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Different methods for the calculation of sample size for simple logistic regression (LR) with one normally distributed continuous covariate give different results. Sometimes the difference can be large. Furthermore, some methods require the user to specify the prevalence of cases when the covariate equals its population mean, rather than the more natural population prevalence. We focus on two commonly used methods and show through simulations that the power for a given sample size may differ substantially from the nominal value for one method, especially when the covariate effect is large, while the other method performs poorly if the user provides the population prevalence instead of the required parameter. We propose a modification of the method of Hsieh et al. that requires specification of the population prevalence and that employs Schouten's sample size formula for a t-test with unequal variances and group sizes. This approach appears to increase the accuracy of the sample size estimates for LR with one continuous covariate.

The UK Medical Research Council (MRC) randomized trial of gastric surgery, ST01, compared conventional (D1) with radical (D2) surgery. Sample size estimation was based upon the consensus opinion of the surgical members of the design team, which suggested that a change in 5-year survival from 20% (D1) to 34% (D2) could be realistic and medically important. On the basis of these survival rates, the sample size for the trial was 400 patients. However, this trial was exceptional in the way that a survey of surgeons' opinions was made at the start of the trial, in 1986, and again before results were analysed but after termination of the trial in 1994. At the initial survey, the three surgeons from the trial steering committee and 23 other surgeons experienced in treating gastric carcinoma were given detailed questionnaires. They were asked about the expected survival rate in the D1 group, anticipated difference in survival from D2 surgery, and what difference would be medically important and influence future treatment of patients. The consensus opinion of those surveyed was that there might be a survival improvement of 9.4%. In 1994, prior to closure of the trial, and before any survival information was disclosed, the survey was repeated with 21 of the original 26 surgeons. At this second survey, the opinion of the trial steering committee was that 9.5% difference was more realistic. This was in accord with the opinion of the larger group, which remained little changed since 1986. The baseline 5-year D1 survival was thought likely to be about 32%, which corresponded closely to the actual survival of recruited patients. Revised sample size calculations suggested that, on the basis of these more recent opinions, between 800 and 1200 patients would have been required. Both surveys assessed the level of treatment benefit that was deemed to be sufficient for causing surgeons to change their practice. This showed that the 13% difference in survival used as the study target was clinically relevant, but also indicated that many clinicians would remain unwilling to change their practice if the difference is only 9.5%. The experience of this carefully designed trial illustrates the problems of designing long-term, randomized trials. It raises interesting questions about the common practice of basing sample size estimates upon the beliefs of a trial design committee that may include a number of enthusiasts for the trial treatment. If their opinion of anticipated effect sizes drives the design of the trial, rather than the opinion of a larger community of experts that includes sceptics as well as enthusiasts, there is likely to be a serious miscalculation of sample size requirements. © 2000 Cancer Research Campaign

Six patients with lumbosacral hemivertebrae were treated by one-stage anterior and posterior excision of the hemivertebrae. Long-term follow-up is reported. Overall, correction of the lumbosacral curve was 46%, including one case of pseudarthrosis and subsequent loss of correction. More importantly, truncal imbalance was restored unless other congenital thoracic anomalies were present. New methods of calculating rib cage shift on the pelvis as well as vertebral column displacement from the sagittal plane are presented.

In 1995-1996, the authors mailed a food frequency questionnaire to 3.5 million American Association of Retired Persons members who were aged 50-69 years and who resided in one of six states or two metropolitan areas with high-quality cancer registries. In establishing a cohort of 567,169 persons (340,148 men and 227,021 women), the authors were fortunate in that a less-than-anticipated baseline response rate (threatening inadequate numbers of respondents in the intake extremes) was offset by both a shifting and a widening of the intake distributions among those who provided satisfactory data. Reported median intakes for the first and fifth intake quintiles, respectively, were 20.4 and 40.1 (men) and 20.1 and 40.0 (women) percent calories from fat, 10.3 and 32.0 (men) and 8.7 and 28.7 (women) g per day of dietary fiber, 3.1 and 11.6 (men) and 2.8 and 11.3 (women) servings per day of fruits and vegetables, and 20.7 and 156.8 (men) and 10.5 and 97.0 (women) g per day of red meat. After 5 years of follow-up, the cohort is expected to yield nearly 4,000 breast cancers, more than 10,000 prostate cancers, more than 4,000 colorectal cancers, and more than 900 pancreatic cancers. The large size and wide intake range of the cohort will provide ample power for examining a number of important diet and cancer hypotheses.

