Prevalence Threshold and the Geometry of Screening Curves

The relationship between a screening tests' positive predictive value, $\rho$, and its target prevalence, $\phi$, is proportional - though not linear in all but a special case. In consequence, there is a point of local extrema of curvature defined only as a function of the sensitivity $a$ and specificity $b$ beyond which the rate of change of a test's $\rho$ drops precipitously relative to $\phi$. Herein, we show the mathematical model exploring this phenomenon and define the $prevalence$ $threshold$ ($\phi_e$) point where this change occurs as: $\phi_e=\frac{\sqrt{a\left(-b+1\right)}+b-1}{(\varepsilon-1)}$ where $\varepsilon$ = $a$+$b$. From the prevalence threshold we deduce a more generalized relationship between prevalence and positive predictive value as a function of $\varepsilon$, which represents a fundamental theorem of screening, herein defined as: $\displaystyle\lim_{\varepsilon \to 2}{\displaystyle \int_{0}^{1}}{\rho(\phi)d\phi} = 1$ Understanding the concepts described in this work can help contextualize the validity of screening tests in real time, and help guide the interpretation of different clinical scenarios in which screening is undertaken

Infant cognitive, motor and language development at 2 years of age following conception through assisted reproductive technologies (ART) relative to natural conception : findings from the prospective, longitudinal, cohort “3D-Study”

Objectifs : L’impact a long terme des techniques de procréation médicalement assistée (PMA) en ce qui concerne le développement neurologique des enfants demeure source de controverse. Cette étude vise à évaluer et comparer le développement cognitif, moteur, et verbal des enfants âgés de 2 ans issus des techniques de PMA par rapport à ceux issus par une conception naturelle. Méthodes: L’étude de cohorte prospective « 3D » a été menée entre 2010-2012. 2,366 femmes enceinte on été recrutées, dont 278 ont utilisé la PMA: stimulation ovarienne (OS), insémination intra-utérine (IUI), fertilisation in-vitro (IVF), injection intra-cytoplasmique du sperme (ICSI) ou maturation in-vitro (IVM). La conception naturelle a été définie comme une grossesse spontanée. Le développement cognitif, moteur et verbal a été comparé entre les groupes de PMA vs. conception naturelle a l’aide des outils standardisés et validés suivants : “The Bayley Scales of Infant and Toddler Development, 3rd ed. (BSID-III)” ainsi que des “MacArthur-Bates Communicative Development Inventories”. Des modèles de régression linéaire ajustés évaluant l’impact des techniques de PMA sur les issus du neurodéveloppement ont été utilisés, tenant compte de la conception naturelle comme groupe de référence. Résultats: Un total de 175 enfants dans le groupe PMA (62,9%) et 1.345 enfants dans le groupe de conception naturelle (64,4%) ont subi une évaluation neurodéveloppementale à 24 mois de vie. En ajustant pour les variables potentiellement confondantes, la PMA n’a eu aucun effet statistiquement significatif sur les scores de l’échelle cognitive BSID-III [B1 (SE) = -1,60 (0,9), p = 0,08], de l’échelle motrice [B1 (SE) = -1,33 (1,0), p = 0,18] ou dans les scores linguistiques du MacArthur-Bates [B1 (SE) = - 0,28 (2.1), p = 0,89]. Aucune différence significative n'a été observée en comparant les techniques de PMA individuelles ou la conception sous-fertile, ni lorsqu’on compare les techniques in-vivo ou in-vitro (p> 0,05). Conclusion : Dans cette étude de cohorte prospective, les enfants nés suite a la PMA semblent avoir un développement cognitif, moteur et verbal similaire aux enfants nés après la conception naturelle à l’âge de 2 ans. Ces résultats pourraient être utiles dans le counseling clinique des patients utilisant des techniques de PMA.Objective: Whether assisted reproductive techniques (ART) have an impact on infants’ long-term neurodevelopmental outcomes remains controversial. In this study, we compared infants’ cognitive, motor, and language development at 2 years of age following ART relative to natural conception. Methods: The prospective cohort “3D-Study” was carried out from 2010-2012. 2,366 pregnant women were recruited, of which 278 conceived with ART: ovarian stimulation (OS), intrauterine sperm insemination (IUI), in-vitro fertilization (IVF), intra-cytoplasmic sperm injection (ICSI) or in-vitro maturation (IVM). Natural conception was defined as the unassisted establishment of pregnancy. Cognitive, motor, and language neurodevelopmental outcomes were compared between ART and natural conception groups at 24 months using “The Bayley Scales of Infant and Toddler Development, 3rd ed. (BSID-III)” and the “MacArthur-Bates Communicative Development Inventories”. Adjusted linear regression models evaluated the effect of ART on neurodevelopmental outcomes, using natural conception as reference. Results: 175 infants in the ART group (62.9%) and 1,345 infants in the natural conception group (64.4%) underwent neurodevelopmental assessment at 24 months of age. After adjusting for relevant confounders, infants born after ART showed no difference in BSID-III cognitive scores [B1(SE)=-1.60(0.9), p=0.08], composite motor scores [B1(SE)=-1.33(1.0), p=0.18] or MacArthur-Bates language scores [B1(SE)=-0.28(2.1), p=0.89]. No statistically significant difference was observed when comparing independent ART techniques or subfertile conceptions, nor comparing in-vivo or in-vitro techniques (p>0.05). Conclusion: In this prospective cohort, infants born after ART had no significant differences in cognitive, motor, and language development relative to infants born following natural conception at 2 years of age. These findings may be useful in the clinical counseling of patients undergoing ART