Current issues in the design and interpretation of clinical trials

Though there have been considerable improvements in the use of statistical methods for clinical trials in recent years, there remain major practical difficulties in the design and interpretation of many trials. This paper concentrates on problems relating to randomisation, the overemphasis on significance testing, and the inadequate size of many trials. Each topic is illustrated by examples from recent trials.

Biochemical and haematological response to alcohol intake

In a clinical survey of 7735 middle-aged men, alcohol consumption has been related to 25 biochemical and haematological measurements obtained from a single blood sample. Most measurements showed some association with alcohol consumption, gamma-glutamyl transferase (GGT) being the most strongly associated. Lead, mean corpuscular haemoglobin (MCH), mean corpuscular volume, high-density lipoprotein-cholesterol (HDL-C), urate and aspartate transaminase also showed substantial associations with alcohol intake. Using a discriminant analysis technique, a simple score based on five variables (GGT, HDL-C, urate, MCH and lead) provided the best discrimination between heavy drinkers (e.g. more than three pints of beer daily) and occasional drinkers, but still failed to identify more than half of the heavy drinkers. This combined score may prove a useful measure of an individual's biochemical/haematological response to alcohol consumption for use in epidemiological and clinical studies of alcohol related disorders. The use of such indices should complement but not replace measures of alcohol intake derived from questionnaires.

Blood lead concentration, blood pressure, and renal function

Blood lead concentrations were related to blood pressure and indicators of renal function in a clinical survey of 7735 middle aged men from 24 British towns. There was no overall evidence that blood lead concentrations were associated with systolic or diastolic blood pressure (r = +0.03 and +0.01, respectively). In the 74 men with a blood lead concentration of 1.8 mumol/l (37.3 micrograms/100 ml) or more there was some suggestion of increased hypertension, but this did not reach significance. Blood lead concentration did not have any relation with serum creatinine concentration. Moderate increases in blood lead concentration were associated with small increases in mean serum urate concentration and small decreases in mean serum urea concentration; these associations were both reduced when alcohol consumption was taken into account. There is no indication that exposure to lead at concentrations commonly encountered in British men is responsible for impaired renal function or increased blood pressure.

Reduction in exposure to lead from drinking water and its effect on blood lead concentrations

The water supply in Ayr (Scotland, UK) was plumbosolvent and many dwellings in Ayr contained lead pipes. In 1981 treatment of the water supply to reduce its plumbosolvency was initiated. Measurements of water and blood lead concentrations were made before and subsequent to the treatment. Most of the measurements made before and after water treatment began were made on water samples from the same dwellings and blood samples from the same women. Water treatment produced a sharp fall in water lead concentrations and a decrease in the median blood lead concentration from 21 to 13 micrograms/100 ml. Two women had higher than expected blood lead concentrations, both these women had been removing old paint. Women who had lead pipes removed from their dwellings all showed substantial decreases in their blood lead concentrations. The curvilinearity of the relation between blood lead and water lead concentrations is confirmed. Even relatively low (less than 40 micrograms/l) water lead concentrations may make a substantial contribution to blood lead concentrations.

Multiple regression in geographical mortality studies, with allowance for spatially correlated errors

In order to provide clues to the aetiology of a disease, mortality indices for different areas are often related to explanatory variables by using multiple regression. However, mortality in nearby areas may be similar for reasons not attributable to the covariates, so the errors will not be independent. This paper suggests a way of finding a parameterized form for the correlated error structure by examining the residuals from an ordinary least squares regression. Such a model is then fitted by using maximum likelihood. An example based on cardiovascular mortality in British towns is used to illustrate the problem and our solution.

Effects of tap water lead, water hardness, alcohol, and cigarettes on blood lead concentrations

A survey of middle-aged men in 24 British towns has found pronounced geographical variation in blood lead concentrations. Towns with the highest mean blood lead concentrations have soft water supplies and have the highest water lead concentrations. Individual blood lead can be considerably increased by raised household tap water lead concentrations. Mean blood lead is estimated to be 43% higher for men when the concentration of lead in first-draw domestic tap water is 100 micrograms/l compared with a zero concentration. Individual blood lead is also affected by alcohol consumption and cigarette smoking, such that on average these two life-style habits together contribute an estimated 17% to the blood concentration of lead in middle-aged men. Lead in water should be given greater priority in any national campaign to reduce lead exposure.

