Sture Holm

A simple sequentially rejective multiple test procedure

This paper presents a simple and widely ap- plicable multiple test procedure of the sequentially rejective type, i.e. hypotheses are rejected one at a tine until no further rejections can be done. It is shown that the test has a prescribed level of significance protection against error of the first kind for any combination of true hypotheses. The power properties of the test and a number of possible applications are also discussed.

A simple model for fatigue life

A simple model to handle fatigue-life length problems is discussed. The characteristic property of the model is that it combines the Palmgren-Miner rule with time invariance. The model is applied to situations with both random strength and random load. The randomness in the life is generated by the random strength and not by the random load. The only property of the random load that affects the life is its damage intensity, which is independent of the particular realization in the ergodic-load case. The damage intensity is even independent of the distribution of the random function, provided its level-crossing intensity is known. Particular attention is given to simple random strength models. In general, the exhaustion density is a random function, but in the simple models the only randomness that appears in the strength is either randomness in the time scale or randomness in the amplitude scale. The model is well-suited for comparative calculations under different load conditions, since it connects fatigue life for random loads to fatigue life for periodically oscillating loads, which is usually measured in experiments. >

Evaluation of the cohort size in phase I dose escalation trials based on laboratory data.

A survey of Phase I dose escalation trials published since 1995 shows that there is great disparity in all aspects of the design of the studies, and the cohort sizes range from 2 to 16 subjects with a great variety in the distribution between active and placebo‐treated subjects. This study investigates the impact of the cohort size on Type I error and power in Phase I dose escalation trials based on laboratory data, with the hospitalization‐induced increase in hepatic enzyme levels taken into consideration. The power of a Phase I dose escalation trial is very low, and only events with a very high probability of occurrence are detectable with acceptable power. For studies with cohort sizes smaller than 6 active subjects, there is much to gain with the inclusion of 1 extra subject, but for more than 10 subjects, little is gained by increasing the cohort size. With increasing cohort sizes, the probability of spontaneous non‐drug‐related events also increases, and this background rate needs to be considered when evaluating the trial.

Pitting corrosion: Comparison of treatments with extreme value distributed responses.

In this article we develop statistical extreme-value theory as a method to validate and improve experiments with extremal responses, and to extrapolate and compare results. Our main motivation is corrosion tests performed at Volvo Car Company. Localized, or “pitting,” corrosion can limit the usefulness of aluminum, magnesium, and other new lightweight materials and makes judicious choice of alloys and surface treatments necessary. Standard methods for evaluating corrosion tests are based on weight loss due to corrosion and ANOVA. These methods fail in two ways. The first is that it usually is not weight loss but the risk of perforation (i.e., the depth of the deepest pit) that is of interest. The second is that the standard ANOVA assumption of homogeneity of variances typically is not satisfied by pit depth measurements, and that normality does not give credible extrapolation into extreme tails.

Multiple Confidence Sets Based on Stagewise Tests

Abstract Recent years have seen suggested constructions of multiple confidence sets related to stagewise multiple tests by some authors. These methods are a type of mixture between test and confidence interval methods, because confidence interval statements are made only for some parameters, whereas test statements for fixed parameter values are made for the other parameters. In this article I define a concept—confidence directional set—giving a confidence bound for one parameter, which may depend on other parameters. Using this concept, one can construct multiple confidence sets, which are always confidence set statements and not test statements for fixed parameter values. The confidence sets correspond exactly to stagewise tests, which is theoretically appealing. Special examples of the general technique are given for the independent test statistic case and for comparison of a number of treatments to a control in the case of normally distributed observations with the same variance.

A test of independence for stratigraphic sequences with respect to embedded Markov chains

Identification of cyclic sequences gives valuable insight into depositional associations of stratigraphic facies. An embedded Markov chain is a reasonable general model for facies transitions. But a model with independent random occurrences of facies is not an appropriate null hypothesis to be tested to show the presence of cycles because of definitional restriction in transition observations to only those between different facies. This is a common stratigraphic situation and the problem has been raised recently by several authors. We present here a test statistic for null hypothesis derived from the concept of “partial independence” and inherent to the model of embedded Markov processes.

Generation of random processes for fatigue testing

In fatigue testing there is a need to generate multivariate random processes meeting certain conditions on distributions, crossing properties and regularity. In this paper it is demonstrated how these conditions can be satisfied. The required process is generated by a random time deformation working on a Gaussian process.

A step-down test for effects in unreplicated factorial designs

Abstract In textbooks it is often suggested that estimates of effects obtained in two-level factorial experiments should be illustrated by a half-normal plot. The effects corresponding to the estimates with biggest absolute values and deviating from a straight line on the plot should be selected as important. We make a formal statistical procedure in this spirit by using a suitable mathematical construction, which can be illustrated in the graph. Thus we may find effects which are significant with a chosen multiple level of significance. This means that there is a given small risk of declaring significant any factor effects, which are in fact void, independent of how many and which effects are possibly missing. There is some mathematics behind the method, but its use is very practical and simple.

Confidence sets of fixed size with predetermined confidence level

In this paper a three stage method to obtain a confidence sets of given form and size, with a preassigned confidence coefficient, is suggested for the case of normally distributed observations from populations with different means and common unknown variance. The method is quite general, and it allows for most common forms of confidence sets. Asymptotic properties of the random sample sizes of the method are studied and compared to the same properties of other methods with the same aim.

Incidence of Second Primary Malignancies in Patients with Neuroendocrine Tumours

Background: An association between neuroendocrine tumours (NET) and increased risk of developing second primary malignancies (SPM) has been recognised. Methods: This was a retrospective review of our institutional prospectively maintained database of NET patients. We identified patients who had been diagnosed with both neuroendocrine and any additional malignancies via examination of patient notes. Results: Clinical data for 169 patients were analysed. After exclusion of patients known to have hereditary tumour predisposition syndromes, 29 SPM were identified in 26 patients (15.38%), the commonest being colorectal (n = 6), breast and renal carcinomas (both n = 5). SPM were classified as previous, synchronous or subsequent relative to NET diagnosis. Rates of SPM in pancreatic and small-bowel NET patients were comparable (15.7 vs. 19.6%, p = 0.78). A person-year methodology was used to compare observed numbers of SPM against expected values generated from age- and sex-specific incidence tables, with standardised incidence ratios (SIR) and 95% confidence intervals (CI) calculated. SPM incidence was significantly elevated in the synchronous subset (SIR 2.732, CI 1.177-5.382) whilst significantly fewer NET patients had a cancer history compared to the general population (SIR 0.4, CI 0.241-0.624). No overall differences were evident between observed and expected incidences of subsequent SPM (SIR 0.36, CI 0.044-1.051). The incidence of synchronous colorectal cancers was markedly elevated (SIR 13.079, CI 4.238-30.474). Conclusions: Our data support the use of colonoscopy in the diagnostic work-up of NET patients in anticipation of a colorectal SPM. The mechanistic underpinnings of this clinical phenomenon require further genetic investigation, and consideration of this knowledge in patient management pathways is warranted.