A comment on: statistical evaluation of biomarkers as surrogate endpoints: a literature review by C. J. Weir and R. J. Walley, Statistics in Medicine 2006; 25:183-203.
Explore the source record for details and available documents.
Biomarkers↗
Biomedical subjects
Susanne Ditlevsen
Publications and source records attributed to Susanne Ditlevsen.
Modeling the euglycemic hyperinsulinemic clamp by stochastic differential equations.
The Euglycemic Hyperinsulinemic Clamp (EHC) is the most widely used experimental procedure for the determination of insulin sensitivity. In the present study, 16 subjects with BMI between 18.5 and 63.6 kg/m(2) have been studied with a long-duration (5 hours) EHC. In order to explain the oscillations of glycemia occurring in response to the hyperinsulinization and to the continuous glucose infusion at varying speeds, we first hypothesized a system of ordinary differential equations (ODEs), with limited success. We then extended the model and represented the experiment using a system of stochastic differential equations (SDEs). The latter allow for distinction between (i) random variation imputable to observation error and (ii) system noise (intrinsic variability of the metabolic system), due to a variety of influences which change over time. The stochastic model of the EHC was fitted to data and the system noise was estimated by means of a (simulated) maximum likelihood procedure, for a series of different hypothetical measurement error values. We showed that, for the whole range of reasonable measurement error values: (i) the system noise estimates are non-negligible; and (ii) these estimates are robust to changes in the likely value of the measurement error. Explicit expression of system noise is physiologically relevant in this case, since glucose uptake rate is known to be affected by a host of additive influences, usually neglected when modeling metabolism. While in some of the studied subjects system noise appeared to only marginally affect the dynamics, in others the system appeared to be driven more by the erratic oscillations in tissue glucose transport rather than by the overall glucose-insulin control system. It is possible that the quantitative relevance of the unexpressed effects (system noise) should be considered in other physiological situations, represented so far only with deterministic models.
Blood Glucose↗
Parameter estimation of feedback gain in a stochastic model of renal hemodynamics: differences between spontaneously hypertensive and Sprague-Dawley rats.
Proximal tubular pressure shows periodic self-sustained oscillations in normotensive rats but highly irregular fluctuations in spontaneously hypertensive rats (SHR). Although we have suggested that the irregular fluctuations in SHR represent low-dimensional deterministic chaos in tubuloglomerular feedback (TGF), they could also arise from other mechanisms, such as intrinsic instabilities in preglomerular vessels or inputs from neighboring, coupled nephrons. To test this possibility, we applied a parameter estimation procedure to a model of TGF, where a stochastic process was added to represent mechanisms not included explicitly in the model. In its deterministic version, the model can have chaotic dynamics arising from TGF. The model introduces random fluctuations into a parameter that determines the gain of TGF. The model shows a rich variety of dynamics ranging from low-dimensional deterministic oscillations and chaos to high-dimensional random fluctuations. To fit the data from normotensive rats, the model must introduce only a small variation in the feedback gain, and its estimates of that gain agree well with experimental values. These results support the use of the deterministic model of nephron dynamics in normotensive rats. In contrast, the irregular tubular pressure fluctuations in SHR were best described by a model dominated by random parameter fluctuations. The results point to the failure of simple mathematical models of nephron dynamics adequately to describe processes that are important for the irregular tubular pressure fluctuations and the need to consider other factors, such as differences in vascular function or nephron-nephron interactions, in further work on this problem.
Animals↗
Estimation of the input parameters in the Feller neuronal model.
The stochastic Feller neuronal model is studied, and estimators of the model input parameters, depending on the firing regime of the process, are derived. Closed expressions for the first two moments of functionals of the first-passage time (FTP) through a constant boundary in the suprathreshold regime are derived, which are used to calculate moment estimators. In the subthreshold regime, the exponentiality of the FTP is utilized to characterize the input parameters. The methods are illustrated on simulated data. Finally, approximations of the first-passage-time moments are suggested, and biological interpretations and comparisons of the parameters in the Feller and the Ornstein-Uhlenbeck models are discussed.
Action Potentials↗
A mathematical model of the euglycemic hyperinsulinemic clamp.
BACKGROUND: The Euglycemic Hyperinsulinemic Clamp (EHC) is the most widely used experimental procedure for the determination of insulin sensitivity, and in its usual form the patient is followed under insulinization for two hours. In the present study, sixteen subjects with BMI between 18.5 and 63.6 kg/m(2) were studied by long-duration (five hours) EHC. RESULTS: From the results of this series and from similar reports in the literature it is clear that, in obese subjects, glucose uptake rates continue to increase if the clamp procedure is prolonged beyond the customary 2 hours. A mathematical model of the EHC, incorporating delays, was fitted to the recorded data, and the insulin resistance behaviour of obese subjects was assessed analytically. Obese subjects had significantly less effective suppression of hepatic glucose output and higher pancreatic insulin secretion than lean subjects. Tissue insulin resistance appeared to be higher in the obese group, but this difference did not reach statistical significance. CONCLUSION: The use of a mathematical model allows a greater amount of information to be recovered from clamp data, making it easier to understand the components of insulin resistance in obese vs. normal subjects.
Blood Glucose↗
Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model.
The stochastic Ornstein-Uhlenbeck neuronal model is studied, and estimators of the model input parameters, depending on the firing regime of the process, are derived. Closed expressions for the Laplace transforms of the first two moments of the normalized first-passage time through a constant boundary in the suprathreshold regime are derived, which is used to define moment estimators. In the subthreshold regime, the exponentiality of the first-passage time is utilized to characterize the input parameters. In the threshold regime and for the Wiener process approximation, analytic expressions for the first-passage-time density are used to derive the maximum-likelihood estimators of the parameters. The methods are illustrated on simulated data under different conditions, including misspecification of the intrinsic parameters of the model. Finally, known approximations of the first-passage-time moments are improved.
