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BFS Statistical Analysis A Statistical Analysis of Benign Fasciculation Syndrome (BFS) Patrick Bohan PO Box 331 109 Raven Way Buena Vista, Colorado, USA 719-966-5167 pbohan1@gmail.com Abstract: Defining and understanding neurological disorders has been a medical mystery. Benign Fasciculation Syndrome (BFS) is one such disorder. BFS is sometimes referred to as Peripheral Nerve Hyperexcitability (PNH). BFS or PNH is a neurological disorder and its cause is not entirely understood, but it theorized that the cause may stem from an imbalance between potassium and sodium at the nerve endings. This imbalance is what causes involuntary impulses that consequently stimulate the nerve endings causing them to fire and twitch. Other BFS symptoms include muscle fatigue, cramps, pins and needles, muscle vibrations, headaches, itching, sensitivity to temperatures, numbness, muscle stiffness, muscle soreness and pain. Like most neurological disorders, there is no cure for BFS. The purpose of this writing is to 1 BFS Statistical Analysis better define and understand the relationship between BFS symptoms, body parts affected by BFS, the potential causes of BFS, and potential remedies for BFS. To accomplish this task, a survey was conducted and data was obtained from 125 people who have been diagnosed with BFS or have BFS like symptoms. The data was analyzed using a simple statistical analysis to find the mean, median, mode, standard deviation, variance, range, percentile rank, skewness, standard error, and coefficient of variance for each symptom, body part affected, and potential remedy. The data was also modeled using a linear regression analysis to determine if there is correlation between symptoms, potential causes or triggers, body parts affected by BFS, and potential remedies. Sources of Information: Since there are few medical publications on BFS, I rely on information posted by fellow BFS sufferers on two user sites. I only used information in this writing that has been corroborated by a multitude of BFS sufferers. After all, the people suffering from BFS are obviously the experts on the syndrome. The internet user sites are listed below: Facebook: https://www.facebook.com/#!/groups/88467288815/ Internet: http://www.nextination.com/aboutbfs/ 2 BFS Statistical Analysis Background: BFS sufferers live in fear because similar symptoms can be found in other crippling and deadly disorders such as Parkinson Disease, Amyotrophic Lateral Sclerosis (ALS), Multiple Sclerosis (MS), and even brain tumors. Because of this, many BFS patients have been forced to undergo advanced medical testing including Magnetic Resonance Imaging (MRI) performed on the brain as well as an Electromyography (EMG) to rule out other neurological disorders. Anyone with BFS, or doctors that have studied BFS, will tell you that “benign” is a bad word to describe the disorder. People may not die from BFS, but it can be debilitating. In fact, many BFS sufferers have similar symptoms to other neurological disorders including Nueromyotonia (NMT), Benign Cramp Fasciculation Syndrome (BCFS), fibromyalgia, Reflex Sympathetic Dystrophy (RSD), stiff person syndrome, continuous muscle fiber activity, continuous motor nerve discharges, and Isaac Syndrome. Many remedies attempted to relieve BFS symptoms are exactly the same as those remedies used for NMT, BCFS, RSD and other neurological disorders. At this time there is no evidence that BFS sufferers are any more likely to acquire other more serious neurological disorders, such as ALS or MS, than any “normal” person. Purpose: 3 BFS Statistical Analysis Most BFS sufferers have been to multiple general practitioners and neurologists looking for answers but have failed to receive any logical explanations. Since BFS is benign there are no or very few studies on the disorder and therefore, doctors do not have any answers. After each doctor visit the medical files of BFS sufferers are put in a file cabinet and locked away. How is this going to find a cure for BFS? It will not! I have also come to realization that doctors are not necessarily the best mathematicians to find solutions by comparing and reviewing data (conversely, I do not understand medicine as well as doctors). In fact, since doctors do not compare the medical records of people with similar ailments (I am not blaming doctors because I realize they may not have the tools to accomplish this task), they treat each patient like a guinea pig using a trial error approach to find a drug regimen that may work to alleviate some symptoms. And yes, what works for one person afflicted with BFS may not necessarily work for another person afflicted with BFS, so it is hard to pin point a treatment regimen for BFS sufferers. If, on the other hand, doctors were supplied the results of this study, they would better understand a starting point to treat their patients. For instance, the results indicate that people whose BFS symptoms get worse due to a sickness will have more success using benzodiazepine drugs to alleviate symptoms than other drug classifications. However, benzodiazepine