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The formation of virus-laden colloidal respiratory microdroplets - the sneeze or cough virulets and their evaporation driven miniaturization in the open air are found to have a significant impact on the community transmission of COVID-19 pandemic.We simulate the motions and trajectories of virulets by employing laminar fluid flow coupled with droplet tracing physics. A force field analysis has been included considering the gravity, drag, and inertial forces to unleash some of the finer features of virulet trajectories leading to the droplet and airborne transmissions of the virus. Furthermore, an analytical model corroborates temperature (T) and relative humidity (RH) controlled droplet miniaturization.The study elucidates that the tiny (1-50 µm) and intermediate (60-100 µm) size ranged virulets tend to form bioaerosol and facilitate an airborne transmission while the virulets of larger dimensions (300 to 500 µm) are more prone to gravity dominated droplet transmission. Subsequently, the mapping between the T and RH guided miniaturization of virulets with the COVID-19 cases for six different cities across the globe justifies the significant contribution of miniaturization-based bioaerosol formation for community transmission of the pandemic.

Hypothesis Mixing of a chemical trigger of lower surface tension into a microdroplet with relatively higher surface tension can cause a rapid spreading of the droplet on a liquid-sublayer to form a host of metastable liquid morphologies such as sheets, toroids, threads, or droplets. Subsequently, such metastable fluidic objects break into a collection of droplets to form microemulsions. Experiments Introduction of surfactant loaded water or long-chain alcohols into an oleic acid microdroplet stimulate a rapid spreading of the same on a water sublayer, which helps in the formation of a metastable liquid sheet connected to a liquid toroid. Much like slipping films, the liquid sheet dewets the water underlayer through the formation of holes before they grow and coalesce to form liquid ribbons. While such liquid structures eventually break into an array of microdroplets, the liquid toroid expands before undergoing a Plateau-Rayleigh instability to form microdroplets. Findings A single step self-organization process in which a chemical trigger can convert a microdroplet into a liquid-toroid on a water surface, in absence of any rotational influence. A symmetric to asymmetric transition in toroid morphology is observed due to the changeover of laminar to turbulent flow regimes with the reduction in viscosity of fluid-sublayer or variation in chemical triggers. The toroid cross-section and droplet spacing after the toroid breakup follow a length scale evaluated from a linear stability analysis.

A resistive touchpad was developed employing paper, pencil graphite, and polydimethylsiloxane (PDMS). A pair of flexible substrates with one side coated with conducting graphite and the other with insulating polymer, were assembled with the help of an intercalated polymer spacer having holes which, allowed the inner graphitic layers of the paper surfaces to come in contact with each other upon touching or pressing. An external electrical circuit was designed to detect the variations in the output electrical resistances. The resistive pad was further modified to develop a point-of-care-testing (POCT) device to detect the hand tremors associated with the neurological disorders such as Parkinson’s disease. The proof-of-concept POCT pad showed variations in the electrical resistance due to the variation in contact area at the inner conductive layers of the paper surface when pressed with a pair of human fingers experiencing tremors. Simplified circuit-models have been discussed to explain the operating principles of the resistive pad and the POCT device. The response from the detection unit helped in evaluating the real time hand tremor levels of patients. The POCT prototype was able to detect the early to chronic stages and severity of tremor and thus is capable of detecting diverse neurological disorders.

We investigate the formation and breakup of a liquid jet originating from an orifice and migrating along and perpendicular to the direction of gravity by conducting three-dimensional numerical simulations. In case of the perpendicular injection, jet follows a parabolic path due to the influence of gravity. In this case, both symmetric and asymmetric perturbations are observed on the liquid surface, which in turn lead to jet breakup forming droplets of varying sizes. It is found that the jet breakup length increases with increase in the Weber and the Ohnesorge numbers. The horizontal distance of the liquid jet released from the same vertical height also increases with increasing the value of the Weber number. Increasing the Bond number significantly increases the curvature of the jet trajectory. An interesting phenomena is observed; the detached drops from the main jet exhibit rolling motion, as well as, shape oscillations while migrating along their trajectories.

