Corneal cross-linking versus standard care in children with keratoconus - a randomised, multicentre, observer-masked trial of efficacy and safety (KERALINK): a statistical analysis plan

Background: The KERALINK trial tests the hypothesis that corneal cross-linking (CXL) treatment reduces the progression of keratoconus in comparison to standard care in patients aged 10–16 years. This article describes the statistical analysis plan for this trial as an update to the published protocol. It is written before the end of the patient follow-up, while the outcome of the trial is still unknown. Design and methods: KERALINK is a randomised controlled, observer-masked, multicentre trial in progressive keratoconus comparing epithelium-off CXL with standard care, including spectacles or contact lenses as necessary for best-corrected acuity. Keratoconus is a disorder of the shape of the cornea in which the normally round domeshaped clear front window of the eye (cornea) thins progressively leading to a cone-like bulge. This impairs the ability of the eye to focus properly, causing reduced vision which requires spectacle or contact lens wear or, in a minority of patients, eventually corneal replacement by a transplant for best vision. The primary outcome measure is the between-group difference in K2 at 18 months adjusted for K2 at baseline examination. K2 is the value of the steepest corneal meridian as measured on Pentacam topography. Secondary outcomes are keratoconus progression, time to keratoconus progression, visual acuity, refraction, apical corneal thickness and adverse events. Patient-reported effects will be explored by questionnaires. We describe in detail the statistical aspects of KERALINK: the outcome measures, the sample size calculation, general analysis principles, the planned descriptive statistics and statistical models, and planned subgroup and sensitivity analyses. Discussion: The KERALINK statistical analysis will provide comprehensive and precise information on the relative effectiveness of the two treatments. The plan will be implemented in May 2020 when follow-up for the trial is completed. Trial registration: EudraCT, 2016-001460-11. Registered on 19 May 201

Planck 2018 results. IX. Constraints on primordial non-Gaussianity

We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: f_(NL)^(local) = −0.9 ± 5.1; f_(NL)^(equil) = −26 ± 47; and f_(NL)^(ortho) = −38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ <  40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarization-only bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5σ. Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is g_(NL)^(local) = (−5.8 ± 6.5) × 10⁴ (68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the ΛCDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations

Exploiting Cross Correlations and Joint Analyses

In this report, we present a wide variety of ways in which information from multiple probes of dark energy may be combined to obtain additional information not accessible when they are considered separately. Fundamentally, because all major probes are affected by the underlying distribution of matter in the regions studied, there exist covariances between them that can provide information on cosmology. Combining multiple probes allows for more accurate (less contaminated by systematics) and more precise (since there is cosmological information encoded in cross-correlation statistics) measurements of dark energy. The potential of cross-correlation methods is only beginning to be realized. By bringing in information from other wavelengths, the capabilities of the existing probes of dark energy can be enhanced and systematic effects can be mitigated further. We present a mixture of work in progress and suggestions for future scientific efforts. Given the scope of future dark energy experiments, the greatest gains may only be realized with more coordination and cooperation between multiple project teams; we recommend that this interchange should begin sooner, rather than later, to maximize scientific gains.Comment: Report from the "Dark Energy and CMB" working group for the American Physical Society's Division of Particles and Fields long-term planning exercise ("Snowmass"

Planck 2018 results. III. High Frequency Instrument data processing and frequency maps

This paper presents the High Frequency Instrument (HFI) data processing procedures for the Planck 2018 release. Major improvements in mapmaking have been achieved since the previous Planck 2015 release, many of which were used and described already in an intermediate paper dedicated to the Planck polarized data at low multipoles. These improvements enabled the first significant measurement of the reionization optical depth parameter using Planck-HFI data. This paper presents an extensive analysis of systematic effects, including the use of end-to-end simulations to facilitate their removal and characterize the residuals. The polarized data, which presented a number of known problems in the 2015 Planck release, are very significantly improved, especially the leakage from intensity to polarization. Calibration, based on the cosmic microwave background (CMB) dipole, is now extremely accurate and in the frequency range 100–353 GHz reduces intensity-to-polarization leakage caused by calibration mismatch. The Solar dipole direction has been determined in the three lowest HFI frequency channels to within one arc minute, and its amplitude has an absolute uncertainty smaller than 0.35 μK, an accuracy of order 10−4. This is a major legacy from the Planck HFI for future CMB experiments. The removal of bandpass leakage has been improved for the main high-frequency foregrounds by extracting the bandpass-mismatch coefficients for each detector as part of the mapmaking process; these values in turn improve the intensity maps. This is a major change in the philosophy of “frequency maps”, which are now computed from single detector data, all adjusted to the same average bandpass response for the main foregrounds. End-to-end simulations have been shown to reproduce very well the relative gain calibration of detectors, as well as drifts within a frequency induced by the residuals of the main systematic effect (analogue-to-digital convertor non-linearity residuals). Using these simulations, we have been able to measure and correct the small frequency calibration bias induced by this systematic effect at the 10⁻⁴ level. There is no detectable sign of a residual calibration bias between the first and second acoustic peaks in the CMB channels, at the 10⁻³ level