Practical experience of randomization in cancer trials: an international survey

The results from an international survey of 15 major cancer centres have clarified how randomization is being implemented in cancer trials. As regards the mechanics of obtaining treatment assignment for each patient a system of telephone registration to a central randomization office was widely used. We also advise formal checks for patient eligibility immediately before treatment assignment, and subsequent written confirmation of randomization to the investigators. As regards statistical methods, stratification of randomization by one or two prognostic factors (and institution in multicentre trials) is commonplace. Most centres used the standard approach of random permuted blocks within strata though some others used "dynamic" institution-balancing or "minimization" methods instead. The value of stratified allocation is chiefly for the trial's credibility in having comparable treatment groups, rather than for statistical efficiency. One should avoid overstratification and use only the really important prognostic factors. One essential is that randomization should in practice work for every patient, so undue complexity is to be avoided.

Ethnic differences in certified sickness absence

The certified sickness absence of 4482 employees in one plant of a large manufacturing company in South-east England was studied for 12 months. The absences in the principal ethnic groups, Caucasian, Asian, and West Indian were compared. After standardisation for age and job grade in each department the Asians had twice the spells per man and nearly twice the days lost per man compared with the Caucasians. Compared with the Caucasians there was slightly more absence in West Indians. Various factors affect absence, and one reason for these differences may be that the three ethnic groups appreciate painful or unpleasant stimuli to a different degree.

Some studies of maternal and infant lead exposure in Glasgow

In two studies in the city of Glasgow, 236 mothers and their newly born infants and 117 mothers and their 6-weeks old children's environmental lead exposure were examined. In both studies blood lead concentrations were found to correlate significantly with the cube root of the domestic water lead concentrations. In the first study, multiple regression analyses of maternal blood lead and cord blood lead concentrations on other variables showed a significant negative correlation with gestational age. It was also noted that there was an annual fluctuation in maternal blood lead concentration with highest values in the autumn. In the second study, similar relationships were found. Although there was no association between blood lead and sex, age, place of birth or feeding method, as in the previous study, a significant association between social class and blood lead was found. This could be explained on the basis of the significant correlation between water lead and social class. In those mothers who breast fed, breast milk lead concentrations were found to correlate significantly with blood lead concentrations where breast milk lead was around one tenth of blood lead concentration. These studies emphasise the importance of water lead in the economy of environmental lead exposure to mothers and their unborn and newly born infants.

Long term survival analysis: the curability of breast cancer

Methods of survival analysis for long-term follow-up studies are illustrated by a study of mortality in 3878 breast cancer patients in Edinburgh followed for up to 20 years. The problems of life tables, advantages of hazard plots and difficulties in statistical modelling are demonstrated by studying the relationship between survival and both clinical stage and initial menopausal status at diagnosis. To assess the 'curability' of breast cancer, mortality by year of follow-up is compared with expected mortality using Scottish age-specific death rates. Techniques for analysing such relative survival data include age-corrected life tables, ratio of observed to expected deaths and excess death rates. Finally, an additive hazard model is developed to incorporate covariates in the analysis of relative survival and curability.

Interim analyses for randomized clinical trials: the group sequential approach

For many clinical trials interim analyses are undertaken periodically, one purpose being to determine whether to stop the trial early because of a substantial treatment difference. There exist group sequential designs for such trials, on simple approach being to decide in advance on a maximum number of analyses and then to apply repeated significance tests to the accumulating data. To allow for repeated testing one uses a more stringent (nominal) significance level as a stopping rule. Power calculations based on results for normal group sequential designs obtained by numerical integration, enable one to determine the number of patients to be evaluated between analyses. There appears to be little advantage in analysing trial data on more than five occasions unless one anticipates the possibility of an extremely large treatment difference. As an alternative to having a constant nominal significance level throughout a trial, one could have more stringent significance levels at early stages and less stringent levels at the last one or two analyses. For a trial of adequate overall size and power there appears to be no statistical advantage to be gained from this approach.

