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Immersion biotesting has long been used to challenge packages, particularly cans, for pinholes and channel leaks. Such testing for all types of plastic packaging may not be appropriate because some packages (e.g., aseptic, hot fill) are not exposed to water. As the food-packaging industry develops alternative environmental biotests there is a need to benchmark them against traditional immersion testing. The purpose of this research was to examine the threshold of critical-defect dimensions using artifically created channel leaks of 10 and 20 μm and 5- and 10-mm lengths sealed into plastic pouches which were subsequently tested by immersion at 102 and 106 CFU of motile and nonmotile Pseudomonas fragi TM849 per ml. Forty-four percent (44%) of the pouches tested became contaminated, indicating the threshold defect value is below 10 μm. Microbial ingress was significant (P < .05) for motile test organisms with a concentration of 106 CFU/ml. The interaction of concentration and time was also significant at 102 CFU/ml at 30 min exposure and 106 CFU/ml at 15 min. Channel length was not statistically significant. The markedly greater contamination rate using immersion testing versus that of aerosol testing highlights the importance of using test methods that reflect environmental exposure conditions of the packages.

When toxicity data are not available for a chemical mixture of concern, U.S. Environmental Protection Agency (EPA) guidelines allow risk assessment to be based on data for a surrogate mixture considered “sufficiently similar” in terms of chemical composition and component proportions. As a supplementary approach, using statistical equivalence testing logic and mixed model theory we have developed methodology to define sufficient similarity in dose—response for mixtures of many chemicals containing the same components with different ratios. Dose—response data from a mixture of 11 xenoestrogens and the endogenous hormone, 17s-estradiol are used to illustrate the method.

Fixed-ratio ray designs have been used for detecting and characterizing interactions of large numbers of chemicals in combination. Single-chemical dose-response data are used to predict an “additivity curve” along an environmentally relevant ray. A “mixture curve” is estimated from the mixture dose-response data along the ray. A test of additivity is equivalent to a test of coincidence of these two curves, which is based on the traditional hypothesis testing framework that assumes additivity in the null hypothesis and rejects with evidence of interaction. However, failure to reject may be due to lack of statistical power, making the claim of additivity problematic. As a solution we have developed rigorous methodology to test for additivity using statistical equivalence testing logic in which additivity is claimed based on pre-specified biologically important additivity margins, if the data support such a claim. Using the principle of confidence interval inclusion, a confidence region about the difference of meaningful functions of model parameters from the mixture model and that predicted under additivity is computed. When the confidence region is completely contained within the additivity margins then additivity is claimed with a Type I error rate chosen a priori to be some acceptably small value. The method is illustrated using an environmentally relevant fixed-ratio mixture of nine haloacetic acids where cytotoxic response is measured.

The general question of appropriate criteria for the development of models from a designed experiment is considered. Since models that are found in this setting are generally not mechanistic but rather empirical in nature, the arbitrary requirement of hierarchy may often lead to a model choice that is inferior in terms of satisfying the goals of the experiment. The non-hierarchial model may be no less interpretable than a hierarchial one and may allow for appreciably better predictive capability. Leaving highly insignificant terms in the model for the sake of hierarchy can increase standard errors and result in poor prediction. Parsimony in empirical modeling is often an important virtue. The broader research question revolves around the choice of criteria for model building, variable selection and model discrimination. Copyright © 2005 John Wiley & Sons, Ltd.

Exposure to mixtures of chemicals is an important and relevant environmental issue. Of particular interest is the detection and characterization of departure of biological effects from additivity. Methodology based on the assumption of additivity is used in fitting single-chemicaldata. Interactionsare determined and characterized by making comparisons between the observed and predicted responses at mixtures along a fixed ratio ray of the component substances. Two simultaneous tests are developed for testing for any departure from additivity. Multiple comparisons procedures are used to compare observed responses to that predicted under additivity. A simultaneous confidence band on the predicted responses along the mixture ray is also developed. The methods are illustrated with cytotoxicity data that arise when human epidermal keratinocytes are exposed to a mixture of arsenic, chromium, cadmium, and lead. Synergistic, antagonistic, and additive cytotoxicities were observed at different dose levels of the four-metal mixture.

To evaluate health effects of chemical mixtures, such as multiple heavy metals in drinking water, we have been developing efficient and accurate hazard identification strategies. Thus, in this study, we determine the cytotoxicity of arsenic, cadmium, chromium, and lead, and characterize interactions among these metals in human epidermal keratinocytes. Three immortal keratinocyte cell lines (RHEK-1, HaCaT, and NM1) and primary keratinocytes (NHEK) were used. A statistical approach applying an additivity response surface methodology was used to test the validity of the additivity concept for a 4-metal mixture. Responses of the 4 keratinocyte strains to the metal mixture were highly dose-dependent. A growth stimulatory effect (hormesis) was observed in RHEK-1, NM1, and NHEK cells with the metal mixture at low concentrations (low ppb range). This hormesis effect was not significant in HaCaT. As the mixture concentration increased, a trend of additivity changed to synergistic cytotoxicity in all 4 cell strains. However, in NHEK, RHEK-1, and HaCaT, at the highest mixture concentrations tested, the responses to the metal mixtures were antagonistic. In NM1, no significant antagonistic interaction among the metals was observed. To explore a mechanistic basis for these differential sensitivities, levels of glutathione and metallothioneins I and II were determined in the keratinocyte cell strains. Initial data are consistent with the suggestion that synergistic cytotoxicity turned to antagonistic effects because at highest mixture exposure concentrations cellular defense mechanisms were enhanced.

