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SUMMARY The general theory of scheduling examinations for the diagnosis of disease is formulated with respect to the optimal spacing between examinations. This same theory is also applicable, with a change in language, to the inspection of equipment and the scheduling of patients under surveillance with disease. Optimal scheduling programmes are investigated using a weighted utility function which is linear in the probabilities both of finding a case at examination and of being clinically incident between examinations. If disease incidence is independent of time, then a necessary and sufficient condition for the intervals to be equally spaced is that the sensitivity of the examination be unity. The equations for finding the optimal intervals are derived and depend on the distribution of the pre-clinical sojourn times and the sensitivity of the test. If the sojourn distribution is exponential, the optimal intervals are equal except for the first and last intervals.

There has been an explosive growth in the development of statistical methodology over the past several decades. Research in both medicine and public health, in which the involvement of biostatisticians has increased dramatically during this period, has been both a beneficiary of this new methodology as well as a source of new problems. The contributions of statistical methodology in design, implementation, and analysis as they relate to the role that biostatistics and biostatisticians now play in the field of medical research are addressed. We comment on: (1) the acceptance by the medical community that biostatistical concepts are an integral part of sound medical research; (2) the sometimes unrealistic expectations placed on biostatistics and biostatisticians given limited resources and/or limited control; (3) some controversies among biostatisticians; and (4) the need for emphasizing the design and implementation phases of medical investigations.

In order to investigate the current state of the art in clinical cancer research, a survey of comparative cancer clinical trials was conducted using a MEDLINE literature search of the 6-month interval from July to December of 1985. Data were obtained primarily from the published abstracts. The major observations from the study are as follows. First, trials in cancer research are published in an extraordinarily wide range of journals covering most of the major medical specialties in addition to the many cancer specialty journals. Second, randomization is now used quite extensively. It is the predominant method of control in chemotherapy trials and in trials reported in cancer journals. However, its use is much less common in other specialties, especially surgery, so efforts to popularize randomization in these specialties would be beneficial. Third, sample sizes are highly variable, and the median sample size (96 patients) is too small to reliably detect and evaluate moderate treatment advances. Finally, our survey reveals that published trials show an inordinately large proportion of breakthroughs in treatment compared with the generally accepted view that only slow progress is being made in developing effective cancer treatments. Our view is that this result reflects the strong tendency to publish only studies with positive results. This hypothesis is supported by the fact that in nonrandom trials there tend to be more positive conclusions and an absence of a strong association between conclusions and sample size.

A new model of centrality is proposed for networks. The centrality measure is based on the “information” contained in all possible paths between pairs of points. The method does not require path enumeration and is not limited to the shortest paths or geodesies. We apply this measure to two examples: a network of homosexual men diagnosed with AIDS, and observations on a colony of baboons. Comparisons are made with “betweenness” and “closeness” centrality measures. The processes by which structural changes in networks occur over time are also discussed.

The Eastern Cooperative Oncology Group (ECOG) initiated a program in 1976 to involve community hospitals in multi-institutional clinical trials. The community hospitals can be characterized as generally having no tradition of participating in clinical trials of cancer therapy, whereas the ECOG member institutions are university hospitals or major treatment centers. More than 100 community hospitals participated in 97 randomized trials involving 4506 patients from November 1976 through February 1981. Comparisons between the community hospitals and the ECOG member institutions indicate that the quality of participation was similar, as measured by rates of ineligibility, compliance with the protocol, and submission of data. Objective measures of outcome, such as survival, response, and toxicity, were also comparable. We conclude that under the mechanism adopted by the ECOG, it is possible to include community hospitals in clinical trials of cancer therapy without reducing the quality of the data or compromising the therapeutic outcomes.

The execution of clinical trials is perhaps the most difficult way of carrying out a scientific experiment. This is especially true of chronic diseases, such as breast cancer, which require long-term follow-up and large numbers of patients. As a result, it is necessary to involve many physicians who can contribute patients to these studies. Unfortunately, many physicians are not comfortable participating in randomized studies because they feel the patient-physician relationship may be compromised. This paper discusses new ways of planning randomized clinical trials which do not interfere with the patient-physician relationship. The new designs are called 'randomized consent' or 'prerandomized' designs. The study designs are discussed from the point of view of statistical efficiency and the new ethical problems which may arise.