A combined experimental and computational study is presented to identify the salient features of the adsorption of water molecules from a humid gas on the surface of a film of cadmium sulfide nanoparticles (CdSNPs). It is well known that, apart from showing exquisite optical and electrical properties, CdSNPs are also capable of adsorbing humidity from the gas or vapors. In the present study, we explore the variation in the electrical conductivity of a film of CdSNPs with the variation in the flowrate of a humid gas, which can lead to the development of a humidity or a flowrate sensor. The computational study shows that the increase in the concentration of adsorbed molecules with the enhancement in the flowrate of the humid gas can lead to a variation in the electrical conductance of the CdSNP film. The adsorption of water molecules on the sensor is correlated with the band bending of the CdSNP film owing to the ionization of the adsorbed molecules on the sensor surface. The electrical conductance of the sensor is found to vary in the range of 55–95% when the flowrate of the humid gas is varied from ∼200 to 600 L/min, at a relative humidity of ∼97%. A logarithmic dependence of the flowrate of the humid gas with the concentration of the water molecules adsorbed on the film surface is found to explain the experimental observations.

Spatially-referenced geostatistical responses that are collected in environmental sciences research are often subject to detection limits, where the measures are not fully quantifiable. This leads to censoring (left, right, interval, etc.), and various ad hoc statistical methods (such as choosing arbitrary detection limits, or data augmentation) are routinely employed during subsequent statistical analysis for inference and prediction. However, inference may be imprecise and sensitive to the assumptions and approximations involved in those arbitrary choices. To circumvent this, we propose an exact maximum likelihood estimation framework of the fixed effects and variance components and related prediction via a novel application of the Stochastic Approximation of the Expectation Maximization (SAEM) algorithm, allowing for easy and elegant estimation of model parameters under censoring. Both simulation studies and application to a real dataset on arsenic concentration collected by the Michigan Department of Environmental Quality demonstrate the advantages of our method over the available naive techniques in terms of finite sample properties of the estimates, prediction, and robustness. The proposed methods can be implemented using the R package CensSpatial .

Microfluidic electrolyzers have been fabricated using graphite coated paper electrodes to electrolyze sea water into oxygen (O2) and hydrogen (H2) when integrated with a photovoltaic (PV) cell. The ‘open’ electrolyzer (OME) consists of a microchannel confined by a pair of graphite electrodes, which is drawn with the help of pencil tips. A sea water microdroplet has been dispensed at the junction of the electrodes while the PV cell is integrated to the electrodes to supply current. The microscale width of channel generates a high intensity electric field even at a lower potential, which facilitates the microdroplets to electrolyze into H2 and O2 near the cathode and anode. The rate of production of the gases increased with field intensity. In the ‘close’ electrolyzer (CME), the paper decorated with graphite electrodes is covered with a substrate embedded with polymeric microchannels. The microcapillaries are placed closer to the anode and cathode for in situ separation of H2 and O2. The economic, flexible, and metal-free micro-electrolyzer facilitates the water-splitting at a much lower applied voltage at an efficiency of 1–2%. Use of multiple separation channels in CME for production and separation of H2 and O2 shows the potential for micro-very-large-scale-integration (μ-VLSI).