Effects of alcohol and smoking on blood lead in middle-aged British men

A survey of middle-aged men in 24 British towns showed a strong association between blood lead concentrations, alcohol consumption, and cigarette smoking. The association with alcohol persisted after age, social class, body mass index, cigarette smoking, water lead concentrations, and the town of residence had been taken into account. There was an independent but less pronounced association between cigarette smoking and blood lead concentrations after adjustment for the other factors. The possible mechanisms include a decreased excretion of lead due to alcohol-induced hepatic dysfunction and an increased lead intake from cigarette smoking. These findings have implications for widespread measurement of blood lead concentrations in adults in the community and for all studies attempting to relate blood lead concentrations to environmental exposure.

Differences in physical characteristics, perinatal histories, and social backgrounds between children with growth hormone deficiency and constitutional short stature

Four hundred and forty-nine children with heights below -2.5 SD were identified by screening for height a total population of 48221 in three Scottish cities. Children participating in the study could be classified into 5 groups: severe growth hormone deficiency (n = 13), partial growth hormone deficiency (n = 25), low birthweight short stature (n = 34), constitutional short stature (n = 178), and short stature associated with some underlying disease (n = 106). Children with growth hormone deficiency tended to be shorter, were more likely to be obese, were growing more slowly, more often were the products of an abnormal pregnancy, and were less socially disadvantaged than constitutionally short children. Their parents were also more likely to have sought medical advice about the short stature. These findings have important implications for improved case-finding of children suffering from growth-hormone deficiency, who in this study accounted for about 10% of all short but otherwise normal children who came from non-disadvantaged communities.

British Regional Heart Study: cardiovascular risk factors in middle-aged men in 24 towns

The British Regional Heart Study seeks to define risk factors for cardiovascular disease, to examine their interrelationships, and to explain the geographic variations in cardiovascular disease in Britain. A clinical survey of men aged 40-59 in 24 British towns was carried out and preliminary data from the survey analysed. On a town basis cardiovascular mortality was associated with mean systolic blood pressure and the prevalence of heavy cigarette smoking and heavy alcohol consumption. No such association was seen for body mass index or mean serum total cholesterol or high-density-lipoprotein cholesterol concentration. Cigarette smoking and alcohol intake and, to a less degree, systolic blood pressure were related to the social class (percentage of manual workers) of a town, and these factors may determine to some extent the increased risk of cardiovascular disease in manual workers. Blood pressure in individual subjects was affected predominantly by age, body mass index, and alcohol intake. Body mass index appeared to affect blood pressure to a greater extent than alcohol intake and did so with a consistent and positive linear trend. Nevertheless, the differences between towns in mean blood pressure readings appeared to be more closely associated with variations in the prevalence of heavy drinking than with variations in body mass index. Alcohol intake and body mass index explained only a part of the striking differences between towns in mean blood pressure readings, and some important "town"factors remained unexplained.

Studies of water quality and cardiovascular disease in the United Kingdom

The British Regional Heart Study aims at determining factors responsible for the marked regional variations in cardiovascular disease in Great Britain. PHASE I is a retrospective study of cardiovascular mortality with water quality (hardness and more than 20 other water parameters have been studied), climate, air pollution, socio-economic and genetic factors. An association between water hardness and cardiovascular mortality is reaffirmed, towns with soft water tending to have higher death rates than towns with hard water. This relationship is somewhat weakened after allowing for climatic and socio-economic factors but remains statistically significant for both coronary heart disease and stroke. After adjustment for other factors, soft water areas (around 0.25 mmol/l) have a 10-15% higher cardiovascular mortality that areas of medium hardness (around 1.70 mmol/l) whereas any further increase beyond 1.70 mmol/l has little extra lowering effect on cardiovascular mortality.

The British Regional Heart Study: cardiovascular mortality and water quality

The Regional Heart Study aims at determining the factors responsible for the marked regional variations in coronary heart disease and stroke in Great Britain. This report is concerned with mortality (1969-1973) from cardiovascular disease in 253 towns in England, Wales and Scotland with particular reference to water quality (hardness), climate, air pollution, socio-economic and genetic (blood group) factors. The preliminary results reaffirm an association between water hardness and cardiovascular (CV) mortality, with towns with soft water tending to have hgiher CV death rates than towns with hard water. Multiple regression analysis shows that this relationship is somewhat weakened after allowing for rainfall, temperature and socio-economic factors but that it remains statistically significant for both coronary heart disease and stroke. A study of 13 towns with artificially softened water supplies indicates that their CV mortality is no higher than in neighbouring towns without softened water. A study of the prevalence of risk factors for cardiovascular disease is being carried out in 25 British towns selected to represent all the variations in CV mortality and water hardness and representing all major geographic regions of Britain. The incidence of CV disease in the 7,500 men aged 40-59 years in this study will be related to personal and environmental risk factors. Preliminary data show an association between mean blood pressure levels and CVD mortality rates.