Stomatitis is a common consequence of chemotherapy and a condition for which there is little effective treatment. Although the management of patients with other chemotherapy-related toxicities has improved in recent years, the incidence of stomatitis is increasing because of more intensive treatment and is often a dose limiting factor in chemotherapy. The authors assessed the efficacy of a homeopathic remedy, TRAUMEEL S(R), in the management of chemotherapy-induced stomatitis in children undergoing bone marrow transplantation.A randomized, placebo-controlled, double-blind clinical trial was conducted in 32 patients ages 3-25 years who had undergone allogeneic (16 patients) or autologous (16 patients) stem cell transplantation. Of the 30 evaluable patients, 15 were assigned placebo, and 15 were assigned TRAUMEEL S both as a mouth rinse, administered five times daily from 2 days after transplantation for a minimum of 14 days, or until at least 2 days after all signs of stomatitis were absent. Stomatitis scores were evaluated according to the World Health Organization grading system for mucositis.A total of five patients (33%) in the TRAUMEEL S treatment group did not develop stomatitis compared with only one patient (7%) in the placebo group. Stomatitis worsened in only 7 patients (47%) in the TRAUMEEL S treatment group compared with 14 patients (93%) in the placebo group. The mean area under the curve stomatitis scores were 10.4 in the TRAUMEEL S treatment group and 24.3 in the placebo group. This difference was statistically significant (P0.01).This study indicates that TRAUMEEL S may reduce significantly the severity and duration of chemotherapy-induced stomatitis in children undergoing bone marrow transplantation.

Cell proliferation in the human colorectum can be measured using bromodeoxyuridine (BrdU) or proliferating cell nuclear antigen (PCNA) assays. Using data from the National Cancer Institute's Polyp Prevention Trial, these two assays are compared using correlation coefficients and variance components analysis. Adjusting for fixed as well as for the random effects of between-biopsy and scoring variation, the estimated correlation is 0.46 for the log labeling index and 0.45 for log proliferative height. This is an estimate of the highest correlation that can be achieved by taking multiple biopsies scored by multiple scorers. For single biopsies, the estimated correlation is 0.16 and 0.10, respectively. There are significant differences between the variance components for the two assays. For example, for log labeling index, PCNA has a lower variation between biopsies than BrdU, but higher variation between scorings. When used in a clinical or epidemiological setting, it is important to take multiple biopsies at multiple time points.

To determine if Kaposi's sarcoma-associated herpesvirus (KSHV) prevalence is correlated with the 9-fold difference in the incidence of classic Kaposi's sarcoma observed among Israeli Jewish populations, we conducted a cross-sectional KSHV seroprevalence survey in a population of 166 HIV-seronegative healthy subjects from the general population (26 women, 140 men). Eight individuals (4.8%) (all men) were seropositive for KSHV; differences between men and women were not statistically significant. If we consider the sensitivity and specificity of the assays, the corrected prevalence would be 6.1% (95% confidence interval 2.0-10.1). We noticed a non-statistically 5.5-fold difference between individuals above and below 40 years of age, but did not find an association with the incidence of classic KS among the Israeli Jewish sub-population, according to their origin. This suggests that KSHV is only necessary, albeit not sufficient, cause of classic Kaposi's sarcoma.