drugs are not 4 BFS Statistical Analysis as helpful in patients who believe their symptoms get worse due to stress – anti-convulsants may work better. We live in a verbal society, but numeric analysis is needed to solve the complex problems and mysteries of life. Having doctors understand these differences for treating BFS would be one purpose for writing this paper. Therefore, I created a survey to anonymously obtain the medical records of BFS sufferers into one location so we can statistically analyze the data to better define and understand the ailment. I completely understand that scientists, doctors, and researchers are spending most of their time trying to solve Parkinson’s disease, ALS, and MS since these diseases are, without question, much worse. Once there are cures for these diseases, then it is possible that cures for BFS could follow shortly afterwards. However, it is debatable as to whether or not this approach to solving the mysteries of neurological disorders is the best or most logical. As an engineer, I saw many projects fail because we tried to design products that incorporated too many features. This created many design complications and ultimately these projects failed. On the other hand, multiple products that focused on particular features were more successful, and over the course of time the features can eventually be incorporated into one product (for example - the phone camera). This approach to problem solving saved the company both in cost and time to market. The same 5 BFS Statistical Analysis can be said of medicine – maybe it makes more sense to focus on less complicated disorders such as BFS or RSD and apply what is learned to more complicated neurological disorders such as ALS and MS. This seems to be a fundamental issue when trying to solve problems (in my opinion) – everyone wants to hit a home run instead of making small incremental advances, regardless of the profession. Hopefully, the analysis included in this paper will provide one of those small incremental advances in not only understanding BFS, but the mysteries of all neurological disorders. The Survey: A survey was created in Google Docs and can be found at the following link: https://spreadsheets.google.com/spreadsheet/viewform?hl=en_US&au thkey=CJvBgaQM&formkey=dElCQkFBRWlvY1ZSTThKTmNsbEg4d0E6M Q#gid=0 I will keep the survey open indefinitely with the hope that we can continue to grow the sample size and therefore, better understand the disorder. I will periodically update the data on my website (links to specific types of data are listed throughout this paper). 6 BFS Statistical Analysis The Survey can also be reached from my BFS webpage: http://patrickbohan.home.bresnan.net/BFS.htm. Click on the link “BFS Survey”. Data: The excel data file for all 125 responses can be found on my BFS website: http://patrickbohan.home.bresnan.net/BFS.htm. Click on the link “Survey Data” and open the first tab titled “BFS”. This is the data file that will be statistically analyzed except when remedy or treatment variables are being analyzed. I use the data on the “BFS No Zero” tab to statistically analyze remedy or treatment variables (this will be explained in this text). Data points with brackets “[]” around them were identified as outliers because these responses were outside plus or minus 3 standard deviations from the mean for all tested variables. Most outliers were determined from the parameters: Symptom Averages, Body Part Averages, and or Remedy Averages. A handful of other outliers were determined by running a statistical analysis on each variable. Outliers are omitted from any statistical analysis. Data Summary: 7 BFS Statistical Analysis The statistical analysis data for each parameter can be found at: http://patrickbohan.home.bresnan.net/BFS.htm. Click on the link “Survey Data” and view the excel file tab titled “Data Summary” to find a statistical summary of all parameters in the survey. The tab “Calculate” contains the averages for all parameters in the survey. A lot of the statistics on the “Data Summary” tab are irrelevant. For instance, statistical data for variables that had yes or no responses (1 or 0 answers respectively) are for the most part irrelevant. Variables such as EMG, MRI, Sickness, Flu Shot, Chemicals, Exercise, Altitude, Stress, History, Spine Injury, Sex, Remedies, and Missing had yes / no responses – meaning other than the statistical average, most of the other statistical results have very little meaning. Even statistical results for variables that had multiple response options such as variables Region or Day are for the most part irrelevant. More relevant results for these parameters can be found on the “Calculate” tab, which merely computes statistical averages. On the “Calculate” tab the results to these questions are sorted to determine for instance, how many people in the survey where from Europe or North America. The “Calculate” tab results are shown below in Table I below (the classification of variables, ie General (G), will be defined later and are color coded on the “Data Summary” and “Calculate” tabs): 8 BFS