Further experience with discriminant functions in differential diagnosis of hypercalcaemia

Transfer of hypercalcemia discriminant functions between local hospitals

Transferability of discriminant functions is potentially useful both from an economical point of view and because, in general, medical knowledge, in this case discriminant functions, should be transferable. In the present study we have evaluated the transferability of discriminant functions, estimated from routine laboratory analysis, age and sex in two consecutively recorded populations with hypercalcemia including 162 and 257 patients with hypercalcemia. Discriminant functions were developed for each sex to distinguish between hypercalcemia associated with malignancy and hypercalcemia associated with other medical diseases. The total diagnostic accuracy in Herlev was 82 and 78%, in women and men, and increased to 87 and 86% in both sexes considering cases classified with posterior probability levels of 60%. In Hvidovre the total diagnostic accuracy was 81 and 84% in women and men, and increased to 83 and 89% at posterior probability levels higher than 60%. Transfer of the discrimination functions between the hospitals was followed by a decrease in diagnostic accuracy of 6-16%. At a posterior probability of 60% the diagnostic accuracies were 79% or more in the receiving hospital, in both sexes, except for men in Hvidovre. In relation to these results the concept of genuine and non-genuine transfer factors is introduced and discussed.

Filtering clinically significant hypercalcaemia from non-significant hypercalcaemia at the laboratory level

In an earlier study it was shown, that, in a hospital population, only about 30% of patients with hypercalcaemia had the diagnosis identified and so an alarm filter was developed, at the laboratory level, to differentiate between clinically significant and clinically non-significant hypercalcaemia. The filter correctly classified 84% and 77% of women and men with hypercalcaemia, respectively, with respect to the clinical significance of the hypercalcaemia. The sensitivity and the specificity of the discriminant functions were 90% and 73% in women and 80% and 67% in men. The alarm filter was based on a two-step procedure. The patients were primarily classified by the discriminant functions into one of the following medical diagnoses related to hypercalcaemia: primary hyperparathyroidism, malignancy, and transient hypercalcaemia. Based on this classification the patients were characterized as having either a clinically significant or non-significant hypercalcaemia. The alarm filter was based on two discriminant functions. The discriminant variables were phosphate, albumin, protein, LD, and a haemoglobin in women, and albumin, protein, ALP, and age in men. Missing values were estimated. The discriminant variables were selected from 17 possible discriminant variables, all measured by routine, and age. The study group comprised 257 patients with hypercalcaemia, consecutively registered, during half a year. The classification efficiency of the discriminant functions were based on comparison of results obtained by cross-validation of the discriminant functions, and the medical diagnosis decided by the clinicians in the respective departments of the hospital. The medical diagnoses were based on principles and definitions generally used in the departments with no knowledge of the results assessed by the discriminant functions.

Differential diagnosis of hypercalcemia

The differential diagnosis of hypercalcemia has expanded to over 25 separate disease states, with primary hyperparathyroidism and malignancy accounting for 80-90% of all hypercalcemic patients. Primary hyperparathyroidism comprises the majority of hypercalcemic patients among the ambulatory population, but malignancy accounts for up to 65% of such patients in the hospital. Factors favoring primary hyperparathyroidism include a family history of hyperparathyroidism or multiple endocrine neoplasia, a history of childhood radiation to the head and neck, the postmenopausal state, a history of renal calculi or peptic ulcer, hypertension, the induction of hypercalcemia by thiazides, or an asymptomatic patient with a prolonged, stable mild hypercalcemia. The usefulness of the serum calcium, parathyroid hormone, chloride, phosphorus, serum 25-OHD, and 1,25-(OH)2D, and urinary calcium in the differential diagnosis of hypercalcemia is discussed. The pitfalls of an excessive reliance on the serum PTH in diagnosing hyperparathyroidism are stressed. The discriminant values of the serum calcium, chloride, phosphorus, and parathyroid hormone are explored, with the serum parathyroid hormone, chloride, and calcium proving most useful in separating primary hyperparathyroidism from other forms of hypercalcemia. Multivariate discriminant analysis using the serum calcium, phosphorus, and chloride and the hematocrit achieves an accuracy of 95-98% and is the most economical method of identifying hyperparathyroidism. The addition of the amino-terminal or intact PTH assay increases the accuracy to 99% and is essential in the presence of renal insufficiency.

