A study of the radiographic aluminum equivalent values of the mandible

A longitudinal study of bone changes in the mandible was conducted. Duplicate radiographs were taken at 3-month intevals with the use of a positioning instrument, which included an aluminum calibrating wedge. The in-duplicate values obtained over the investigation period made it possible to assess the precision of the method and to analyze effects that take place with time. Significant bone changes were observed in seven volunteers between various observation periods at intervals of 6 and 9 months

Optimal time-points in clinical trials with linearly divergent treatment effects.

In repeated measures studies, equidistant time-points do not always yield efficient treatment effect estimators. In the present paper, the optimal allocation of time-points is calculated for a small number of repeated measures, different covariance structures and linearly divergent treatment effects. The gain in efficiency of the treatment effect estimator by using optimally allocated time-points instead of equidistant time-points or by adding optimally spaced measures (at the expense of patients) is then computed. The assumed covariance structure is crucial for the results. For a compound symmetric covariance structure a large gain in efficiency is obtained by adding repeated measures at the end of the study. For a first-order auto-regressive covariance structure, highly efficient treatment effect estimators are obtained with only two repeated measures, i.e. at the start and at the end of the study. For a first-order auto-regressive covariance structure including measurement error, the gain in efficiency by adding optimally spaced measures depends on the covariance parameter values. The gain in efficiency is similar with or without a random intercept. For a fixed study budget, the commonly used design with more than two equally spaced measures was never optimal for the linear cost function and covariance structures that were used. If the covariance structure is unknown, the optimal design based on a first-order auto-regressive covariance structure with measurement error is preferable in terms of robustness against misspecification of the covariance structure. The numerical results are illustrated by two examples

Optimal designs for clinical trials with second-order polynomial treatment effects

The effect of adding intermediate measures on the efficiency of treatment effect estimation is considered for a second-order polynomial treatment effect, equidistant time-points, different covariance structures and two optimality criteria, assuming either a fixed sample size or a fixed budget. The benefit of adding intermediate measures (at the expense of subjects) depends strongly on the assumed covariance structure and is hardly affected by the two used optimality criteria (D, or c). For a fixed sample size, the increase in efficiency by adding intermediate measures is large for a compound symmetric structure and small for a first-order auto-regressive structure. For a first-order auto-regressive structure with measurement error, the results depend on the covariance parameter values. For a fixed budget and linear cost function, the design with only three measures per subject is often highly efficient. if the structure resembles compound symmetry and the cost per subject is eight or more times larger than the cost per repeated measure, however, more than three measures are required to obtain highly efficient treatment effect estimators. If the covariance structure is unknown, the optimal design based on a first-order auto-regressive structure with measurement error is preferable in terms of robustness against misspecification of the covariance structure. Given a design with three repeated measures and a second-order polynomial treatment effect, equidistant time-points are either optimal (D-s-) or highly efficient (c-optimality criterion). The results are illustrated by a practical example

Optimal number of repeated measures and group sizes in clinical trials with linearly divergent treatment effects

The effect of number of repeated measures on the variance of the generalized least squares (GLS) treatment effect estimator is considered assuming a linearly divergent treatment effect, equidistant time-points and either a fixed number of subjects or a fixed study budget. The optimal combination of group sizes and number of repeated measures is calculated by minimizing this variance subject to a linear cost function. For a fixed number of subjects, the variance of the GLS treatment effect estimator can be decreased by adding intermediate measures per subject. This decrease is relatively large if a) the covariance structure is compound symmetric or b) the structure approaches compound symmetry and the con-elation between two repeated measures does not exceed 0.80, or c) the correlation between two repeated measures does not exceed 0.60 if the time-lag goes to zero. In case the sample sizes and number of repeated measures are limited by budget constraints and the covariance structure includes a first-order auto-regression part, two repeated measures per subject yield highly efficient treatment effect estimators. Otherwise, it is more efficient to have more than two repeated measures. If the covariance structure is unknown, the optimal design based oil a first-order auto-regressive structure with measurement error is preferable in terms of robustness against misspecification of the covariance structure. The numerical results are illustrated by three examples

Randomized clinical trials with a pre- and a post-treatment measurement: repeated measures versus ANCOVA models

Repeated measures (RM) and ANCOVA models are compared with respect to treatment effect estimation in randomized clinical trials with a pre- and a post-treatment measure. The covariance matrices of repeated measures are assumed to be I) homogeneous or II) heterogeneous across groups. In situation I, ANCOVA is preferred to RM, because the estimated variance of the treatment effect estimator is unbiased for ANCOVA and biased downwards for RM. In situation II, RM with Kenward and Roger's adjustment is preferred to ANCOVA, because the ANCOVA variance estimator does not correct for unknown pre-treatment expectation. The results are illustrated with an example

Endothelium-dependent vasodilatation, plasma markers of endothelial function, and adrenergic vasoconstrictor responses in type 1 diabetes under near-normoglycemic conditions

It is unknown whether and to what extent changes in various endothelial functions and adrenergic responsiveness are related to the development of microvascular complications in type 1 diabetes. Therefore, endothelium-dependent and endothelium-independent vasodilatation, endothelium-dependent hemostatic factors, and one and two adrenergic vasoconstrictor responses were determined in type 1 patients with and without microvascular complications. A total of 34 patients with type 1 diabetes were studied under euglycemic conditions on two occasions (11 without microangiopathy, 10 with proliferative and preproliferative retinopathy previously treated by laser coagulation, 13 with microalbuminuria, and 12 healthy volunteers also were studied). Forearm vascular responses to brachial artery infusions of N(G)-monomethyl-L-arginine (L-NMMA), sodium nitroprusside, acetylcholine (ACh), clonidine, and phenylephrine were determined. The ACh infusions were repeated during coinfusion of L-arginine. Furthermore, plasminogen activator inhibitor type 1 (PAI-1) activity, tissue plasminogen activator antigen levels, von Willebrand factor antigen levels, tissue factor pathway inhibitor (TFPI) activity, and endothelin-1 levels were measured. No differences in endothelium-dependent or endothelium-independent vasodilatation or adrenergic constriction were observed between the diabetic patients and the healthy volunteers. In comparison to the first ACh infusion, the maximal response to repeated ACh during L-arginine administration was reduced in the diabetic patients, except in the patients with proliferative and preproliferative retinopathy previously treated by laser coagulation. In these patients, the combined infusion of L-arginine and ACh resulted in an enhanced response. TFPI activity was elevated, and PAI-1 activity was reduced in the type 1 diabetic patients. Furthermore, PAI-1 activity was positively correlated with urinary albumin excretion (r = 0.48, P < 0.01) and inversely correlated with the vasodilatory response to the highest ACh dose (r = -0.37, P < 0.05). The response to the highest ACh and L-NMMA dose were positively correlated with mean arterial blood pressure (r = 0.32, P < 0.01; r = 0.41, P < 0.01, respectively). Forearm endothelium-dependent and endothelium-independent vasodilatation and adrenergic responsiveness were unaltered in type 1 diabetic patients with and without microvascular complications. Relative to healthy control subjects, endothelium-dependent vasodilatation was depressed during a repeated ACh challenge (with L-arginine coinfusion) in the diabetic patients without complications or with microalbuminuria. In contrast, this vasodilatation was enhanced in the patients with retinopathy. Elevation of TFPI was the most consistent marker of endothelial damage of all the endothelial markers measured