Early randomized Phase II cancer chemoprevention trials which assess short-term biological activity are critical to the decision process to advance to late Phase II/Phase III trials. We have adapted published Bayesian interim analysis methods (Spiegelhalter et al., J. R. Statist. Soc A, 1994; 157: 357-416) which give greater flexibility and simplicity of inference to the monitoring of randomized controlled Phase II trials using intermediate endpoints. The Bayesian stopping rule is designed to stop the trial more quickly when the evidence suggests ineffectiveness rather than when it suggests biological activity, thus allowing resources to be concentrated on those agents that show the most promise in this early stage of testing. We investigate frequentist performance characteristics of the proposed method through simulation of randomized placebo controlled trials with a growth factor intermediate end-point using mean and variance values derived from the literature. Simulation results show expected error rates and trial size similar to other commonly used group sequential methods for this setting. These results suggest that the Bayesian approach to interim analysis is well suited for monitoring small randomized controlled Phase II chemoprevention trials for early detection of either inactive or promising agents.

This chapter reviews work of Carroll, Freedman, Kipnis, and Li (1998) on the statistical analysis of the relationship between dietary intake and health outcomes. In the area of nutritional epidemiology, there is some evidence from biomarker studies that the usual statistical model for dietary measurements may break down due to two causes: (a) systematic biases depending on a person's body mass index; and (b) an additional random component of bias, so that the error structure is the same as a one-way random effects model. We investigate this problem, in the context of (1) the estimation of the distribution of usual nutrient intake; (2) estimating the correlation between a nutrient instrument and usual nutrient intake; and (3) estimating the true relative risk from an estimated relative risk using the error-prone covariate. While systematic bias due to body mass index appears to have little effect, the additional random effect in the variance structure is shown to have a potentially important impact on overall results, both on corrections for relative risk estimates and in estimating the distribution usual of nutrient intake. Our results point to a need for new experiments aimed at estimation of a crucial parameter.

We assessed components of total variability of bromodeoxyuridine (BrdUrd) and proliferating cell nuclear antigen (PCNA) assays of rectal mucosal proliferation in a subset of 390 participants from the U. S. National Cancer Institute's multicenter Polyp Prevention Trial. Biopsies were blindly double-scored by two technicians. For those participants for whom at least one evaluable biopsy was obtained, a mean of 2.0 and 2.6 biopsies, and 6.2 and 8.7 crypts/biopsy were evaluated, respectively, with the BrdUrd and PCNA assays. Factors such as clinical center, scorer, and month of biopsy collection significantly affected the observed values of the labeling index (LI) and proliferative height (PH). Therefore, it is essential to control or adjust for these variables in proliferation studies. Sources of random variation for LI and PH measures remaining after the aforementioned factors include between-participant variation and several sources of within-participant variation, including variation over time, between biopsies, and between multiple measurements on the same biopsy. Both LI and PH measurements exhibited substantial variability over time, between biopsies, and from reading-to-reading of the same biopsy. When other sources of variability have been accounted for, the PCNA LI seems to have little between-participant variation. This brings into question its utility as a marker in colorectal cancer studies. The PCNA PH showed significant between-participant variability and may hold some promise as a useful marker in colorectal cancer studies. Results for BrdUrd were less conclusive. The BrdUrd LI showed marginally significant between-participant variation, whereas the corresponding variation for PH was nonsignificant.

Motivated by a meta-analysis of animal experiments on the effect of dietary fat and total caloric intake on mammary tumorigenesis, we explore the use of sandwich estimators of variance with conditional logistic regression. Classical conditional logistic regression assumes that the parameters are fixed effects across all clusters, while the sandwich estimator gives appropriate inferences for either fixed effects or random effects. However, inference using the standard Wald test with the sandwich estimator requires that each parameter is estimated using information from a large number of clusters. Since our example violates this condition, we introduce two modifications to the standard Wald test. First, we reduce the bias of the empirical variance estimator (the middle of the sandwich) by using standardized residuals. Second, we approximately account for the variance of these estimators by using the t-distribution instead of the normal distribution, where the degrees of freedom are estimated using Satterthwaite's approximation. Through simulations, we show that these sandwich estimators perform almost as well as classical estimators when the true effects are fixed and much better than the classical estimators when the true effects are random. We achieve simulated nominal coverage for these sandwich estimators even when some parameters are estimated from a small number of clusters.