Recent advances in quality technology have resulted from considering the variation of a response variable as well as its mean value. Current research dealing with the analysis of data involving noise factors has mostly been confined to models with normally distributed responses. The research described herein focuses on development of methodology for time-to-event data. Once model parameters have been estimated, optimization of the pertinent aspects of the event time distribution can be used to reduce the effect of the noise factors.

Test organism motility, concentration, aerosol exposure time, hole diameter and length were evaluated to determine their influence on microbial ingress into a flexible plastic pouch. Microtubes with 10- and 20-μm hole diameters and of 5- and 10-mm lengths were used as defects in 128 flexible pouches. A bioaerosol with a 2.68-μm mean particle size comprised of 102 or 106 CFU/ml source concentrations of motile or nonmotile Pseudomonas fragi TM 849 was introduced into a 119,911-cm3 chamber for exposures of 15 or 30 minutes. Six pouches showed test organism growth after a 72-h incubation period. Microbial ingress was significant (P < .05) for motile test organisms with source concentrations of 106 CFU/ml.

Alphabetic optimality has become an important component of experimental design in the case of the standard linear model. Many design criteria have been developed in order to produce optimal designs based on either parameter estimation or the prediction of a response. However, relatively little attention has been devoted to developing designs in the nonlinear model case (e.g. logistic regression model). D-optimality is the only criterion that has received much attention in the literature for the logistic regression model. This paper develops optimal designs for the logistic model based on the prediction of a response. Comparisons are made between different optimal designs by computing efficiencies based on certain optimality criteria. The robustness properties for some of the newly created designs are also investigated. Finally, the development of optimal designs for asymmetric regions of the logistic regression model is presented.

In in vitro testing, no pharmacologic synergism has been found for the combination of cisplatin and etoposide in P388 leukemia in contrast to the demonstration of therapeutic synergism in the same model. No pharmacologic synergism has been found for the same combination in the treatment of four small-cell lung-cancer cell lines, although clinical results obtained using this combination in small-cell lung cancer and other cancers suggest a therapeutic advantage. The popular concept of synergy, implying a therapeutic advantage, is different from the pharmacologic meaning, which generally implies that less drug is required in a combination for an equal effect. Therapeutic advantage may be obtained regardless of whether drugs are synergistic in the pharmacologic sense in the treatment of a tumor. To gain a more comprehensive insight into concepts of drug interaction, it is important to recognize that the type of drug interaction seen is dependent on the drug doses used and may vary with the treatment of different cell lines. All of these factors complicate the use of the word synergism, or any associated term, in a categorical manner to describe the effects of combinations of antineoplastic drugs.

The risk-reducing effect of a potential reduced-risk tobacco product (PRRP) can be investigated conceptually in a long-term, prospective study of disease risks among cigarette smokers who switch to a PRRP and in appropriate comparison groups. Our objective was to provide guidance for establishing the fundamental design characteristics of a study intended to (1) determine if switching to a PRRP reduces the risk of lung cancer (LC) compared with continued cigarette smoking, and (2) compare, using a non-inferiority approach, the reduction in LC risk among smokers who switched to a PRRP to the reduction in risk among smokers who quit smoking entirely. Using standard statistical methods applied to published data on LC incidence after smoking cessation, we show that the sample size and duration required for a study designed to evaluate the potential for LC risk reduction for an already marketed PRRP, compared with continued smoking, varies depending on the LC risk-reducing effectiveness of the PRRP, from a 5-year study with 8000-30,000 subjects to a 15-year study with

Pretreatment with either pyridostigmine (PYR) or physostigmine (PHY) followed by atropineoxime therapy is very effective in reducing the lethality of organophosphorus nerve agents. The therapeutic efficacy of scopolamine (SCP) versus azaprophen (AZA), when used in conjunction with PHY and PYR (PHY/PYR) combination pretreatment, was evaluated in guinea pigs challenged with 2 half-lethal doses of soman. Maximum postsoman decrement of rotarod performance was measured. Response surface methodology was employed to describe the relationship between the decrement and the PHY/PYR dosages. Results show that AZA is a more effective pretreatment adjunct at the behavioral deficit-free doses tested, AZA or SCP is as effective with PHY alone as with a PHY/PYR combination. Thus, PYR adds essentially nothing to the carbamate combination against soman-induced behavioral deficit.