A distribution-free, multivariate discriminating method. Initial experience with the discrimination of patient groups by 2 or more clinical chemical parameters

We communicate a distribution-free quasi graphic procedure for obtaining a linear discriminating function. The method is based on the following considerations: Suppose a group A is to be separated from a group B using two parameters X and Y. The centre of each group is defined as the median (or mean or mode) of its points. Of all straight lines passing through any point of A and any point of B those are retained which intersect the segment joining the centres of A and B. For each of these the number of wrongly allocated points is calculated (i.e. the points which do not lie on the same side of the straight line as their group centres). In this way one obtains straight lines with maximal separating power (for the two groups given). Finally, each optimal line is rotated in such a way that its defining points are also correctly allocated. If more than two parameters are available a stepwise procedure can be used: the distance from the separating straight line obtained from the first two parameters is introduced as a new parameter, which is then combined with the third parameter to yield a new discriminating function which depends on all three parameters. Iterating this step one can combine any number of parameters. The method was implemented on a personal computer. It was first applied to a textbook model (chances of survival for M. haemolyticus neonatorum estimated by concentrations of haemoglobin and bilirubin in cord blood).(ABSTRACT TRUNCATED AT 250 WORDS)

Differential laboratory diagnosis of hypercalcemia

It is proposed that this review will adopt the following format: establishment of hypercalcemia. This demands a discussion of the problem of normal ranges, the usage of either total calcium or ionized calcium in making this decision and where total calcium is used whether adjustment of this value for serum protein concentration should be used and if so, the formulae which have been cited to perform this. Having established hypercalcemia why is it necessary to differentiate this? This will involve reviewing those clinical situations in which differentiation of hypercalcemia has been attempted and will include an attempt to produce an up to date indication of conditions in which hypercalcemia has been described. When hypercalcemia has been established the laboratory tests which have been further used to discriminate will be divided into single tests such as N- or C- terminal parathormone, 1,25- dihydroxycholecalciferol, cyclic AMP; the combination tests which have been used including phosphate clearance, chloride vs. bicarbonate etc. proceeding to those groups which have used discriminant function to help in the decision making; dynamic testing will also be discussed particularly with reference to steroid suppression but will also include other known suppressants such as Mithramycin and Calcitonin. A final section will be included attempting to assess overall the present state of art in differentiating laboratory diagnosis of hypercalcemia and will also attempt to highlight those areas which appear to be most fruitful areas of progress in the future.

On the transportability of linear discriminant functions

Different methods can give different results for the same analyte, and inconsistent answers may be obtained if such results are used in linear discriminant functions. This is an important factor to consider when transporting linear discriminant functions from one laboratory to another; the example of alkaline phosphatase activity and the differential diagnosis of hypercalcaemia has recently been given. This study shows that results obtained by the method recommended by the Scandinavian Committee on Enzymes for alkaline phosphatase may be used in the calculation of the discriminant functions used for the differential diagnosis of hypercalcaemia and considers other factors that may affect the discrimination. It is concluded that, with care, linear discriminant functions may be transported from one laboratory to another.

Ectopic parathyroid adenomas

Two cases of parathyroid tumours occurring in unusual situations are described. Such cases may cause difficulty in both the diagnosis and the surgical treatment of hyperparathyroidism. The cases described illustrate the importance of a definitive aetiological diagnosis in hypercalcaemia, if appropriate surgery is to be performed. The value of discriminant function analysis and hydrocortisone suppression tests are discussed.

Hydrocortisone suppression test and discriminant analysis in differential diagnosis of hypercalcaemia

Experience is reported of the hydrocortisone suppression test in 140 hypercalcaemic patients, comprising 98 new cases of hyperparathyroidism and 42 cases of non-parathyroid malignant disease. The diagnostic accuracy of the test was compared in 168 patients with that of discriminant analysis, the discriminant functions being derived from plasma inorganic phosphate, alkaline phosphatase, chloride, bicarbonate, and urea, and the erythrocyte sedimentation rate. The hydrocortisone test and discriminant analysis each achieved a diagnostic accuracy of about 93% in 148 patients with either non-parathyroid malignant disease or hyperparathyroidism without osteitis fibrosa. When both tests pointed to the same diagnosis, they were wrong in less than 1% of cases. The hydrocortisone test was not helpful in patients with osteitis fibrosa. Both tests can be performed in any hospital with reliable standard laboratory services. Used in combination they have a high predictive value in distinguishing hypercalcaemia of parathyroid origin from that due to non-parathyroid malignant disease and have not led to errors of clinical importance. They should continue to play a major role in the differential diagnosis of hypercalcaemia until a prompt and reliable service finally establishes parathyroid hormone assay as the definitive laboratory procedure.

Discriminant analysis

Discriminant analysis (DA) is a pattern recognition technique that has been widely applied in medical studies. It allows multivariate observations ("patterns" or points in multidimensional space) to be allocated to previously defined groups (diagnostic categories). The relationships between DA and other multivariate statistical techniques of interest in medical studies will be briefly discussed. The main emphasis is on linear discriminant functions (LDF). The theoretic assumptions underlying DA using LDFs will be presented, and the effect of violations to these assumptions will be reviewed in detail. Alternative methods will be presented when violations cause serious problems. It has been shown that the familiar LDF is fairly robust to departures from the assumptions. The application of the LDF in less than ideal situations therefore often does not cause much harm (if the violations are not too grotesque). Another set of problems reviewed is how to estimate the misallocation probabilities when using discriminant functions. The selection of the "best" subset of variables out of the complete set will be discussed. Practical guide lines are given based on the theoretic studies reviewed. When possible, available computer programs for various problems of DA will be indicated. The review does not aim at covering all medical studies where DA has been applied, since emphasis is on the practical conclusions of the theory of DA.