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.     

Studies of the mortality of A-bomb survivors. 8. Cancer mortality, 1950-1982

This study extends an earlier one by 4 years (1979-1982) and includes mortality data on 11,393 additional Nagasaki survivors. Significant dose responses are observed for leukemia, multiple myeloma, and cancers of the lung, female breast, stomach, colon, esophagus, and urinary tract. Due to diagnostic difficulties, results for liver and ovarian cancers, while suggestive of significant dose responses, do not provide convincing evidence for radiogenic effects. No significant dose responses are seen for cancers of the gallbladder, prostate, rectum, pancreas, or uterus, or for lymphoma. For solid tumors, largely due to sex-specific differences in the background rates, the relative risk of radiation-induced mortality is greater for women than for men. For nonleukemic cancers the relative risk seen in those who were young when exposed has decreased with time, while the smaller risks for those who were older at exposure have tended to increase. While the absolute excess risks of radiation-induced mortality due to nonleukemic cancer have increased with time for all age-at-exposure groups, both excess and relative risks of leukemia have generally decreased with time. For leukemia, the rate of decrease in risk and the initial level of risk are inversely related to age at exposure.     

Testing for a trend in tumor prevalence rates: I. Nonlethal tumors

In the analysis of animal carcinogenicity studies, the standard survival-adjusted test for a dose-related trend in the prevalence of nonlethal tumors is the Hoel-Walburg test, which stratifies on age at death by grouping survival times into intervals. An alternative analysis assesses trend on the basis of the likelihood score test under a logistic model for the prevalence function, which adjusts for survival by including age at death as a continuous regression variable. Extensive simulations demonstrate that the test based on modeling the prevalence log-odds as a linear function of age is more powerful than the Hoel-Walburg test, regardless of the intervals used by the latter to stratify the data. Without incorporating a continuity correction, the size of each test often exceeds the nominal level, especially when the mortality patterns differ across dose groups. Corrected versions of the tests operate at conservative levels, where the degree of conservatism varies with the distribution of the data. When the mortality patterns for the dose groups are similar, both tests have essentially the same power to detect a trend in tumor prevalence rates. However, when mortality varies with dose, the logistic regression test with a linear age term is more powerful than the Hoel-Walburg test, and this gain in power increases as the dose-specific mortality patterns become more disparate.     

Utilizing Cause-of-Death Information to Estimate Conditional Probabilities of Disease and Death

Conditional probabilities that do not require the assumption of independence among competing risks for identifiability are proposed for the analysis of carcinogenesis bioassay data as a reasonable adjustment for deaths or other removals due to competing risks. These conditional probabilities permit consideration of one type of tumor at a time, but in such a way that inferences are relevant to actual experimental conditions under which other diseases and causes of death are present and operating. The importance of assigning cause of death in bioassays is demonstrated by the fact that it allows the definition and identification of functions useful in the interpretation of carcinogenesis data, without requiring that a disease of interest be independent from competing risks. However, one proposed conditional probability does require sacrifice data for its identifiability.     

Responses of the beagle to protracted irradiation. I. Effect of total dose and dose rate

The effects of protracted exposure to 60Co gamma rays on survival and tumor induction in the beagle were investigated. Total accumulated doses of 450, 1050, 1500, and 3000 cGy were given at rates of 3.8, 7.5, 12.8, and 26.3 cGy/day. Hazard models were used to identify trends in mortality associated with radiation exposure. The probability of an acute death (related to hematopoietic aplasia) was positively associated with the total dose received and the rate at which the dose was delivered. Once an animal survived the initial hematopoietic effects of radiation exposure, the risk of death from causes other than cancer, while elevated, was far less responsive than the neoplastic end points. No relationship between tumor or chronic nontumor deaths and dose rate could be identified. However, survival curves for tumor mortality did separate into a pattern clearly dependent on the accumulated dose.     