Recent studies have shown that pretreatment with either pyridostigmine (PYR) or physostigmine (PHY) followed by atropineoxime therapy is very effective in reducing the lethality of nerve agents. The therapeutic efficacy of a PHY and PYR combination pretreatment was evaluated in guinea pigs challenged with two LD50s of soman. Endpoints measured were percentage of acetylcholinesterase inhibition induced by the pretreatment and survival up to 24 hr postchallenge. Response surface methodology was employed to describe the relationship between each endpoint and the pretreatment combination. Although both carbamates contributed to blood acetylcholinesterase inhibition, PHY alone protected as well as the optimal dose of the combination.

Physostigmine (PHY) has the advantage over pyridostigmine of minimizing OP-induced incapacitation because it penetrates into the CNS. However, physostigmine is behaviorally toxic at relatively low concentrations. It is anticipated that this could be offset by a cholinolytic to prevent behavioral deficit due to the carbamate pretreatment alone. The therapeutic efficacy of physostigmine/azaprophen pretreatment therapy was evaluated in soman-challenged guinea pigs. Response surface methodology was employed to describe the relationship of the pretreatment combination with duration of incapacitation. The significance of the combination relative to PHY alone was evaluated in addition to dose combinations that yield optimal time to recovery. Analysis of the fitted response surface indicated that combination pretreatment with these compounds significantly reduces the time to recovery after soman challenge versus pretreatment with PHY alone.

Several assumptions, defined and undefined, are used in the toxicity assessment of chemical mixtures. In scientific practice mixture components in the low-dose region, particularly subthreshold doses, are often assumed to behave additively (i.e., zero interaction) based on heuristic arguments. This assumption has important implications in the practice of risk assessment, but has not been experimentally tested. We have developed methodology to test for additivity in the sense of Berenbaum (Advances in Cancer Research, 1981), based on the statistical equivalence testing literature where the null hypothesis of interaction is rejected for the alternative hypothesis of additivity when data support the claim. The implication of this approach is that conclusions of additivity are made with a false positive rate controlled by the experimenter. The claim of additivity is based on prespecified additivity margins, which are chosen using expert biological judgment such that small deviations from additivity, which are not considered to be biologically important, are not statistically significant. This approach is in contrast to the usual hypothesis-testing framework that assumes additivity in the null hypothesis and rejects when there is significant evidence of interaction. In this scenario, failure to reject may be due to lack of statistical power making the claim of additivity problematic. The proposed method is illustrated in a mixture of five organophosphorus pesticides that were experimentally evaluated alone and at relevant mixing ratios. Motor activity was assessed in adult male rats following acute exposure. Four low-dose mixture groups were evaluated. Evidence of additivity is found in three of the four low-dose mixture groups. The proposed method tests for additivity of the whole mixture and does not take into account subset interactions (e.g., synergistic, antagonistic) that may have occurred and cancelled each other out.

Robust statistical methods are important to the evaluation of toxicological interactions (i.e., departures from additivity) among chemicals in a mixture. However, different concepts of joint toxic action as applied to the statistical analysis of chemical mixture toxicology data or as used in environmental risk assessment often appear to conflict with one another. A unifying approach for application of statistical methodology in chemical mixture toxicology research is based on consideration of change(s) in slope. If the slope of the dose-response curve of one chemical does not change in the presence of other chemicals, then there is no interaction between the first chemical and the others. Conversely, if the rate of change in the response with respect to dose of the first chemical changes in the presence of the other chemicals, then an interaction is said to exist. This concept of zero interaction is equivalent to the usual approach taken in additivity models in the statistical literature. In these additivity models, the rate of change in the response as a function of the i(th) chemical does not change in the presence of other chemicals in a mixture. It is important to note that Berenbaum's (1985, J. Theor. Biol. 114, 413-431) general and fundamental definition of additivity does not require the chemicals in the mixture to have a common toxic mode of action nor to have similarly shaped dose response curves. We show an algebraic equivalence between these statistical additivity models and the definition of additivity given by Berenbaum.

Environmental exposures generally involve chemical mixtures instead of single chemicals. Statistical models such as the fixed-ratio ray design, wherein the mixing ratio (proportions) of the chemicals is fixed across increasing mixture doses, allows for the detection and characterization of interactions among the chemicals. In this study, we tested for interaction(s) in a mixture of five organophosphorus (OP) pesticides (chlorpyrifos, diazinon, dimethoate, acephate, and malathion). The ratio of the five pesticides (full ray) reflected the relative dietary exposure estimates of the general population as projected by the US EPA Dietary Exposure Evaluation Model (DEEM). A second mixture was tested using the same dose levels of all pesticides, but excluding malathion (reduced ray). The experimental approach first required characterization of dose-response curves for the individual OPs to build a dose-additivity model. A series of behavioral measures were evaluated in adult male Long-Evans rats at the time of peak effect following a single oral dose, and then tissues were collected for measurement of cholinesterase (ChE) activity. Neurochemical (blood and brain cholinesterase [ChE] activity) and behavioral (motor activity, gait score, tail-pinch response score) endpoints were evaluated statistically for evidence of additivity. The additivity model constructed from the single chemical data was used to predict the effects of the pesticide mixture along the full ray (10-450 mg/kg) and the reduced ray (1.75-78.8 mg/kg). The experimental mixture data were also modeled and statistically compared to the additivity models. Analysis of the 5-OP mixture (the full ray) revealed significant deviation from additivity for all endpoints except tail-pinch response. Greater-than-additive responses (synergism) were observed at the lower doses of the 5-OP mixture, which contained non-effective dose levels of each of the components. The predicted effective doses (ED20, ED50) were about half that predicted by additivity, and for brain ChE and motor activity, there was a threshold shift in the dose-response curves. For the brain ChE and motor activity, there was no difference between the full (5-OP mixture) and reduced (4-OP mixture) rays, indicating that malathion did not influence the non-additivity. While the reduced ray for blood ChE showed greater deviation from additivity without malathion in the mixture, the non-additivity observed for the gait score was reversed when malathion was removed. Thus, greater-than-additive interactions were detected for both the full and reduced ray mixtures, and the role of malathion in the interactions varied depending on the endpoint. In all cases, the deviations from additivity occurred at the lower end of the dose-response curves.

