Response Surface Methodology-A Statistical Tool for the Optimization of Responses - Juniper Publishers

 Addiction & Rehabilitation Medicine - Juniper Publishers

Abstract

Experimentation plays a significant role in Science and Technology, which is an application of handling experimental units, and then the determination of one or more responses from that. In every experiment, some inputs (x) transform into results that have one or more observable response variables (y). Therefore, from the results, the conclusion can be drawn by experiment. For obtaining an unbiased conclusion a researcher needs to plan & design the experiment and analyze the results obtained. When dealing with a continuous range of values then the true connection between y and x’s might not be known. In such cases, statistical analysis like Response Surface Methodology plays a crucial role, which is a combination of statistical and mathematical techniques useful for designing and analyzing problems where a response of interest is affected by several variables, and the objective is to optimize this response. It generally helps in reviewing the empirical relationship among one or more measured responses and various independent variables in the form of a polynomial equation. Mapping of those responses associated with the experimental domain helps in generating an optimized method.

Introduction

Response Surface Methodology [1-9] (RSM) plays a crucial role, which is a combination of statistical and mathematical techniques useful for designing and analyzing problems where a response of interest is affected by several variables, and the objective is to optimize this response. It generally helps in reviewing the empirical relationship among one or more measured responses and various independent variables in the form of a polynomial equation. Mapping of those responses associated with the experimental domain helps in generating an optimized method.

The wide applications of RSM are in particular situations where numerous input variables strongly impact some performance measures of the method. Thus, the performance measures are called the response. The input variables are termed independent variables, and they are elements of the control of the researcher. The arena of RSM comprises the experimental approach for exploring the range of the independent variables, an empirical statistical model to create a suitable relationship between the results and the independent variables, and optimization of the methods with suitable independent variable values that yield desirable values of the response.

In maximum RSM conditions, the relationship between the independent variables and the response is unknown. Thus, the initial step of RSM is to identify a suitable guess for the right functional relationship between the independent variables and the responses. Generally, a low-order polynomial equation of the independent variables is employed. If the response is well demonstrated by a linear function of the independent variables, then the opting function is the first-order model [10].

If the system is with curvature, then a higher degree polynomial must be followed, for example, the second-order model [11-12].

Steps involved in designing of an experiment

a. Consider variables in the experimental criteria and notify how they are related to each other

b. Write a precise, testable hypothesis for the experiment

c. Design experimental actions to operate independent variable

d. Allocate subjects to groups

e. Plan how the dependent variable can be measured

Experiments are context-dependent, and apt experimental design will affect all of the considerations of the experimental system to yield data that is valid and relevant for research.

Types of RSM [13]

Standard Full 2^nd Order Polynomial Model

It is starting point for many design points, which is based on a modified quadratic equation where each output parameter is a quadratic function of the input variables. The result obtained from this method is satisfactory when changes in output variables are made gently.

In this model, write the output parameter function in terms of input variable as given below, where, f is a quadratic polynomial function:

output = f (inputs)

Kriging Model

It is a multi-dimensional interpolation model that associates a polynomial model analogous to one of the standard response levels, which is stated as a comprehensive model of the design space, plus a detailed local deviation that can intercept design points of the model.

The method denotes the output parameter as a function of input variables as given below:

output = f (inputs) + z(inputs)

Where f is a quadratic polynomial function and z is the deviation term

Meanwhile, this model fits the contact surfaces at all design points, so it will always give appropriate goodness of fit criterion. Which has improved results than the standard response surface model, if the output elements are stronger and nonlinear. The major disadvantage is that fluctuations can occur on the response surface. Figure 1 shows the behavioral pattern of the function related to this model. where the behavior of the estimated function comprises a general function (f) combined with a local function (z).

Non-Parametric Regression Model

It tends to be a general class of RSM model, where the epsilon (Ԑ) tolerance forms a fine covering around the output response surface and spreads around it. This covering space should comprise all the design sample points. Instability regression is created to estimate the regression function directly, which means instability regression can directly study the effect of independent variables on a dependent parameter without notifying a particular function to create the relationship between the independent and dependent variables. Figure 2 shows the behavioral outline of the function related to the non-parametric regression model. The behavior of the predictable function consists of a principal response surfaces with a margin of tolerance on both side.