Weighted p-value adjustments for animal carcinogenicity trend test

A typical animal carcinogenicity experiment routinely analyzes approximately 10-30 tumor sites. Comparisons of tumor responses between dosed and control groups and dose-related trend tests are often evaluated for each individual tumor site/type separately. p-Value adjustment approaches have been proposed for controlling the overall Type I error rate or familywise error rate (FWE). However, these adjustments often result in reducing the power to detect a dose effect. This paper proposes using weighted adjustments by assuming that each tumor can be classified as either class A or class B based on prior considerations. The tumors in class A, which are considered as more critical endpoints, are given less adjustment. Two weighted methods of adjustments are presented, the weighted p adjustment and weighted alpha adjustment. A Monte Carlo simulation shows that both weighted adjustments control the FWE well. Furthermore, the power increases if a treatment-dependent tumor is analyzed as in class A tumors and the power decreases if it is analyzed as in class B tumors. A data set from a National Toxicology Program (NTP) 2-year animal carcinogenicity experiment with 13 tumor types/sites observed in male mice was analyzed using the proposed methods. The modified poly-3 test was used to test for increased carcinogenicity since it has been adopted by the NTP as a standard test for a dose-related trend. The unweighted adjustment analysis concluded that there was no statistically significant dose-related trend. Using the Food and Drug Administration classification scheme for the weighted adjustment analyses, two rare tumors (with background rates of 1% or less) were analyzed as class A tumors and 11 common tumors (with background rates higher than 1%) as class B. Both weighted analyses showed a significant dose-related trend for one rare tumor.     

Toxicity of 241Am in male C57BL mice: relative risk versus 226Ra

A life-span study on male C57BL mice after injection of various doses of 241Am was conducted. The effects on life span were evaluated and the incidence of tumors was determined by procedures that take competing risks into account. Bone tumors were induced in the mice by injections of 22 and 58 Bq 241Am per g. The mice died early from nonneoplastic diseases at the higher dose levels (190, 373, and 1197 Bq 241Am/g). Additionally, spontaneously occurring tumors such as liver carcinomas, lymphosarcomas, and lymphoreticulosarcomas occurred at an enhanced rate with increasing dose level. The data for survival time after 241Am injection and death with bone tumor were compared to data collected previously for 226Ra-injected mice of the same C57BL strain. This enabled direct comparison in the same strain of the effects of the bone-surface seeker 241Am to the effects of the bone-volume seeker 226Ra. The proportional hazards model was applied and the rate of death with bone tumor was 12.9 +/- 5.2 times higher after 241Am injection than after 226Ra injection if the regression covariate was the average dose to the skeleton. The relative risk was 3.5 +/- 1.7 if regressed on the injected radioactivity. The mortality rate after 241Am injection was 20.4 +/- 3.6 times higher than after 226Ra injection if regressed on average dose to the skeleton.     

Mortality among the liquidators of the Chernobyl accident: dose dependences and groups of the potential risk

Dynamics of the mortality and the mortality radiation risks among male emergency workers of 1986-1987 years of entrance to the Chernobyl zone is analyzed. The average dose of external gamma-exposure for this cohort equals 128 mGy. The size of the cohort at the beginning of the follow-up in 1992 was 47820 persons. For the follow-up period 1992-2006 statistically significant radiation risks of death rates have been estimated: for the mortality from all causes, the excess relative risk per Gy (ERR/Gy) equals 0.42 with 95% confidence interval (95% CI) (0.14-0.72); for the mortality from solid cancers ERR/Gy = 0.74, 95% CI (0.03-1.76); and for the mortality from the circulatory system diseases ERR/Gy = 1.01, 95% CI (0.51-1.57). Based on these estimates the risk groups were ranked among all Russian emergency workers (160 thousand persons): the group of the potential radiation risk with doses more than 150 mGy (33488 persons) and the group of the high radiation risk with doses more than 240 mGy (6054 persons).     

