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This paper describes a new method of assigning patients to treatment and control groups to minimize differences between the groups, not only in the number of patients but in patient characteristics. Testing the method by computer simulations, using data on 40 patients with 15 variates each, demonstrates a four- to fivefold reduction of the probability of severe imbalance, relative to randomization. Minimization can maintain tight control of one variate, comparable to the currently acceptable experimental design of blocking, while reduCing the probability of severe imbalance in the other 14 variates by a factor of 3. It also compares favorably with accepted methods regarding susceptibility to experimenter bias. Therefore, it is suggested that minimization should replace randomization in assigning patients in clinical trials.

An attempt has been made to develop tritiated derivatives of Synkavit (menadiol sodium diphosphate, MNDP) of high specific activity as a radioactive drug. This paper summarizes the preliminary biological and physical studies, with emphasis on approximate radiation dosimetry and the necessary preliminary testing, and then gives an account of the clinical investigations and the trials carried out so far, which correspond essentially to Phases I and II trials for a chemotherapeutic agent. In all, 214 patients with different sites and types of advanced and recurrent, inoperable, histologically verified malignant tumours including reticuloses have been treated with doses of at least 1 Ci of the various preparations. Among the 203 evaluable treated cases, some form of response was observed in 23 out of 151 (15·2%) receiving the drug by intravenous injections and 13 out of 52 (25%) after intra-arterial injections. For the sites and types of malignant diseases which showed responses after either intravenous or intra-arterial administration among the 55 patients surviving at least 3 months after the first injection, some form of response was observed in 32 but only 5 of these showed either a “complete” or a “partial” response. It is concluded that further investigation is desirable. It is suggested that clinical trials with randomization should be carried out for inoperable cases of carcinoma of the colon and of the pancreas.

Twenty children, while hospitalized with pneu monia, were treated by randomization with graded dosages of oral ampicillin; five each received 50, 100, 150, or 200 mg/kg daily in four equally divided doses for at least five days. The peak serum levels rose from a mean of 1 mcg/ml with 50 mg/kg per day to 4 to 7 mcg/ml with 200 mg/kg per day. Mild to moderate diarrhea, encountered in two of the five patients of each study group, was apparently unrelated to dose, and did not hinder absorption of the drug to a clinically significant degree.

1. Thirty acutely depressed patients were treated with imipramine and amitriptyline for periods of three weeks each in a double blind cross-over design. Twenty-four patients completed the six weeks study period. Clinical improvement on a highly significant level occurred for both drugs. No significant differences could be noted between drugs with the exception of a near significant difference existing at the ten day interval, amitriptyline producing more improvement than imipramine. However, this difference disappeared at the twenty day period. Amitriptyline appears to produce improvement somewhat faster than imipramine, but after about three weeks, imipramine has caught up with amitriptyline. Improvement with both drugs occurred within the first three weeks and could be maintained for another three weeks by the other agent, i.e., drugs were interchangeable after the first three week period. 2. The clinical change noted by the physician may not correspond with the subjective change reported by the patient. The patient may feel improved even though this improvement may not be noticeable to the physician. Even if noticeable, the patient may attribute more importance to such an improvement than does the physician. 3. A cross-over design appears to be inadequate in studies in which one may expect major change to occur within the initial study period. Furthermore, randomization of patients, according to a given criteria, does not necessarily provide randomization for other criteria (e.g., psychological test results in this study).

Analysis of the temperature characteristic of β-galactoside transport has prompted the proposal of a diffusional mechanism for the randomization of lipid molecules in the membrane.

The results of this trial do not indicate that patients treated with mebanazine have shown any better response than those given a placebo. Sixty-four percent. of the patients given placebo were "Improved" compared with 52 per cent. of those given mebanazine. These overall results do not differ significantly, but the results for re-admission patients show the proportion of patients "Improved" in the placebo groups to be significantly greater than the proportion "Improved" in the mebanazine group, at the 5 per cent. level of significance. This is a somewhat surprising finding which may be associated with the effects of randomization of treatments to patients at the commencement of the trial. No serious side-effects were encountered in the trial dose of 20 mg. daily. This contrasts with the findings of Cooper and Keddie (1964) who observed instances of serious hypotensive collapse in a dosage of 30 mg. daily. This implies that the therapeutic dose may closely approximate the toxic dose, thus contra-indicating the use of this drug. We are of the opinion that there is some urgency for further controlled trials, perhaps conducted along similar lines, to be undertaken to assess the effectiveness of other antidepressant drugs in current use.