Prolonged 1-phenylalanine mustard (L-PAM) administration as an adjuvant to mastectomy in the management of patients with primary breast cancer and pathologically positive axillary nodes was evaluated by a prospective, randomized, clinical trial. Treatment failures occurred in 22 per cent of 108 patients receiving placebo and 9.7 per cent of 103 women given L-PAM (p = 0.01). A statistically significant difference (p = 0.02) existed in favor of L-PAM relative to disease-free interval. In premenopausal women, the difference with respect to disease-free interval of treated and control groups was highly significant (p = 0.008). A treatment failure occurred in 30 per cent of premenopausal patients receiving placebo and 3 per cent of those treated with L-PAM (p = 0.008). Whereas a similar trend was observed in postmenopausal patients, the difference is not statistically significant. Thus, L-PAM has been demonstrated to be effective in the treatment of women with primary breast cancer, particularly those who are premenopausal. Results were achieved with minimal undesirable side effects.

In 1979, two of the eight municipal wells servicing Woburn, Massachusetts, were discovered to be contaminated with several chlorinated organics. Shortly afterwards, the town was found to have an elevated rate of childhood leukemia. Using recent information about the space—time distribution of water from the two contaminated wells, we find positive statistical associations between access to this water and the incidence rates of childhood leukemia, perinatal deaths (1970–1982), two of five categories of congenital anomalies, and two of nine categories of childhood disorders. We find no associations with spontaneous abortions, low birth weight, or the other categories of congenital anomalies and childhood disorders. This article discussed these results and other features of the data relevant to their interpretation.

The Eastern Cooperative Oncology Group, composed of major cancer treatment centers, has an outreach program which involves community hospitals in ongoing cancer clinical trials. A prevalence survey was carried out in February 1981 among 104 community hospitals and 21 member institutions to determine the characteristics of patients being treated, their staffing, and reasons why patients were not on protocol studies. The survey sampled 25 (50) consecutive patients from community hospitals (member institutions). The purpose of the study was to assess the impact of a community cancer control program. The results of the study demonstrated that 16% of patients surveyed in the affiliated community hospitals were being treated on a research protocol. In addition, a further 35% had their treatment plan influenced by a protocol. Consequently protocols have impacted directly or indirectly on 51% of the patients. The corresponding figures in member institutions were 23% and 38% for a total of 61%. In studying protocol availability, it was found that 66% of all patients were ineligible for any protocol. Of patients eligible for a protocol but not registered on one, 52% were not registered because of physician preference for a specific treatment. The affiliates surveyed were shown to be on average half as large as member institutions in terms of number of beds and staff size. Also, staff/patient ratios are generally smaller in the community hospitals. The median age of patients was considerably lower than SEER incidence data. Also, elderly patients were slightly more prevalent in community hospitals than in member institutions. A clear relationship between disease stage and age in breast cancer patients was noted with the representation of early-stage disease much higher in young women.

We outline the methods of Bayesian inference for applications to case-control studies. These methods appear as the natural way of making inferences, since much of the controversy that surrounds a specific case-control study is subjective. We derive conjugate prior distributions of exposure, posterior distributions of the ratio of the odds of being incident with a disease both with and without exposure to a potential causal agent, and convenient approximations. In particular, we show how one may carry out 'case-control studies' without necessarily having a control group. We illustrate these ideas with the data that first showed the relationship between in utero exposure to diethylstilbestrol and cancer of the vagina in young girls.