We performed a meta-analysis on data extracted from 97 reports of experiments, involving a total of 12,803 mice or rats, studying the effect on mammary tumor incidence of different types of dietary fatty acids. Fatty acids were categorized into saturated, monounsaturated, n-6 polyunsaturated, and n-3 polyunsaturated. We modeled the relation between tumor incidence and percentage of total calories from these fatty acids using conditional logistic regression and allowing for varying effects between experiments, and for each fatty acid we estimated the effect of substituting the fatty acid calories for nonfat calories. Our results show that n-6 polyunsaturated fatty acids (PUFAs) have a strong tumor-enhancing effect and that saturated fats have a weaker tumor-enhancing effect. The n-3 PUFAs have a small protective effect that is not statistically significant. There is no significant effect of monounsaturated fats. n-6 PUFAs have a stronger tumor-enhancing effect at levels under 4% of total calories, but an effect is still present at intake levels greater than 4% of calories. In addition, when the intake of n-6 PUFAs is at least 4% of calories, the n-6 PUFA effect remains stronger than the saturated fat effect.

The 2 x 2 factorial design has been advocated for improving the efficiency of clinical trials. Most such trials are designed on the assumption that there is no interaction between the levels of the factors and outcome. This assumption is often problematic, however, because interactions are usually possible in clinical trials and the sample sizes often used provide little power in testing for interactions. We consider the use of Bayesian methods for the design and analysis of 2 x 2 factorial clinical trials. This approach avoids the need to dichotomize one's assumptions that interactions either do or do not exist and provides a flexible approach to the design and analysis of such clinical trials. Exact results are developed for balanced factorial designs with normal response. Approximations are then presented for factorial designs based on the logistic model for binary response or the proportional hazards model for time-to-event data. The resulting approximate posterior distributions are normal and hence no extensive computations are required. Suggestions for specification of prior distributions are presented.

Researchers have proposed a broad range of molecular, cellular and histological markers as surrogate end-points for cancer (SECs). The effect of an intervention on a 'valid' SEC is concordant with its effect on cancer incidence. The validity of a potential SEC is determined primarily by the extent to which the marker is a necessary event on the causal pathway to cancer. Colorectal adenomatous polyp formation is an example of a reasonably valid SEC because these lesions are obligate precursors of most large bowel malignancies. However, the existence of a plausible major alternative causal pathway--one bypassing the potential SEC--weakens inferences from that marker to cancer. Moreover, unless the pathway to cancer operates nearly exclusively through the SEC, an SEC that is valid for one intervention or exposure may not be valid for another. Metabolic, ecological, observational epidemiological and intervention studies may yield data that are useful in revealing these causal interrelations of intervention (exposure), SEC and cancer. Empirical studies of three questions are pertinent: (1) What is the relation of the SEC to cancer? (2) What is the relation of the intervention (exposure) to the SEC? (3) To what extent does the SEC mediate the relation between the intervention (exposure) and cancer? Data on SEC measurement error are important in ascertaining the extent to which marker results have been attenuated by such error. It is essential to carry out these studies to evaluate potential SECs (such as epithelial cell hyperproliferation) with plausible major alternative pathways to cancer. At the present time, definitive evidence on etiology and prevention will emerge only from studies with cancer end-points or SECs that are, by and large, necessary steps on the causal pathway to malignant disease.