A review of abstracts and papers reporting clinical trials of new anticancer agents reveals that only a small percentage have been controlled. Arguments against employing randomized controls in such trials are understandable but hardly valid at the present stage in cancer research. Randomization of drugs tested or dosage regimens at the earliest stages of clinical use is needed to evaluate relative therapeutic efficacy and toxicity. Potent ethical arguments also require that when a new drug is tried, patients should be given a 50–50 chance of receiving the conceivably better standard therapy. An important and subtle consideration, that of how long to continue a controlled trial, requires continued development of the study-design process and new uses of peer review.

In an experiment in which treatments are applied and observed in a sequential manner, if not all treatment combinations may be placed (run) in adjacent positions then the usual technique of full randomization cannot be carried out. In such instances some technique of randomization, constrained by the requirements of adjacency on the various treatment combinations, is desired in order that the properties of the statistical analysis may be determined. This paper presents methods of constrained randomization for 2 n—p factorial experiments in blocked designs when the requirment (imposed by the nature of the process under investigation) on adjacent treatment combinations restricts the number of factor levels which may be changed from run to run (treatment combination to adjacent treatment combination). The method of constrained randomization provides a basis for a statistical analysis utilizing the randomization model, which results in unbiased estimates of treatment effects and an unbiased estimate of experi...

Response selection was studied independently of the stimulus by asking subjects to generate random sequences of letters or numbers. Experiment 1 varied rate of letter generation from ½ sec. to 4 sec. per item and showed that the redundancy of the sequence increased linearly with rate. Experiment 2 added random generation of letters as a secondary task to paced card sorting. Information load per card was varied from 1 through 2 to 4 to 8 alternatives, with sorting rate held constant. As predicted, the redundancy of the sequences generated increased linearly with sorting load. Experiment 3 varied number of items to be randomized. Rate of random generation increased systematically from 2 to 4 to 8 alternatives, but levelled out beyond this point, showing no difference between 16 and 26. In general, these results suggest a response-selection mechanism of limited informational capacity.

The paper is concerned with randomized experiments with one treatment. Two randomization schemes are considered: randomized pairs and unrestricted randomization. If effective at all, the treatment is supposed to affect the conditional distribution of the “experimental” variable Y given another variable X, called “predictor”. The distribution of X is not affected by the treatment. Using the general theory published elsewhere, the paper deduces the locally asymptotically optimal test of the hypothesis that the treatment has no effect. Apart from the usual difficulties connected with asymptotic tests (how large must N be?), the theory is easily applicable in many “live” cases even though the conditional distribution of Y given X may contain nuisance parameters and be of unusual form.

A pediatric formulation of clindamycin was evaluated in comparison to ampicillin sodium in treatment of otitis media. Ampicillin and clindamycin were provided in identical numbered bottles and dispensed to 271 children. The randomization procedures employed for assignment of therapeutic regimen yielded two groups which were remarkably similar in relation to age, sex, and clinical severity of disease. No significant differences in clinical response to therapy were observed even when data were evaluated with regard to specific organisms isolated. Clindamycin proved to be effective therapy for otitis media due to penicillin-sensitive and penicillin-resistant Staphylococcus aureus, epidermidis, and Diplococcus pneumoniae . Differences between the two regimens in the response of otitis media caused by Hemophilus influenzae were noted. We would not recommend clindamycin for routine treatment of otitis media caused by H influenzae .

A randomization technique to help reduce possible bias was used in dose-finding trials of a new cancer chemotherapeutic agent, hydroxyurea. The drug was given at fixed starting doses of 12.5, 25.0, 37.5, and 50.0 mg. per kilogram for a 6 week period by the oral and parenteral routes to 110 patients. Only downward modification of doses was allowed according to a fixed protocol. Leukopenia was the most common toxicity observed at doses of 25.0 mg. per kilogmm or more and appeared slightly more often in patients receiving the drug parenterally. The actual total dose administered was approximately the same at 25.0, 37.5, and 50.0 mg. per kilogram, and no difference in toxicity was noted between the single daily and three times daily oral administration. Recalculation of the dose by surface area indicated the biologically active dose to be about 1.4 Gm. per square meter. For hydroxyurea administered to adults, no better prediction of toxicity was noted for the dose calculated for individual patients on surface area when compared to the dose based on milligrams per kilogram. These procedures in dose-finding trials are recommended: the usc of randomized assignment of patients, fixed nonescalating doses and the inclusion of a low (ineffective) dose (12.5 mg. per kilogram), and separation of drug toxicity from natural disease progression.