Neural Network Model

It represents a mathematical practice based on natural neural networks in the human brain, which connects every input variable to weights by arrows. Which can find the inactive or active hidden functions, that are the threshold elements allows the output function to connect or disconnect based on a set of their input variables. Finally, every time the procedure is repeated. It adjusts these weight functions to diminish the error between the response levels with the design points. Figure 3 shows the behavioral algorithm of the cellular network model, which consists of input variables, hidden functions, and output functions.

Sparse Grid Model

It is a type of adaptive response surface, which can continuously correct itself automatically. It usually needs extra design points than other methods. The capability of it is that it adjusts the design points only in the directions that requires. For which, it requires less design points to complete the same quality response level. This model is also fit for cases that contain multiple discontinuities.

Methods of RSM [14]

RSM is often a step-wise procedure where the response surface points remote from the optimum. This method focuses on the travel from the existing point to the optimum point with a sequence.

There are two methods for getting the optimum point:

i. The method of steepest ascent

ii. The method of steepest descent

i. Method of Steepest Ascent: It is a course of moving consecutively in the direction of the extreme increase in the response to the optimum response, which is indicated in Figure 4.

ii. Method of steepest descent: It is a course of moving consecutively to minimize the response, which is indicated in (Figure 5).

Types of response surface modeling [15-16]

i. Central Composite Design (CCD)

ii. Box-Behnken Design (BBD)

i. Central Composite Design (CCD)

The central composite design is the most widespread and adaptable response surface design and maximum researchers pick this design. The central composite design was published by Box and Wison in the year 1951. A central composite design always has 2 levels and k influencing factors. It comprises axial points and center points. Initially, produce a 2^k factorial or a 2^k-p fractional factorial design, and then affix extra runs denoted to as axial points (Figure 6). The 2^k and 2^k-p part of the design permits to fit of first-order terms and relations. Similarly, the axial points help to the extra level required to fit the second-order model.

ii. Box-Behnken Design (BBD)

It is the famous response surface method for a three-level factor, suitable for the second-order model to the response. In 1960, Box and Behnken were first established this method. It is a blend of two-level factorial designs with incomplete block designs. The advantage of this design is it does not contain corner points, which means any points at the out of the cubic region formed by the two-level factorial level combinations (Figure 7).

Data analysis

After finishing the experimental work by a suitable RSM design, the output responses may be modelled and the data is fitted with polynomial equation to find the relation between the responses and factors studied. ANOVA is used to test the statistical significance of the model. ANOVA allows the decision of inclusion or exclusion of coefficient of linear terms, interaction terms and quadratic terms in the model based on p-value. If the p-value is less than 0.05 means the response is affected by the varying levels of the input parameters, and that terms have to include in the regression model or else if p-value is greater than 0.05 declares no effects of varying levels of input factors on response, and that should be eliminated from the regression model [17].

Multiple regression model can be adjusted by coefficient of determination values like R², adjusted R² and predicted R². The variation of output response based on the input factors will be explained by R² value. Addition of new terms to the regression model will increases the R² value. Adjusted R² is the modified version of R², which helps in the adjustment of terms in the regression model, adjusted R² get increased, if the added terms improve the model. Predicted R² indicates how well a regression model predicts output responses for new observations and is calculated by removing each observation from the data set systematically. R² is always higher than adjusted and predicted R² values. The difference between the predicted and adjusted R² values should be less than 0.2 in order to obey the fit statistics. Adequate precision measures signal to noise ratio and a ratio of greater than 4 is desirable which tells that the model can be used to navigate the design space. When the error provided by the regression model lack of fit is significantly lower than a random pure error (p-value > 0.05), it indicates that the regression model is well fitted. Lake of fit data must be non-significant and it can be estimated only when replicas usually for centra point are included in the experimental design [18].