Studies using surrogate end points of malignant disease may be smaller, shorter, and less expensive than studies with incident cancer end points. Researchers have proposed a broad range of histological, cellular, and molecular markers as surrogate end points for cancer (SECs). We define a valid SEC as follows: the effect of an intervention on (or the association of a risk factor with) the SEC is concordant with its effect on (or association with) incident cancer. Adenomatous polyps and persistent human papillomavirus infections are examples of reasonably valid SECs (for colorectal and cervical cancer, respectively) because these markers are necessary precursors of most of these malignancies. Inferences from other potential SECs, however, are problematic if there exist major alternative causal pathways to malignancy bypassing the SEC. Furthermore, in such circumstances, an SEC that is valid for one intervention or exposure may not be valid for another. Even for those end points without such major alternative pathways, an intervention could differentially affect two intermediate markers on the same pathway, thus disturbing the concordance between its effect on a given SEC and its effect on cancer. Thus, an understanding of the causal structure underlying the relations of interventions/exposures, potential SECs, and cancer is critical in evaluating SECs. Three questions are pertinent to elucidating this structure: (a) What is the relation of the SEC to cancer? (b) What is the relation of the intervention/exposure to the SEC? and (c) To what extent doses the SEC mediate the relation between the intervention/exposure and cancer? Ecological, metabolic, observational epidemiological, and intervention studies may provide data relevant to one or more of these questions. Data on SEC variability are critical in evaluating whether marker findings have been attenuated by random sources of intra-individual variation. We emphasize the importance of conducting studies, especially SEC-cancer and intervention/exposure-SEC-cancer mediation studies, to evaluate problematic SECs such as epithelial cell hyperproliferation. For some time to come, hard and policy-relevant evidence on cancer etiology and prevention will emerge only from studies with cancer end points or, at a somewhat lower level of certainty, SECs that are (for the most part) obligatory steps on the causal pathway to malignant disease.

The Polyp Prevention Trial (PPT) is a multicenter randomized controlled trial examining the effect of a low-fat (20% of total energy intake), high-fiber (18 g/1000 kcal), high-vegetable and -fruit (5-8 daily servings) dietary pattern on the recurrence of adenomatous polyps of the large bowel, precursors of most colorectal malignancies. Eligibility criteria include one or more adenomas removed within 6 months of randomization; complete nonsurgical polyp removal and complete colonic examination to the cecum at the qualifying colonoscopy: age 35 years of more; no history of colorectal cancer, inflammatory bowel disease, or large bowel resection; and satisfactory completion of a food frequency questionnaire and 4-day food record. Of approximately 38,277 potential participants with one or more polyps recently resected, investigators at eight clinical centers randomized 2,079 (5.4%; 1,037 in the intervention and 1,042 in the control arm) between June 1991 and January 1994, making the PPT the largest adenoma recurrence trial ever conducted. Of PPT participants, 35% are women and 10% are minorities. At study entry, participants averaged 61.4 years of age; 14% of them smoked, and 22% used aspirin. At the baseline colonoscopy, 35% of participants had two or more adenomas, and 29% had at least one large (of = 1 cm) adenoma. Demographic, behavioral, dietary, and clinical characteristics are comparable across the two study arms. Participants have repeat colonoscopies after 1 (T(1)) and 4 (T(4)) years of follow-up. The primary end point is adenoma recurrence; secondary end points include number, size, location, and histology of adenomas. All resected lesions are reviewed centrally by gastrointestinal pathologists. The trial provides 90% power to detect a reduction of 24% in the annual adenoma recurrence rate. The primary analytic period, on which sample size calculations were based is 3 years (T(1) to T(4)), which permits a 1-year lag time for the intervention to work and allows a more definitive clearing of lesions at T(1), given that at least 10-15% of polyps may be missed at baseline. The final (T(4)) colonoscopies are expected to be completed in early 1998.

We determined the role, if any, of 1 and 5 instillations of intravesical mitomycin C in the treatment of newly diagnosed superficial bladder cancer.A multicenter randomized clinical trial was done involving 502 patients with newly diagnosed superficial bladder cancer. After complete transurethral resection patients with newly diagnosed superficial bladder cancer. After complete resection patients were randomized into 1 of 3 treatment arms: no further treatment, 1 instillation of mitomycin C at resection and 1 instillation at resection and at 3-month intervals for 1 year (total 5 instillations). The dose of mitomycin C used was 40 mg./40 ml. water. End points were interval to first superficial recurrence, recurrence rate (defined as the number of positive cystoscopies per year) and progression-free interval rate (progression defined as the development of muscle invasive or metastatic disease, or death from bladder cancer).After median followup of 7 years 1 and 5 instillations of mitomycin C resulted in decreased recurrence rates and increased recurrence-free interval. The benefit of mitomycin C was observed in patients at low, medium and high risk for subsequent recurrence. There was suggestive but not conclusive evidence that 5 instillations of mitomycin C offered a slight advantage over 1 instillation.Our analysis confirms the positive benefit of mitomycin C to decrease the number of subsequent recurrences and increase the recurrence-free interval.

