A support vector machine-based cure rate model for interval censored data.

The mixture cure rate model is the most commonly used cure rate model in the literature. In the context of mixture cure rate model, the standard approach to model the effect of covariates on the cured or uncured probability is to use a logistic function. This readily implies that the boundary classifying the cured and uncured subjects is linear. In this article, we propose a new mixture cure rate model based on interval censored data that uses the support vector machine to model the effect of covariates on the uncured or the cured probability (i.e. on the incidence part of the model). Our proposed model inherits the features of the support vector machine and provides flexibility to capture classification boundaries that are nonlinear and more complex. The latency part is modeled by a proportional hazards structure with an unspecified baseline hazard function. We develop an estimation procedure based on the expectation maximization algorithm to estimate the cured/uncured probability and the latency model parameters. Our simulation study results show that the proposed model performs better in capturing complex classification boundaries when compared to both logistic regression-based and spline regression-based mixture cure rate models. We also show that our model's ability to capture complex classification boundaries improve the estimation results corresponding to the latency part of the model. For illustrative purpose, we present our analysis by applying the proposed methodology to the NASA's Hypobaric Decompression Sickness Database.

On the estimation of interval censored destructive negative binomial cure model.

In this article, a competitive risk survival model is considered in which the initial number of risks, assumed to follow a negative binomial distribution, is subject to a destructive mechanism. Assuming the population of interest to have a cure component, the form of the data as interval-censored, and considering both the number of initial risks and risks remaining active after destruction to be missing data, we develop two distinct estimation algorithms for this model. Making use of the conditional distributions of the missing data, we develop an expectation maximization (EM) algorithm, in which the conditional expected complete log-likelihood function is decomposed into simpler functions which are then maximized independently. A variation of the EM algorithm, called the stochastic EM (SEM) algorithm, is also developed with the goal of avoiding the calculation of complicated expectations and improving performance at parameter recovery. A Monte Carlo simulation study is carried out to evaluate the performance of both estimation methods through calculated bias, root mean square error, and coverage probability of the asymptotic confidence interval. We demonstrate the proposed SEM algorithm as the preferred estimation method through simulation and further illustrate the advantage of the SEM algorithm, as well as the use of a destructive model, with data from a children's mortality study.

On the integration of decision trees with mixture cure model.

The mixture cure model is widely used to analyze survival data in the presence of a cured subgroup. Standard logistic regression-based approaches to model the incidence may lead to poor predictive accuracy of cure, specifically when the covariate effect is non-linear. Supervised machine learning techniques can be used as a better classifier than the logistic regression due to their ability to capture non-linear patterns in the data. However, the problem of interpret-ability hangs in the balance due to the trade-off between interpret-ability and predictive accuracy. We propose a new mixture cure model where the incidence part is modeled using a decision tree-based classifier and the proportional hazards structure for the latency part is preserved. The proposed model is very easy to interpret, closely mimics the human decision-making process, and provides flexibility to gauge both linear and non-linear covariate effects. For the estimation of model parameters, we develop an expectation maximization algorithm. A detailed simulation study shows that the proposed model outperforms the logistic regression-based and spline regression-based mixture cure models, both in terms of model fitting and evaluating predictive accuracy. An illustrative example with data from a leukemia study is presented to further support our conclusion.

On the parameter estimation of Box-Cox transformation cure model.

We propose an improved estimation method for the Box-Cox transformation (BCT) cure rate model parameters. Specifically, we propose a generic maximum likelihood estimation algorithm through a non-linear conjugate gradient (NCG) method with an efficient line search technique. We then apply the proposed NCG algorithm to BCT cure model. Through a detailed simulation study, we compare the model fitting results of the NCG algorithm with those obtained by the existing expectation maximization (EM) algorithm. First, we show that our proposed NCG algorithm allows simultaneous maximization of all model parameters unlike the EM algorithm when the likelihood surface is flat with respect to the BCT index parameter. Then, we show that the NCG algorithm results in smaller bias and noticeably smaller root mean square error of the estimates of the model parameters that are associated with the cure rate. This results in more accurate and precise inference on the cure rate. In addition, we show that when the sample size is large the NCG algorithm, which only needs the computation of the gradient and not the Hessian, takes less CPU time to produce the estimates. These advantages of the NCG algorithm allows us to conclude that the NCG method should be the preferred estimation method over the already existing EM algorithm in the context of BCT cure model. Finally, we apply the NCG algorithm to analyze a well-known melanoma data and show that it results in a better fit when compared to the EM algorithm.

A time-dependent survival analysis for early prognosis of chronic wounds by monitoring wound alkalinity.