The dosing of combination therapies is commonly undertaken empirically by practising physicians, and a coherent algorithm to approach the problem of combination dosing is currently lacking. Current methods of evaluating multiple drug combinations in clinical trials fail to provide information regarding the location of more effective doses when the combination is not found to differ from the standard, even though the absence of a difference does not necessarily mean the new combination is ineffective. Moreover, in studies where the new combination is found more effective, often a large proportion of the study participants obtain no benefit from the trial. Even with early stopping rules, the time these subjects spend on inferior treatments can have lasting detrimental effects, leading to problems with patient enrolment and adherence to study protocol. This paper describes an evolutionary operation (EVOP) direct-search procedure to titrate combination doses within individual patients. The Nelder-Mead simplex direct-search algorithm is used to titrate combinations of drugs within individual subjects. Desirability functions are utilized to define the main response of interest and additional responses or constraints. Statistical methodology for determining whether the titrated treatment combination has resulted in an improvement in subject response and for evaluating for therapeutic synergism is developed. Inferences can then be made about the efficacy of the combination or about the individual drugs that comprise the combination. The advantages of this approach include affording every patient the potential to benefit from the combination under study and permitting the consideration of multiple endpoints simultaneously.

In this paper we focus on the use of a two-stage procedure for logistic regression that emphasizes predicting response through the use of the Q-optimality criterion. The use of D-optimality in the first stage is primarily to allow best possible parameter estimates as one enters the second stage. However, it is important to understand that there are many ways to formulate the two-stage procedure. It may involve any optimality criterion in either stage. In fact, theoretically, one need not stop at two stages. It was our intention in this paper to demonstrate the potential in the two-stage procedure in cases in which good initial parameter estimates are not available. Those investigators who are interested in the software for the two-stage procedure described here should contact Dr. William R. Myers.

The efficacy of diazepam (DZ) and scopolamine (SCP), in combination with atropine (ATR)+oxime therapy, against soman-induced seizure/convulsive activity and associated brain damage has been demonstrated, but the efficacy of each against the incapacitating effects of soman has not been addressed. Thus, the therapeutic efficacies of SCP (5 doses; 0-0.86 mg/kg) and DZ (5 doses; 0-5 mg/kg), when each was used in conjunction with ATR (3 doses; 0.5-8 mg/kg) + 2-PAM (25 mg/kg) therapy, were compared in groups of pyridostigmine pretreated guinea pigs exposed to 1.6, 2.0, 2.5, or 3.2 LD50s of soman. Response surface methodology was employed to describe the relationship between soman-induced incapacitation and the ATR/DZ or ATR/SCP dosages. Incapacitation was measured by toxicity scores assigned by three graders to test animals at 60 min postsoman. Results show that as the dosage of SCP increased, the mean toxicity scores decreased. Also, within the indicated dose ranges used, the efficacy of SCP was not dependent on the presence of ATR. In contrast, ATR alone was found to be more effective than when combined with DZ at any dose, and indicates that DZ might be temporarily contributing to soman-induced incapacitation. These findings suggest that in guinea pigs, SCP could replace ATR or DZ, or both, as therapy against soman-induced incapacitation.

Diazepam (DZ) and scopolamine (SCP) are known to be beneficial when each is used in combination with atropine (AT) + oxime therapy against intoxication by soman, but the efficacy of each might be expected to vary with the dosage of AT. Thus, the therapeutic efficacy of SCP (5 doses; 0–0.86 mg/kg) versus DZ (5 doses; 0 - 5 mg/kg), when used in conjunction with AT (3 doses; 0.5 - 8 mg/kg) + 2-PAM (25 mg/kg) therapy, was tested in groups of pyridostigmine pretreated guinea pigs exposed to 1.6, 2.0, 2.5 or 3.2 LD50s of soman. Response surface methodology was employed to describe the relationship between lethality and the AT/DZ or AT/SCP dosages. Results show that within the indicated dose ranges used, the efficacy of SCP is not dependent on the presence of AT, whereas AT is needed for DZ to maintain die lowest probability of death. These findings suggest that in guinea pigs SCP could supplement AT or replace DZ as therapy against nerve agent intoxication.

