General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference

<p>Frequentists’ inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point estimators, which, in many but not all cases, are related to asymptotic Normal distributions ensured by central limit theorems. Although previous literature has established various forms of central limit theorems for statistical inference in super population models, we still need general and convenient forms of central limit theorems for some randomization-based causal analyses of experimental data, where the parameters of interests are functions of a finite population and randomness comes solely from the treatment assignment. We use central limit theorems for sample surveys and rank statistics to establish general forms of the finite population central limit theorems that are particularly useful for proving asymptotic distributions of randomization tests under the sharp null hypothesis of zero individual causal effects, and for obtaining the asymptotic repeated sampling distributions of the causal effect estimators. The new central limit theorems hold for general experimental designs with multiple treatment levels, multiple treatment factors and vector outcomes, and are immediately applicable for studying the asymptotic properties of many methods in causal inference, including instrumental variable, regression adjustment, rerandomization, cluster-randomized experiments, and so on. Previously, the asymptotic properties of these problems are often based on heuristic arguments, which in fact rely on general forms of finite population central limit theorems that have not been established before. Our new theorems fill this gap by providing more solid theoretical foundation for asymptotic randomization-based causal inference. Supplementary materials for this article are available online.</p

Lysosomal Delivery of a Lipophilic Gemcitabine Prodrug Using Novel Acid-Sensitive Micelles Improved Its Antitumor Activity

Stimulus-sensitive micelles are attractive anticancer drug delivery systems. Herein, we reported a novel strategy to engineer acid-sensitive micelles using a amphiphilic material synthesized by directly conjugating the hydrophilic poly­(ethylene glycol) (PEG) with a hydrophobic stearic acid derivative (C18) using an acid-sensitive hydrazone bond (PHC). An acid-insensitive PEG-amide-C18 (PAC) compound was also synthesized as a control. 4-(<i>N</i>)-Stearoyl gemcitabine (GemC18), a prodrug of the nucleoside analogue gemcitabine, was loaded into the micelles, and they were found to be significantly more cytotoxic to tumor cells than GemC18 solution, likely due to the lysosomal delivery of GemC18 by micelles. Moreover, GemC18 in the acid-sensitive PHC micelles was more cytotoxic than in the acid-insensitive PAC micelles, which may be attributed to the acid-sensitive release of GemC18 from the PHC micelles in lysosomes. In B16–F10 melanoma-bearing mice, GemC18-loaded PHC or PAC micelles showed stronger antitumor activity than GemC18 or gemcitabine solution, likely because of the prolonged circulation time and increased tumor accumulation of the GemC18 by the micelles. Importantly, the <i>in vivo</i> antitumor activity of GemC18-loaded PHC micelles was significantly stronger than that of the PAC micelles, demonstrating the potential of the novel acid-sensitive micelles as an anticancer drug delivery system

Synthesis of Sterically Protected Xanthene Dyes with Bulky Groups at C‑3′ and C‑7′

Substitution of the xanthene scaffold with bulky groups at C-3′ and C-7′ is expected to protect the electrophilic central methine carbon against nucleophilic attack and inhibit stacking. However, such structures are not readily prepared via traditional xanthene syntheses. We have devised an alternative and convenient synthesis to enable facile preparation of this subset of xanthene dyes under mild conditions and in good yields

Size of the at-risk population for each SU in the Auvergne region, as defined by mean number of live births per year between 1999 and 2006 (source: INSEE).

<p><i>Q</i>1:≤ 17; <i>Q</i>2:> 17 and ≤ 35; <i>Q</i>3:> 35 and ≤ 70; <i>Q</i>4:> 70.</p

<i>TC_a</i> of Kulldorff’s spatial scan.

<p><i>TC_a</i> measured for four combinations of two relative risks (RR) and two annual incidences of birth defects: low RR = 3 and high RR = 6; low incidence = 0.48% births per year and high incidence = 2.26% births per year.</p

Summary statistics of usual Power, <i>AUC_EP</i>, <i>TC_a</i> and <i>TC_c</i>.

<p>Results for four combinations of two relative risks (RR) and two annual incidences of birth defects: low RR = 3 and high RR = 6; low incidence = 0.48% births per year and high incidence = 2.26% births per year.</p

Values of <i>f(s)</i> and <i>g(s)</i> for simulation <i>s = 1: 1000</i>.

<p>The simulations displayed before the vertical plain line lead to null rejection (<i>p</i>—<i>value</i> < 0.05). They are sorted by increasing number of FP SUs. The dotted line represent the last simulation resulting in a detected cluster without FP SUs. The functions <i>f</i>(<i>s</i>) and <i>g</i>(<i>s</i>) represent respectively the computation of <i>TC_a</i> and <i>TC_c</i> over the <i>m</i>′ simulations. (a) simulated cluster with the maximum value of <i>TC_a</i>—<i>TC_c</i> and (b) simulated cluster with the minimum value of <i>TC_a</i>—<i>TC_c</i>.</p

Performance indicators and size of at-risk population.

<p>Indicators are measured for four combinations of two relative risks (RR) and two annual incidences of birth defects: low RR = 3 and high RR = 6; low incidence = 0.48% births per year and high incidence = 2.26% births per year.</p

Histological and RT-PCR results of TH- and GAP 43 expression.

<p>Data were expressed as means ± SD.</p><p>* <i>P<0.05</i> vs. Sham-operated group;</p>†<p><i>P<0.05</i> vs. MI-GFP group.</p

Representative images for infarcted hearts at 8 wk time point after MI.

<p>(A) Macroscopical view of the infarcted heart. (B) Masson’s trichrome staining of infarcted area.</p