The objective is to determine whether monitoring wound alkalinity between visits may help prognosticate chronic wound healing. The alkalinity of 167 wounds during the first 3 visits was assessed using disposable DETEC® pH. Wounds grouped by frequency of alkaline results were compared by % wound size reduction during each visit and 120-day healing probability. The Cox proportional hazards model for time-dependent variables was used to generate non-healing probability curves, where variables are binary (alkaline/non-alkaline, infection/no infection), categorical (wound type), and continuous (wound area); the response is time to complete wound healing; and the event of interest is complete wound healing in 120 days. Results show that wounds with frequent alkaline results have significantly smaller % size reduction per visit. Logistic regression shows an increase in 120-day healing probability with fewer alkaline results. Survival analysis shows that the instantaneous healing rate of non-alkaline or non-alkaline transitioning wounds is 1.785, 2.925, and 5.908 times that of alkaline or alkaline-transitioning wounds for 1, 2, and 3 alkalinity measurements, respectively. Furthermore, the concordance statistic of each survival model shows that goodness of fit increases with more alkalinity measurements. Overall, frequent wound alkalinity assessments may serve as a novel way to prognosticate wound healing outcomes.

A New Non-Linear Conjugate Gradient Algorithm for Destructive Cure Rate Model and a Simulation Study: Illustration with Negative Binomial Competing Risks.

In this paper, we propose a new estimation methodology based on a projected non-linear conjugate gradient (PNCG) algorithm with an efficient line search technique. We develop a general PNCG algorithm for a survival model incorporating a proportion cure under a competing risks setup, where the initial number of competing risks are exposed to elimination after an initial treatment (known as destruction). In the literature, expectation maximization (EM) algorithm has been widely used for such a model to estimate the model parameters. Through an extensive Monte Carlo simulation study, we compare the performance of our proposed PNCG with that of the EM algorithm and show the advantages of our proposed method. Through simulation, we also show the advantages of our proposed methodology over other optimization algorithms (including other conjugate gradient type methods) readily available as R software packages. To show these, we assume the initial number of competing risks to follow a negative binomial distribution although our general algorithm allows one to work with any competing risks distribution. Finally, we apply our proposed algorithm to analyze a well-known melanoma data.

A wound alkalinity measurement to predict non-healing wound outcomes.

OBJECTIVE: As wound pH could influence wound healing rates, this study examined the alkalinity of the entire wound during patients' follow-up visits to predict the final non-healing outcome. METHOD: Wound alkalinity of patients with diabetic foot ulcers (DFUs), venous leg ulcers, and other wounds during three follow-up visits within a four week period was recorded. All wounds were followed until 12 weeks to confirm that healed wounds did not relapse. The alkalinity of various wounds over multiple visits with varying durations was compared with final wound status to assess whether one-time wound alkalinity measurement could predict non-healing wounds. The effect of wound types, infection, age and sex on such determinations was also studied. RESULTS: A total of 96 patients were included in this study. Based on probability variations of pre- and post-test non-healing outcomes from multiple visits over 12 weeks, second visit assessment gave the highest increase in risk of non-healing for an alkaline test result (+8.0%) and decrease in risk of non-healing for a non-alkaline test result (-19.7%). Moreover, a second visit (7-21 days from first visit) showed a greater change in risk for non-healing based on alkaline and non-alkaline test results (+15.7% and -38.1% respectively), compared with a visit within seven days (+6.3% and -12.5%, respectively). Wound type, infection, age and sex did not affect the prognostic ability of wound alkalinity. CONCLUSION: The results of this study support that a single wound alkalinity measurement during the second visit (7-21 days from first visit) can be used to predict non-healing wounds. Wound alkalinity may be routinely assessed to predict non-healing wounds and to determine whether the wounds are healing as expected following initial treatment.

A two-way flexible generalized gamma transformation cure rate model.

We propose a two-way flexible cure rate model. The first flexibility is provided by considering a family of Box-Cox transformation cure models that include the commonly used cure models as special cases. The second flexibility is provided by proposing the wider class of generalized gamma distributions to model the associated lifetime. The advantage of this two-way flexibility is that it allows us to carry out tests of hypotheses to select an adequate cure model (within the family of Box-Cox transformation cure models) and a suitable lifetime distribution (within the wider class of generalized gamma distributions) that jointly provides the best fit to a given data. First, we study the maximum likelihood estimation of the generalized gamma Box-Cox transformation (GGBCT) model parameters. Then, we use the flexibility of our proposed model to carry out power studies to demonstrate the power of likelihood ratio test in rejecting mis-specified models. Furthermore, we study the bias and efficiency of the estimators of the cure rates under model mis-specification. Our findings strongly suggest the importance of selecting a correct lifetime distribution and a correct cure rate model, which can be achieved through the proposed two-way flexible model. Finally, we illustrate the applicability of our proposed model using a data from a breast cancer study and show that our model provides a better fit than the existing semiparametric Box-Cox transformation cure model with piecewise exponential approximation to the lifetime distribution.