Background and objective: With the recent surge in availability of large biomedical databases mostly derived from electronic health records, the need for the development of scalable marginal survival models with faster implementation cannot be more timely. The presence of clustering renders computational complexity, especially when the number of clusters is high. Marginalizing conditional survival models can violate the proportional hazards assumption for some frailty distributions, disrupting the connection to a conditional model. While theoretical connections between proportional hazard and accelerated failure time models exist, a computational framework to produce both for either marginal or conditional perspectives is lacking. Our objective is to provide fast, scalable bridged-survival models contained in a unified framework from which the effects and standard errors for the conditional hazard ratio, the marginal hazard ratio, the conditional acceleration factor, and the marginal acceleration factor can be estimated, and related to one another in a transparent fashion. Methods We formulate a Weibull parametric frailty likelihood for clustered survival times that can directly estimate the four estimands. Under a nonlinear mixed model specification with positive stable frailties powered by Gaussian quadrature, we put forth a novel closed form of the integrated likelihood that lowered the computational threshold for fitting these models. The method is illustrated on a real dataset generated from electronic health records examining tooth-loss. Results: Our novel closed form of the integrated likelihood significantly lowered the computational threshold for fitting these models by a factor of 12 (36 compared to 3 min) for the R package parfm, and a factor of 2400 for Gaussian Quadrature (4.6 days compared to 3 min) in SAS. Moreover, each of these estimands are connected by simple relationships of the parameters and the proportional hazards assumption is preserved for the marginal model. Our framework provides a flow of analysis enabling the fit of any/all of the 4 perspective-parameterization combinations. Conclusions We see the potential usefulness of our framework of bridged parametric survival models fitted with the Static-Stirling closed form likelihood. Bridged-survival models provide insights on subject-specific and population-level survival effects when their relation is transparent. SAS and R codes, along with implementation details on a pseudo data are provided.

Pre-decorating graphene-oxide (GO) flakes on silicon (Si) substrate led to the pattern directed dewetting of ultrathin polystyrene (PS) films. The size and periodicity of the PS droplets on the GO flakes were found to be much smaller than the same on the homogeneous Si substrate. Interestingly, when the dewetted PS droplets were exposed to UV-Ozone (UVO), polystyrene/polystyrene-oxide (PS/PSO) nanostructures of size less than 100 nm with sub-micron periodicity were formed. The UVO exposure facilitated, (i) catalytic conversion of PS into the lower molecular weight PS/PSO; (ii) heating beyond the glass transition temperature of PS/PSO because the UV rays concentrated at the GO-PS interface owing to the translucency (opacity) of the PS droplets (GO flakes); (iii) rapid spreading, thermal expansion, and breaking of PS/PSO droplets to form GOPSO nanocomposites. The nanocomposites enhanced the Raman signals of rhodamine6G (Rh6G) dye, which could be the highest among the recently reported chemical pathway of Surface-Enhanced-Raman-Scattering (SERS) of graphene and its derivatives. Density-of-states (DOS) computations uncovered that the defects induced strain effects on GO, confinement of light at the GO-PS/PSO interface, and the band gap reduction of GO cumulatively engendered the SERS effect.

The frequency of breathing and peak flow rate of exhaled air are necessary parameters to detect chronic obstructive pulmonary diseases (COPDs) such as asthma, bronchitis, or pneumonia. We developed a lung function monitoring point-of-care-testing device (LFM-POCT) consisting of mouthpiece, paper-based humidity sensor, micro-heater, and real-time monitoring unit. Fabrication of a mouthpiece of optimal length ensured that the exhaled air was focused on the humidity-sensor. The resistive relative humidity sensor was developed using a filter paper coated with nanoparticles, which could easily follow the frequency and peak flow rate of the human breathing. Adsorption followed by condensation of the water molecules of the humid air on the paper-sensor during the forced exhalation reduced the electrical resistance of the sensor, which was converted to an electrical signal for sensing. A micro-heater composed of a copper-coil embedded in a polymer matrix helped in maintaining an optimal temperature on the sensor surface. Thus, water condensed on the sensor surface only during forcible breathing and the sensor recovered rapidly after the exhalation was complete by rapid desorption of water molecules from the sensor surface. Two types of real-time monitoring units were integrated into the device based on light emitting diodes (LEDs) and smart phones. The LED based unit displayed the diseased, critical, and fit conditions of the lungs by flashing LEDs of different colors. In comparison, for the mobile based monitoring unit, an application was developed employing an open source software, which established a wireless connectivity with the LFM-POCT device to perform the tests.