Diagnostic plots [19]

a. Normal probability plot: These plots indicate whether the residuals follow normal distribution represented by a straight line. S-shaped curve indicates that transformation of response is necessary to provide better analysis.

b. Residual Vs. Predicted plot: A graph is plotted between residuals and predicted response values in ascending order denoted by a random scatter.

c. Residuals Vs. Run: This is a plot of residuals versus experimental run order denoted by a random scatter.

d. Predicted Vs. Actual: The plot is drawn between predicted versus actual response values.

e. Box-Cox plot for power transforms: This plot is for power transformation based on the best λ value and if a 95% confidence interval around this λ includes 1 then transformation is not recommended.

f. Residual Vs. Factor: This is a plot of residuals versus any factor of choice denoted by a random scatter. If the curvature effect is seen it indicates that the contribution of the independent factor is not taken into consideration.

g. Model graph [20]: To interpret the selected model various graphs are provided in the design expert software. For factorial designs, the most commonly used graphs are one factor, interaction, and cube. For response surface and mixture designs 2D Contour and 3D Surface plots are used.

h. Perturbation plot: These plots compare all factor effects at a particular point in design space and the response is plotted by varying only 1 factor over its range and keeping all other factors constant. The steepest slope or curvature indicates the response is sensitive to that factor and the flat line indicates the response is not affected by that factor.

i. One factor effects plot: These plots show linear effects by changing the levels (-1 : low, +1 high) of a factor and predicting the responses.

j. Interaction graph: These plots appear as two nonparallel lines which indicates that one factor effect depends on another factor level.

k. Contour plot: It is a 2D representation of response plotted against numeric factor combination which shows the relationship between responses.

l. 3D Surface plot: It is a contour plot projection which gives shape along with contour and color.

m. Cube plot: It shows the predicted values from the coded model for the combinations of -1 and +1 levels of any 3 factors.

Optimization by desirability functions approach

This approach finds a factor setting that provides the most desirable response. Each response is assigned a number between 0-1 for a completely undesirable to desirable or ideal response value. Finally overall desirability is obtained by combining the individual response desirabilities using a geometric mean [21].

Conclusion

RSM can be used for the approximation of both experimental and numerical responses. Two steps are necessary, the definition of an approximation function and the design of the plan of experiments. The success of RMS depends on an estimation of y at different locations in the response surface. Therefore, the experimenter can draw a conclusion about whether the system contains optimum or improvement in response. Before any experimenter starts the analysis of the response surface, the application of RMS first begins with investigation of factors or variables. In order to obtain an efficient experiment, unimportant independent variables need to be separated from important ones. One should never start an analysis of the surface until significant factors are identified. After that, the response surface study can start. Four steps for response surface analysis are (1) perform a statistically designed experiment, (2) estimate the coefficients in the response surface equation, (3) check on the adequacy of the equation (via a lack-of-fit test), and (4) study the response surface in the region of interest. Besides statistical and mathematical techniques the graphical representation of the response surface is also helpful in finding answers to problems. Due to broader applications in real-word problems, RMS will continue to attract statisticians, engineers, and scientists in order to develop, improve, and optimize new or existing products and processes.

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Addiction Needs Brain Neuroscience, Gene Sequencing, Research on Pharmaceutical Influences on Dopamine, Serotonin and the Inter Communication of the Billions of Microbes in the Stomach on the Brain to Improve Recovery Outcomes - Juniper Publishers

 Addiction & Rehabilitation Medicine - Juniper Publishers  

Opinion

The number of persons afflicted with addiction is growing with an estimated 40 Million diagnosed patients and another 80 million risky substance users. One third of America. It is costing America an estimated $486 Billion annually. Most of the money is going to the Judicial system and not treatment or research on better treatments. An estimated 600,000+ die from addiction annually (more than the Vietnam war). It causes 71 other diseases of all kinds. And less than 10% of people with addiction fail to ever get help for it. In 2010, the United States spent $43.8 billion to treat diabetes which affects 25.8 million people, $86.6 billion to treat cancer which affects 19.4 million people and an estimated $107.0 billion to treat heart conditions which affect 27.0 million people, but only $28.0 billion to treat addiction which affects 40.3 million people.Addiction is still a highly stigmatizing illness and is still perceived by most people even medical professionals as a character defect, moral weakness, or inability to self-control. Organized Medicine has done little training of interns and residents about the disease (some improvement in recent years). It’s the least likely health category to be asked about in annual physicals as is the brain itself. How often have you ever had a physician ask you when is the last time you had your head examined? More often that phrase is meant to be either funny or denigrating to whom its directed. Ironically, it’s the single most important organ in the body. You can live without most every other organ even your heart (which can be replaced). You cannot get a new brain. That is in part the result of the fact that the brain is the single most important part of your body. And it is also the single most complicated thing in the entire universe as it has more connections in its cerebral folds than stars in the Milky Way Galaxy.