This paper applies the theory of semi-Markov processes to the construction of a stochastic model for interpreting data obtained from clinical trials. The model characterizes the patient as being in one of a finite number of states at any given time with an arbitrary probability distribution to describe the length of stay in a state. Transitions between states are assumed to be chosen according to a stationary finite Markov chain.Other attempts have been made to develop stochastic models of clinical trials. However, these have all been essentially Markovian with constant transition probabilities which implies that the distribution of time spent during a visit to a state is exponential (or geometric for discrete Markov chains). Markov models need also to assume that the transitions in the state of a patient depend only on absolute time whereas the semi-Markov model assumes that transitions depend on time relative to a patient. Thus the models are applicable to degenerative diseases (cancer, acute leukemia), while Markov models with time dependent transition probabilities are applicable to colds and epidemic diseases. In this paper the Laplace transforms are obtained for (i) probability of being in a state at timet, (ii) probability distribution to reach absorption state and (iii) the probability distribution of the first passage times to go from initial states to transient or absorbing states, transient to transient, and transient to absorbing. The model is applied to a clinical study of acute leukemia in which patients have been treated with methotrexate and 6-mercaptopurine. The agreement between the data and the model is very good.

Data from studies of the duration of unmaintained remissions in human acute leukemia have been analyzed according to a murine L1210 leukemia model system. The pattern of recurrence follows an exponential distribution. The slope of recurrence (λ) was more shallow and the guarantee time (G) was longer for the intensive combination treatments (VAMP and BIKE) than for single drug treatment (vincristine and prednisone). The presented model provides the clinician with another potential tool for the analysis of the effectiveness of therapy on human leukemia.

SUMMARY Consider data arranged into k 2 x 2 contingency tables. The principal result is the derivation of a statistical test for making an inference on whether each of the k contingency tables has the same relative risk. The test is based on a conditional reference set and can be regarded as an extension of the Fisher-Irwin treatment of a single 2 x 2 contingency table. Both exact and asymptotic procedures are presented. The analysis of k 2 x 2 contingency tables is required in several contexts. The two principal ones are (i) the comparison of binary response random variables, i.e. random variables taking on the values zero or one, for two treatments, over a spectrum of different conditions or populations; and (ii) the comparison of the degree of association among two binary random variables over k different populations. Cochran (1954) has investigated this problem with respect to testing if the success probability for each of two treatments is the same for every contingency table. Cochran's recommendation is that the equality of the two success probabilities should be tested using the total number, summed over all tables, of successes for one of the treatments. Cochran considers the asymptotic distribution of the total number of successes, for one of the treatments, conditional on all marginals being fixed in every table. He recommends this technique whenever the difference between the two populations on a logistic or probit scale is nearly constant for each contingency table. The constant logistic difference is equivalent to the relative risk being equal for each table. Mantel & Haenlszel (1959), in an important paper discussing retrospective studies, have also proposed an asymptotic method for analysing several 2 x 2 contingency tables. Their worlk on this problem was evidently done independently of Cochran, for their method is exactly the same as Cochran's except for a modification dealing with the correction factor associated with a finite population. Birch (1964) and Cox (1966) clarified the problem by showing, that under the assumption of constant logistic differences for each table, same relative risk, the conditional distribution of the total number of successes, for one of the treatments, leads to a uniformly most powerful unbiased test. Birch and Cox also derived the exact probability distribution of this conditional random variable under the given model. In this paper, we investigate the more general situation where the difference between the logits in each table is not necessarily constant. Procedures are derived for making an inference with regard to the hypothesis of constant logistic differences. Both the exact and asymptotic distributions are derived for the null and nonnull cases. This problem has been discussed by several investigators. A constant logistic difference corresponds to no interaction between the treatments and the k populations. The case k = 2 corresponds to one in which Bartlett (1935) has derived both an exact and an asymptotic procedure. Norton (1945)

1. Introduction and summary. Recently there has been much activity dealing with the tabulation of the bivariate normal probability integral. D. B. Owen [3], [4] has summarized many of the properties of the bivariate normal distribution function and tabulated an auxiliary function which enables one to calculate the bivariate normal probability integral. In addition, the National Bureau of Standards [1] has compiled extensive tables of the bivariate normal integral drawn from the works of K. Pearson, Evelyn Fix and J. Neymaln, and H. H. Germond. In this same volume, D. B. Owen has contributed an extensive section on applications. It is the purpose of this paper to present three charts, which will enable one to easily compute the bivariate normal integral to a maximum error of 10-2. This should be sufficient for most practical applications. Owen and Wiesen [5] have also presented charts with a similar objective; however, as pointed out below, we believe the charts presented here lend themselves more easily to visual interpolation. Actually the motivation for these charts came from the Owen and Wiesen work. 2. Notation and formulas. We present here notation and useful formulas relating to the bivariate normal integral. Let X and Y be random variables following a bivariate normal distribution with zero means, unit variances, and correlation coefficient p. Then