In measuring food intake, three common methods are used: 24-hour recalls, food frequency questionnaires and food records. Food records or 24-hour recalls are often thought to be the most reliable, but they are difficult and expensive to obtain. The question of interest to us is to use the food records or 24-hour recalls to examine possible systematic biases in questionnaires as a measure of usual food intake. In Freedman, et al. (1991), this problem is addressed through a linear errors in variables analysis. Their model assumes that all measurements on a given individual have the same mean and variance. However, such assumptions may be violated in at least two circumstances, as in for example the Women's Health Trial Vanguard Study and in the Finnish Smokers' Study. First, some studies occur over a period of years, and diets may change over the course of the study. Second, measurements might be taken at different times of the year, and it is known that diets differ on the basis of seasonal factors. In this paper, we will suggest new models incorporating mean and variance offsets, i.e., changes in the population mean and variance for observations taken at different time points. The parameters in the model are estimated by simple methods, and the theory of unbiased estimating equations (M-estimates) is used to derive asymptotic covariance matrix estimates. The methods are illustrated with data from the Women's Health Trial Vanguard Study.

In this paper we describe the design and monitoring of two large randomized trials being conducted through the British Medical Research Council (MRC) Cancer Trials Office. In particular we discuss the issues involved in the design of the trials, specifying the null and alternative hypotheses and how the design has influenced the monitoring procedure used. From these two examples, and some other MRC experiences, we suggest some basic considerations which could be applied to many MRC and other trials.

We explore the use of a statistical model proposed by Kokoska (1987, Biometrics 43, 525-534) for the analysis of animal cancer chemoprevention experiments. We show, using an example, that the results derived from the method can be sensitive to the parametric forms of the distributions that are assumed, particularly to the distribution of the number of tumors per animal. We propose goodness-of-fit tests to aid in the choice of the distributions.

The anatomic description of the extent of tumor spread (tumor staging) assists clinical management, facilitates communication among physicians, is an essential part of randomized controlled trials, and may help in the counseling patients and their families. However, in recent years, additional "prognostic factors" have been defined, many of which assess or reflect the biologic behavior of malignant neoplasms. Other measures of tumor biochemistry address the natural history of neoplastic development and often are included in a discussion of new prognostic factors. This review article summarizes current knowledge and thinking related to tumor prognostic factors in four areas by providing: (1) a definition and principles of anatomic spread of tumor (staging) and some suggestions for improvement, (2) a description of some examples of additional factors of prognostic significance, (3) some statistical methods to evaluate prognostic factors, and (4) an examination of the possible future of summary statements of outcome (i.e., prognostic indexes).

This paper explores the extent to which application of statistical stopping rules in clinical trials can create an artificial heterogeneity of treatment effects in overviews (meta-analyses) of related trials. For illustration, we concentrate on overviews of identically designed group sequential trials, using either fixed nominal or O'Brien and Fleming two-sided boundaries. Some analytic results are obtained for two-group designs and simulation studies are otherwise used, with the following overall findings. The use of stopping rules leads to biased estimates of treatment effect so that the assessment of heterogeneity of results in an overview of trials, some of which have used stopping rules, is confounded by this bias. If the true treatment effect being studied is small, as is often the case, then artificial heterogeneity is introduced, thus increasing the Type I error rate in the test of homogeneity. This could lead to erroneous use of a random effects model, producing exaggerated estimates and confidence intervals. However, if the true mean effect is large, then between-trial heterogeneity may be underestimated. When undertaking or interpreting overviews, one should ascertain whether stopping rules have been used (either formally or informally) and should consider whether their use might account for any heterogeneity found.

We describe the application of Bayesian methods to the monitoring and analysis of a trial of treatment for patients with advanced colorectal carcinoma. We discuss the choice of prior distribution and justify the use of a truncated normal distribution with a probability mass at zero difference. The stopping rule, based on the trials of the posterior distribution and a chosen range of equivalence, yields an upper boundary very close to the Pocock group sequential boundary. The Bayes stopping rule is quite sensitive to the amount of probability mass at zero in the prior distribution.

