. 1995–2000 matched multiple birth dataset (the largest dataset available for multiple births). Cox proportional hazard models were applied to estimate the adjusted hazard ratios (aHR) of perinatal death (stillbirth and neonatal death) comparing gestational hypertensive vs. non-hypertensive pregnancies controlling for maternal characteristics and twin cluster-level dependence.

Results

Comparing births in gestational hypertensive vs. non-hypertensive twin pregnancies, perinatal mortality rates were significantly lower (1.20% vs. 3.38%), so were neonatal mortality (0.72% vs. 2.30%) and stillbirth (0.48% vs. 1.10%) rates. The aHRs (95% confidence intervals) were 0.34 (0.31–0.38) for perinatal death, 0.31 (0.27–0.34) for neonatal death, and 0.45 (0.38–0.53) for stillbirth, respectively. The protective effect of gestational hypertension against perinatal death became weaker over advancing gestational age; the aHRs in very preterm (<32 weeks), mild preterm (32–36 weeks) and term (37+ weeks) births were 0.29, 0.48 and 0.76, respectively. The largest risk reductions in neonatal mortality were observed for infections and immaturity-related conditions.

Conclusions

Gestational hypertension appears to be beneficial for fetal survival in twin pregnancies, especially in those ending more prematurely or for deaths due to infections and immaturity-related conditions. Prospective studies are required to rule out the possibility of unmeasured confounders.