On the Optimal Timing of Futility Interim Analyses

<p>Futility analyses provide a mechanism to stop a trial early because of low likelihood to achieve its efficacy objective. They are usually motivated by ethical and economic purposes, so that stopping a trial with poor efficacy could save patients and resources for other promising trials. There are various methods to address futility analyses in the literature but most focus on equally spaced interim looks. We consider a constrained optimization framework where the timing and the futility boundary are decided jointly to balance the risks between stopping trials which should continue, and continuing trials which should stop. The average sample size is used as a key parameter, which is evaluated under different degrees of power loss. Alternative objective functions and constraints are compared to assess the operating characteristics of the optimal futility scheme. Numerical results for single and multiple futility looks are provided. Supplementary materials for this article are available online.</p

Ablation of Sim1 neurons reduces activity.

<p>Total and ambulatory activity of iDTR mice (gray line) and Sim1creiDTR mice (black line) was measured using metabolic cages at wk6 (A, D) and wk 12 (B, E). Average total (C) and ambulatory (F) activity at wk 6 and wk 12 (n = 4 for each group, *p<0.05; **p<0.01). Error bars indicate SEM for all figures. Means for each condition were compared using repeated measures two-way ANOVA with Bonferroni post-test. Total activity is any movement producing a beam break in the horizontal plane and ambulatory activity is any movement producing sequential horizontal beam breaks of different beams.</p

Generation of Sim1creiDTR mice and experimental schedule.

<p>(A) Sim1cre mice were crossed with homozygous iDTR mice to generate Sim1creiDTR mice and iDTR littermates. (B) Mouse genotyping shows that the cre gene product of 250 bp is expressed in Sim1creiDTR mice, while a normal product of 550 bp is amplified from iDTR mice that do not express cre. (C) Detailed experimental schedule. 6-week-old female mice were entered into the study (Wk1). Cannulation and DT injection took place at Wk5. Body weight and food intake were measured weekly before and after injection of DT. Energy expenditure was measured at wk 6 and wk 12. Body and brown adipose tissue temperature and body composition were measured before the mice were sacrificed. (D) Coronal sections of iDTR mouse brain stained with DAPI showing a dense PVH, with decreased density in Sim1creiDTR mice (G). Immunofluorescence staining with an antibody to SIM1 in PVH (E, H), SON (F, I), MeA (J, M), MePD and MePV (K, N). Quantitation of cell number in each region (L, O, n = 3 for each group, *p<0.05; **p<0.01). Scale bar: 200 µm for D, G; 40 µm for E, H, J, K, M, N; and 20 µm for F, I.</p

Ablation of Sim1 neurons reduces resting energy expenditure, body and BAT temperature.

<p>Resting energy expenditure for individual mice was calculated as described in the results (A, n = 4 for each group, *p<0.05, **p<0.01). (B) Rectal temperature and BAT temperature were measured (n = 7 for each group, *p<0.05). Error bars indicate SEM for all figures. Means for each condition were compared using repeated measures two-way ANOVA with Bonferroni post-test (A) and a two-tailed <i>t</i>-test, with Welch's correction (B).</p

Ablation of Sim1 neurons causes hyperphagic obesity.

<p>(A) Growth curves and (B) weekly food intake of Sim1creiDTR versus iDTR mice. 2.5 ng DT was ICV injected at wk 5. Body weight and food intake were measured weekly on a chow diet (n = 7 for each group, *p<0.05). (C) Hypothalamic mRNA expression of Sim1creiDTR mice versus iDTR mice (n = 4 for each group, *p<0.05). (D) Representative images of iDTR and Sim1creiDTR mice (wk 14). (E) Relationship between final body weight and hypothalamic <i>Sim1</i> mRNA levels of Sim1creiDTR mice and iDTR mice. (F) Feeding efficiency calculated as the ratio between weekly body weight change (g) and food intake (g) (n = 7 for each group, *p<0.05). (G) Body composition measured by NMR (n = 4 for each group, *p<0.05; **p<0.01). Error bars indicate SEM for all figures. Means at each time point or condition were compared by a two-tailed <i>t</i>-test, with Welch's correction.</p

Ablation of Sim1 neurons decreases hypothalamic expression of <i>OXT</i> and <i>TRH</i>.

<p>(A) mRNA expression of obesity-related genes in the hypothalamus (n = 4 for each group, *p<0.05). (B) Immunofluorescence staining of OXT in iDTR versus Sim1creiDTR mice. Error bars indicate SEM. Means for each condition were compared by a two-tailed <i>t</i>-test, with Welch's correction.</p

Ablation of Sim1 neurons reduces energy expenditure.

<p>Energy expenditure measured in CLAMS cages over a 72-hr period in the pre-obese state at wk 6 (A–D) and in the obese state wk 12 (E–H). Measures during light and dark cycles are presented separately. VO₂, VCO₂ and metabolic rate were normalized to body weight (n = 4 for each group, *p<0.05). Error bars indicate SEM for all figures. Means for each condition were compared by a two-tailed <i>t</i>-test, with Welch's correction.</p

Response of Sim1creiDTR and iDTR mice to high fat diet.

<p>(A) Food intake and (B) energy intake of Sim1creiDTR and iDTR mice. Mice were fed with chow for a week, switched to HF for a week, then back to chow(n=6 for each group). (C) Average daily body weight change of Sim1creiDTR and iDTR mice when fed with a chow diet or HF diet (n=6 for each group). (D)(E)Daily food intake (E) and energy intake (F) of Sim1creiDTR and iDTR mice fed with mixed diet of chow and HF (n=7 to 9 for each group). * p<0.05.</p

Immunofluorescence and quantitation of <i>SIM1</i> neurons in PVN and SON of iDTR and Sim1Cre mice.

<p>(A) PVN of iDTR mice shows robust expression of <i>SIM1</i>, (B) <i>SIM1</i> staining was dramatically decreased in PVN of Sim1creiDTR mice. Robust expression of <i>SIM1</i> was observed in SON of both iDTR (C) and Sim1creiDTR mice (D). (E) Quantitation of <i>SIM1</i> positive neurons in PVN and SON reveals similar numbers of <i>SIM1</i> positive neurons in SON of both iDTR and Sim1Cre mice but a significant decrease in SIM1 neurons of PVN of Sim1Cre mice relative to iDTR mice (n=3 for each group, * p<0.05). Scale bar: 40 µm for A, B; and 20 µm for C, D.</p

The constructed miR adenovirus did not affect the expression of certain apoptosis-related proteins, but significantly decreased cleavage of caspase-3.

<p>(<b>A</b>) There was significantly decreased cleavage of caspase-3 in Ad-mFas-mTNFR1-miRNA treated mice and combined interference group at 72 h after MHV-3 infection. (<b>B</b>) Both Ad-mFas-mTNFR1-miR and combined interference with the two adenoviral miRNAs did not affect the expression of pro-apoptotic proteins, including Bax and Bad, and anti-apoptotic proteins, including Bcl-2 and c-IAP2 at 72 h after MHV-3 infection. The average protein expression from Negative miRNA control group was designated as 1. *<i>P</i> <0.05.</p