To study multiple immune parameters in mice subjected to severe hemorrhage without fluid resuscitation.Controlled animal study. Anesthetized, female mice were hemorrhaged by tail bleeding. Immune parameters (spleen T-cell proliferation and activation, intracellular calcium flux, cytokine production, peritoneal neutrophil respiratory burst, and survival after intra-abdominal septic challenge) were measured at 24, 48, and 72 hrs after hemorrhage.T-cell proliferation was decreased in animals after two 20% blood volume hemorrhages, 30 mins apart; single 30%, 40%, and 50% blood volume hemorrhages did not depress proliferation. "Helper/inducer" T cells from twice-hemorrhaged mice showed decreased expression of activation antigens (interleukin-2 receptor, Ia) after mitogen stimulation. In contrast, "suppressor/cytotoxic" T cells displayed increased activation, shown by augmented expression of interleukin-2 receptor and Ia antigens. Leukocyte production of prostaglandin E2, a mediator frequently implicated in immune down-regulation, was unaffected by hemorrhage. Secretion of tumor necrosis factor-alpha (TNF-alpha) in culture was increased when cells were harvested 48 hrs after injury. Intracellular calcium flux in stimulated lymphocytes was decreased 24 hrs after hemorrhage, suggesting deranged intracellular signal transduction. Respiratory burst activity of peritoneal neutrophils was unchanged following hemorrhage. When animals were subjected to septic challenge, the survival rate was markedly decreased after two hemorrhages (when sepsis was induced 24 hrs after hemorrhage). By 72 hrs posthemorrhage, most of the immunologic alterations, including resistance to septic challenge, had resolved.This uninstrumented hemorrhagic shock model allows quantification of multiple immune derangements. Immune suppression was identified after two smaller (20% blood volume) hemorrhages, but not after a single, larger hemorrhage. Immune derangements are maximal at 24 hrs posthemorrhage, and resolve in the subsequent 48 hrs.

A dual-exposure drug treatment of cell lines in tissue culture provides a possible method for determining schedule dependency. This is suggested by results of treatment of human small cell lung carcinoma NIH H209 and murine L1210 leukemia cell lines with cisplatin, a non-schedule-dependent drug, and etoposide, a schedule-dependent drug. Nonlinear least squares was used to estimate the dose-response surface. The estimated regression coefficients for the effect of the first dose compared to that of the second dose support the premise that cisplatin is not schedule dependent. Unlike cisplatin, the second dose of etoposide was shown to be more effective than the first dose in the human small cell carcinoma line. This agrees with known clinical results where multiple etoposide dosing has been shown to be more effective and confirms schedule dependency. This methodology, or a refinement, may offer another tool for studying schedule dependency of drugs using tissue culture methods.

The delta method is utilized to construct an asymptotic 100(1 - alpha)% confidence interval for the response at the stationary point of a quadratic response surface. The end-points of the interval can be found directly, compared to other more, computationally intense procedures that result in a conservative interval. The coverage probability associated with intervals constructed in this manner from studies with relatively small numbers of observations is investigated via a simulation study. Finally, the methodology is illustrated with an example involving the evaluation of a combination of cytotoxic agents in the treatment of murine L1210 leukemia.

A pretreatment combination of physostigmine and azaprophen (6-methyl-6-azabicyclo[3.2.1]octan-3-ol-2,2-diphenylpropionate), a novel cholinolytic, was evaluated for its ability to minimize soman-induced incapacitation and lethality in guinea pigs. This was accomplished by using response surface methodology to model and analyze the combination, varying physostigmine from 0 to 194 micrograms/kg, azaprophen from 0 to 5 mg/kg, and soman from 30 to 150 micrograms/kg. One hundred percent survival was achieved against 5 LD50 of soman using as little as 100 micrograms/kg of physostigmine in the presence of 5 mg/kg azaprophen. Both survival and soman-induced incapacitation were similarly affected by this pretreatment combination. For both endpoints, greater efficacy was achieved with the combination than could be achieved with either component alone (therapeutic synergism). This suggests that such a pretreatment combination may prove very efficacious against soman-induced lethality and incapacitation in higher species.

Analysis of repeated measures data using a mixed model includes specifying a form for the covariance matrix of the within-subject observations. This reduction in the number of estimated parameters from the unspecified structure may improve the efficiency of inferences made. An implementation of this technique has been incorporated in the MIXED procedure of the SAS® statistical package, and includes a wide range of options for the structure of the covariance matrix. It is demonstrated that draftman's display plots and/or plots in a coordinate system with parallel axes can aid in visualizing the dispersion structure.

The dose-response surface for a combination of drugs is a multidimensional figure. Consequently, it is not possible to view such a surface using orthogonal axes when the number of dimensions exceeds 3. Parallel axes have been used to represent hyperdimensional figures. This paper reports on the use of parallel coordinate axes to plot the dose-response surface and its contours of constant response (isobols) for a combination of drugs. It is shown that patterns formed by intersecting line segments in the parallel system can aid in the interpretation of the fitted dose-response surface. More generally, analytic results are developed that permit the ready visualization and characterization of interaction effects of a polynomial model.