Statistical Analysis Table I: ―Calculate‖ Tab Results __________________________________________________ __________________________________________________ ___________________ General (G): Age: 38.74 Sex: 64.5% Male Region: 68% North America; 1.6% South America; 26.4% Europe; 0.8% Europe; 3.2% Oceania MRI: 56.8% Yes EMG: 66.9% Yes Years with symptoms: 3.49 years Years diagnosed: 2.23 years Causes / Triggers (CA): Flu shot: 10.4% Chemicals: 4.8% Prescription drugs: 20.8% Neck/Spine injury: 13.6% Sickness: 28.8% Exercise: 20% 9 BFS Statistical Analysis Stress: 72.6% History: 19.2% Other: 20% The sum of causes adds to more than 100% because people selected multiple potential causes (this is okay). Stressers (ST): Sickness 3.86 (out of 10) Exercise: 5.59 Stress: 6.83 Symptoms (S): Twitching: 7.64 (out of 10) Pins and Needles: 3.72 Cramps: 3.34 Muscle Fatigue: 3.97 Headaches: 2.85 Itching: 2.13 Numbness: 2.79 Muscle Stiffness: 3.98 Muscle Vibrations/Buzzing: 4.7 10 BFS Statistical Analysis Muscle Pain/Soreness: 4.52 Sensitivity to Temperature: 3.06 Symptom Average: 3.87 Body Part (B): Feet: 5.68 (out of 10) Lower Leg: 7.28 Upper Leg: 5.15 Hip/Butt: 3.83 Back: 3.29 Abdomen: 2.88 Chest: 2.43 Head/Neck: 3.53 Hands: 4.4 Arms / Shoulders: 4.83 Body Average: 4.32 Remedies (RE): Benzodiazepine: 3.91 (out of 10, for those that tried the treatment); 54.5% did not try the method Anti-Convulsant: 2.56; 57.7% Anti-Depressant: 2.11; 54.1% 11 BFS Statistical Analysis Potassium Channel: 1.4; 87.8% Sleeping Pills: 3.02; 66.7% Muscle Relaxant: 2.2; 66.4% Homeopathic: 2.2; 63.4% Supplements: 2.27; 25.2% Diet: 2.03; 48% Acupuncture: 2.14; 82.1% Massage: 2.35; 50% Yoga: 2.46; 71.5% Remedy Average: 2.39; 6.5% Various (V): Time: 4.91 (People feel their symptoms are slightly improving over time since a 5 means that symptoms have stayed the same) Day: 32% Morning; 29.6% Day/Evening; 38.4% Night (Time when symptoms are worse) Remedies: 15.2% of people said that certain remedy treatments made their symptoms worse. Missing: 9.6% of people said that a remedy solution that worked for them was not included in the survey. Altitude: 5.6% of people said their symptoms got worse at altitude. 12 BFS Statistical Analysis ________________________________________________________ ________________________________________________________ __________________ However, for many parameters, just knowing the mean (average) does not really describe the variable without knowing more about the result such as its standard deviation. For instance, if a child scored 5 points below the average on a test, this does not tell us much statistically without understanding how the class did as a whole. If the child’s test result was within one standard deviation of the class average, than the child’s result would still rank in the middle of the class (a C grade – see Figure 1). If, on the other hand, the result was over 2 standard deviations away from the mean, than the child’s result would rank in the bottom of the class (a D or F grade). Thus, understanding the standard deviation, variance, and standard error of the class distribution would be extremely helpful. Let’s examine the results of one parameter on the “Data Summary” tab, Twitching (Figures 2 and 3 below summarize the data results for the variable twitching). The question in the survey for the variable twitching specifically reads “Enter a number from 1 to 10 on how much the symptom twitching affects you? A 1 means the symptom does not affect you at all, and a 10 means the symptom occurs 24/7”. For the 13 BFS Statistical Analysis rest of this writing I will refer to this question simply as “twitching”. The results of the variable twitching are summarized below in Table II: Table II: ―Data Summary‖ Tab Results for Twitching __________________________________________________ __________________________________________________ ___________________ i Mean – 7.64 The mean is the arithmetic average. In the case of twitching the mean is 7.64. Hence, BFS sufferers, on average, feel twitching in their body’s 76.4% of the time. The mean is also illustrated in Figure 2; it is the point at which the red bell cure line is at its maximum point. ii Median – 8 The median is the result at which 50 percent of the survey responses are above the result and 50 percent are below the result. In the case of twitching the median result is 8. Hence, 50% are the responses to the survey question twitching were below 8 and 50% of the responses were above 8. This is illustrated in Figure 2. iii Mode – 10 14 BFS Statistical Analysis The mode is the most common response or the response with the highest occurrence or frequency. The most common answer for twitching was 10 (the symptom happens 24/7). This is also illustrated in Figure 2. iv Standard Deviation—SD – 2.52 The standard deviation is a measure of the variability of a set of responses around their mean. If responses cluster tightly around the mean score, the standard deviation is smaller than it would be with a more diverse group of responses from the mean. Any results outside of the mean plus or minus three standard deviations is v considered an outlier and discarded from the analysis. Figure 1 shows a common bell curve or what is sometimes referred to as a normal distribution curve, probability density function, or Gaussian distribution (µ is the mean and σ is the standard deviation). Figure 2 is the bell curve for the variable twitching. For twitching, the standard deviation is 2.52 (3 standard deviations is equal to 7.6). Hence, the mean plus 3 standard deviations is equal to 15.2 and the mean minus 3 standard deviations is equal to 0. Obviously, 100% of the data responses for the twitching question lie within this range since all answers had to be between 1 and 10 (no outliers). 