Maternal vitamin D intake and mineral metabolism in mothers and their newborn infants

Pregnant women receiving daily supplements of 400 IU (10 microgram) of vitamin D2 from the 12th week of pregnancy had plasma calcium concentrations higher at 24 weeks but similar at delivery to those in control pregnant women who did not receive the supplements. Infants of the women receiving the supplements had higher calcium, lower phosphorus, and similar magnesium concentrations on the sixth day of life and a lower incidence of hypocalcaemia than infants of the control women. Plasma concentrations of 25-hydroxycholecalciferol, which showed a seasonal variation, were higher in mothers and infants in the treated group. Cord-blood calcium, magnesium, phosphorus, and 25-hydroxycholecalciferol concentrations correlated with maternal values at delivery. Breast-fed infants had higher calcium and magnesium and lower phosphorus and 25-hydroxycholecalciferol concentrations than artificially fed infants. A defect of dental enamel was found in a high proportion of infants (many of whom had suffered from hypocalcaemia) born to the control women. These results suggest that vitamin D supplementation during pregnancy would be beneficial for mothers, whose intake from diet and skin synthesis is appreciably less than 500 IU of vitamin D daily.

British Regional Heart Study: geographic variations in cardiovascular mortality, and the role of water quality

In a study of regional variations in cardiovascular mortality in Great Britain during 1969-73 based on 253 towns the possible contributions of drinking water quality, climate, air pollution, blood groups, and socioeconomic factors were evaluated. A twofold range in mortality from stroke and ischaemic heart disease was apparent, the highest mortality being in the west of Scotland and the lowest in south-east England. A multifactorial approach identified five principal factors that substantially explained this geographic variation in cardiovascular mortality-namely, water hardness, rainfall, temperature, and two social factors (percentage of manual workers and car ownership). After adjustment for other factors cardiovascular mortality in areas with very soft water, around 0.25 mmol/l (calcium carbonate equivalent 25 mg/l), was estimated to be 10-15% higher than that in areas with medium-hard water, around 1.7 mmol/l (170 mg/l), while any further increase in hardness beyond 1.7 mmol/l did not additionally lower cardiovascular mortality.Thus a negative relation existed between water hardness and cardiovascular mortality, although climate and socioeconomic conditions also appeared to be important influences. Cross-sectional and prospective surveys of 7500 middle-aged men from 24 towns are in progress and will permit further exploration of these geographic differences, especially with regard to personal risk factors such as blood pressure, blood lipid concentrations, and cigarette smoking.

Factors influencing household water lead: a British national survey

From a survey of 2,831 households in Great Britain, a quantitive assessment was made of the combined influence of lead piping, acidity of water supply, and other factors on houselhold water lead levels. Estimates are provided of the effects that remedial measures would have on blood lead levels in the population.

Long-term survival of patients with breast cancer: a study of the curability of the disease

A retrospective analysis was made of 3878 cases of breast carcinoma first seen in Edinburgh from 1954 to 1964. During this time there was a policy to treat breast cancer by simple mastectomy and x-ray therapy, and over 90% of cases classified as international stages I and II were so treated. The mortality in these women was compared with that in an equivalent normal population using Scottish national age-specific death rates. For every year of follow-up within 20 years of initial treatment there was an excess mortality from all causes. There was an overall excess mortality of 58% among patients with breast cancer 15-20 years after initial treatment, and 20 times more deaths occurred in this period from breast cancer than in a normal population. For patients disease-free after 15 years there was still a 28% excess mortality from all causes. Factors known to be of major prognostic significance for five-year survivorship had less influence than might have been expected when the ratio of observed to expected deaths was considered for longer periods of follow-up. The effect of clinical staging (I, II, or III), though initially marked, largely disappeared by the 10th year of follow-up, and after allowing for age there was no evidence beyond 10 years of an effect on survival of the original stage of the disease. Similarly, the effect of tumour size on survival disappeared after 10 years. Women who were premenopausal at presentation still had a significant excess of deaths in the fourth quinquennium of follow-up. In the menopausal and postmenopausal groups combined there was still a small non-significant excess of deaths from all causes after 15 years but this almost disappeared when patients who had already relapsed were excluded. In terms of overall mortality only patients who have undergone the menopause before presentation and who are disease-free 15 years after primary treatment may prove to be cured by conventional techniques such as simple mastectomy and postoperative radiotherapy.

