Constant risk differences in the analysis of animal tumorigenicity data

In a typical tumorigenicity study, most tumors are not observable in live animals and only a single (terminal) sacrifice is performed. This paper proposes a nonparametric, survival-adjusted analysis for these data that focuses on tumor incidence and yet does not require data on cause of death or assumptions about the tumor's lethality. The tumor onset/death process is most naturally characterized in terms of the tumor incidence rate and the death rates for tumor-free and tumor-bearing animals. The proposed approach, however, reparameterizes the problem in terms of the incidence rate, the death rate for tumor-free animals, and the difference between the death rates for tumor-free and tumor-bearing animals (i.e., the risk difference). The advantage of this alternative formulation is that a full likelihood analysis is possible with as few as one sacrifice time if the risk difference is assumed to be constant with respect to time. Data from the large ED01 study suggest that reasonable results can be obtained under the assumption of constant risk differences.     

Semiparametric estimation in copula models for bivariate sequential survival times

Sequentially observed survival times are of interest in many studies but there are difficulties in analyzing such data using nonparametric or semiparametric methods. First, when the duration of followup is limited and the times for a given individual are not independent, induced dependent censoring arises for the second and subsequent survival times. Non-identifiability of the marginal survival distributions for second and later times is another issue, since they are observable only if preceding survival times for an individual are uncensored. In addition, in some studies a significant proportion of individuals may never have the first event. Fully parametric models can deal with these features, but robustness is a concern. We introduce a new approach to address these issues. We model the joint distribution of the successive survival times by using copula functions, and provide semiparametric estimation procedures in which copula parameters are estimated without parametric assumptions on the marginal distributions. This provides more robust estimates and checks on the fit of parametric models. The methodology is applied to a motivating example involving relapse and survival following colon cancer treatment.     

Distinguishing effects on tumor multiplicity and growth rate in chemoprevention experiments

In some types of cancer chemoprevention experiments and short-term carcinogenicity bioassays, the data consist of the number of observed tumors per animal and the times at which these tumors were first detected. In such studies, there is interest in distinguishing between treatment effects on the number of tumors induced by a known carcinogen and treatment effects on the tumor growth rate. Since animals may die before all induced tumors reach a detectable size, separation of these effects can be difficult. This paper describes a flexible parametric model for data of this type. Under our model, the tumor detection times are realizations of a delayed Poisson process that is characterized by the age-specific tumor induction rate and a random latency interval between tumor induction and detection. The model accommodates distinct treatment and animal-specific effects on the number of induced tumors (multiplicity) and the time to tumor detection (growth rate). A Gibbs sampler is developed for estimation of the posterior distributions of the parameters. The methods are illustrated through application to data from a breast cancer chemoprevention experiment.     

Mapping quantitative trait loci in the case of a spike in the phenotype distribution

A common departure from the usual normality assumption in QTL mapping concerns a spike in the phenotype distribution. For example, in measurements of tumor mass, some individuals may exhibit no tumors; in measurements of time to death after a bacterial infection, some individuals may recover from the infection and fail to die. If an appreciable portion of individuals share a common phenotype value (generally either the minimum or the maximum observed phenotype), the standard approach to QTL mapping can behave poorly. We describe several alternative approaches for QTL mapping in the case of such a spike in the phenotype distribution, including the use of a two-part parametric model and a nonparametric approach based on the Kruskal-Wallis test. The performance of the proposed procedures is assessed via computer simulation. The procedures are further illustrated with data from an intercross experiment to identify QTL contributing to variation in survival of mice following infection with Listeria monocytogenes.     

B16 melanoma development in black mice exposed to low-level microwave radiation

The effect of low-level microwave exposure, 2,450 MHz, at a power density of 1 mW/cm2 and specific absorption rate of 1.2 mW/g, continuous waves (CW) or pulsed waves (PW), 2.5 h/day, 6 sessions/week until death (up to 690 h of irradiation), has been studied in black C57/6J mice with B16 melanoma. The results show that no significant effects are observed on tumor development or on survival times compared to controls, or between CW- and PW-treated animals.     