Femtosecond laser-assisted cataract surgery compared with phacoemulsification: the FACT non-inferiority RCT

BACKGROUND: Cataract surgery is one of the most common operations. Femtosecond laser-assisted cataract surgery (FLACS) is a technique that automates a number of operative steps. OBJECTIVES: To compare FLACS with phacoemulsification cataract surgery (PCS). DESIGN: Multicentre, outcome-masked, randomised controlled non-inferiority trial. SETTING: Three collaborating NHS hospitals. PARTICIPANTS: A total of 785 patients with age-related cataract in one or both eyes were randomised between May 2015 and September 2017. INTERVENTION: FLACS (n = 392 participants) or PCS (n = 393 participants). MAIN OUTCOME MEASURES: The primary outcome was uncorrected distance visual acuity in the study eye after 3 months, expressed as the logarithm of the minimum angle of resolution (logMAR): 0.00 logMAR (or 6/6 if expressed in Snellen) is normal (good visual acuity). Secondary outcomes included corrected distance visual acuity, refractive outcomes (within 0.5 dioptre and 1.0 dioptre of target), safety and patient-reported outcome measures at 3 and 12 months, and resource use. All trial follow-ups were performed by optometrists who were masked to the trial intervention. RESULTS: A total of 353 (90%) participants allocated to the FLACS arm and 317 (81%) participants allocated to the PCS arm attended follow-up at 3 months. The mean uncorrected distance visual acuity was similar in both treatment arms [0.13 logMAR, standard deviation 0.23 logMAR, for FLACS, vs. 0.14 logMAR, standard deviation 0.27 logMAR, for PCS, with a difference of -0.01 logMAR (95% confidence interval -0.05 to 0.03 logMAR; p = 0.63)]. The mean corrected distance visual acuity values were again similar in both treatment arms (-0.01 logMAR, standard deviation 0.19 logMAR FLACS vs. 0.01 logMAR, standard deviation 0.21 logMAR PCS; p = 0.34). There were two posterior capsule tears in the PCS arm. There were no significant differences between the treatment arms for any secondary outcome at 3 months. At 12 months, the mean uncorrected distance visual acuity was 0.14 logMAR (standard deviation 0.22 logMAR) for FLACS and 0.17 logMAR (standard deviation 0.25 logMAR) for PCS, with a difference between the treatment arms of -0.03 logMAR (95% confidence interval -0.06 to 0.01 logMAR; p = 0.17). The mean corrected distance visual acuity was 0.003 logMAR (standard deviation 0.18 logMAR) for FLACS and 0.03 logMAR (standard deviation 0.23 logMAR) for PCS, with a difference of -0.03 logMAR (95% confidence interval -0.06 to 0.01 logMAR; p = 0.11). There were no significant differences between the arms for any other outcomes, with the exception of the mean binocular corrected distance visual acuity with a difference of -0.02 logMAR (95% confidence interval -0.05 to 0.00 logMAR) (p = 0.036), which favoured FLACS. There were no significant differences between the arms for any health, social care or societal costs. For the economic evaluation, the mean cost difference was £167.62 per patient higher for FLACS (95% of iterations between -£14.12 and £341.67) than for PCS. The mean QALY difference (FLACS minus PCS) was 0.001 (95% of iterations between -0.011 and 0.015), which equates to an incremental cost-effectiveness ratio (cost difference divided by QALY difference) of £167,620. LIMITATIONS: Although the measurement of outcomes was carried out by optometrists who were masked to the treatment arm, the participants were not masked. CONCLUSIONS: The evidence suggests that FLACS is not inferior to PCS in terms of vision after 3 months' follow-up, and there were no significant differences in patient-reported health and safety outcomes after 12 months' follow-up. In addition, the statistically significant difference in binocular corrected distance visual acuity was not clinically significant. FLACS is not cost-effective. FUTURE WORK: To explore the possible differences in vision in patients without ocular co-pathology. TRIAL REGISTRATION: Current Controlled Trials ISRCTN77602616. FUNDING: This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 25, No. 6. See the NIHR Journals Library website for further project information. Moorfields Eye Charity (grant references GR000233 and GR000449 for the endothelial cell counter and femtosecond laser used)

Femtosecond Laser-Assisted Cataract Surgery Versus Phacoemulsification Cataract Surgery (FACT): A Randomized Noninferiority Trial