For the past 40 years, there has been confusion on the differences between tests of significance and tests of hypotheses to the point where data interpretation is presented as an accept-reject process. This paper discusses the case of inference for a simple experiment, the paired design. It gives a rationale of the significance tester, and proceeds to a comparison of three tests of significance which can be viewed as competitors in the case of this design. These are the sign test, S, the Wilcoxon test, W, and the Fisher randomization test, R. The conclusion is that there is indeed an ordering of the tests, which is R preferred to W preferred to S. The S test should never be used if the others are possible. An Appendix gives a proof of monotonicity of the R test with respect to a shift alternative.

Background: Evidence for an effect of zinc supplementation on growth in every young infants in developing countries is scarce and inconsistent. In Bangladesh, the highest incidence of Low Birth Weight (LBW) is the main cause of neonatal mortality and morbidity. It is hypothesized that LBW neonates is zinc deficient and that might adversely affect postnatal growth. The present study was carried out to measure the effect of zinc supplementation on LBW neonates during the first month of life and to observe the growth pattern of supplemented (zn) with non supplemented group. Aim and Objective: It is supported by literates that zinc has an effective positive role in the growth and development in children. But evaluation of the effect of zinc on weight gain in LBW not done so our primary objectives are. (1) The study was done to measure the effectiveness of zinc supplementation on weight gain in low birth weight neonates. (2) To list low birth weight (LBW) babies admitted in neonatal ward of Pediatrics Department of Sher-E-Bangla Medical College Hospital, Barisal during one clander year. (3) To supplement Zinc in a group low birth weight neonate and to compare with another group of low birth weight neonate will receive placebo for a period of 28 days along with necessary treatment for both groups. (4) To compare the study group with control to find out where and when zinc have contributed to weight gain, side effect of supplementation and acceptance of supplementation by the neonates. Materials and methods : In a randomized, double-blind, placebo-controlled trial study of the effect of zinc on weight gain in low birth weight neonates. The study was carried out in the neonatal ward of pediatrics department of Sher-E-Bangla Medical College, Barisal, Bangladesh. The duration of the study was from May '05 to May '07. The research proposal was approved by Faculty of Post-graduate Medical Science and Research, Dhaka University. Ethical clearance was obtained from Bangladesh Medical Research Council (BMRC). One hundred low birth weight neonates were included in this study and the same number of controls matched for birth weight sex, types to LBW, feeding pattern was studied. After randomization and pair matched neonates were grouped into two groups, 100 neonates were included in group A and 100 neonates in group B. In the first 28 days of life, the A group received Syrup D 1 2.5ml/day in and B group received syrup D 2 2.5ml/day. The syrup administered to the study neonate in two groups were prepared by Orion Laboratories Ltd. drug manufacturing company. Syrup D 1 2.5ml contains zinc 5mg was given to A group and Placebo (D 2 ) for B group. The two syrups were indistinguishable in taste and color and code of syrup 'D 1 ' and 'D 2 ' was kept strictly confidential with the pharmacist. The parents or care giver were instructed to feed syrup D 1 2.5ml or syrup D 2 every morning at 10 am to their neonate up to 28 days. Measurement of weight of case and control without cloth before feeding at 9a.m after 3 days, 7 days, 14 days, 21 days and 28 days and recorded in a record form. The overall supervision was maintained by researcher. At the end of the study the code of syrup was decoded and found 'D 2 ' for Placebo and D 1 > for zinc. Data were analyzed by using statistical software SPSS. Result : Among the study subjects 54% of them were male and 46% were female, of them 78% were preterm, and were 22% IUGR. The mean (±SD) birth weight was 1789.50 ± 228.89gm is for cases and controls. Three days after birth, weight decreases to (1610.50 ± 255.38gms) in cases and to (1613.00 ± 215.04 gms) in controls. More weight gain in cases than controls was observed after 7 days of birth. Highly significant weight gain after 21 days (2261.50 ± 296.14 gms) in cases than controls (2165.50 ± 243.47 gms) and 28 days (2665.00 ± 331.52 gms) in cases observed than controls (2374.00 ± 410.07 gms). So mean weight after 21st and 28th days of cases was significantly higher (P

Randomization, often specified as an indispensable requirement in experimental design, is required only when the order or position of the experimental unit influences the performance of the unit. Randomization, when required, may give an arrangement that is obviously undesirable and one that may doom the particular experimental program. A system of constrained randomization is proposed that eliminates the undesirable arrangements without sacrificing the customary gains achieved by randomization.