Nonparametric estimation of the survival function when cause of death is uncertain

A nonparametric estimator for the survival function, accommodating censored survival times and uncertainty in the assignment of cause of death, is proposed. For example, in a carcinogenicity experiment the data on each animal may consist of an observed age-at-death and some indication of the probability that the tumor type under study caused death. An estimator of the net survival function, for time-to-death due to the cause of interest, is developed. Under certain assumptions, the proposed estimator is consistent and asymptotically normally distributed. Monte Carlo simulations were used to compare this estimator with the Kaplan-Meier estimator. Forcing the cause of death to be specified with certainty, as required by the Kaplan-Meier estimator, may result in substantial biases.     

Exploring Migration Data Using Interval-Censored Time-to-Event Models

Abstract: Ecologists and wildlife biologists rely on periodic observation of radiocollared animals to study habitat use, survival, movement, and migration, resulting in response times (e.g., mortality and migration) known only to occur within an interval of time. We illustrate methods for analyzing interval-censored data using data on the timing of fall migration (from spring-summer-fall to winter ranges) for white-tailed deer (Odocoileus virginianus) in northern Minnesota, USA, during years 1991–1992 to 2005–2006. We compare both nonparametric and parametric methods for estimating the cumulative distribution function of migration times, and we suggest a parametric (cure rate) model that accounts for conditional (facultative) migrators as a potential alternative to traditional parametric models. Lastly, we illustrate methods for exploring the effect of environmental covariates on migration timing. Models with time-dependent covariates (snow depth, temp) were sensitive to the treatment of the data (as interval-censored or known event times), suggesting the need to account for interval-censoring when modeling the effect of these covariates.     

Estimation with correlated censored survival data with missing covariates

Incomplete covariate data are a common occurrence in studies in which the outcome is survival time. Further, studies in the health sciences often give rise to correlated, possibly censored, survival data. With no missing covariate data, if the marginal distributions of the correlated survival times follow a given parametric model, then the estimates using the maximum likelihood estimating equations, naively treating the correlated survival times as independent, give consistent estimates of the relative risk parameters Lipsitz et al. 1994 50, 842-846. Now, suppose that some observations within a cluster have some missing covariates. We show in this paper that if one naively treats observations within a cluster as independent, that one can still use the maximum likelihood estimating equations to obtain consistent estimates of the relative risk parameters. This method requires the estimation of the parameters of the distribution of the covariates. We present results from a clinical trial Lipsitz and Ibrahim (1996b) 2, 5-14 with five covariates, four of which have some missing values. In the trial, the clusters are the hospitals in which the patients were treated.     

Generalized Rank Transformations for Tests of Survival

The asymptotic equivalence of nonparametric tests and parametric tests based on rank-transformed data (CONOVER and IMAN , 1981) can be extended to the case of censoring. This paper presents generalized rank transformations for analyses of censored data, of interval-censored data and of survival data with uncertain causes of death. A Monte Carlo study and an analysis of leukemia remission times demonstrate excellent agreement of suggested procedures with GEHAN 'S (1965) and PRENTICE 'S (1978) tests.     

Nonparametric methods for survival/sacrifice experiments

In many carcinogenicity studies, the time to disease occurrence is not clinically observable; a survival/sacrifice experiment is considered for nonparametric inference about the rate of disease occurrence. A multistate model for disease development and death is considered and an algorithm of the EM type for maximum likelihood estimation is obtained. Questions of identifiability and estimability are addressed. Under the model, interval hazards for disease occurrence are identifiable for intervals defined by the sacrifice times. A score test is developed appropriate for the comparison of two groups with respect to disease development without need of any assumption concerning lethality of the disease concerned.     