There were 375 cases in the series of breast cancer patients diagnosed from 1921 to 1953 at the Yale-New Haven Medical Center for which information was available for the following four variables: axillary lymph node status, nuclear grade, sinus histiocytosis and tumor size. Patients were classified according to a favorable or unfavorable status with respect to each of these four variables. With one exception, the survival distribution for the 16 resulting groups of patients could be reasonably approximated by a simple exponential distribution. This implies that the mortality rate can be used for analytical purposes as a summary of the survival pattern for a group of cases. Using statistical methods for analyzing factorial experiments, we found that each of the four variables influenced survival and that the order of importance was axillary node status, tumor size, sinus histiocytosis and nuclear grade. No interaction was judged important. Based on an assumption of exponential survival, a mathematical model was developed which made meaningful survival prediction possible (by taking disease status at time of mastectomy into account). The mathematical model was further used for ranking combinations of conditions of the four variables in order of prognostic importance.

(1969). Some Pitfalls in the Evaluation of Screening Programs. Archives of Environmental Health: An International Journal: Vol. 19, No. 3, pp. 412-415.

Under the usual assumptions for the recovery of inter-block information there may exist two independent variance-ratio tests for testing every null hypothesis pertaining to the treatments. A method is suggested for combining two independent tests, and an example shows the gain in power from using the second test. Exact confidence limits are given for the ratio of the inter-block variance to the intra-block variance.

SIUMMARY It is assumed that a chronic disease progresses from a pre-clinical state to a clinical state. If an individual, having pre-clinical disease, participates in an early detection programme, the disease may be detected in the pre-clinical state. The potential benefit of a screening programme is related to the lead time gained by early diagnosis. A stochastic model is developed for early detection programmes which leads to an estimate of the mean lead time as a function of observable variables. An investigation is also made of a non-progressive disease model in which individuals in a pre-clinical state may not necessarily advance to the clinical state. At the present time special diagnostic procedures are available for early detection of some chronic diseases. For example, chest X-rays have long been used to detect tuberculosis. Currently, there are many public health programmes to detect women having cancer of the uterine cervix by using Papanicolaou smears; other programmes designed to test for glaucoma and diabetes are in wide use. An especially interesting programme for early detection of breast cancer using soft tissue X-rays, mammography, is now being conducted by the Health Insurance Plan of Greater New York; see Shapiro, Strax & Venet (1967). The aim of all such programmes is to detect the disease earlier than it normally would be detected, the motivation being that earlier detection may result in a cure or better prognosis. Unfortunately, with only a few exceptions we know of no chronic disease in which unambiguous evidence has been coLlected showing that early detection has resulted in significantly improved prognosis. Even in cancer of the uterine cervix, the results are not without question, because the survival rate had been increasing before the widespread introduction of the Papanicolaou smear. It is the purpose of this paper to discuss statistical considerations associated with the evaluation of such early detection programmes. Attention is confined to screening programmes where an individual is examined only once. In a future paper, we shall examine problems associated with screening programmes where an individual is examined periodically. It will be assumed that a person having a particular chronic disease can be regarded as

This paper discusses procedures for analyzing factorial experiments, where the experiment deals with the life testing of components or equipment. These procedures assume an underlying general distribution of “times-to-failure”, of which the exponential, Weibull, and extreme value distributions are special cases. Statistical tests and confidence procedures are outlined, and an example illustrating the procedure for life-test results of glass capacitors is included. Small sample approximations, which are adequate for practical applications, are given for the proposed procedures. This is shown empirically by generating thousands of life-test experiments on an electronic computer. An empirical sampling investigation is given of the robustness of the proposed procedures. From the sampling results, it is concluded that these techniques are sensitive (non-robust) to departures from the original assumptions on the probability distribution of failure-times. An investigation is also given of a transformation which ...