A Fokker-Planck feedback control framework for optimal personalized therapies in colon cancer-induced angiogenesis.

In this paper, a new framework for obtaining personalized optimal treatment strategies in colon cancer-induced angiogenesis is presented. The dynamics of colon cancer is given by a Itó stochastic process, which helps in modeling the randomness present in the system. The stochastic dynamics is then represented by the Fokker-Planck (FP) partial differential equation that governs the evolution of the associated probability density function. The optimal therapies are obtained using a three step procedure. First, a finite dimensional FP-constrained optimization problem is formulated that takes input individual noisy patient data, and is solved to obtain the unknown parameters corresponding to the individual tumor characteristics. Next, a sensitivity analysis of the optimal parameter set is used to determine the parameters to be controlled, thus, helping in assessing the types of treatment therapies. Finally, a feedback FP control problem is solved to determine the optimal combination therapies. Numerical results with the combination drug, comprising of Bevacizumab and Capecitabine, demonstrate the efficiency of the proposed framework.

Predictive evaluation of multicomponent direct compress model tablets by integrating sphere UV-Vis spectroscopy and chemometrics.

BACKGROUND: Control of the pharmaceutical manufacturing process and active pharmaceutical ingredients (API) is essential to product formulation and bioavailability. OBJECTIVE: The aim of this study is to predict tablet surface API concentration by chemometrics using integrating sphere UV-Vis spectroscopy, a non-destructive and contact-free measurement method. METHODS: Riboflavin, pyridoxine hydrochloride, dicalcium phosphate anhydrate, and magnesium stearate were mixed and ground with a mortar and pestle, and 100 mg samples were subjected to direct compression at a compaction pressure of 6 MPa at 7 mm diameter. The flat surface tablets were then analyzed by integrating sphere UV-Vis spectrometry. Standard normal variate (SNV) normalization and principal component analysis were applied to evaluate the measured spectral dataset. The spectral ranges were prepared at 300-800 nm and 500-700 nm with SNV normalization. Partial least squares (PLS) regression models were constructed to predict the API concentrations based on two previous datasets. RESULTS: The regression vector of constructed PLS regression models for each API was evaluated. API concentration prediction depends on riboflavin absorbance at 550 nm and the excipient dicalcium phosphate anhydrate. CONCLUSION: Integrating sphere UV-Vis spectrometry is a useful tool to process analytical technology.

A simplified stochastic EM algorithm for cure rate model with negative binomial competing risks: An application to breast cancer data.

In this article, a long-term survival model under competing risks is considered. The unobserved number of competing risks is assumed to follow a negative binomial distribution that can capture both over- and under-dispersion. Considering the latent competing risks as missing data, a variation of the well-known expectation maximization (EM) algorithm, called the stochastic EM algorithm (SEM), is developed. It is shown that the SEM algorithm avoids calculation of complicated expectations, which is a major advantage of the SEM algorithm over the EM algorithm. The proposed procedure also allows the objective function to be split into two simpler functions, one corresponding to the parameters associated with the cure rate and the other corresponding to the parameters associated with the progression times. The advantage of this approach is that each simple function, with lower parameter dimension, can be maximized independently. An extensive Monte Carlo simulation study is carried out to compare the performances of the SEM and EM algorithms. Finally, a breast cancer survival data is analyzed and it is shown that the SEM algorithm performs better than the EM algorithm.

A non-contact device for fast screening of wound infections.

Screening for wound infection relies on the expertise of the provider. Clinical diagnosis of infections based on wound swab/biopsy results often takes a few days and may not assess the full wound. There is a need for a non-invasive tool that can quickly and accurately diagnose wound infection. Leukocyte esterase strips are used to identify various infectious diseases. However, it is not clear whether infected wounds also have elevated leukocyte esterase activities as compared with non-infected wounds. To achieve the objective, a device was developed to detect elevated leukocyte esterase activities in wounds by measuring wound exudates adsorbed onto wound dressings in 3 minutes. The efficacy of the device in assessing leukocyte esterase activities across various chronic wounds was tested. Such measurements were unaffected by the type of underlying wound dressing. By correlating the device outputs with clinical adjudication of infection, we found that this device had high positive predictive values for diagnosing wound infection in a wide variety of chronic wounds. In addition, a positive device output increases the probability of detecting infected wounds, while the negative device output reduces the probability of detecting infected wounds. This rapid non-contact and disposable diagnostic tool may serve as a rapid and accurate indication of infection in the chronic wound.

