Bridge Designs for Modeling Systems With Low Noise

<div><p>For deterministic computer simulations, Gaussian process models are a standard procedure for fitting data. These models can be used only when the study design avoids having replicated points. This characteristic is also desirable for one-dimensional projections of the design, since it may happen that one of the design factors has a strongly nonlinear effect on the response. Latin hypercube designs have uniform one-dimensional projections, but are not efficient for fitting low-order polynomials when there is a small error variance. <i>D</i>-optimal designs are very efficient for polynomial fitting but have substantial replication in projections. We propose a new class of designs that bridge the gap between <i>D</i>-optimal designs and <i>D</i>-optimal Latin hypercube designs. These designs guarantee a minimum distance between points in any one-dimensional projection allowing for the fit of either polynomial or Gaussian process models. Subject to this constraint they are <i>D</i>-optimal for a prespecified model.</p></div

Joint distribution of p21 and hif1α in the study population.

<p>No expression (−), Positive (+).</p

Relation of clinical data to genes expression in the presence or absence of hypoxia.

<p>Average of each parameter in the study groups is shown. p-values determined by the bootstrap are marked by the letter a.</p

Association between hypertension, proteinuria, abnormal fetoplacental Doppler and IUGR with the expressions of the different genes in the maternal plasma.

<p>For p21, hif1α, VEGF and mdm2, logistic regression statistic was used.</p>*<p>For ERCC, Fisher's test was used. Significant results (p<0.05) in bold.</p

Gene's expression in the maternal plasma of twin pregnancies.

<p>Fisher's exact test for the expression of the different genes in hypoxia versus normal twin pregnancies. No expression (−), positive expression (+).</p

Prevalence of mRNA expressions in normal and hypoxic pregnancies.

<p>The number of cases (n) and percentage of cases (%) in each group with no expression (−) and positive expression (+). χ² tests are shown, significant results (p<0.05). NS, not significant.</p