In paired comparisons of a treatment and control, it frequently happens that the two members of each pair can be classified into distinguishable types. The completely randomized design, which assigns the members of each pair at random to treatment and control, then may by chance assign the treatment primarily to subjects of one type and thereby confound treatment and type. This difficulty can be avoided by restricting the randomization. We find that such restriction is desirable by analyzing several of the standard tests (Wilcoxon, t, and tests for dichotomous response) for efficiency and deficiency.

The present study is an analysis of 204 consecutive cases. A final evaIuation of this clinica material was made February I, 1961. Thus, there is a five to twenty year follow-up of patients. All clinicai diagnoses were confirmed by histopathologic study. The series does not represent a11 patients \vith breast cancer seen in the Tumor CIinic and treated at the University of Oregon Medical School (UOMS). To illustrate this point, the distribution of all breast cancer patients treated during representative years 1950 to rg5r is shown in Table I. Selection of Cases. The clinical criteria of operability that governed decisions of the Tumor Board were more IiberaI than the Haagensen criteria [zl]. The size of tumor and clinical staging in combination were not considered absolute determinants. Adverse local signs, except for the occasiona fulminant and unquestioned inflammatory carcinoma, did not negate primary radical mastectomy. Nor did pregnancy, by definition, preclude operation. Once a cIinica1 judgment of operabiIity had been reached, the patients were hospitalized at the teaching hospital. The rotation of service assignments in hospital of visiting staff surgeons and the closely integrated activities of full time surgeons led to a randomization of treated patients at this point. A precise definition of the technic and the extent of so-called radical mastectomy was not established as a fixed operational policy. Thus, distinctive differences in surgica1 philosophy and operative

The use of Monte Carlo and other statistical procedures that depend on randomization of the observed data has been inhibited by uncertainty about the validity of random numbers generated by a computer. In the empirical test performed here, computer-generated numbers appeared to be just as “random” as those available in the Rand tables that are a conventional standard source of random numbers.

The possible role of specific saturated fatty acids in the development of atherosclerosis in rabbits has been assessed. Special fats were prepared by randomizing corn oil with pure trilaurin (L), trimyristin (M), tripalmitin (P), and tristearin (S), yielding oils of similar iodine value (102 ± 2) but differing in the predominating saturated fatty acids. Rabbits were fed for 8 weeks on diets consisting of chow augmented with 2% cholesterol and 6% of fats L, M, P, and S. Other groups of rabbits were fed diets in which corn oil (CO) or randomized corn oil (R) were used as the cholesterol vehicle. In a series of four experiments with a cholesterol-containing diet, the four different saturated fats were more atherogenic than either native or randomized corn oil. The palmitic acid-rich fat (P) was somewhat more atherogenic than were the other special fats. This observation was also true when the atherogenicity of the various fats was expressed as a function of the degree of hypercholesteremia they induced. The aortic cholesterol ester was elevated in all six groups of rabbits (27–40% vs. 5% in normal rabbits) and could not be correlated with severity of atheromata; however, the average total cholesterol content of the thoracic aorta did correspond to the degree of atherosclerosis. Average serum cholesterol levels were lower in the special fat groups than they were in the rabbits fed corn oil. Possibly the presence in these diets of relatively large amounts of unsaturated fatty acids masks the specific hypercholesteremic effects of saturated fatty acids.

The purpose of this expository paper is to explain methods of randomization for two-level factorial experiments in various designs when the treatment combinations are applied and observed in sequence and when not all treatment may follow one another...

SUMMARY Randomization models for 2 x 2 tables in the matched and unmatched cases are proposed and, in terms of these models, the usual large sample statistical tests are shown to be conservative. The likelihood surface for the unmatched case is discussed. In the matched case, the model takes more explicit account of the effect of the matching criteria used in the trial than do the more familiar probability models. A simple analogue in the case of continuous measurements is indicated.

With few observations involving a large number of variables the T 2 test for the multivariate two-sample problem may not exist. Some alternative tests based on randomization methods are suggested and two of these are applied to an example. Also, valid randomization tests can be obtained by using subgroups of permutations; this provides a simple method for reducing computation which is desirable when the sample sizes are not small.

When one observes values of a function, he usually expects to make inferences from these values to other values, or to characteristics of the function as a whole. Unless useful assumptions about the function can be made, one can make such inferences only if randomization has been used. Two problems, that of numerical integration and that of measuring goodness of fit, are discussed from the randomization viewpoint. * Paper presented in part at meeting of the Institute of Mathematical Statistics, Princeton, N. J., April 20, 1956.