Major increases in the time between administration of two modalities, radiation and cyclophosphamide (CP), from 1 to 7 days and in the overall time of delivery of 3 courses of combined therapy from 24 to 35 days were carried out in rats with hepatoma 3924A without major loss of therapeutic effectiveness. Cure rates of 50% or greater could be maintained even though treatment was given over much longer time periods. The radiation was given as hyperfractionated, split-course schedules which were devised by increasing the number of 250 rad fractions over a 2-day period. In one series of experiments these 2-day schedules were given at 11-day intervals for 3 courses on days 0 and 1, 11 and 12, 22 and 23; and CP (150 mg/kg) was given 1 day after each of the 3 radiation courses on days 2, 13, and 24. In the second series of experiments radiation was given on days 0 and 1, 14 and 15, 28 and 29; and this was alternated with 3 single doses of CP given 1 week after each of the 3 courses of radiation, on days 7, 21 and 35. Increasing the total radiation dose from 6000 to 7500 rad in the series given CP 1 day after each of three courses of radiation results in an increase in total tumor cure rates from 50% to 60%. The tumor cure rate in the series given CP 7 days after radiation increased from 10% to 70% when the total radiation dose was increased from 6000 to 7500 rad. Increasing the total radiation dose from 6000 to 7500 rad increased the magnitude of the acute skin reaction as well as the duration of recovery. However, the skin reactions for both the 6000 and 7500 rad were acceptable. Host toxicity and normal tissue reaction were within acceptable limits for both modalities. The results of these studies, therefore, indicate that excessive toxicity, one of the major deterrents to the effective combined utilization of these two primary means of cancer management, may be avoided by temporal separation of delivery while maintaining tumor cure rates of 50% or greater.

Sample size characteristics for the performance of time to event response surface studies are determined where both proportional hazards and quadratic surfaces apply. Single drug activity is evaluated through the use of confidence intervals and computer simulations are employed to assess design characteristics including optimum location, grouping and censoring. Confidence intervals can be reliably constructed for the smallest sample size considered (n=48). Power considerations applicable to pre clinical studies are presented with discussion of extensions including clinical applications.

In certain survival studies the percentage of right-hand single censoring and the frequency of survival assessment, which results in the grouping of otherwise distinct failure times, is under experimental control. It is important to determine the consequences of the use of the Peto-Breslow approximate likelihood function in the analysis of studies with grouped and censored observation. A Monte Carlo study was performed to simulate the response surface analysis of data generated under the assumption of Cox's proportional hazard model. Fortuitous reductions in the mean squared error of the model parameters with slight grouping and censoring are observed.

Response surface methods were employed to model survival data obtained in guinea pigs following subcutaneous exposure to soman (GD; 30-84.6 micrograms/kg) with various treatment regimens (i.e., atropine/pralidioxime chloride [ATR/2-PAM] combinations, given im, 1 min post-GD). The analysis of the proportions of surviving animals in the various groups revealed that the use of individual treatment agents (i.e., ATR or 2-PAM) was effective in increasing survival. The level of GD exposure altered the nature of the ATR/2-PAM interaction. Exploration of the response surface indicates that the optimal treatment combinations (greater than 94% survival) of ATR/2-PAM change as a function of GD exposure in the following manner: GD 30 micrograms/kg-ATR/2-PAM, 217 mg/kg/0 mg/kg; GD 42.4 micrograms/kg-179/29 mg/kg; mg/kg; GD 60 micrograms/kg-148/83 mg/kg; GD 84.6 micrograms/kg-168/150 mg/kg. At higher exposures of GD (greater than 42.4 micrograms/kg), therapeutic synergy was observed with the use of the treatment combinations, as compared to optimal single agent treatments. Evaluation of the apparent toxicities of treatment combinations can also be determined in this procedure. RSM is not geometrically restricted by the number of variables under consideration. A variety of experimental designs, when used in conjunction with RSM, permit the modeling of multiple responses and provide estimates of optimal therapeutic modalities subject to constraints (e.g., behavioral toxicity).

The interaction of 5-fluorouracil and cyclophosphamide in the treatment of L1210 and P388 leukemias was studied using response surface methodology. Single dose treatment of each drug was administered simultaneously or with a 24-hr interval between 5-fluorouracil and cyclophosphamide to the advanced tumors or at various times after L1210 inoculation. While at low doses the action of the combination of the two drugs was greater than expected, there was no therapeutic synergism if the drugs were given together (optimum doses cyclophosphamide 366 mg/kg and 364 mg/kg, respectively, in advanced L1210 and P388 leukemias) or in the early tumor when cyclophosphamide was given 24 hours after 5-fluorouracil. In the advanced tumor, using the regimen employing a 24-hr interval between drugs, therapeutic synergism could be demonstrated (optimum doses 5-fluorouracil 130 mg/kg followed by cyclophosphamide 248 mg/kg in advanced L1210 leukemia and 5-fluorouracil 110 mg/kg followed by cyclophosphamide 263 mg/kg in advanced P388 leukemia). The evidence generated suggested that improved therapy could be found in two separate regions of the treatment space, raising the possibility of more than one mechanism of drug interaction. The location of the optimal treatment depended on the tumor burden at the time treatment was initiated. A shift from one region to the other occurred after 4-6 days of tumor growth when the original inoculum was 10(5) i.p. L1210 cells. Another more obvious conclusion that can be drawn is that treatment was less effective as the tumor became more advanced. The notion that different tumor stages may require different ratios of drugs in a clinically useful combination should receive attention.