Highlights • TP53 mutations are common in serous endometrial tumors. • Endometrial tumors with micro and macrometastasis are more likely than tumors with ITC only to have LVSI. • No patient with ITC only disease had a recurrence in the study time frame., Objectives Lymph node (LN) metastasis and genomic profiles are important prognostic factors in endometrial cancer (EMCA). However, the prognostic significance of low volume metastasis found in sentinel lymph nodes (SLN) is unknown. We sought to determine if genomic mutations were associated with metastatic volume. Methods Surgically staged women with EC who were enrolled in both a SLN clinical trial and tumor sequencing protocol were eligible. Relevant targets were enriched by a custom designed Agilent SureSelect hybrid capture enrichment library using standard protocols. Three specific gene mutations were evaluated, TP53, PTEN and PIK3CA in the primary tumor of patients with LN negative, LN positive and ITC disease. Results 42 patients were eligible; of these, 7 (16.7%) had ITC only and 7 (16.7%) had micrometastatic or macrometastatic (LN positive) disease. No differences were seen in TP53, PIK3CA or PTEN between groups. All ITC patients with TP53 mutations were of non-endometrioid histology (2/7). Deeper myometrial invasion and lymph vascular space invasion were more likely to occur in the LN positive group (p

C-terminal binding proteins 1 and 2 (CtBP1 and CtBP2) are transcriptional regulators that activate or repress many genes involved in cellular development, apoptosis, and metastasis. NADH-dependent CtBP activation has been implicated in multiple types of cancer and poor patient prognosis. Central to understanding activation of CtBP in oncogenesis is uncovering how NADH triggers protein assembly, what level of assembly occurs, and if oncogenic activity depends upon such assembly. Here, we present the cryoelectron microscopic structures of two different constructs of CtBP2 corroborating that the native state of CtBP2 in the presence of NADH is tetrameric. The physiological relevance of the observed tetramer was demonstrated in cell culture, showing that CtBP tetramer-destabilizing mutants are defective for cell migration, transcriptional repression of E-cadherin, and activation of TIAM1. Together with our cryoelectron microscopy studies, these results highlight the tetramer as the functional oligomeric form of CtBP2.

In studies involving nonparametric testing of the equality of two or more survival distributions, the survival curves can exhibit a wide variety of behaviors such as proportional hazards, early/late differences, and crossing hazards. As alternatives to the classical logrank test, the weighted Kaplan-Meier (WKM) type statistic and their variations were developed to handle these situations. However, their applicability is limited to cases where the population membership is available for all observations, including the right censored ones. Quite often, failure time data are confronted with missing population marks for the censored observations. To alleviate this, a new WKM-type test is introduced based on imputed population marks for the censored observations leading to fractional at-risk sets that estimate the underlying risk for the process. The asymptotic normality of the proposed test under the null hypothesis is established, and the finite sample properties in terms of empirical size and power are studied through a simulation study. Finally, the new test is applied on a study of subjects undergoing bone marrow transplantation.

Transitions from spinodal to pattern-guided dewetting of a bilayer of ultrathin films (

A versatile graphene coated glass microswimmer displayed directed motions under the influence of applied electric field, chemical potential gradient and external magnetic field. The directed chemical locomotion took place from the region of lower to higher pH with speed ∼13 body lengths per second due to asymmetric catalytic decomposition of dilute hydrogen peroxide across the motor surface. The negative surface potential of graphene coated motor developed an electrical double layer in an alkaline medium which in turn engendered electrophoretic mobility towards anode when the external electrostatic field was applied. Inclusion of sparsely populated ferromagnetic iron nanoparticles on the surface of the motor offered the magnetic remote control on the motion. The coupled in situ and external controls enabled the motor to develop complex motions in diverse open and confined environments. For example, the motor could approach, pick-up, tow, and release a heavy cargo inside microchannel. Remarkably, the motor (∼67 μg) could successfully drive out a ∼1000 times heavier payload (∼0.67 mg) displaying the ability to overcome the drag force of ∼2619 pN with the help of coupled in situ and remote guidance.

