An improved measure for comparing diagnostic tests.

We present a loss based method for comparing the predictive performance of diagnostic tests. Unlike standard assessment mechanisms, like the area under the receiver-operating characteristic curve and the misclassification rate, our method takes specific advantage of any information that can be obtained about misclassification costs. We argue that not taking costs into account can lead to incorrect conclusions, and illustrate with two examples.

Improving the practice of classifier performance assessment.

In this note we use examples from the literature to illustrate some poor practices in assessing the performance of supervised classification rules, and we suggest guidelines for better methodology. We also describe a new assessment criterion that is suitable for the needs of many practical problems.

Causal indicators in quality of life research.

Quality of Life (QOL) questionnaires contain two different types of items. Some items, such as assessments of symptoms of disease, may be called causal indicators because the occurrence of these symptoms can cause a change in QOL. A severe state of even a single symptom may suffice to cause impairment of QOL, although a poor QOL need not necessarily imply that a patient suffers from all the symptoms. Other items, for example anxiety and depression, can be regarded as effect indicators which reflect the level of QOL. These indicators usually have a more uniform relationship with QOL, and therefore a patient with poor QOL is likely to have low scores on all effect indicators. In extreme cases it may seem intuitively obvious which items are causal and which are effect indicators, but often it is less clear. We propose a model which includes these two types of indicators and show that they behave in markedly different ways. Formal quantitative methods are developed for distinguishing them. We also discuss the impact of this distinction upon instrument validation and the design and analysis of summary subscales.

Factor analysis, causal indicators and quality of life.

Exploratory factor analysis (EFA) remains one of the standard and most widely used methods for demonstrating construct validity of new instruments. However, the model for EFA makes assumptions which may not be applicable to all quality of life (QOL) instruments, and as a consequence the results from EFA may be misleading. In particular, EFA assumes that the underlying construct of QOL (and any postulated subscales or 'factors') may be regarded as being reflected by the items in those factors or subscales. QOL instruments, however, frequently contain items such as diseases, symptoms or treatment side effects, which are 'causal indicators'. These items may cause reduction in QOL for those patients experiencing them, but the reverse relationship need not apply: not all patients with a poor QOL need be experiencing the same set of symptoms. Thus a high level of a symptom item may imply that a patient's QOL is likely to be poor, but a poor level of QOL need not imply that the patient probably suffers from that symptom. This is the reverse of the common EFA model, in which it is implicitly assumed that changes in QOL and any subscales 'cause' or are likely to be reflected by corresponding changes in all their constituent items; thus the items in EFA are called 'effect indicators.' Furthermore, disease-related clusters of symptoms, or treatment-induced side-effects, may result in different studies finding different sets of items being highly correlated; for example, a study involving lung cancer patients receiving surgery and chemotherapy might find one set of highly correlated symptoms, whilst prostate cancer patients receiving hormone therapy would have a very different symptom correlation structure. Since EFA is based upon analyzing the correlation matrix and assuming all items to be effect indicators, it will extract factors representing consequences of the disease or treatment. These factors are likely to vary between different patient subgroups, according to the mode of treatment or the disease type and stage. Such factors contain little information about the relationship between the items and any underlying QOL constructs. Factor analysis is largely irrelevant as a method of scale validation for those QOL instruments that contain causal indicators, and should only be used with items which are effect indicators.

Effects of treatments by calcium and sex hormones on vertebral fracturing in osteoporosis.

Lateral radiographs of the thoracic and lumbar spine were taken periodically in 49 patients with osteoporosis. Thirty patients were postmenopausal, and 19 nonmenopausal with osteoporosis due to steroids, male hypogonadism, alcoholism, thyrotoxicosis or unknown cause. Patients were studied before, during and after treatment with high calcium alone, or with combined calcium and sex steroids. Calcium was given as effervescent calcium lactate gluconate, and sex hormones as oestradiol valerate, testosterone oenanthate, or methenolone oenanthate. A total of 964 films covering 409 patient-years were available for measurement. On each vertebra, deformity due to loss of anterior height was measured and assigned to one of four grades. For the time interval between each consecutive pair of films, a patient's vertebral fracture rate score was calculated and expressed per thousand patient-years. In comparison with the corresponding pretreatment fracture rate score, both the postmenopausal and the nonmenopausal groups who had not received sex hormones previously, failed to show significant changes (p = 0.144; p = 0.017) on high calcium alone during mean periods of 4.3 and 2.8 years respectively. If the first 2 years on high calcium were excluded for the postmenopausal group, they still failed to show a reduction in fracture rate score (observed for a mean period of 5.0 years; p = 0.04). When treated with combined calcium and sex hormones, both postmenopausal and nonmenopausal groups showed a lower fracture rate score of 20 and 207 respectively when compared with the pretreatment levels of 1500 and 1697 (in mean treatment periods of 3.2 and 4.4 years; p less than 0.001 in each case). When given high-dose calcium alone, but after treatment with sex hormones as well, the postmenopausal group showed no change in fracture rate score from pretreatment (in a mean of 3.1 years; p = 0.069); however the nonmenopausal group still showed a significant reduction in fracture rate score from 1697 to 42 over a mean period of 2.3 years (p = 0.001). The postmenopausal group, after stopping all treatment, showed a higher fracture rate score of 1286 (in a mean of 2.6 years) than did those on combined calcium and sex hormones, in whom the fracture rate score was 20 (in a mean of 3.2 years; p = 0.008). A subgroup of 11 patients with osteoporosis of both the menopausal and nonmenopausal types, had data both before (in a mean of 5.5 years) and during (for a mean of 2.5 years) treatment with calcium alone; the fracture rate scores were 1473 and 918 (p = 0.247).(ABSTRACT TRUNCATED AT 400 WORDS)