(1974). An Analysis of the Game of Tennis. The American Statistician: Vol. 28, No. 4, pp. 130-134.

Physostigmine (PHY) is currently being evaluated as a potential pretreatment against nerve agent challenge. Although it might provide increased protection against nerve agent-induced incapacitation, it is nonetheless behaviorally toxic itself. Addition of a cholinolytic adjunct is expected to significantly reduce this behavioral toxicity. The efficacy of pretreatment regimens (PRG) (composed of PHY in combination with either scopolamine (SCP) or trihexyphenidyl (artane; ART] was evaluated in guinea pigs challenged with soman (98 ug/kg, sc; 3.5 LD50) to determine the dose of PHY and adjunct required for optimal efficacy as well as the better of the two adjuncts. Three different endpoints were measured on each animal: (1) whether or not the animal survived up to 24 hours post challenge, (2) severity of incapacitation, and (3) time to recovery. The survival data revealed no significant differences between the two adjuncts and PHY against soman, but the data suggests that a pretreatment combination of PHY and ART is likely to give a greater therapeutic index than one containing SCP. Furthermore, since ART is less toxic behaviorally, it would most likely be better tolerated as a pretreatment with PHY in non-agent exposed subjects. The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. In conducting the work described in this report, the investigators adhered to the "Guide for the Care and Use of Laboratory Animals" as promulgated by the Committee on Revision of the Guide for Laboratory Animal Facilities and Care of the Institute of Laboratory Animal Resources, National Research Council.

The CSF pressure-volume (P-V) function was evaluated before and after cardiac arrest in 15 cats. The CSF volume change was produced by bolus loading (loading rate, greater than 0.1 mL/s) of the CSF space. Comparison of the CSF P-V function before and after cardiac arrest was made over a CSF pressure range of 5 to 46 mm Hg and for a CSF volume change of up to 9% of total CSF volume. After cardiac arrest, all CSF P-V curves were well described by the mathematical model konwn to be valid under normal physiological conditions. In eight animals, there was no significant difference between the prearrest and postarrest P-V functions. For the seven animals demonstrating a significant difference between prearrest and postarrest P-V data, all but one of the postarrest P-V curves were within the normal range. These results suggest that the shape of the CSF P-V curve is not substantially altered by cardiac arrest. We conclude that under normal circumstances material properties of brain tissue are the most important factors in determining the configuration of the CSF P-V curve and that under normal circumstances cerebral hemodynamic factors do not affect the shape of this curve.

We tested serial bone-marrow samples from 47 adults with acute myeloblastic leukemia in remission for reactivity with heteroantiserums to leukemia-associated antigens, to determine whether imminent relapse could be detected in patients with acute leukemia. Of 26 patients who relapsed by standard morphologic criteria, 21 had increased immunoreactivity of bone marrow for one to six months (mean, 3.7 months) before relapse. High concordance was observed between a positive test and relapse during the period of study (chi-square = 27.53, P

The approach of preliminary test estimation has been suggested by Ellerton and Myers (1977) as a means for controlling the size of the J-criterion of the estimator ŷ of the true response,ηIn this paper, the j-criterion associated with the response estimator employed by Ellerton and Myers is evaluated and comparisons made with the j-criteria of several procedures which fit one model all the time. The comparisons suggest that preliminary test estimation offers much advantage over “first-order” procedures when there are enough observations available to fit a second-order model.

Response-surface methodology (RSM) techniques provide a useful statistical approach for the design and analysis of experiments involving multiple variables. Although it has been used for some time in the areas of chemical engineering and agriculture, RSM has only recently been applied to the solution of biological problems. Here we have utilized RSM to investigate the interaction of two direct-acting, monofunctional alkylating agents [ethyl methanesulfonate (EMS) and ethylnitrosourea (ENU)] in Chinese hamster V79 cells with respect to the in vitro induction of sister chromatid exchanges (SCEs). A factorial design was employed in which the cells were exposed to the agents singly and in simultaneous combinations for 4 h. The cells were collected for SCE determination 30 h after treatment. The analysis revealed concentration-dependent increases in SCEs for both of the agents, with ENU being the more effective on an equimolar basis. In addition, single- and multiple-agent interactions were detected. The most important finding was that over the treatment range studied, a significant negative interaction occurs between EMS and ENU with regard to SCE induction. It is suggested that RSM not only may be useful in determining the statistical relevance of experimental variables but also may generate hypotheses the evaluation of which could provide additional insights into the underlying mechanisms involved.