a) Over 100 billion nerve cells

b) More connections than stars

c) Information travels ~ 268 miles/hour

d) Brain is 2% of body’s weight, but uses 20-30% of your calories

e) Loses an average of 85,000 cells/day

Columbia calculated that risky substance use- and addiction-related spending accounted for 10.7 percent of federal, state and local spending, and that for every dollar federal and state governments spent, 95.6 cents went to pay for the consequences of substance use; only 1.9 cents was spent on any type of prevention or treatment. The taxpayer tab for government spending on the consequences of risky substance use and addiction alone totals almost $1,500 a year for every person in America. Nearly one- third (32.3 percent) of all hospital inpatient costs are attributable to substance use and addiction. So, what is addiction anyway and how best to treat it. Many theories have been advanced over the decades. One thing we now know is that the basic outline of an inpatient standard 4-6 week stay in a treatment program with an admixture of cognitive testing; individual therapy, group therapy, AA or other self-help group, drug testing, family therapy, etc. (with many additions like yoga, equine therapy, gourmet nutritious meals, etc.) about 60 % of patients discharged will relapse in six months or longer. Our outcome success rate has been stuck at that general level since 1980. There has been little real progress with the exception of interventions aimed at the brain. That is because addiction is a complex brain disorder. There is something going on in the brain which is still not completely understood. No small wonder in that the brain again is far more complicated than your heart, lungs, stomach, kidneys, etc. Some research has led to progress in the treatment in the brain though it still needs further work and evaluation. Here is a sample of more scientifically validated therapies aimed specifically at the brain itself. This new type of treatment is aimed at impacting the brain itself and is referred to as Medication Assisted Treatment (MAT). Its less time intensive, less costly and does interfere with dopamine reception in the brain in different ways. Dopamine is primarily responsible for the euphoric effect one gets when drinking or using drugs. But the brain is still vastly more complicated than taking a pill or injection to cure addiction. It appears to be a first step to assist the patient, however. Next, we need to look at some great research on identical twins raised apart. Here the data is pretty clear that such twin pairs have a high probability of becoming addicted to alcohol or drugs regardless of their upbringing or location. In other words, identical twin with a specific combination of 89 genes in their DNA have between a 40%-75% probability of becoming addicted based on their genes. A simple way to think about this is that a person with normal genes (not the 89 that appear to predispose a person) can say drink a 12-ounce beer with little effect while the person with those 89 genes has a 4X euphoric effect. So, seeking to better understand what allows those 89 genes to express is an area of future research. Also why do drugs like cocaine have a much higher rate of addiction in identical twins. Likely the power of cocaine on dopamine and a sense of euphoria is a factor that needs to be better understood. America’s approach to addressing risky substance use and providing addiction treatment has evolved outside of the mainstream public health and medical systems. As a result:

a. Most primary providers of intervention and treatment for risky substance use and addiction do not have the requisite training or qualifications to implement the existing range of evidence-based practices and face many organizational and structural barriers to providing services;

b. Most health professionals do not implement evidence-based addiction care practices;

c. Performance and outcome measures that should be a routine part of quality assurance in mainstream medicine are limited and rarely implemented in addiction treatment;

d. The pharmaceutical industry lacks the incentive to develop new and effective pharmaceutical interventions for addiction treatment; and

e. Insurance coverage for evidence-based intervention, treatment and disease management is inadequate. Because of the vast chasm between the health care system and approaches to preventing risky substance use or treating addiction, medical professionals fail to address risky substance use or addiction or take responsibility for intervention or treatment, risky substance use is addressed primarily in terms of its consequences and addiction treatment providers are not held to the same standards as providers of mainstream medical care. The ultimate goal we must achieve is to deploy Neuroscience and genetics with evidence-based interventions if we are to find a more successful outcome for our patients.