PURPOSE: To report the 3-month results of a randomized trial (Femtosecond Laser-Assisted Cataract Trial [FACT]) comparing femtosecond laser-assisted cataract surgery (FLACS) with standard phacoemulsification cataract surgery (PCS). DESIGN: Multicenter, randomized controlled trial funded by the UK National Institute of Health Research (HTA 13/04/46/). PARTICIPANTS: Seven hundred eighty-five patients with age-related cataract. METHODS: This trial took place in 3 hospitals in the UK National Health Service (NHS). Randomization (1:1) was stratified by site, surgeon, and 1 or both eyes eligible using a secure web-based system. Postoperative assessments were masked to the allocated intervention. The primary outcome was unaided distance visual acuity (UDVA) in the study eye at 3 months. Secondary outcomes included corrected distance visual acuity, complications, and patient-reported outcomes measures. The noninferiority margin was 0.1 logarithm of the minimum angle of resolution (logMAR). ISRCTN.com registry, number ISRCTN77602616. MAIN OUTCOME MEASURES: We enrolled 785 participants between May 2015 and September 2017 and randomly assigned 392 to FLACS and 393 to PCS. At 3 months postoperatively, mean UDVA difference between treatment arms was -0.01 logMAR (-0.05 to 0.03), and mean corrected distance visual acuity difference was -0.01 logMAR (95% confidence interval [CI], -0.05 to 0.02). Seventy-one percent of both FLACS and PCS cases were within ±0.5 diopters (D) of the refractive target, and 93% of FLACS and 92% of PCS cases were within ±1.0 D. There were 2 posterior capsule tears in the PCS arm and none in the FLACS arm. There were no significant differences between arms for any secondary outcome. CONCLUSIONS: Femtosecond laser-assisted cataract surgery is not inferior to conventional PCS surgery 3 months after surgery. Both methods are as good in terms of vision, patient-reported health, and safety outcomes at 3 months. Longer-term outcomes of the clinical effectiveness and cost-effectiveness are awaited

Planck 2018 results. VIII. Gravitational lensing

We present measurements of the cosmic microwave background (CMB) lensing potential using the final Planck 2018 temperature and polarization data. Using polarization maps filtered to account for the noise anisotropy, we increase the significance of the detection of lensing in the polarization maps from 5σ to 9σ. Combined with temperature, lensing is detected at 40σ. We present an extensive set of tests of the robustness of the lensing-potential power spectrum, and construct a minimum-variance estimator likelihood over lensing multipoles 8 ≤ L ≤ 400 (extending the range to lower L compared to 2015), which we use to constrain cosmological parameters. We find good consistency between lensing constraints and the results from the Planck CMB power spectra within the ΛCDM model. Combined with baryon density and other weak priors, the lensing analysis alone constrains σ₈Ω_m^(0.25) = 0.589 ± 0.020 (1σ errors). Also combining with baryon acoustic oscillation data, we find tight individual parameter constraints, σ₈ = 0.811 ± 0.019, H₀ = 67.9_(−1.3)^(+1.2) km s⁻¹ Mpc⁻¹, and Ω_m = 0.303_(−0.018)^(+0.016). Combining with Planck CMB power spectrum data, we measure σ₈ to better than 1% precision, finding σ₈ = 0.811 ± 0.006. CMB lensing reconstruction data are complementary to galaxy lensing data at lower redshift, having a different degeneracy direction in σ₈ − Ω_m space; we find consistency with the lensing results from the Dark Energy Survey, and give combined lensing-only parameter constraints that are tighter than joint results using galaxy clustering. Using the Planck cosmic infrared background (CIB) maps as an additional tracer of high-redshift matter, we make a combined Planck-only estimate of the lensing potential over 60% of the sky with considerably more small-scale signal. We additionally demonstrate delensing of the Planck power spectra using the joint and individual lensing potential estimates, detecting a maximum removal of 40% of the lensing-induced power in all spectra. The improvement in the sharpening of the acoustic peaks by including both CIB and the quadratic lensing reconstruction is detected at high significance

Planck 2018 results. V. CMB power spectra and likelihoods

We describe the legacy Planck cosmic microwave background (CMB) likelihoods derived from the 2018 data release. The overall approach is similar in spirit to the one retained for the 2013 and 2015 data release, with a hybrid method using different approximations at low (ℓ   800 ranges of the power spectrum, or the preference for more smoothing of the power-spectrum peaks than predicted in ΛCDM fits. These are shown to be driven by the temperature power spectrum and are not significantly modified by the inclusion of the polarization data. Overall, the legacy Planck CMB likelihoods provide a robust tool for constraining the cosmological model and represent a reference for future CMB observations

Making Maps Of The Cosmic Microwave Background: The MAXIMA Example

This work describes Cosmic Microwave Background (CMB) data analysis algorithms and their implementations, developed to produce a pixelized map of the sky and a corresponding pixel-pixel noise correlation matrix from time ordered data for a CMB mapping experiment. We discuss in turn algorithms for estimating noise properties from the time ordered data, techniques for manipulating the time ordered data, and a number of variants of the maximum likelihood map-making procedure. We pay particular attention to issues pertinent to real CMB data, and present ways of incorporating them within the framework of maximum likelihood map-making. Making a map of the sky is shown to be not only an intermediate step rendering an image of the sky, but also an important diagnostic stage, when tests for and/or removal of systematic effects can efficiently be performed. The case under study is the MAXIMA data set. However, the methods discussed are expected to be applicable to the analysis of other current and forthcoming CMB experiments.Comment: Replaced to match the published version, only minor change