Motivated by recent developments on dimension reduction (DR) techniques for time series data, the association of a general deterrent effect towards South Carolina (SC)'s registration and notification (SORN) policy for preventing sex crimes was examined. Using adult sex crime arrestee data from 1990 to 2005, the the idea of Central Mean Subspace (CMS) is extended to intervention time series analysis (CMS-ITS) to model the sequential intervention effects of 1995 (the year SC's SORN policy was initially implemented) and 1999 (the year the policy was revised to include online notification) on the time series spectrum. The CMS-ITS model estimation was achieved via kernel smoothing techniques, and compared to interrupted auto-regressive integrated time series (ARIMA) models. Simulation studies and application to the real data underscores our model's ability towards achieving parsimony, and to detect intervention effects not earlier determined via traditional ARIMA models. From a public health perspective, findings from this study draw attention to the potential general deterrent effects of SC's SORN policy. These findings are considered in light of the overall body of research on sex crime arrestee registration and notification policies, which remain controversial.

Background There is a lack of consensus in the literature as to how to define drinking outcomes in clinical trials. Typically, separate statistical models are fit to assess treatment effects on several summary drinking measures. These summary measures do not capture the complexity of drinking behavior. We used the COMBINE study to illustrate a statistical approach for examining treatment effects on high-resolution drinking data. Methods This is a secondary data analysis of COMBINE participants randomly assigned to naltrexone, acamprosate, with medical management and/or combined behavioral intervention (CBI). Using a Poisson hurdle model, abstinence and number of drinks were simultaneously modeled as a function of treatment and covariates. An emphasis was placed on the evaluation of “risky drinking” (3 drinks/day for women and 4 for men). Results During treatment, naltrexone increased the odds of abstinence vs placebo naltrexone (OR = 1.35 [1.06, 1.65]) but receiving CBI in addition to naltrexone (vs not) obscured this effect; thus, the naltrexone effect was largest in the group not receiving CBI (OR = 1.87 [1.29, 2.46]). Naltrexone vs placebo naltrexone also reduced the risk of drinking in those who resumed risky drinking (RR = 0.58 [0.24, 0.93]) and increased the odds of maintaining low risk drinking (OT = 1.99 [1.07, 2.90]). Both effects were strongest in the absence of CBI when only “medical management” was provided. Conclusions The hurdle model is an appropriate statistical tool for assessing the effect of treatment on the two part drinking process, abstinence and number of drinks. When applied to COMBINE, results bolster the use of naltrexone in promoting abstinence and reduction in risky drinking.

A combined experimental and computational study is presented to uncover the dewetting kinetics of the PS/PMMA system by changing the film thickness of the PMMA under layer. On the low M w PMMA ( M w = 15 kg/mol) layer, the dewetting velocity of PS film firstly rapidly decreases (regime I), and then becomes almost invariant (regime II) with the increase of the film thickness of the liquid lower layer. Experiments suggest that the transition from regime I to regime II is correlative with the property of the solid substrates. The linear stability analysis of thin bilayers uncovers a bimodal behaviour of the instability under the experimental conditions and changeover of dominant mode of instability from one interface to the other is the major reason behind the switching of regimes. The nonlinear simulations closely mimic the experimental interfacial morphologies and suggest two different pathways of hole growth for regimes I and II under experimental condition. The simulations also indicate that the rapid reduction in the dewetting velocity is because of the increased excursion or penetration of the upper layer into the lower layer near the three phase contact line as the viscous resistance at the more viscous PMMA layer reduces with its increasing thickness. A qualitative match is thus found between the experimental and theoretical trends of the dewetting velocities. In addition, the experiments show that on a high M w PMMA ( M w = 365 kg/mol) layer, the kinetics of hole growth of the PS layer is not affected by the PMMA layer thickness.

