Walter H. Carter

Response surface methodology: 1966–1988

Response sarfxe methodology (RSM) is a collection of tools developed in the 1950s for the purpose of determining optimum operating conditions in applications in the chemical industry. This article reviews the progrrss of RSM in the general areas of experimental design and analysis and indicates how its role has been affected by advanccs in other fields of applied statistics. Current areas of research in RSM are highlighted. and areas for future research are discussed.

Analysis of survival data with nonproportional hazard functions.

The log-rank test or the proportional hazard model is a valuable, widely accepted method for analyzing time-to-response data from comparative clinical trials. When the hazard ratio is constant in time, this procedure is optimal. Indiscriminate or unthinking use of this approach results in problems in the determination of treatment differences. For example, when the true survival curves intersect, the hazard ratio cannot be constant, i.e., the hazard functions are not proportional. It is shown that by considering time-by-treatment interactions we gain flexibility in describing the relationships among hazard functions. In this paper we demonstrate with the results of a clinical trial how available methodology can be used to permit tests for the appropriateness of the model and to enable informative analysis of such data.

Early Diagnosis of Relapse in Acute Myeloblastic Leukemia — Serologic Detection of Leukemia- Associated Antigens in Human Marrow

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 less than 0.001). The median time to relapse after a positive test was four months, as compared with the median remission duration of 19 months for the whole group (P less than 0.02, Petos log-rank analysis). Serologic detection of leukemia-associated antigens in marrow may be a reliable indicator of imminent relapse in acute myeloblastic leukemia.

Application of Response Surface Methods for Evaluating the Interactions of Soman, Atropine, and Pralidioxime Chloride

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).

Two Graphical Techniques Useful in Detecting Correlation Structure in Repeated Measures Data

Abstract 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 draftmans display plots and/or plots in a coordinate system with parallel axes can aid in visualizing the dispersion structure.

Protective effects of freeze dried swordfish on methylmercury chloride toxicity in rats

This study quantifies selenium in swordfish and examines its prophylactic effect on methylmercury poisoning in rats. It was found that swordfish have twice as much selenium as mercury, and that a diet which included freeze-dried swordfish protected rats from the toxic effects of methylmercury.

Efficacy comparison of scopolamine and diazepam against soman-induced debilitation in guinea pigs

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.

Solid tumor models for the assessment of different treatment modalities: XXIII. A new approach to the more effective utilization of radiotherapy alternated with chemotherapy.

This study with the rat hepatoma 3924A demonstrated the marked improvement in tumor cure rates and control of tumor growth that can be achieved by the addition of cyclophosphamide (CP) to multiple fractions of radiation per day (MFD) schedules given intermittently. MFD radiation was delivered over a 2-day period followed by CP (150 mg/kg or 0.9 g/m2) 1 day later; this combined course was repeated at 11-day intervals (to allow for gastrointestinal tract and bone marrow recovery) for a total of 3 courses over a 23-day period. Cure rates of 30, 50 and 60% were achieved with total radiation doses of 4500, 6000 and 7500 rad, respectively, when the MFD radiation was given with CP. No cures and no complete responses were realized when the same intermittent MFD schedules for radiation were employed up to 9000 rad without CP. Other groups of 10 animals each were treated with daily fractions of 100, 150, 188, 250 and 375 rad given on days 0-9, 11-20 and 22-31. A 150 mg/kg or 0.9 g/m2 dose of CP was given after each course of daily radiation on days 10, 21 and 32 in the combined treatment groups. No complete responses or tumor cures occurred with radiation alone given daily for total radiation doses, which were increased from 3000 to 11,250 rad. Only the highest radiation dose given, 375 rad per day to a total of 11,250 rad, resulted in a complete response rate and tumor cure rate of 50% when CP was added. The addition of CP to the daily fractionation schedules reduced the total dose needed to give a growth delay of 100 days by 39% (5600 rad versus 9200 rad). The addition of CP to the intermittent MFD schedules further reduced the total dose needed to give a growth delay of 100 days to 4200 rad. Major improvements in some types of cancer treatment may be realized if we can develop clinical protocols for the alternate use of chemotherapy and radiotherapy as we have done successfully in our experimental program. The finding that intermittent MFD radiation schedules are as effective as daily schedules when given alone suggests that greater flexibility of patient management in clinical radiotherapy may be possible without a major loss of therapeutic effectiveness. These alternated fractionated schedules offer the possibility of optimizing treatment in terms of patient convenience and economy as well as the potential for improving the effectiveness of the interaction of radiotherapy with radiosensitizers, radioprotectors, and hyperthermia in addition to chemotherapy.

Efficacy comparison of scopolamine (SCP) and diazepam (DZ) against soman-induced lethality in guinea pigs.

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 the lowest probability of death. These findings suggest that in guinea pigs SCP could supplement AT or replace DZ as therapy against nerve agent intoxication.

Solid tumor models for the assessment of different treatment modalities. XXII. The alternate utilization of radiotherapy and chemotherapy

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.