Updated Mortality Analyses of Pernis Epidemiological Data on Human Exposures to Aldrin and Dieldrin

An extensive clinical and epidemiological study of workers engaged in the manufacturing and formulation of aldrin and dieldrin, the Pernis study, provides occupational hygiene and biological monitoring data on individual exposures over the years of employment and provides the opportunity to investigate dose response relationships for these chemicals. The human epide miological mortality data on these workers, who were exposed to fairly substan tial lifetime average daily doses of aldrin and dieldrin, suggest that low dose exposures do not significantly increase human mortality and may even de crease the human mortality hazard rate. While hormesis from low dose expo sure to aldrin and dieldrin is not statistically significant, it is observed in the raw data and in the best fitting dose response models. The decrease in risk suggests increased survival time at low doses of aldrin and dieldrin. Using an upper bound on cancer potency based on mouse liver tumors, the U.S. Environmental Protection Agency (EPA) estimated that lifetime average daily doses (LADDs) of 0.0000625 and 0.00625?µg/kg body weight/day would correspond to increased cancer risks of 0.000001 and 0.0001, respectively. However, the best estimate from the Pernis epidemiological data is that LADDs of 0.0000625 and 0.00625?µg/kg body weight/day correspond to no increase in cancer risk and a decrease in the probability of mortality from all causes by the age of 70 years. At low doses of aldrin and dieldrin, the estimated decrease in mortality in a reference period of 70 years is more than 1000 times larger than the U.S. EPA's upper bound on the increase in the lifetime probability of cancer.     

Partner status and survival after cancer: A competing risks analysis

ObjectiveThe survival benefits of having a partner for all cancers combined is well recognized, however its prognostic importance for individual cancer types, including competing mortality causes, is less clear. This study was undertaken to quantify the impact of partner status on survival due to cancer-specific and competing mortality causes.MethodsData were obtained from the population-based Queensland Cancer Registry on 176,050 incident cases of ten leading cancers diagnosed in Queensland (Australia) from 1996 to 2012. Flexible parametric competing-risks models were used to estimate cause-specific hazards and cumulative probabilities of death, adjusting for age, stage (breast, colorectal and melanoma only) and stratifying by sex.ResultsBoth unpartnered males and females had higher total cumulative probability of death than their partnered counterparts for each site. For example, the survival disadvantage for unpartnered males ranged from 3% to 30% with higher mortality burden from both the primary cancer and competing mortality causes. The cause-specific age-adjusted hazard ratios were also consistent with patients without a partner having increased mortality risk although the specific effect varied by site, sex and cause of death. For all combined sites, unpartnered males had a 46%, 18% and 44% higher risk of cancer-specific, other cancer and non-cancer mortality respectively with similar patterns for females. The higher mortality risk persisted after adjustment for stage.ConclusionsIt is important to better understand the mechanisms by which having a partner is beneficial following a cancer diagnosis, so that this can inform improvements in cancer management for all people with cancer.     

On the efficiency of age-adjusted tests in animal carcinogenicity experiments

Based on asymptotic relative efficiency calculations, Ryan (1985, Biometrics 41, 525-531) concludes that, in the analysis of animal carcinogenicity experiments, age-adjusted tests of tumor rates should be routinely preferred to simple proportions tests for both lethal and nonlethal tumors. We recalculate the asymptotic efficiencies of the simple proportions test relative to the log-rank test for the lethal tumor case. For a simplified model it is shown that the relative efficiency may be easily computed as a function of the crude tumor rate and the survival rate at the time of terminal sacrifice. More generally, we calculate by numerical quadrature the asymptotic relative efficiency for all models considered by Ryan and, using simulations, examine the relevance of asymptotic efficiencies to typical sample sizes. Contrary to the numerical results of Ryan, we find, for experiments with good survival and typical tumor rates, that the relative efficiencies are greater than 95%, usually about 99%. In the nonlethal tumor case, similar results follow from Ryan for tumor rates and survival rates typically encountered in practice. As it is often difficult to determine whether or not a tumor is lethal, we conclude for equal interim mortality rates, that the simple proportions test is usually adequate in evaluating animal carcinogenicity experiments.     