Statistical methods in diagnosis.

Motivations are presented for exploring formal statistical methods for use in medical diagnosis and the advantages and disadvantages are discussed. A brief review is presented of classical linear discriminant analysis, quadratic discriminant analysis, logistic regression, nearest neighbour and kernel methods, recursive partitioning methods, the independence model, regularized discriminant analysis, structured conditional probability distributions, methods for categorical data, and other methods. Criteria on which a choice might be made are presented and methods for assessing diagnostic performance are outlined. Particular applications of screening and chromosome analysis are used as illustrations and available software is described.

Screening for vertebral osteoporosis using individual risk factors. The Multicentre Vertebral Fracture Study Group.

Osteoporosis is a major cause of ill health in postmenopausal women. Several risk factors for osteoporosis have been identified, and they have been widely recommended as a means of identifying subgroups of postmenopausal women who might benefit from prophylaxis and therapy. Evidence to support this use of risk factors is currently lacking, however. We have constructed and evaluated a profile of putative risk factors as a means of identifying women attending general practitioners who have sustained vertebral fractures. The overall prevalence of vertebral fractures in the 1012 women (mean age 64.4 years) studied was 7.8%. Women who had sustained vertebral fractures in this population were significantly (p less than 0.05) older and shorter than those without fractures. They reported a significantly (p less than 0.05) earlier menopause, lower parity and a greater prevalence of hyperthyroidism. However, the best screening instrument devised was not sufficiently predictive to warrant widespread use.

Contradictory correlations between derived scales.

In a clinical trial one scale of pain relief is scored backwards relative to another (high on one corresponding to low on the other), with a consequent large negative correlation. But two derived scales of total pain, obtained by multiplying average pain relief on each scale by duration of pain (common to both pain relief measurements) gave an almost zero correlation. This apparent contradiction is explained by the inverse relationship between the pain relief scales and the large differences in duration of pain experienced by the patients.

Who gets renal bone disease before beginning dialysis?

To identify patients at risk from renal bone disease we compared the demographic characteristics of 243 patients with end stage renal failure grouped according to the presence (97 (40%] or absence of severe renal bone disease as judged by histological criteria. Youth, female sex, tubulointerstitial types of nephropathy, and a long duration of uraemia were all identified as significant independent risk factors for the development of bone disease. The relative risks from being female and having tubulointerstitial renal disease were separately identifiable when the estimated observation of renal failure was short (less than four years). The identification of patients at high risk from bone disease may clarify the pathogenesis and treatment strategies of renal osteodystrophy.

A comparison of two methods of discriminant analysis applied to binary data.

The results of applying classical linear discriminant analysis and kernel discriminant analysis to several real sets of multivariate binary data are presented. Classical discriminant analysis is intrinsically parametric and is usually presented as being well-suited to continuous variables; it is also well-known to be optimal when the (two) classes have normal distributions with identical covariance matrices. The kernel method, on the other hand, is nonparametric and, in the form used here, is ideally suited to binary data. The apparent error rates of the kernel method are found to be consistently less than those of the classical method. However, when the true error rates are estimated either by applying the classifiers to independent test sets, or by the leaving-one-out method from the design sets, no significant difference is discernible between the two types of classifier.

Statistical tests in experimental psychiatric research.

It is pointed out that the subjects used in psychiatric research experiments are usually drawn in such a way as to invalidate many of the commonly applied statistical tests. The necessarily non-statistical component of any inference is noted, and the area where one might hope for an exact statistical inference is identified. A class of tests permitting such inferences is described. Their theoretical and practical advantages are outlined.

Interaction of light and temperature on seed germination of Rumex obtusifolius L.

Germination of Rumex obtusifolius L. seeds (nutlets) is low in darkness at 25° C. Germination is stimulated by exposure to 10 min red light (R) and also by a 10-min elevation of temperature to 35° C. A 10-min exposure to far-red light (FR) can reverse the effect of both R (indicating phytochrome control) and 35° C treatment. Fluence-response curves for this reversal of the effect of R and 35° C treatments are quantitatively identical. Treatment for 10 min with light of wavelenght 680, 700, 710 and 730 nm, after R and 35° C treatment, demonstrates that germination induced by 35° C treatment results from increased sensitivity to a pre-existing, active, far-red-absorbing form of phytochrome (Pfr) in the seeds.