Bayesian inference on age-specific survival for censored and truncated data

1. Traditional estimation of age-specific survival and mortality rates in vertebrates is limited to individuals with known age. Although this subject has been studied extensively using effective capture-recapture and capture-recovery models, inference remains challenging because of large numbers of incomplete records (i.e. unknown age of many individuals) and because of the inadequate duration of the studies. 2. Here, we present a hierarchical model for capture-recapture/recovery (CRR) data sets with large proportions of unknown times of birth and death. The model uses a Bayesian framework to draw inference on population-level age-specific demographic rates using parametric survival functions and applies this information to reconstruct times of birth and death for individuals with unknown age. 3. We simulated a set of CRR data sets with varying study span and proportions of individuals with known age, and varying recapture and recovery probabilities. We used these data sets to compare our method to a traditional CRR model, which requires knowledge of individual ages. Subsequently, we applied our method to a subset of a long-term CRR data set on Soay sheep. 4. Our results show that this method performs better than the common CRR model when sample sizes are low. Still, our model is sensitive to the choice of priors with low recapture probability and short studies. In such cases, priors that overestimate survival perform better than those that underestimate it. Also, the model was able to estimate accurately ages at death for Soay sheep, with an average error of 0.94 years and to identify differences in mortality rate between sexes. 5. Although many of the problems in the estimation of age-specific survival can be reduced through more efficient sampling schemes, most ecological data sets are still sparse and with a large proportion of missing records. Thus, improved sampling needs still to be combined with statistical models capable of overcoming the unavoidable limitations of any fieldwork. We show that our approach provides reliable estimates of parameters and unknown times of birth and death even with the most incomplete data sets while being flexible enough to accommodate multiple recapture probabilities and covariates.     

Simple parametric survival analysis with anonymized register data: A cohort study with truncated and interval censored event and censoring times

Background

To preserve patient anonymity, health register data may be provided as binned data only. Here we consider as example, how to estimate mean survival time after a diagnosis of metastatic colorectal cancer from Norwegian register data on time to death or censoring binned into 30 day intervals. All events occurring in the first three months (90 days) after diagnosis were removed to achieve comparability with a clinical trial. The aim of the paper is to develop and implement a simple, and yet flexible method for analyzing such interval censored and truncated data.

Methods

Considering interval censoring a missing data problem, we implement a simple multiple imputation strategy that allows flexible sensitivity analyses with respect to the shape of the censoring distribution. To allow identification of appropriate parametric models, a χ²-goodness-of-fit test--also imputation based--is derived and supplemented with diagnostic plots. Uncertainty estimates for mean survival times are obtained via a simulation strategy. The validity and statistical efficiency of the proposed method for varying interval lengths is investigated in a simulation study and compared with simpler alternatives.

Results

Mean survival times estimated from the register data ranged from 1.2 (SE = 0.09) to 3.2 (0.31) years depending on period of diagnosis and choice of parametric model. The shape of the censoring distribution within intervals did generally not influence results, whereas the choice of parametric model did, even when different models fit the data equally well. In simulation studies both simple midpoint imputation and multiple imputation yielded nearly unbiased analyses (relative biases of -0.6% to 9.4%) and confidence intervals with near-nominal coverage probabilities (93.4% to 95.7%) for censoring intervals shorter than six months. For 12 month censoring intervals, multiple imputation provided better protection against bias, and coverage probabilities closer to nominal values than simple midpoint imputation.

Conclusion

Binning of event and censoring times should be considered a viable strategy for anonymizing register data on survival times, as they may be readily analyzed with methods based on multiple imputation.