Total radiation (4500 rad) and cyclophosphamide doses (450 mg/kg or 2.7 g/m2) were held constant over a 24-day period in rat hepatoma 3924A using radiation schedules in which 1500 rad were given over a 1- to 2-day period in 1-8 fractions, repeated at 11-day intervals, with or without cyclophosphamide. Reducing the rad per fraction resulted in a reduced incidence of complete tumor response and tumor cures, and a reduction in the magnitude of skin response. Cure rates were 40, 10, 0, and 0%, respectively, for the 1500, 750, 500, and 250 rad per fraction groups without cyclophosphamide. When the 1500, 750, 500, 375, 250, and 188 rad per fraction groups were given 150 mg/kg cyclophosphamide day 1 after radiation, major increases occurred in tumor cures, with the cure rates being 80, 80, 80, 70, 60, and 50%, respectively. The addition of cyclophosphamide did not significantly alter skin reaction to radiation. The higher rad per fraction schedules were more effective in controlling metastatic dissemination when radiation was used alone. The addition of cyclophosphamide markedly reduced metastatic dissemination in both high and low-dose per fraction schedules. Optimal treatment levels were estimated from analysis of fitted response surfaces, and the quantitative interrelationship betweenmore » normal tissue reaction, probability of tumor cure, and associated relative hazard to the host estimated from the results of these analytical methods. Hyperfractionated radiation dose schedules with dose/fraction in the clinical range combined with cyclophosphamide can significantly increase the therapeutic ratio and prevent metastatic dissemination compared with radiation alone as a result of the increased effectiveness of combined modality therapy on the tumor, without a concomitant increase in normal tissue reaction.« less

In this presentation, statistical methods for designing and analyzing experiments evaluating a mixture of drugs/chemicals are discussed. These methods are promising in that they are not limited by the number of interacting agents in the combination. Several examples are given and a discussion of the results follows.

Immune suppression occurs frequently after major injury and undoubtedly contributes to infection and mortality in trauma patients. Prevention of such suppression may lead to decreased infection and improved survival in trauma patients surviving the immediate insult of injury. Suppressor-cell activation appears to play a key role in immune suppression after major injury. For several years we have studied the effects on immune functions after injury of various drugs which have been shown in the immunologic literature to have inhibitory effects on suppressor cell populations. H2-antagonists may inhibit suppressor cell activation by blocking surface H2-receptors, which are present in higher numbers on suppressor cells than on helper cells. Prostaglandin inhibitors may block the multiple immune suppressive effects of prostaglandins, particularly PGE2. Immunological studies suggest that low-dose cyclophosphamide selectively inhibits the proliferation of suppressor T cells. Our previous work suggested that such drugs preserve cell-mediated immune functions after injury. In experiments reported here, we utilized a standard hindlimb crush injury and amputation in mice, followed in 24 hrs by polymicrobial septic challenge using cecal ligation and 23-gauge needle puncture (CLP). Nontraumatized (control) mice had a 36.2% mortality after CLP; when crush injury/amputation was followed by CLP in 24 hrs the mortality rose to 63.8% (p less than 0.0035). When mice were given 24 hrs before crush/amputation: cimetidine, an H2-antagonist (10 mg/kg/day); ibuprofen, a prostaglandin blocker (5 mg/kg/day); or cyclophosphamide (2.5 mg/kg/day), and a second dose on the day of trauma, with CLP 24 hrs later, subsequent mortality was not different from the mortality in nontraumatized, control mice (p less than 0.0035).(ABSTRACT TRUNCATED AT 250 WORDS)

Current statistical procedures used in the construction of isobolograms do not use recent advances in mathematical statistics. The variability in the experimental data is either ignored or incompletely accounted for in the analyses. The decision procedures currently used to characterize the type of interaction between two agents do not permit the determination of the level of statistical significance associated with a given conclusion. Furthermore, the often formidable sample size is not exploited in the current isobologram methodology. Statistical techniques exist that may be used to construct isobolograms and decision procedures with a reliable level of significance. An isobologram is a contour of constant response of the underlying dose-response surface. Consequently, response surface methods (RSM) are useful in the estimation and analysis of isobolograms. The interaction between ethanol and chloral hydrate in female ICR mice was evaluated using the RSM approach by fitting the logistic model to quantal data. The loss of righting reflex was quantitated in mice 30 min after coadministration of the two drugs, injected IP on a body weight basis (mg/kg). The study consisted of 39 groups with 6 animals per group. Analysis of our data supports the conclusion of synergy between the drugs as reported by others; however, our results were obtained with a significantly smaller number of animals. These studies also demonstrate that response surface modeling can be used for determining additivity, synergism, and antagonism at a given preselected level of significance.

Statistical methods for fitting nonlinear functions to data generated by correlated response variates are discussed. Estimation of the model parameters is performed with an iterative two-stage scheme. The estimation procedure accommodates both within-unit and between-unit variability in fitting a response surface. Under regularity conditions the procedure yields asymptotically normal, strongly consistent estimators. If desired a patterned variance-covariance matrix can be assumed and incorporated into the model. The methods are illustrated by an analysis of data from a study of the combined effects of hepatotoxins in which between- and within-subject measurements are recorded.