Approximate Bayesianity of Frequentist Confidence Intervals for a Binomial Proportion

<p>The well-known Wilson and Agresti–Coull confidence intervals for a binomial proportion <i>p</i> are centered around a Bayesian estimator. Using this as a starting point, similarities between frequentist confidence intervals for proportions and Bayesian credible intervals based on low-informative priors are studied using asymptotic expansions. A Bayesian motivation for a large class of frequentist confidence intervals is provided. It is shown that the likelihood ratio interval for <i>p</i> approximates a Bayesian credible interval based on Kerman’s neutral noninformative conjugate prior up to <i>O</i>(<i>n</i>^{− 1}) in the confidence bounds. For the significance level α ≲ 0.317, the Bayesian interval based on the Jeffreys’ prior is then shown to be a compromise between the likelihood ratio and Wilson intervals. Supplementary materials for this article are available online.</p

Effects of thaspine and reference compounds on the HCT116 cell cycle.

<p>Effects of thaspine and reference compounds on the HCT116 cell cycle.</p

Thaspine induces wide-spread activation of caspase-3 in spheroids.

<p>HCT116 spheroids with homogeneous diameters were formed using the hanging drop technique as described <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007238#pone.0007238-Herrmann1" target="_blank">[40]</a>. Five days after formation spheroids were compact and contained proliferating cells only in the surface layers (Ki67 staining, top left). Spheroids were treated with drugs for the times indicated, fixed, sectioned and stained for active caspase-3. Thaspine was used at 20 µM, doxorubicin at 20 µM, and cisplatin at 40 µM.</p

<i>In vivo</i> induction of tumor apoptosis by thaspine.

<p>(A) Induction of apoptosis in HCT116 tumors <i>in vivo</i>. SCID mice were injected with 10 mg/kg thaspine. Mice were sacrificed after 48 hours and tumors stained for active caspase-3 (upper panel: thaspine treated mice; lower panel: PBS injected mice). (B, C) SCID mice carrying HCT116 tumors (B) or FaDu head-neck carcinoma tumors (C) were injected with 10 mg/kg of thaspine or with PBS and the levels of human caspase-cleaved CK18 (CK18-Asp396) were determined in mouse plasma 48 hours after treatment using ELISA. The antibodies used to detect CK18-Asp396 do not bind mouse CK18. Four mice in each group; bars represent S.D. (D) SCID mice carrying FaDu tumors were treated with 10 mg/kg of thaspine (day 1, arrow) and tumor volume was calculated; black circles: untreated mice, red squares: treated mice (4 mice in each group). Error bars are presented as unidirectional for figure clarity. Animals were sacrificed when tumors were approximately 1 cm³ according to local animal welfare regulations. Statistical significance was calculated using Student's t-test.</p

Influence of resistance mechanisms on cytotoxic potency of thaspine and standard topoisomerase inhibitors.

<p>The resistance factor was defined as the IC₅₀ value in the resistant subline divided by that in its parental cell line. The IC₅₀ of thaspine on the parental cell lines were between 1–3 µM. Topo II, Topoisomerase II; P-gp, P-glycoprotein (ABCB1); MRP, multidrug resistance-associated protein (ABCC1). For details on cell lines and calculations of resistance factors, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007238#pone.0007238-Wickstrm1" target="_blank">[22]</a>. CCRF-CEM are not resistant to camptothecin <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007238#pone.0007238-Jonsson1" target="_blank">[21]</a>, which was therefore not included. The experiments were repeated twice.</p

Thaspine is a topoisomerase inhibitor.

<p>(A) Connectivity Map (CMAP) results after treatment with thaspine. The bar view is constructed from 6100 horizontal lines, each representing a single treatment and ordered according to their corresponding enrichment to the query signatures generated after thaspine treatment. Black horizontal lines in the barview represent the individual instances for ellipticine and camptothecin when the thaspine expression signature was used as query signature. Score according to the CMAP database; (B) inhibition of topoisomerase I activity: 1: plasmid +5U topoisomerase I; 2: plasmid; 3: plasmid +5U topoisomerase I+DMSO (1 µm); 4. Marker for nicked plasmid; 5: plasmid +5U topoisomerase I +50 µM thaspine; 6: plasmid +5U topoisomerase I +25 µM thaspine; 7: plasmid +5U topoisomerase I +10 µM thaspine; 8: plasmid + DMSO (1 µm). Topoisomerase I primarily induced nicked plasmid DNA, note the inhibition by thaspine. (C) inhibition of topoisomerase II activity: 1: plasmid +15U topoisomerase II; 2: plasmid; 3: plasmid +15U topoisomerase II + DMSO (1 µm); 4. Marker for nicked plasmid; 5: plasmid +15U topoisomerase II +50 µM thaspine; 6: plasmid +15U topoisomerase II +25 µM thaspine; 7: plasmid +15U topoisomerase II +10 µM thaspine; 8: plasmid + DMSO (1 µm). Topoisomerase II primarily induced nicked plasmid DNA, note the inhibition by thaspine.</p

Induction of apoptosis by thaspine.

<p>(A) chemical structure of thaspine (NSC76022); (B) induction of caspase-cleaved CK18 by thaspine, cisplatin, doxorubicin and mechlorethamine in HCT116 colon carcinoma cells. Treatment was for 24 hours with the indicated concentrations of compounds. Cells were lysed and CK18-Asp396 was determined using the M30 CytoDeath ELISA. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007238#s2" target="_blank">Results</a> are shown with S.D. from triplicate determinations. Similar results (including the biphasic response to doxorubicin) were observed in independent experiments.</p

Induction of the mitochondrial apoptosis pathway by thaspine.

<p>(A) loss of mitochondrial membrane potential in thaspine-treated HCT116 cells. Control and thaspine-treated cells (10 µM, 18 hours) were stained with tetramethyl-rhodamine ethyl ester (TMRE) and fluorescence was measured by flow cytometry; (B) Release of cytochrome c to the cytosol of thaspine-treated cells. Cells were treated with 10 µM thaspine for 7 or 16 hours. Cytochrome c was quantified in mitochondrial and cytosolic fractions by Western blotting. (C) thaspine induces the active conformation of Bak and Bax. Cells were treated with 10 µM thaspine, fixed and stained with conformation-specific antibodies to Bak and Bax. Note induction of the active conformation of both molecules by thaspine (<i>red arrows</i>: immunofluorescent signal in untreated cells; <i>green arrows</i>: immunofluorescent signal in drug-treated cells). (D) Inhibition of thaspine-induced apoptosis by siRNA to Bik and Bid. Cells were transfected with siRNAs in triplicate 96 well plates and treated with thaspine or solvent (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007238#s4" target="_blank">Material and Methods</a>). After 24 hours the levels of caspase-cleaved CK18 were determined using the M30 CytoDeath ELISA.</p

Compounds in the NCI Natural Product Set that induce caspase cleavage of CK18 in HCT116 cells.

<p>Compounds in the NCI Natural Product Set that induce caspase cleavage of CK18 in HCT116 cells.</p

Cytotoxic effects of digitoxin.

<p>A: Cytotoxic effects of digitoxin (0.1 µM) expressed as Survival Index % (<i>vs.</i> untreated control cells) in the various leukaemia types (T-ALL, B precursor ALL, AML and CLL) and PBMC using the standard 72 h assay. B: Effects of therapeutically achievable digitoxin concentrations against leukaemic cells from patients and CCRF-CEM cell line over six days with daily medium change.</p