     

The negative systemic effect of BCGcw inoculated intraperitoneally

Summary The present studies describe a systemic effect of BCGcw inoculated intraperitoneally by observing its influence on the development of Morris hepatomas inoculated intramuscularly. In none of our studies did we observe an inhibition of tumor growth. Instead, an enhancement of tumor growth was seen with four antigenically distinct Morris hepatomas (3924a, 9098, 7777, and 5123tc) in two strains of inbred rats (Buffalo and ACI). Extensive studies with Morris hepatoma 3924a showed consistent enhancement of intramuscular tumor growth in eight of eight experiments with a tumor cell dose of 1×10⁵ and a BCGcw dose of 900 g. In BCGcw-inoculated animals, palpable tumors (1–2 g) were detected approximately 1 week earlier than in controls, and significantly larger tumor masses were noted on the day of sacrifice. With the threshold dose of cells, 1×10⁴, an increase in tumor incidence was observed. It was not necessary for the host to be immunized with BCGcw prior to tumor inoculation as enhancement of tumor growth occurred when the BCGcw were inoculated the same day or 7 days after tumor inoculation. Splenectomized animals also demonstrated BCGcw-mediated enhancement of tumor growth. BCGcw immunization blocks the induction of tumor-specific immunity. When 3924a ascites tumor cells were inoculated intradermally into normal animals, no tumor growth was observed and tumor-specific immunity resulted. When 3924a ascites tumor cells were inoculated intradermally into BCGcw-immunized animals, progressive intradermal tumors grew in all the animals, implying that tumor-specific immunity was not induced. The administration of BCGcw did not effect established tumor-specific immunity to line 3924a as assessed by tumor-specific rechallenge resistance. Studies with an allograft system showed that the ACI tumor 3924a would not grow in normal Buffalo rats, but transient tumor growth was observed when the Buffalo rats were immunized with BCGcw. The abbreviations used are: BCGcw, bacillus Calmette-Guérin cell walls attached to oil droplets; MLC, mixed lymphocyte culture; MER, methanol extract residue; IM, intramuscular; IP, intraperitoneal; ID, intradermal; Con-A, concanavalin-A     

Naloxone prolongs the survival time of mice treated with neuroblastoma

The effect of naloxone on tumor growth and survival time was studied in mice with neuroblastoma tumors. Daily s.c. injections of either 5, 10, 15, or 20 mg/kg naloxone were initiated either 2 weeks prior to tumor cell inoculations (pre-treated groups) or one week after tumor transplantation (post-treated groups). The S20Y cell line, cloned from A/Jax murine C1300 neuroblastoma, was utilized and each animal was inoculated with 10⁶ cells. All mice in the saline- tumor and naloxone post-treated groups, developed tumors within 3 weeks after tumor cell inoculation. In the naloxone pre-treated groups, 4 of 12 mice exposed to 20 mg/kg, 2 of 12 mice exposed to 15 mg/kg, and 1 of 12 mice exposed to 10 mg/kg, did not develop tumors within the 91-day post-inoculation period. Three animals in the 20 mg/kg naloxone pre-treated group developed tumors between 43 and 63 days after tumor cell inoculation. Tumor dimensions were often reduced in naloxone-treated animals but a dose-response relationship was not found in regard to the magnitude of alterations in tumor size. At the time of death, tumor sizes of control and naloxone-exposed mice were similar. In general, tumor-bearing mice receiving naloxone lived longer than saline-tumor controls, with animals receiving higher drug dosages surviving for the longest time. In contrast to a mean survival time of 27 days for controls, naloxone pre-treated groups had increases in survival times of 25–61%, whereas naloxone post- treated groups exhibited increases of 20–40%. The median day of death for all mice exposed to naloxone was prolonged by 21–75%, occuring 6–21 days after the 28-day median for saline-tumor controls. These results suggest that naloxone, a non-addictive compound, is an effective agent in modulating neoplasia.     

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.     

Parametric analysis of the survival time of irradiated animals

The work deals with the parametric analysis of the irradiated animal survival data. Several forms of radiation death are considered. The life-span distribution has been derived using a special type Markovian model. Conditions for identifiability of the distribution and properties of maximum likelihood estimates of unknown parameters are discussed.     

Susceptibility dynamics in neonatal BALB/c mice infected with Cryptosporidium parvum.