On a probability Model for Classifying the Unknown Causes of Death Due to Two Competing Risks into Assignable Causes

A probability model to classify the otherwise unclassified causes of death due to two competing risks R₁ and R₂ has been evolved in this paper. A simple model based on Poisson inputs has been illustrated by numerical illustrations. Further generalization of the model with more than two competing risks is straightforward for the given model.     

Solid cancer mortality associated with chronic external radiation exposure at the French atomic energy commission and nuclear fuel company

Studies of nuclear workers make it possible to directly quantify the risks associated with ionizing radiation exposure at low doses and low dose rates. Studies of the CEA (Commissariat à l'Energie Atomique) and AREVA Nuclear Cycle (AREVA NC) cohort, currently the most informative such group in France, describe the long-term risk to nuclear workers associated with external exposure. Our aim is to assess the risk of mortality from solid cancers among CEA and AREVA NC nuclear workers and its association with external radiation exposure. Standardized mortality ratios (SMRs) were calculated and internal Poisson regressions were conducted, controlling for the main confounding factors [sex, attained age, calendar period, company and socioeconomic status (SES)]. During the period 1968-2004, there were 2,035 solid cancers among the 36,769 CEA-AREVA NC workers. Cumulative external radiation exposure was assessed for the period 1950-2004, and the mean cumulative dose was 12.1 mSv. Mortality rates for all causes and all solid cancers were both significantly lower in this cohort than in the general population. A significant excess of deaths from pleural cancer, not associated with cumulative external dose, was observed, probably due to past asbestos exposure. We observed a significant excess of melanoma, also unassociated with dose. Although cumulative external dose was not associated with mortality from all solid cancers, the central estimated excess relative risk (ERR) per Sv of 0.46 for solid cancer mortality was higher than the 0.26 calculated for male Hiroshima and Nagasaki A-bomb survivors 50 years or older and exposed at the age of 30 years or older. The modification of our results after stratification for SES demonstrates the importance of this characteristic in occupational studies, because it makes it possible to take class-based lifestyle differences into account, at least partly. These results show the great potential of a further joint international study of nuclear workers, which should improve knowledge about the risks associated with chronic low doses and provide useful risk estimates for radiation protection.     

Modeling the effect of dose on the lifetime tumor rate from an animal carcinogenicity experiment

The proportion of tumor-bearing animals in a chronic bioassay is often used as a basis for assessing risk at human exposure levels that are below the experimental range. However, such a crude experimental tumor rate can be biased by dose-related differences in the nontumor mortality. To adjust tumor rates for competing mortality, Kodell, Gaylor, and Chen (1986, Biometrics 42, 867-873) propose a standardized tumor rate, calculated separately in each dose group from dose-specific estimates of the tumor prevalence and mortality functions. This paper extends the approach of Kodell et al, by developing a method of modeling the standardized rate as a function of dose. An advantage of this approach is that it leads to estimates that are monotone in dose. In addition, by modeling the lifetime risk as a function of dose directly, it is possible to obtain estimates for the risk at dose levels outside the experimental range, such as for low-dose extrapolation, and estimation of the "tumorigenic dose 50" (TD50). A semiparametric model is developed, as well as the nonparametric alternative of isotonic regression. Simulations are provided to show the relative bias and precision of the two approaches to that of Kodell et al.     

Probabilistic Analysis of Human Health Risks Associated with Background Concentrations of Inorganic Arsenic: Use of a Margin of Exposure Approach