Stochastic EM algorithm for generalized exponential cure rate model and an empirical study.

In this paper, we consider two well-known parametric long-term survival models, namely, the Bernoulli cure rate model and the promotion time (or Poisson) cure rate model. Assuming the long-term survival probability to depend on a set of risk factors, the main contribution is in the development of the stochastic expectation maximization (SEM) algorithm to determine the maximum likelihood estimates of the model parameters. We carry out a detailed simulation study to demonstrate the performance of the proposed SEM algorithm. For this purpose, we assume the lifetimes due to each competing cause to follow a two-parameter generalized exponential distribution. We also compare the results obtained from the SEM algorithm with those obtained from the well-known expectation maximization (EM) algorithm. Furthermore, we investigate a simplified estimation procedure for both SEM and EM algorithms that allow the objective function to be maximized to split into simpler functions with lower dimensions with respect to model parameters. Moreover, we present examples where the EM algorithm fails to converge but the SEM algorithm still works. For illustrative purposes, we analyze a breast cancer survival data. Finally, we use a graphical method to assess the goodness-of-fit of the model with generalized exponential lifetimes.

Predictive evaluation of powder X-ray diffractograms of pharmaceutical formulation powders based on infrared spectroscopy.

BACKGROUND: To ensure quality and stability, monitoring systems are recommended to analyze pharmaceutical manufacturing processes. OBJECTIVE: This study was performed to predict powder X-ray diffraction (PXRD) patterns of formulation powders through attenuated total reflectance (ATR)-infrared (IR) spectroscopy in a nondestructive manner along with chemometrics. RESULTS: Caffeine anhydrate, acetaminophen, and lactose monohydrate were grinded at six weight ratios. The six sample groups were evaluated using ATR-IR spectroscopy and PXRD analysis. Partial least squares models were constructed to predict the PXRD intensities of the samples from the ATR-IR spectra. The prediction accuracy on the prepared PLS regression models was as high as R2 = 0.993. CONCLUSIONS: Linear relationships were obtained between the prediction data set and reference PXRD intensity at each degree. 2D PLS regression coefficient analysis enabled the analysis of the correlation between PXRD patterns and IR spectra.

A Device to Predict Short-Term Healing Outcome of Chronic Wounds.

Objective: While myriads of studies have suggested that a survey of wound pH environment could indicate wound healing activities, it is not clear whether wound alkalinity can be used as a prognostic indicator of nonhealing wounds. Currently available systems cannot reliably assess the pH environment across wounds, which is the objective of this study. Approach: A disposable device, DETEC® pH, was developed and characterized on its ability to map wound alkalinity by pressing a freshly recovered wound dressing against its test surface. By comparing the wound's alkalinity and size reduction rates (∼7 days) following pH measurement, we assessed the capability of wound alkalinity to prognosticate subsequent short-term wound size reduction rates. Results: The device had high accuracy and specificity in determining the alkalinity of simulated wound fluids soaked onto wound dressing. The type of wound dressing type had an insignificant effect on its detection sensitivity. Upon testing discarded wound dressings from human patients, the device quickly determined alkaline and acidic wounds. Finally, statistical analyses of wound size reduction rates in wounds with various alkalinities confirmed that wound alkalinity has a strong influence on, at least, short-term wound healing activity. Innovation: Without directly contacting the patient, this device provides a quick assessment of wound alkalinity to prognosticate immediate and short-term wound healing activities. Conclusion: DETEC® pH may serve as a prognosis device for wound care specialists during routine wound assessment to predict wound healing progress. This information can assist the decision-making process in a clinical setting and augur well for chronic wound treatment. DETEC® pH can also be used as an aid for home health care nurses or health care providers to screen nonhealing wounds outside clinics.

Probing Spin-State Switching in Fe(phen)2(NCS)2 Thin Film Nanocrystals on Different Substrates by Electrical Conductivity Measurements.