One hundred forty-nine patients of private physicians in Toronto, Canada, who were positive for human immunodeficiency virus (HIV), medically stable, and had CD4 cell counts of700 cells/mm3 participated in a randomized, double-blind trial of placebo versus low-dose (50 U) versus high-dose (100 U) oral interferon-alpha. Treatment allocation was balanced according to baseline CD4 cell count and history of prior antiviral therapy. Patients were observed at 4 and 8 weeks for assessment of adverse events and several measures of disease status, including CD4 cell count, beta 2-microglobulin, weight, and Karnofsky score. We detected neither short-term benefits nor adverse effects from oral interferon-alpha therapy.

By introducing replicate observations into observer agreement studies, one can obtain better measures of observer agreement than heretofore possible. New methodology based on the analysis of latent variables allows a separation of within- and between-observer variation for binary measures of assessment among pairs of observers. Maximum likelihood estimation and hypothesis testing are discussed. The methodology is illustrated using data on the assessment of dysplasia by pathologists.

Survival rates for 22,616 cases of breast cancer listed in the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute were stratified on outcome according to the histologic grade and stage of disease. Two different staging systems, "local, regional, and distant" and a modified American Joint Committee on Cancer (AJCC) system adopted for SEER were used. Relative survival rates were calculated at 5 and 10 years. Patients who were assigned Stage II, Grade 1 had the same survival as those assigned Stage I, Grade 3. Their survival was better than patients assigned Stage I, Grade 4. The 5-year relative survival rate for patients listed as Stage I, Grade 1 was 99% and for patients listed as Stage I, Grade 2, it was 98%. At 10 years, the survival rate of patients assigned Stage I, Grade 1 was 95%. Patients with histologic Grade 1 tumors less than 2 cm in size and with positive axillary lymph nodes had a 5-year survival rate of 99%. As breast tumors increased in size, the histologic grade also increased. The results suggest that in linking histologic grade with stage of disease, the staging system should also be considered. Histologic grade when used in conjunction with stage of disease can improve the prediction of outcome. Our results also indicate that a prognostic index can be created for breast cancer using a combination of stage of disease and histologic grade. The data suggest that only three grades are needed for breast cancer.

We have extracted from the literature data from 100 animal experiments, involving 7838 rats and mice, which compared the effects of different levels of dietary fat and/or calorie intake on the development of mammary tumors. Both higher calorie intake (P less than 0.0001) and higher fat intake (P less than 0.0001) independently increased mammary tumor incidence in Sprague-Dawley rats and in mice, as judged from analyses combining ad libitum feeding experiments and restricted feeding experiments. The effect of fat was two thirds the magnitude of the calorie effect in both Sprague-Dawley rats and mice. In ad libitum feeding experiments, a modest but significant (P less than 0.0001) average increase in body weight was found in animals fed high fat diets. However, these differences in body weight did not correspond to differences in mammary tumor incidence. The effect of log body weight on the log odds of tumor incidence was not significant (P = 0.16), while dietary fat intake significantly increased tumor incidence (P less than 0.0001). The collection of animal experimental data supports the hypothesis that, in mammary tumor development, there is a specific enhancing effect of dietary fat, as well as a general enhancing effect of calories.

This brief article surveys the number and type of injuries sustained by people tripping over uneven or broken paving stones, and warns that the cost of such injuries is considerable. Statistics are provided of cases which were collected retrospectively by analysis of medicolegal reports prepared by the Department of Orthopaedic Surgery at Northwick Park Hospital, Harrow during January to December 1988. Patients seen prospectively in the fracture clinic during January to March 1989 were also included. Twenty Seven factures were found in 24 patients, with one case of anterior dislocation of the shoulder. Over 150 patients are referred to fracture clinics each year for such injuries. The cost of treating such patients can be high. These figures also indicate that far more people injure themselves than actually make a claim, although the number of litigations is rising. Over 10000 claims for compensation for injuries as a direct result of tripping over broken, uneven, or loose paving stones were made against local authorities in England and Wales in 1987. Less than 40% were successful: even so, payment exceeded 10 million pounds in 1987 alone. A plea is made for local authorities to ensure that there is adequate funding for footpath maintenance.