Substantial evidence exists from epidemiological and mechanistic studies supporting a sublinear or threshold dose–response relationship for the carcinogenicity of ingested arsenic; nonetheless, current regulatory agency evaluations have quantified arsenic risks using default, generic risk assessment procedures that assume a linear, no-threshold dose–response relationship. The resulting slope factors predict risks from U.S. background arsenic exposures that exceed certain regulatory levels of concern, an outcome that presents challenges for risk communication and risk management decisions. To better reflect the available scientific evidence, this article presents the results of a Margin of Exposure (MOE) analysis to characterize risks associated with typical and high-end background exposures of the U.S. population to arsenic from food, water, and soil. MOE values were calculated by comparing a no-observable-adverse-effect-level (NOAEL) derived from the epidemiological literature with exposure estimates generated using a probabilistic (Monte Carlo) model. The plausibility and conservative nature of the exposure and risk estimates evaluated in this analysis are supported by sensitivity and uncertainty analyses and by comparing predicted urinary arsenic concentrations with empirical data. Using the more scientifically supported MOE approach, the analysis presented in this article indicates that typical and high-end background exposures to inorganic arsenic in U.S. populations do not present elevated risks of carcinogenicity.     

Temporal trends in net and crude probability of death from cancer and other causes in the Australian population, 1984–2013

BackgroundWhile net probabilities of death in the relative survival framework ignore competing causes of death, crude probabilities allow estimation of the real risk of cancer deaths. This study quantifies temporal trends in net and crude probabilities of death.MethodsAustralian population-based cohort of 2,015,903 people aged 15-89 years, diagnosed with a single primary invasive cancer from 1984 to 2013 with mortality follow-up to 31 December 2014. Survival was analyzed with the cohort method. Flexible parametric relative survival models were used to estimate both probability measures by diagnosis year for all cancers and selected leading sites.ResultsFor each site, excess mortality rates reduced over time, especially for prostate cancer. While both the 10-year net and crude probability of cancer deaths decreased over time, specific patterns varied. For example, the crude probability of lung cancer deaths for males aged 50 years decreased from 0.90 (1984) to 0.79 (2013); whereas the corresponding probabilities for kidney cancer were 0.64 and 0.18 respectively. Patterns for crude probabilities of competing deaths were relatively constant. Although for younger patients, both net and crude measures were similar, crude probability of competing deaths increased with age, hence for older ages net and crude measures were different except for lung and pancreas cancers.ConclusionsThe observed reductions in probabilities of death over three decades for Australian cancer patients are encouraging. However, this study also highlights the ongoing mortality burden following a cancer diagnosis, and the need for continuing efforts to improve cancer prevention, diagnosis and treatment.     

Lifetime Smoking History and Cause-Specific Mortality in a Cohort Study with 43 Years of Follow-Up

BackgroundIn general, smoking increases the risk of mortality. However, it is less clear how the relative risk varies by cause of death. The exact impact of changes in smoking habits throughout life on different mortality risks is less studied.MethodsWe studied the impact of baseline and lifetime smoking habits, and duration of smoking on the risk of all-cause mortality, mortality of cardiovascular diseases (CVD), chronic obstructive pulmonary disease (COPD), any cancer and of the four most common types of cancer (lung, colorectal, prostate, and breast cancer) in a cohort study (Vlagtwedde-Vlaardingen 1965–1990, with a follow-up on mortality status until 2009, n = 8,645). We used Cox regression models adjusted for age, BMI, sex, and place of residence. Since previous studies suggested a potential effect modification of sex, we additionally stratified by sex and tested for interactions. In addition, to determine which cause of death carried the highest risk we performed competing-risk analyses on mortality due to CVD, cancer, COPD and other causes.ResultsCurrent smoking (light, moderate, and heavy cigarette smoking) and lifetime persistent smoking were associated with an increased risk of all-cause, CVD, COPD, any cancer, and lung cancer mortality. Higher numbers of pack years at baseline were associated with an increased risk of all-cause, CVD, COPD, any cancer, lung, colorectal, and prostate cancer mortality. Males who were lifetime persistent pipe/cigar smokers had a higher risk of lung cancer [HR (95% CI) = 7.72 (1.72–34.75)] as well as all-cause and any cancer mortality. A longer duration of smoking was associated with a higher risk of COPD, any and lung cancer [HR (95% CI) = 1.06 (1.00–1.12), 1.03 (1.00–1.06) and 1.10 (1.03–1.17) respectively], but not with other mortality causes. The competing risk analyses showed that ex- and current smokers had a higher risk of cancer, CVD, and COPD mortality compared to all other mortality causes. In addition, heavy smokers had a higher risk for COPD mortality compared to cancer, and CVD mortality.ConclusionOur study indicates that lifetime numbers of cigarettes smoked and the duration of smoking have different impacts for different causes of mortality. Moreover, our findings emphasize the importance of smoking-related competing risks when studying the smoking-related cancer mortality in a general population and that smoking cessation immediately effectively reduces the risk of all-cause and any cancer mortality.     