The contribution of drinking water lead to maternal blood lead concentrations

The association between domestic water lead concentrations and blood lead concentrations has been examined in 232 mothers at delivery. The blood lead was found to vary significantly with the cube root of the water lead. This association was stronger for first flush water lead rather than for running water lead. This study emphasises the danger to mothers and to their children of environmental lead over-exposure in areas of soft acid plumbosolvent water.

Allocation of patients to treatment in clinical trials

This article is intended as a practical guide to the various methods of patient assignment in clinical trials. Topics discussed include a critical appraisal of non-randomized studies, methods of restricted randomization such as random permuted blocks and the biased coin technique, the extent to which stratification is necessary and the methods available, the possible benefits of randomization with a greater proportion of patients on a new treatment, factorial designs, crossover designs, randomized consent designs and adaptive assignment procedures. With all this diversity of approach it needs to be remembered that the effective implementation and reliability of a relatively straightforward randomization scheme may be more important than attempting theoretical optimality with more complex designs.

Size of cancer clinical trials and stopping rules

A recent international survey on the size of clinical trials in cancer showed the frequent problem of slow patient accrual, which remains a major hindrance to progress. The survey also revealed that, although the design of most trials specified a fixed number of patients, subsequent experience revealed a much more flexible approach, with analysis of results, say, every 4--6 months. Conventional sequential methods are hardly ever used and unfortunately most trials proceed without any predetermined stopping rules. Some trial organizers use repeated significance tests on accumulating data as a guide to the detection of treatment differences, an approach that can be adapted to a more rigorous statistical framework as a "group sequential design". The major statistical principle involved is that the more often one analyses the data the greater is the probability of achieving a statistically significant result, even when the two treatments are equally effective. Group sequential designs require the adoption of a more stringent significance level to allow for repeated testing. If one intends up to 10 repeated analyses of the data, only a treatment difference significant at the 1% level would merit a decision to stop the trial. For any trial to implement a stopping rule successfully there must also be prompt feedback and processing of response and survival data ready for up-to-date analysis. Such efficiency is often lacking. The repeated presentation of interim results of a trial to participating investigators can seriously affect their future reaction, especially if there are interesting but non-significant differences. Thus, some secrecy about ongoing results is advisable if trials are to achieve an unbiased conclusion.

Prognosis of patients with acute myocardial infarction admitted to a coronary care unit. I: Survival in hospital

On a basis of history, clinical examination, and the electrocardiogram it was possible to identify groups of patients with acute myocardial infarction with good and bad prognoses as regards hospital survival. Individual adverse factors were age, prevous history of ischaemic heart disease, anterior infarction, persistent sinus tachycardia, pulmonary crepitations, hypotension, and raised venous pressure. Multivariate analysis showed four factors remaining significant--age, tachycardia, hypotension, and pulmonary crepitations. As a result of treatment of cardiac arrest, hospital mortality, which would otherwise have been 20 percent, was 17 percent. Preceding unstable angina did not worsen the immediate prognosis.

Prognosis of patients with acute myocardial infarction admitted to a coronary care unit. II. Survival after hospital discharge

The factors adversely affecting long-term prognosis differed from those affecting outcome of acute infarction. Individual factors were previous history of infarction or hypertension, tachycardia, cardiac arrest, ventricular arrhythmia, atrial fibrillation, 3rd heart sound, raised venous pressure, and pulmonary crepitations. Multivariate analysis reduced these to 6--previous infarct or hypertension, sinus tachycardia, cardiac arrest, ventricular arrhythmia, and artial fibrillation. Of those who survived 5 years, approximately half had angina. Two-thirds of the under 60 survivors were at their normal work.