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. We derive a simple EM-type algorithm for iteratively computing maximum likelihood (ML) estimates and the observed information matrix is derived analytically. Simulation studies demonstrate the robustness of this flexible class against outlying and influential observations, as well as nice asymptotic properties of the proposed EM-type ML estimates. Finally, the methodology is illustrated using an ultrasonic calibration data.

A Bayesian analysis of stochastic volatility (SV) models using the class of symmetric scale mixtures of normal (SMN) distributions is considered. In the face of non-normality, this provides an appealing robust alternative to the routine use of the normal distribution. Specific distributions examined include the normal, student-t, slash and the variance gamma distributions. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo (MCMC) algorithm is introduced for parameter estimation. Moreover, the mixing parameters obtained as a by-product of the scale mixture representation can be used to identify outliers. The methods developed are applied to analyze daily stock returns data on S&P500 index. Bayesian model selection criteria as well as out-of- sample forecasting results reveal that the SV models based on heavy-tailed SMN distributions provide significant improvement in model fit as well as prediction to the S&P500 index data over the usual normal model.

We present a semiparametric analysis of an augmented inverse probability of non-missingness weighted (AIPW) estimator of a survival function for the missing censoring indicator model. Although the estimator is asymptotically less efficient than a Dikta semiparametric estimator, its advantage is the insulation that it offers against inconsistency due to misspecification. We present theoretical and numerical comparisons of the asymptotic variances when there is no misspecification. In addition, we derive the asymptotic variance of the AIPW estimator when there is partial misspecification. We also present a numerical robustness study that confirms the superiority of the AIPW estimator when there is misspecification.

The purpose of this study was to determine levels of oral health knowledge and factors associated with adequate oral health knowledge in adults with diabetes. A convenience sample of 253 adult US residents with diabetes completed an oral health survey to assess their knowledge. Results showed that only 47% of the participants answered five or more (out of a maximum of seven) oral health knowledge items related to diabetes correctly. Participants who received oral health information related to diabetes have 2.9 times the odds of possessing adequate oral health knowledge (i.e., answered five or more items correctly) compared to participants who did not received that information controlling for education and race (OR = 2.86, 95% CI 1.26–6.24, P = 0.008). Given that oral health information provided by health professionals (dental and/or medical) contributes to improve oral health knowledge among adults with diabetes, health professionals should take the opportunity to educate patients with diabetes about the oral manifestations (e.g., dry mouth) and complications (e.g., periodontitis and oral candidiasis) of diabetes and to promote proper oral health behaviors.

Introduction Human laboratory paradigms for examining stress- or cue-reactivity in substance-dependent individuals often involve exposure to pharmacological, psychosocial or physical laboratory procedures or drug paraphernalia. This study examines whether participation in such studies alters drug-seeking behavior and which patient attributes contribute to increased use. Methods In two separate studies, the relationship between participation and drug use post-study were examined. Cocaine-dependent participants received 1 μg/kg of corticotropin releasing hormone intravenously, underwent the Trier Social Stress Task, and were exposed to drug cues and various measures obtained. Cocaine use for 90 days prior and 28 days following the study was assessed. Methamphetamine-dependent participants were exposed to drug cues and various measures obtained. Methamphetamine use for 90 days prior and 14 days following the study was assessed. Weekly drug use was modeled using a 2-state hidden Markov model assuming two possible underlying states at each week. Bayesian estimation was used. Results are presented as posterior mean odds ratios (OR) and 95% credible intervals (CI). Results Participation decreased the odds of remaining in or transitioning to the high use state (cocaine study OR = 0.04 [CI = 0.01, 0.11]; methamphetamine study OR = 0.39 [CI = 0.07, 1.70]). In the cocaine study, older age increased the odds of remaining in or transitioning into the high use state (1.66 [CI = 0.99, 2.96]). In the methamphetamine study, male gender increased the odds (2.70 [CI = 1.10, 6.17]). Conclusion Stress and cue exposure paradigms were associated with a decreased odds of drug use following participation.