Long-term follow-up for brain tumor development after childhood exposure to ionizing radiation for tinea capitis

Ionizing radiation is an established risk factor for brain tumors, yet quantitative information on the long-term risk of different types of brain tumors is sparse. Our aims were to assess the risk of radiation-induced malignant brain tumors and benign meningiomas after childhood exposure and to investigate the role of potential modifiers of that risk. The study population included 10,834 individuals who were treated for tinea capitis with X rays in the 1950s and two matched nonirradiated groups, comprising population and sibling comparison groups. The mean estimated radiation dose to the brain was 1.5 Gy. Survival analysis using Poisson regression was performed to estimate the excess relative and absolute risks (ERR, EAR) for brain tumors. After a median follow-up of 40 years, an ERR/Gy of 4.63 and 1.98 (95% CI = 2.43-9.12 and 0.73-4.69) and an EAR/Gy per 10(4) PY of 0.48 and 0.31 (95% CI = 0.28-0.73 and 0.12-0.53) were observed for benign meningiomas and malignant brain tumors, respectively. The risk of both types of tumors was positively associated with dose. The estimated ERR/Gy for malignant brain tumors decreased with increasing age at irradiation from 3.56 to 0.47 (P = 0.037), while no trend with age was seen for benign meningiomas. The ERR for both types of tumor remains elevated at 30-plus years after exposure.     

A computer program package for relative survival analysis

A computer program package has been constructed for use in patient survival analyses for chronic diseases based on aggregated data. The central concept of the analyses--the relative survival rate--is the ratio of the observed survival rate of the patients to the survival rate expected in a group in the general population similar to the group of patients at the beginning of the follow-up (interval), with respect to age, sex and calendar time. This quantity is used to measure patient survival adjusted for the effect of mortality attributable to the competing risks of death without employing information on causes of death of individual patients. The package contains three alternative methods of estimating the relative survival rates, two different ways of estimating the expectation of life for the patients, and five methods of testing the relative survival patterns using information on the whole follow-up period. Conventional survival and competing risk analysis can also be performed with the package. It is hoped that the package will facilitate standardization of statistical methodology and terminology in long-term survival studies for chronic diseases.     

The analysis of failure times in the presence of competing risks.

Distinct problems in the analysis of failure times with competing causes of failure include the estimation of treatment or exposure effects on specific failure types, the study of interrelations among failure types, and the estimation of failure rates for some causes given the removal of certain other failure types. The usual formation of these problems is in terms of conceptual or latent failure times for each failure type. This approach is criticized on the basis of unwarranted assumptions, lack of physical interpretation and identifiability problems. An alternative approach utilizing cause-specific hazard functions for observable quantities, including time-dependent covariates, is proposed. Cause-specific hazard functions are shown to be the basic estimable quantities in the competing risks framework. A method, involving the estimation of parameters that relate time-dependent risk indicators for some causes to cause-specific hazard functions for other causes, is proposed for the study of interrelations among failure types. Further, it is argued that the problem of estimation of failure rates under the removal of certain causes is not well posed until a mechanism for cause removal is specified. Following such a specification, one will sometimes be in a position to make sensible extrapolations from available data to situations involving cause removal. A clinical program in bone marrow transplantation for leukemia provides a setting for discussion and illustration of each of these ideas. Failure due to censoring in a survivorship study leads to further discussion.