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The Opioid Epidemic - A Generation in Crisis- Juniper Publishers

The Opioid Epidemic - A Generation in Crisis by Oliver Morgan in Global Journal of Addiction & Rehabilitation Medicine - Juniper Publishers

On March 29, 2017 President Donald Trump tapped Governor Chris Christie of New Jersey to lead a commission fighting the opioid addiction crisis. Not a bad choice, as political appointments go. Christie’s heartfelt words about addiction went viral in 2015 during the presidential campaign and won him praise. In his last year as governor, Christie has pursued enlightened policies to help stem the tide of opioid and other drug addiction in New Jersey. He has signed legislation limiting first-time narcotic prescriptions to five days’ worth of opioids, and requiring health insurers to cover at least a minimum of six months of substance abuse treatment.

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Substance Use and Mental Health Treatment Retention among Young Adults - Juniper Publishers

Substance Use and Mental Health Treatment Retention among Young Adults by Siobhan Morse in Global Journal of Addiction & Rehabilitation Medicine - Juniper Publishers

In Western and European cultures where marriage and parenthood are increasingly delayed to the late twenties and early thirties, a distinct developmental stage between adolescence and adulthood has been described as “emerging” or “young” adults [1]. As these individuals make the transition from adolescence to adulthood, when parental or authoritative and protective influences weaken, they begin to explore possible life directions in love, work, and worldviews and a new level of social freedom and responsibility is experienced. The period of emerging adulthood is filled with both opportunities and challenges. Explorations of love, work, and worldviews are fraught with the possibility of romantic rejection, failure to find work that is satisfying and meaningful, and disillusionment with the world’s inequities and realities [1]. Developmental theory suggests that these “younger adults” have less social control and exercise higher levels of impulsivity than their older counterparts.

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Parents with Psychosis: Impact on Parenting & Parent-Child Relationship- A Systematic Review - Juniper Publishers

Parents with Psychosis: Impact on Parenting & Parent-Child Relationship- A Systematic Review by Begum Engure in Global Journal of Addiction & Rehabilitation Medicine - Juniper Publishers

Psychosisis a mental state that is defined as “A severe mental illness, derangement, or disorder involving a loss of contact with reality, frequently with hallucinations, delusions, or altered thought processes, with or without a known organic origin.’’ [1-4]. A psychotic experience or episode is diagnosed when one or more of the following symptoms is present: delusions, hallucinations, disorganized speech (e.g., frequent derailment or incoherence), grossly disorganized or abnormal motorbehaviour (including catatonia) and negative symptoms [1]. Thus, among all, the most common symptoms of psychosis are delusions and hallucinations [1-4].“Psychosis is a term used to cover a range of mental illnesses where psychotic symptoms typically occur.’’ [2]. The primary disorders comprise schizophrenia, schizoaffective disorder, delusional disorders, schizophreniform disorder and brief psychotic disorder. On the other hand, it can be attributable to more general mental health conditions, personality disorders, psychoactive substance or mood disorder for instance major depression or bipolar disorder [2-4]. Schizophrenia is the most common psychotic disorder and it occurs at the same rates across women and men. Thus, as it’s assumed that women and men are affected by psychosis to the same extent, the same holds true for parents (either mothers or fathers).

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E-Cigarettes: Risk Assessment and Possible uses for Patients with Severe COPD - An Update (GJARM) - Juniper Publishers

E-Cigarettes: Risk Assessment and Possible uses for  Patients with Severe COPD - An Update by Thomas Hering in GJARM - Juniper Publishers

Taking market data as a basis, e-cigarettes continue to enjoy major success [1]. Topulmonologists it falls to assess this development, to advise patients adequately and if appropriate to support their use. Even though for long-term risk assessment the state of information is still unsatisfactory, their use has become increasingly established. The clearest statement has been that of the Public Health Authority of the British government: this clear statement published 2015 on e-cigarettes classified their global risk as extremely positive compared to tobacco cigarettes. The risk from consumption of e-cigarettes is assessed as one twentieth of the risk of tobacco cigarettes [2]. According to this, in a hypothetical world where only e-cigarettes were consumed instead of tobacco cigarettes, after the dropping of tobacco-related morbidity and mortality – the mortality would drop by 95%. Instead of the now roughly120 thousand tobacco-related deaths eg. in Germany [3], we would be left with only 6000 “e-cigarettes-deaths.” That is according to the hypothesis, which speaks for itself

But how should pulmonologists classify their use in consultations, how should they advise patients?

Two significant arguments against e-cigarettes state that they constitute

1. A potential gateway drug for youth…
2. A potential risk of cancer from e-cigarette substances, even if it is less 

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