This review analyzes the results of 692 breast cancer patients from the Norwegian Radium Hospital. All cases were diagnosed during the period 1951–1959 and the average follow-up time was just under eight years. All patients received a radical mastectomy and had their diagnoses pathologically confirmed by a separate reviewer. The purpose of this paper is to apply a novel method of analysis in order to infer the longitudinal course of the disease as if it had not been interrupted by treatment. The method allows one to estimate the average times between changes in the biological factors which characterize the natural history of the disease. Applying this method to the Norwegian data has resulted in identifying three pathways of the natural history of the disease. The tumor growth rates differ for these pathways and are in the approximate ratio 1:5:27. Furthermore, we can estimate the potential benefit from earlier diagnosis. Two of the three pathways would seem to benefit from earlier detection.

An increasingly common public health problem is the perception that disease incidence has increased or a cluster of disease has occurred in a community. In most cases, the disease of concern is cancer and a local hazardous waste site or other environmental problem is involved. These problems can be difficult to investigate and public health officials are frequently criticized for their inability to address community concerns. This paper reports a case study of such a situation occurring in the Barlett-Green Acres (BGA) neighborhood of Randolph, Massachusetts. Study data were obtained by interviews in households of persons belonging to a list of alleged cancer cases initially supplied by residents and supplemented using records available in town and state public health offices. One objective of the investigation was to develop methods that may be of value in similar situations arising in other communities. From a list of names compiled prior to and during the investigation, 45 incident cases of cancer were identified and found suitable for analysis. An additional four cases were added from the Massachusetts Cancer Registry. The analysis showed the existence of a cancer cluster, but overall cancer incidence and mortality in the BGA neighborhood were not elevated. Residence history, disease site, and other features of the cancer cases were investigated using methods less sensitive to incomplete reporting than total incidence. No unusual features of the cancer data other than the initiating cluster were identified and no environmental hazard likely to impact the BGA neighborhood was discovered, hence we conclude that the most likely cause of the cancer cluster was random variation in cancer rates.

This paper proposes a new method for planning randomized clinical trials. This method is especially suited to comparison of a best standard or control treatment with an experimental treatment. Patients are allocated into two groups by a random or chance mechanism. Patients in the first group receive standard treatment; those in the second group are asked if they will accept the experimental therapy; if they decline, they receive the best standard treatment. In the analyses of results, all those in the second group, regardless of treatment, are compared with those in the first group. Any loss of statistical efficiency can be overcome by increased numbers. This experimental plan is indeed a randomized clinical trial and has the advantage that, before providing consent, a patient will know whether an experimental treatment is to be used.

At the present time there are a large number of clinical trials being conducted to find better ways of treating cancer. These trials come in many varieties. Some are based on small numbers of patients, others on large number of patients; some are multi-institutional, others are carried out within a single institution; some are randomized, others are non-randomized. However, regardless of the scientific quality and the care with which a trial is carried out, if the clinical investigator claims that the therapy under investigation is beneficial, it is likely to influence patient treatment everywhere. The problem of choosing the “best” treatment for the cancer patient is difficult and for many cancer sites unresolved. One reason for this is that the outcome depends on many factors; e.g. anatomic stage, pathology, demographic factors, physical status of patient, prior history, extra disease symptoms, as well as special characteristics of the natural history of the disease site. One point of universal agreement is that the treatment outcome with most patients is not well predicted because of the wide fluctuations and complex nature of the natural history of the disease. Poorly conducted trials may ignore the influence of characteristics of the natural history of the disease and report a positive effect of therapy which may be an artifact.

One of the most important advances in modern experimental therapeutics is the development and widespread use of clinical trials to evaluate the benefit of therapy. The term “clinical trial” refers to a prospective clinical investigation in which the clinical investigator has control of the assignment of the therapy to the patient. A clinical trial can be contrasted with an observational study where one undertakes a retrospective record review in an attempt to determine the benefit of therapy which has been administered to patients. In general, the use of observational studies to establish the value of therapies is not reliable.