BALB/c Mice were infected as neonates and at different ages to study the susceptibility dynamics in this animal model to Cryptosporidium parvum. When 4-day-old animals were infected with 10(5) C. parvum oocysts, parasites were detected in the terminal ileum when the mice became 14-25 days old (10-21 days post-infection [PI]). The percentage of animals positive for parasites was 100% up to the age of 19 days (15 days PI) but decreased immediately thereafter until no parasites were detected in 26-day-old (22 days PI) or older mice. Parasite load also decreased in these animals from 184.7 parasites per high power field in 14-day-old animals (10 days PI) to 0.22 in 25-day-old (21 days PI) mice. In a second study, some neonatal mice became resistant to C. parvum when infection was attempted at day-10 of age (day-15 of age at sacrifice). The susceptibility to C. parvum decreased until 14 days of age (19 days of age at sacrifice) when mice could no longer be infected. Parasite load also decreased in infected mice from 235.6 parasites per high power field (9 days of age at sacrifice) to 0.25 (18 days of age at sacrifice).     

Standardized tumor rates for chronic bioassays

If crude experimental proportions of animals with tumors from chronic bioassays for carcinogenicity are used for low-dose extrapolation in a risk analysis, different dose-specific patterns of mortality due to competing risks can bias the results. In order to adjust tumor rates for differential mortality across dose groups, Farmer, Kodell, and Gaylor (1982, Risk Analysis 2, 27-34) recommended using nonparametric estimates of probability distributions of times to onset of tumors, with competing causes of death removed, when performing a risk analysis. This paper extends the approach of Farmer et al. by proposing a method for adjusting tumor rates to reflect lifetime or near-lifetime tumor incidences that would be obtained if all dose groups experienced the control mortality rate from causes other than the tumor of interest. Thus, natural mortality due to competing risks is explicitly included, rather than removed. The proposed standardized tumor rates are calculated as a summation of adjusted age-specific probabilities of dying with a tumor during the course of an animal bioassay for carcinogenicity plus the probability of being alive with a tumor at the terminal sacrifice.     

A spatial open-population capture-recapture model

A spatial open-population capture-recapture model is described that extends both the non-spatial open-population model of Schwarz and Arnason and the spatially explicit closed-population model of Borchers and Efford. The superpopulation of animals available for detection at some time during a study is conceived as a two-dimensional Poisson point process. Individual probabilities of birth and death follow the conventional open-population model. Movement between sampling times may be modeled with a dispersal kernel using a recursive Markovian algorithm. Observations arise from distance-dependent sampling at an array of detectors. As in the closed-population spatial model, the observed data likelihood relies on integration over the unknown animal locations; maximization of this likelihood yields estimates of the birth, death, movement, and detection parameters. The models were fitted to data from a live-trapping study of brushtail possums (Trichosurus vulpecula) in New Zealand. Simulations confirmed that spatial modeling can greatly reduce the bias of capture-recapture survival estimates and that there is a degree of robustness to misspecification of the dispersal kernel. An R package is available that includes various extensions.     

FAS/FASL Expression Profile as a Prognostic Marker in Squamous Cell Carcinoma of the Oral Cavity

FAS/FASL altered expression may cause tumor protecting immunomodulation, with a direct impact on patient prognosis. FAS expression was studied in 60 squamous cell carcinomas of the oral cavity. FAS expression did not show a significant association with tumor histopathological characteristics, but was significantly associated with lymph node positivity. FAS expression was significantly associated with disease specific death and negative FAS expression was an independent risk factor, increasing risk 4 times when compared to positive expression. When FAS and FASL expression results were combined, we were able to define high, intermediate and low risk profiles. Disease-free and disease-specific survival were significantly correlated with FAS/FASL expression profiles. The high risk category was an independent marker for earlier disease relapse and disease-specific death, with approximately 4- and 6-fold increased risk, respectively, when compared to the low risk profile. Risk profiles based on FAS/FASL expression showed that high risk was significantly associated with increased disease relapse and death, as well as shorter disease-free or disease-specific survival. This categorization, added to patient clinical data, may facilitate the choice of therapy, minimizing treatment failure and increasing disease control.