Summary Polyaromatic hydrocarbons, including benzo [a] pyrene (BP), are major tobacco carcinogens. Their carcinogenic effects require metabolic activation by cytochrome p450 (CYP) enzymes. Relative CYP isoform expression is related to tissue-specific tobacco-related squamous cell carcinoma (SCC) susceptibility. There have been conflicting reports regarding relative CYP1A1 and CYP1B1 oral expression, and information regarding CYP1B1 expression in oral tissues is limited. To quantify BP- and tobacco-induced CYP1A1 and CYP1B1 expression in oral SCC cells and oral mucosa. Study Design: Real-time qPCR was performed to measure (1) BP-induced CYP1A1 and CYP1B1 mRNA expression in seven oral/other head and neck SCC cell lines (2) CYP1A1 and CYP1B1 mRNA expression in gingiva from 22 smokers and 24 nonsmokers. SCC lines exhibited either similar induction of both isoforms or preferential CYP1A1 induction (CYP1A1-to-CYP1B1 ratios 0.8–4.3). In contrast, gingival tissues from smokers exhibited preferential CYP1B1 induction. Marked interindividual variation in CYP1A1 and CYP1B1 expression was observed among smokers. In vitro conditions may not account for factors that modulate expression in vivo . Interindividual variation in inducible CYP1A1 and CYP1B1 expression may account in part for variation in tobacco-related oral SCC risk.

We derive the asymptotic distributions of a semiparametric Dikta-type estimator and an inverse probability weighted type estimator of a survival function for a missing censoring indicator left truncated model and provide a theoretical comparison study.

A long wave nonlinear theory and simulations on the electric field induced instability of a thin (

This paper studies off-diagonal decay in symmetric Toeplitz matrices. It is shown that if the generating sequence of the matrix is monotone, positive and convex then the monotonicity and positivity are maintained through triangular decomposition. The work is motivated by recent results on explicit bounds for inverses of triangular matrices.

Purpose Intraocular lens (IOL) formulas based on aphakic refraction alone have been proposed as an alternative to biometry-based formulas. The purpose of this study was to determine the relative accuracy of these simplified formulas. Methods Records of patients who received secondary in-the-bag (IOL) implants and for whom aphakic refraction was obtainable were retrospectively studied. The formulas for IOL power calculation by Hug (J Pediatr Ophthalmol Strabismus 2004;41;209-11) and Khan and by AlGaeed (Br J Ophthalmol 2006;90:1458-60; modified to account for greater K values in our population) were compared with the biometry-based Holladay 1 formula by calculating the absolute prediction error for each. Results Twenty eyes met the inclusion criteria. The average age at IOL implantation was 4.8 ± 3.4 years. The mean of the absolute value of the prediction error when we used the Hug's formula was 2.4 ± 2.1 D; with Khan's formula, 2.4 ± 2.0 D; and with biometry, 1.6 ± 1.4 D. None of these differences was statistically significant (paired t test: Hug vs Khan, P = 0.9; biometry vs Hug, P = 0.3; biometry vs Khan, P = 0.2). The absolute prediction error was more than 2 D in 8 of 20 eyes (40%) when we used Hug's formula, 11 of 20 eyes (55%) with Khan's formula, and 5 of 20 eyes (25%) with biometry. Conclusions Although the 0.8 D reduction in accuracy of the refraction-based formulas was not statistically significant, we recommend continued use of biometry-based formulas for IOL power calculation. Aphakic refraction may be used to confirm IOL power prediction when biometry is difficult.

A class of tests is proposed for testing bivariate exponentiality against the bivariate increasing failure rate class of probability distributions. These tests are consistent and asymptotically unbiased against all continuous bivariate increasing failure rate alternatives. They are U-statistics and hence asymptotically normally distributed. Numerical evaluation of critical values and small sample powers of some selected tests have been done using Monte Carlo simulation.