15 BFS Statistical Analysis Sample Size – n - 125 The sample size is equivalent to the number of people that participated in the survey – 125. Remember, the sample size per statistical test may be less than 125 because outliers were omitted from the calculations. The exact sample size per variable is shown on the “Data Summary” tab. vi Standard Error – SE - .230 Standard error is the standard deviation of the values of a given function of the data (parameter), over all possible samples of the same size. This is usually defined by the standard deviation (SD) divided by the square root of the sample size (n). The smaller the standard error the more tightly clustered the data results are around the mean. And conversely, a high standard error means the data distribution is widely dispersed around mean. One would expect to find a large portion of the population (answers to the twitching question) be between the mean plus and minus 3 times the standard error. vii Variance – 6.37 The (population) variance of a random variable is a non-negative number which gives an idea of how widely spread the values of the 16 BFS Statistical Analysis random variable are likely to be; the larger the variance, the more scattered the observations are on average. In other words, variance is a measure of the 'spread' of a distribution about its average (mean) value. The variance for twitching is fairly dispersed because responses covered the entire range of possibilities (1 through 10). This too can be observed by reviewing Figure 2. Percentile Rank – 1 at 0%, 5.875 at 25%, 8 at 50%, 10 at viii 75%, and 10 at 100% A percentile rank is typically defined as the proportion of scores in a distribution that a specific score is greater than or equal to. For percentile rank at 25%, this statistic equals the response where the first 25% (frequency of occurrences) of the sample size population resides. In the case of twitching 25% of the people answered 5.875 or lower. Obviously, the inverse is also true, that 75% of the people answered higher than 5.875 for the variable twitching. Also, for twitching, the percentile rank at 0% is 1, at 50% it is 8, at 75% it is 10, and at 100% it is also 10. This concept can be visualized in Figure 2. ix Inter – Quartile Range – IQR – 4.125 17 BFS Statistical Analysis The inter-quartile range is a measure of the spread of dispersion within a data set. It is calculated by taking the difference between the upper and the lower quartiles. IQR is generally defined as the middle 50% of the data equal to percentile rank at 75% minus percentile rank at 25%. In the case of the variable twitching percentile rank at 75% = 10 and percentile rank at 25% = 5.75. Hence, IQR equals 10 minus 5.875, which equals 4.25. x Range – 9 The range of a sample (or a data set) is a measure of the spread or the dispersion of the observations. It is the difference between the largest and the smallest observed value of some quantitative characteristic and is very easy to calculate. A great deal of information is ignored when computing the range since only the largest and the smallest data values are considered; the remaining data are ignored. The range value of a data set is greatly influenced by the presence of just one unusually large or small value in the sample (outlier). In the twitching example the range of responses were between 1 and 10. Hence, the range is equal to 10 minus 1, which of course equals 9. Once again, this can be seen by viewing the histogram for twitching in Figure 2. xi Coefficient of Variation – CV – 33.03% 18 BFS Statistical Analysis The coefficient of variation (CV) measures the spread of a set of data as a proportion of its mean. It is often expressed as a percentage. It is the ratio of the sample standard deviation to the sample mean. The smaller the coefficient of variance percentage the more tightly clustered the result distribution is around the mean. Conversely, the more dispersed a distribution is around the mean equates to a larger coefficient of variance percentage. For twitching the coefficient of variance result was 33.03%. xii Skewness - -.773 Qualitatively, a negative skew indicates that the tail on the left side of the probability density function (Bell Curve) is longer than the right side and the bulk of the values (possibly including the median) lie to the right of the mean. A positive skew indicates that the tail on the right side is longer than the left side and the bulk of the values lie to the