Spin-state switching mechanism is investigated by measuring the temperature of the electrical conductivity of spin crossover (SCO) material Fe(phen)2(NCS)2 thin films grown on glass, quartz and silicon substrates. The morphology characterized by scanning electron microscopy, clearly reveals the growth of thin films of thickness ~300 nm comprising of nanocrystals, size and distribution of which is dependent on the nature of substrates. The film on quartz is found to have the most uniform growth of nanocrystals of size ~22 nm with a homogeneous distribution. All the films retain the orthorhombic crystal structure as that of bulk with slight distortions in lattice plausibly arising out of the strain. Spin state switching between LS and HS is clearly revealed by the hysteresis loop observed in the temperature dependence of the electrical conductivity in its heating and cooling cycle. The critical temperature of transition between HS and LS states is found to be 162 K, 193 K and 217 K for film on glass, quartz and Si respectively. Film on quartz is found to exhibit a wide hysteresis loop of width ~60 K while that of on silicon exhibits higher transition temperature with narrow hysteresis loop ~14 K. The results are found to be quite inspiring to tune the SCO characteristics to develop molecular switch and memory devices close to room temperature.

Impact of heat on metabolic and hemodynamic changes in transcranial infrared laser stimulation measured by broadband near-infrared spectroscopy.

Transcranial infrared laser stimulation (TILS) has shown effectiveness in improving human cognition and was investigated using broadband near-infrared spectroscopy (bb-NIRS) in our previous study, but the effect of laser heating on the actual bb-NIRS measurements was not investigated. To address this potential confounding factor, 11 human participants were studied. First, we measured time-dependent temperature increases on forehead skin using clinical-grade thermometers following the TILS experimental protocol used in our previous study. Second, a subject-averaged, time-dependent temperature alteration curve was obtained, based on which a heat generator was controlled to induce the same temperature increase at the same forehead location that TILS was delivered on each participant. Third, the same bb-NIRS system was employed to monitor hemodynamic and metabolic changes of forehead tissue near the thermal stimulation site before, during, and after the heat stimulation. The results showed that cytochrome-c-oxidase of forehead tissue was not significantly modified by this heat stimulation. Significant differences in oxyhemoglobin, total hemoglobin, and differential hemoglobin concentrations were observed during the heat stimulation period versus the laser stimulation. The study demonstrated a transient hemodynamic effect of heat-based stimulation distinct to that of TILS. We concluded that the observed effects of TILS on cerebral hemodynamics and metabolism are not induced by heating the skin.

Expectation Maximization Algorithm for Box-Cox Transformation Cure Rate Model and Assessment of Model Misspecification Under Weibull Lifetimes.

In this paper, we develop likelihood inference based on the expectation maximization algorithm for the Box-Cox transformation cure rate model assuming the lifetimes to follow a Weibull distribution. A simulation study is carried out to demonstrate the performance of the proposed estimation method. Through Monte Carlo simulations, we also study the effect of model misspecification on the estimate of cure rate. Finally, we analyze a well-known data on melanoma with the model and the inferential method developed here.

Likelihood inference for COM-Poisson cure rate model with interval-censored data and Weibull lifetimes.

In this paper, we consider a competing cause scenario and assume the number of competing causes to follow a Conway-Maxwell Poisson distribution which can capture both over and under dispersion that is usually encountered in discrete data. Assuming the population of interest having a component cure and the form of the data to be interval censored, as opposed to the usually considered right-censored data, the main contribution is in developing the steps of the expectation maximization algorithm for the determination of the maximum likelihood estimates of the model parameters of the flexible Conway-Maxwell Poisson cure rate model with Weibull lifetimes. An extensive Monte Carlo simulation study is carried out to demonstrate the performance of the proposed estimation method. Model discrimination within the Conway-Maxwell Poisson distribution is addressed using the likelihood ratio test and information-based criteria to select a suitable competing cause distribution that provides the best fit to the data. A simulation study is also carried out to demonstrate the loss in efficiency when selecting an improper competing cause distribution which justifies the use of a flexible family of distributions for the number of competing causes. Finally, the proposed methodology and the flexibility of the Conway-Maxwell Poisson distribution are illustrated with two known data sets from the literature: smoking cessation data and breast cosmesis data.

Quantification of Pharmaceutical Compounds Based on Powder X-Ray Diffraction with Chemometrics.

We propose an approach for the simultaneous determination of multiple components in pharmaceutical mixed powder based on powder X-ray diffraction (PXRD) method coupled with chemometrics. Caffeine anhydrate, acetaminophen and lactose monohydrate were mixed at various ratios. The samples were analyzed by PXRD method in the ranges of 2θ=5.00-30.0 and 35.0-45.0 degrees. Obtained diffractograms were analyzed by conventional peak intensity method, multi curve resolution (MCR)-alternating least squares (ALS) method and partial least squares (PLS) method. Constructed PLS models can most accurately predict the concentrations among different methods used. Each regression vector of PLS correlates not only to the compound of interest but also to the coexisting compounds. The combination of PXRD and PLS methods is concluded to be powerful approach for analyzing multi components in pharmaceutical formulations.