Chemotherapy of non-Hodgkin's lymphomas: Eastern Cooperative Oncology Group experience

The addition of prednisone to the two-drug combination of cyclophosphamide and vincristine increases the number of complete remissions (CR). Patients who had CRs in at least two of the studies, EST 0168 and EST 3472, lived significantly longer than those who had partial remissions. In EST 0168, the survival time correlated strongly with the nodal pattern and cell type, confirming results of Rosenberg and co-workers. EST 1472 confirmed the activity of BCNU in lymphocytic lymphomas; when both agents are combined with prednisone, the induction potential of BCNU is equal to that of cyclophosphamide. In the histiocytic lymphomas, BCNU added to CVP increases the percentage of CRs but it does so at the expense of considerable toxicity. EST 0871 demonstrated that low-dose bleomycin and hexamethylmelamine are active agents in lymphoma and should be combined with other effective combinations in an attempt to improve the CR rate. Finally, our current studies demonstrate that the failure rate in the diffuse or unfavorable lymphomas is higher than that in the more favorable nodular forms.

Variation in the incidence of diverticular disease within the city of Edinburgh

An estimate of the incidence of diverticular disease of the colon was based on all the barium enema examinations in Edinburgh over four years (12 335 cases); using the census data for 1971, incidence rates for the city by age, sex, and electoral ward were calculated. The overall annual incidence rate was 1-55/1000, the rate rising sharply with increasing age. The incidence of diverticular disease varies from ward to ward (range 0-92-2-04/1000), adjacent wards have similar incidence rates and the six wards with the lowest rates are clustered together in the South East of the city. Ward incidence rates have a significant negative association with the percentage of owner occupiers living in that area.

Combination chemotherapy for metastatic breast carcinoma. Prospective comparison of multiple drug therapy with L-phenylalanine mustard

A prospective randomized clinical trial was undertaken in 184 patients with metastatic breast carcinoma to compare single drug chemotherapy with L-phenylalanine mustard (L-PAM) and intermittent combination chemotherapy with cyclophosphamide, methotrexate, and 5-fluourouracil (CMF). All patients had not been previously treated with cytotoxic drugs and all had objectively measurable visceral of soft tissue disease. Of the 93 patients who received CMF, 49 (53%) achieved a complete (14 patients) or partial (35 patients) regression of measurable tumor, for a median duration of 25 weeks. Eighteen of the 91 patients (20%) treated with L-PAM responded, for a median duration of 13 weeks. The toxicity was primarily hematologic, and greater in the CMF group, which also received more cycles of therapy because of the higher rate and duration of response. The overall survival of CMF-treated patients was superior to that of the single drug group. The differences were even greater when the patients were subclassified according to the presence of liver involvement or nonambulatory performance status. The superior antitumor effect of CMF over L-PAM suggests that it may be a more effective drug regimen to be used as an adjuvant to primary therapy.

Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial

In controlled clinical trials there are usually several prognostic factors known or thought to influence the patient's ability to respond to treatment. Therefore, the method of sequential treatment assignment needs to be designed so that treatment balance is simultaneously achieved across all such patients factor. Traditional methods of restricted randomization such as "permuted blocks within strata" prove inadequate once the number of strata, or combinations of factor levels, approaches the sample size. A new general procedure for treatment assignment is described which concentrates on minimizing imbalance in the distributions of treatment numbers within the levels of each individual prognostic factor. The improved treatment balance obtained by this approach is explored using simulation for a simple model of a clinical trial. Further discussion centers on the selection, predictability and practicability of such a procedure.

Clinical studies of 5-fluorouracil + premarin in the treatment of breast cancer

Sixty patients with metastatic or primary inoperable breast cancer not suitable for hormone alteration therapy were blindly randomized between weekly 5-fluorouracil, intravenously, and daily physiologic doses of conjugated estrogens by mouth against weekly 5-fluorouracil, intravenously, and placebo. There was no difference in the survival or the effect on the tumor in the two groups. Numerous factors were analyzed as to their effect on the course of the disease. The number of organ sites of tumor involvement, age of the host, and previous treatment for the disseminated disease were not shown to influence the survival or the results of therapy of either group. However, the duration of the clinical cancer-free period from primary treatment to recurrence, the sites of organ involvement, and the performance status of the patients at the time of entry into the study significantly did influence the survival. There is no evidence in this study that physiologic doses of conjugated estrogens deleteriously influenced the course of the disease.