Randomization has played an important role in social affairs, going back at least to biblical days. The drawing of lots, one of the simplest forms of randomization, has been used publicly in many different contexts. Although the legal use of randomization techniques and lotteries in the United States dates back at least to the mid-19th century, only recently have the federal courts recognized the need for proper randomization to assure fairness, lack of bias, and lack of discrimination. A recent presidential commission has supported the call for all-volunteer armed forces (29), but it appears that the recommendations of this commission are at least several years away from becoming law. In fact, it has been suggested that the present lottery system is retarding any moves toward allvolunteer armed forces by reducing the number of draft-induced volunteers, and thereby necessitating an increase in the number of draftees. So, in the short run, it appears that the draft lottery will be the means by which the United States will man much of itsarmed forces. Since this is the case, it is important that future lotteries achieve equity in selection and that the lack of randomization present in previous lotteries be eliminated. [Indeed, it is interesting to note that several young men have filed suit in federal court, seeking to void the 1970 drawing and to force a new lottery. The basis of these suits is the lack of proper randomization (30).] The 1917 and 1940 Selective Service draft lotteries have served in the past as indications that the commonly held notion of "randomness" is often at variance with the strict statistical meaning. The 1970 draft lottery has not helped to mitigate the doubts of many regarding the equity and fairness of random drawings, although the recent 1971 draft lottery sets a very positive example, which, it is hoped, will counteract the effects of the earlier lotteries. Since randomization does have a role in the everyday workings of society, it is important that the public be educated to accept the proper use of randomization, while rejecting attempts to use chance as a disguise for inequity, bias, and unlawful discrimination. As one step toward this end, future draft lotteries should adhere to a reasonable definition of randomness, and the public should be well informed of the precautions taken to preclude arbitrary features that have marred previous draft lotteries. In addition, it is clearly desirable that the Selective Service provide the public with an official statement giving all relevant details on the design and execution of the lotteries. The most recent draft lottery serves as an admirable model in this regard. Note added in proof: Professor Hans Zeisel has brought to my attention the details of the draft procedure used in Austria-Hungary between 1889 and the start of World War I. This draft procedure was also based on a lottery, with every person liable for the draft (or a representative) drawing a slip of paper on which was recorded a number indicating a place in the draft list. It is conceivable that Selective Service officials, in charge of the World War I lottery in the United States, were familiar with the details of this draft lottery procedure.

The most common type of structural fatigue test program is the experimental construction of an S-N curve and may be divided into two phases: determination of the mean fatigue limit by the staircase method; and determination of the finite life region and its subsequent analysis by regression analysis. The bases for statistical design of experiments require both randomization and, generally, replication. Randomization in sampling of material, specimen assignment to stress levels, and test sequence minimizes the effects of possible bias due to uncontrolled variation in material, laboratory environment, and test procedures. Replication of tests at a given stress level to estimate variability in fatigue life is often impractical. The variability in life may be estimated from regression analysis and used to predict probability of survival at any stress level.

Fifty "random permutations" were prepared for use by the Selective Service System as a basis for a two-stage randomization that preceded the lottery drawing on 1 July 1970. This report identifies the permutations used. It also gives the orders in which calendar dates and numbers were put into and drawn from two drums and the correlations between them.

The loss of HCN and DCN from 2,4,6-d3-phenyl isocyanide is preceded by H/D randomization in the large majority of k-states which could be sampled in this study.

A prospective clinical study was performed documenting the incidence of diarrhea, vomiting, and skin rashes relative to varied dosage schedules of orally administered ampicillin. Four hundred children were treated by randomization with one of four doses; 100 each received 50, 100, 150, or 200 mg. per kilogram per day administered in four equally divided doses, for a period of at least seven days. Vomiting or severe diarrhea was rare and was not dose related. Mild or moderate diarrhea was commonly encountered in patients regardless of dose. Erythematous maculopapular skin rashes occurred in 3 to 7 per cent of patients; there was some increase in incidence with increasing dosages but not to a significant degree. Urticarial skin rashes occurred in 1 per cent of patients and were unrelated to dose. Perineal moniliasis occurred exclusively in infants in diapers, usually with associated mild diarrhea; the incidence was significantly dose related.

Grundy & Healy (1950) developed a method of ‘restricted randomization’ applicable to factorial experiments of 2n or 3n type laid out either in quasi-Latin squares of size 8 × 8 or 9 × 9, or in blocks of 8 or 9 plots. This method of randomization, while in no way affecting the validity of the normal analysis, prevents the appearance of designs with obviously undesirable features. Grundy & Healy gave an example of a quasi-Latin square inwhich the main effect of one factor corresponded to the pattern