A discussion of some statistical issues in the planning of prevention studies will be presented. Limitations of space necessitate confining topics to: (i) The role of compliance and (ii) theoretical models and mechanism of action. Compliance issues have k e n discussed in several of the preceding articles. The aim of this presentation is to show that compliance is absolutely crucial in the planning of prevention trials. An understanding of the mechanism of action of interventions is important both in the planning and interpretation of prevention trials. One can develop analytical models of different mechanisms of action and use these models to explore how endpoints are affected with knwn inputs. Analytic models can be viewed as the theoretical analogs of animal models. Other aspects of statistical problems associated with cancer prevention trials can be found in Byar (l), and Prentice (2).

Randomized clinical trials are regarded as the most credible way of generating scientific data that compare the benefits of different therapies. However, randomized trials present difficulties in their execution. Often physicians are unwilling to participate in such studies because they do not wish to inform the patient that the treatment program will be chosen by a chance mechanism. They believe that such a discussion may compromise the physician-patient relationship. Alternatives to classic randomized trials have been discussed. Also considered are some aspects of the strategy of clinical experimentation. It has been pointed out that the initiation of definitive Phase III trials made on the basis of little prior expectation of success ("trying something out") tends to generate false-positive results.

A factorial experiment involving $m$ factors such that the $i$th factor has $m_i$ levels is termed an asymmetrical factorial design. If the number of levels is equal to one another the experiment is termed a symmetric factorial experiment. When the block size of the experiment permits only a sub-set of the factorial combinations to be assigned to the experimental units within a block, resort is made to the theory of confounding. With respect to symmetric factorial designs, the theory of confounding has been highly developed by Bose [1], Bose and Kishen [4], and Fisher [11], [12]. An excellent summary of the results of this research appears in Kempthorne [13]. However, these researches are closely related to Galois field theory resulting in (i) only symmetric factorial designs being incorporated into the current theory of confounding; (ii) the common level must be a prime (or power of a prime) number; and (iii) the block size must be a multiple of this prime number. The theory of confounding for asymmetric designs has not been developed to any great degree. Examples of asymmetric designs can be found in Yates [19], Cochran and Cox [9], Li [15], and Kempthorne [13]. Nair and Rao [16] have given the statistical analysis of a class of asymmetrical two-factor designs in considerable detail. Kramer and Bradley [14] discuss the application of group divisible designs to asymmetrical factorial experiments, however their paper is mainly confined to the two-factor case and its intra-block analysis. It is the purpose of this paper, which was done independently of their work, to outline the general theory for using the group divisible incomplete block designs for asymmetrical factorial experiments. The use of incomplete block designs for asymmetric factorial experiments results in (i) no restriction that the levels must be a prime (or power of a prime) number, (ii) no restriction with respect to the dependence of the block size on the type of level, and (iii) unlike the previous referenced works on asymmetric factorial designs, the resulting analysis is simple, does not increase in difficulty with an increasing number of factors, and "automatically adjusts" for the effects of partial confounding. Section 2 states three useful lemmas, Section 3 contains the main results of this paper, and Section 4 outlines the recovery of inter-block information.

Some diseases can be characterized by the patient being in one of a finite number of states; e.g. relapse, remissive, toxic, etc. These states may be both transient and absorbing. Other authors have proposed similar models to describe data dealing with time dependent phenomena which have assumed that the distribution spent within any state is exponential. These models are all Markovian. In this paper we develop non Markovian models which allow arbitrary distri butions within a state. The model is applied to clinical trials of patients with acute leuke mia who are undergoing experimental therapy. The agreement of the model and the data is very good.

Consider two diagnostic procedures having binary outcomes. If one of the tests results in a positive finding, a more definitive diagnostic procedure will be administered to establish the presence or absence of a disease. The use of both tests will improve the overall screening sensitivity when the two tests are independent, compared with employing two tests that are positively correlated. We estimate the correlation coefficient of the two tests and derive statistical methods for testing the independence of the two diagnostic procedures conditional on disease status. The statistical tests are used to investigate the independence of mammography and clinical breast exams aimed at establishing the benefit of early detection of breast cancer. The data used in the analysis are obtained from periodic screening examinations of three randomized clinical trials of breast cancer screening. Analysis of each of these trials confirms the independence of the clinical breast and mammography examinations. Based on these three large clinical trials, we conclude that a clinical breast exam considerably increases the overall sensitivity relative to screening with mammography alone and should be routinely included in early breast cancer detection programs.