Under the global null hypothesis that all covariates are unrelated to the outcome variables, forward stepwise regression procedures should have the property that the probability of selecting a given variable and finding it significant at the a level is equal to a. Because of the problem of underestimating the residual error variance the actual probability can be very different from a. This problem becomes of practical concern when the ratio of the number of variables to the number of observations becomes greater than 0-25, and is more serious for logistic than for linear regression.

SUMMARY Retroperitoneal lymph-node dissection or radiotherapy have long been known to provide equivalent survival for early stage I and stage II nonseminomatous germ-cell tumors. Review of the results from intensive radiological and biochemical surveillance with salvage chemotherapy for stage I tumors demonstrates that the long-term survival rate is equivalent to that achievable by conventional treatment (i.e., 98 per cent survival at 4 years). As relapses have continued to occur in the third and fourth years at the rate of 4 per cent annually, and 4 years is the limit of follow-up, further follow-up is required to be sure of the long-term picture. Prognostic factor analysis demonstrates that venous and lymphatic invasion, the absence of yolk sac differentiation, and the presence of undifferentiated cells are independently important in predicting the frequency of relapse. Using these factors, it was possible to define low-risk groups with relapse rates less than that seen after lymph-node dissection and high-risk groups with 58 per cent frequency of relapse who probably are suitable for adjuvant chemotherapy studies. Review of the results from the use of surveillance in stage I seminoma demonstrated no advantages over prophylactic radiotherapy. However, late toxicity is being demonstrated after radiotherapy and evidence is emerging that the less toxic cisplatinum analogue carboplatin may be as good as radiotherapy for metastatic disease. This offers for the first time a viable alternative to radiotherapy for consideration in the adjuvant setting in stage I seminoma.

One crucial component for a successful clinical trial is that the data gathered have a high level of reliability and completeness. This paper reviews some problems of data management and describes the computer package COMPACT which has been developed to deal with such problems. The package allows range and consistency checks and can monitor complex follow-up schedules. A unique feature of the package is a PROBLEMS file which has use both for identification of queries about the data and of patients with particular characteristics of interest. The ability to monitor drug dosages and to signal deviations from the protocol is of particular value. COMPACT has the syntax necessary to create a 'flat' file for transfer to statistical packages for analysis, and the variable description files for SAS, SPSS and MINITAB. The package is written in standard FORTRAN which enables transfer to different types of mini and micro computer systems.

Records of 3085 patients registered with breast cancer at the Mersey Regional Cancer Registry have been analysed to evaluate the relative importance of possible prognostic factors. In a subgroup of 1759 patients, clinical stage and histological grade are shown to be strongly related to survival after treatment. In addition histological grade is related to the distribution of times to death after treatment. The results of this and 3 other studies have implications for the design and analysis of clinical trials in the primary treatment of breast cancer. Images Fig. 1 Fig. 2 Fig. 3

In a multicentre study, 824 patients with operable rectal cancer were randomized to receive surgery alone, surgery plus a single fraction of 500 rad (5 Gy) and surgery plus 2000 rad (20 Gy) in 10 equal daily, i.e. multiple, fractions. The ratio of abdominoperineal excision to anterior restorative operations was 3:1. There was no evidence of an increased morbidity or mortality following irradiation. The multiple fraction 2000 rad group had tumours which were significantly smaller than those of the other groups. There was also a reduction in the Dukes' C cases in the multiple fraction group. Neither the tumour size nor the lymph node status was altered in the single fraction group.

The logrank test is commonly used in the analysis of clinical trials in chronic diseases such as cancer. Existing tables for the number of patients required in such trials are based on the direct comparison of two proportions. This paper presents tables of numbers required in clinical trials using the logrank test and describes their use. The numbers required are considerably smaller than those in existing tables when the event-free proportions are small, but otherwise comparable.