Action Potentials↗
Stochastic vs. deterministic uptake of dodecanedioic acid by isolated rat livers.
Deterministic and stochastic differential equations models of the uptake of dodecanedioic acid (C12) are fitted to experimental data obtained on nine isolated, perfused rat livers. 11500 mug of C12 were injected as a bolus into the perfusing liver solution. The concentrations of C12 in perfusate samples taken over 2 h from the beginning of the experiments were analyzed by High Performance Liquid Chromatography (HPLC). A two-compartment deterministic model is studied. To include spontaneous erratic variations in the metabolic processes the parameter for the uptake rate is randomized to obtain a stochastic differential equations model. Parameters are estimated in a two-step procedure: first, parameters in the drift part are estimated by least squares; then, the diffusion parameter is estimated using Monte-Carlo simulations to approximate the unknown likelihood function. Parameter estimation is carried out over a wide range of reasonable measurement error variances to check robustness of estimates. It is concluded that the kinetics of dodecanedioic acid, in the experimental conditions discussed, is well approximated by a model including spontaneous erratic variations in the liver uptake rate.
Algorithms↗
Parameter estimation in a stochastic model of the tubuloglomerular feedback mechanism in a rat nephron.
A key parameter in the understanding of renal hemodynamics is the gain of the feedback function in the tubuloglomerular feedback mechanism. A dynamic model of autoregulation of renal blood flow and glomerular filtration rate has been extended to include a stochastic differential equations model of one of the main parameters that determines feedback gain. The model reproduces fluctuations and irregularities in the tubular pressure oscillations that the former deterministic models failed to describe. This approach assumes that the gain exhibits spontaneous erratic variations that can be explained by a variety of influences, which change over time (blood pressure, hormone levels, etc.). To estimate the key parameters of the model we have developed a new estimation method based on the oscillatory behavior of the data. The dynamics is characterized by the spectral density, which has been estimated for the observed time series, and numerically approximated for the model. The parameters have then been estimated by the least squares distance between data and model spectral densities. To evaluate the estimation procedure measurements of the proximal tubular pressure from 35 nephrons in 16 rat kidneys have been analyzed, and the parameters characterizing the gain and the delay have been estimated. There was good agreement between the estimated values, and the values obtained for the same parameters in independent, previously published experiments.
Animals↗
The mediation proportion: a structural equation approach for estimating the proportion of exposure effect on outcome explained by an intermediate variable.
It is often of interest to assess how much of the effect of an exposure on a response is mediated through an intermediate variable. However, systematic approaches are lacking, other than assessment of a surrogate marker for the endpoint of a clinical trial. We review a measure of "proportion explained" in the context of observational epidemiologic studies. The measure has been much debated; we show how several of the drawbacks are alleviated when exposures, mediators, and responses are continuous and are embedded in a structural equation framework. These conditions also allow for consideration of several intermediate variables. Binary or categorical variables can be included directly through threshold models. We call this measure the mediation proportion, that is, the part of an exposure effect on outcome explained by a third, intermediate variable. Two examples illustrate the approach. The first example is a randomized clinical trial of the effects of interferon-alpha on visual acuity in patients with age-related macular degeneration. In this example, the exposure, mediator and response are all binary. The second example is a common problem in social epidemiology-to find the proportion of a social class effect on a health outcome that is mediated by psychologic variables. Both the mediator and the response are composed of several ordered categorical variables, with confounders present. Finally, we extend the example to more than one mediator.
Adult↗
Academic detailing has no effect on prescribing of asthma medication in Danish general practice: a 3-year randomized controlled trial with 12-monthly follow-ups.
BACKGROUND: Educational outreach visits, particularly when combined with social marketing, appear to be a promising approach to modifying health professional behaviour, especially prescribing. Results from previous studies have shown a varying effect. OBJECTIVE: The purpose of the study is to examine the effect of academic detailing as a method of implementing a clinical guideline in general practice. METHODS: A cluster randomized, controlled, blinded study was carried out of the effect of an academic detail visit compared with postal distribution of a guideline for prescribing asthma medication. Half the practices in a Danish county with 100 practices were visited once. The outcome measure was routinely collected data from all Danish pharmacies on the sales of asthma medication. Data were collected monthly for 2 years before to 1 year after the intervention. RESULTS: There was no effect on the pattern of prescription of asthma medicines following the visit, neither immediately nor long term. CONCLUSION: We found no effect of academic detailing as a single intervention.
Asthma↗
Cynical hostility, socioeconomic position, health behaviors, and symptom load: a cross-sectional analysis in a Danish population-based study.
OBJECTIVE: To analyze the cross-sectional association between cynical hostility and high symptom load in a Danish population-based study. Furthermore, the aim was to investigate to what extent health risk behaviors mediated this association. METHODS: Data were based on a postal questionnaire in a Danish random sample of 3426 men and 3699 women aged 40 or 50 years. Cynical hostility was measured by the 8-item Cynical Distrust Scale. High symptom load was assessed by physiological and mental symptoms experienced within the last 4 weeks. Confounders were age and socioeconomic position, while potential mediators were alcohol consumption, smoking, physical activity, and BMI. RESULTS: Higher cynical hostility was associated with self-reported symptom load. Health behaviors did not seem to mediate this effect. Socioeconomic position was a strong confounder for the effect on both health and health behaviors. After adjustment the effects of hostility on health remained with odds ratios of 2.1 (1.7-2.6) for women and 2.3 (1.8-2.8) for men. CONCLUSION: After adjustment for socioeconomic position, cynical hostility has an effect on self-reported high symptom load, and this effect is not mediated by health behaviors.
Adult↗