left of the mean. A zero value indicates that the values are relatively evenly distributed on both sides of the mean, typically but not necessarily implying a symmetric distribution. The larger the absolute value of the skewness magnitude, the more skewed the data is to the right or left (depending on the polarity) in the bell curve. The twitching variable is skewed to the right as 19 BFS Statistical Analysis shown by Figure 2. The example in Figure 1 has no skewness because the bell curve is completely symmetrical. ______________________________________________________ ______________________________________________________ _____________________ Figure 1: Probability Density Function Histogram 50 Normal Fit 45 (Mean=7.63,… 40 35 Frequency 30 25 20 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 Twitching Figure 2: Probability Density Function (Bell Curve) for Twitching 20 BFS Statistical Analysis n 119 (cases excluded: 5 due to missing values) Mean 7.63 Median 8.00 95% CI 7.17 to 8.09 95.7% CI 8.00 to 9.00 SE 0.232 Range 9.0 Variance 6.40 IQR 4.42 SD 2.53 95% CI 2.24 to 2.90 Percentile 0th 1.00 (minimum) CV 33.2% 25th 5.58 (1st quartile) 50th 8.00 (median) Skewness -0.76 75th 10.00 (3rd quartile) Kurtosis -0.50 100th 10.00 (maximum) Shapiro-Wilk W 0.85 p <0.0001 Figure 3: Data Analysis for Twitching Variable What can the data on the “Data Summary” tab tell us? It is very useful to compare data for one parameter versus another parameter within the same group or category of variables (ie symptoms, causes, body parts, and remedies – these groups are color coded on the spreadsheet). For symptom variables we can deduce the most predictable parameter is Itching because it has the lowest standard deviation, variance, and standard error. On the other hand, the parameter Vibration/Buzzing Sensation has the lowest predictability because it has the highest standard deviation, variance, and standard error. This simply means that the responses to Itching are more tightly distributed around the mean than the results to other parameters, especially Vibration/Buzzing Sensation, which had sparsely distributed 21 BFS Statistical Analysis results around the mean. For Body Part affected variables the Chest parameter was the most predictable while the Feet parameter was the least predictable. For Remedy variables the Massage parameter (I did not consider potassium channel drugs because very few people tried them) was the most predictable while the Benzodiazepine variable was the least predictable. This simply means that while benzodiazepine drugs helped many people alleviate their symptoms, but at the same time benzodiazepine drugs did very little to help other people alleviate BFS symptoms creating a large variance in the distribution around the mean result. This does not make benzodiazepine drugs a bad choice to treat BFS. In fact, the opposite may be true since other remedies had lower variances only because they did not work as well (in other words, most people answered lowered numbered results for other remedy variables such as sleeping pills, muscle relaxants, homeopathic treatments, supplements, and so forth. Hence, the results are clustered more tightly around a lower mean value). Therefore, benzodiazepine drugs had more success than any other treatment types because it had a higher mean, but the results were mixed. In this study, parameters with lower means tended to have lower variances, standard deviations, and standard errors. The data on the “Data Summary” tab was calculated from the data on “BFS” tab 22 BFS Statistical Analysis (for all data except remedy variables) and the “BFS No Zero” tab (for remedy variables). Correlation Data: The correlation results for all 125 responses can be found at: http://patrickbohan.home.bresnan.net/BFS.htm. Click on the link “Survey Data” and look at the excel file tab titled “Correlation Results” to find statistical correlation data between variables (t-statistic data). xiii A linear regression model can have two purposes: one to predict future results and or two, to find correlation. Most of the models generated xiv from the BFS survey have very low adjusted R² values (the results are not linear) and are therefore, not very good models to predict future outcomes. On the other hand, linear regression models can give us an idea of which parameters have strong or even weak correlation, and that can be useful information. This is why the t-statistic result for each model simulation is important because the t-statistic is a measure of correlation. Each question in the survey: your age, your sex, how bad you get pins and needles, how well yoga works for you, etc is a variable or 23 BFS Statistical Analysis parameter (I use the two words interchangeably). When modeling variables using a linear regression model, there are two sets of variables - x and y. In the data result array (on the “Correlation Results” tab) the horizontal axis is for y variables and the vertical axis is for x variables (this is reversed from conventional algebra, but it was easier for me to get the data into the table using this reversed format). Only one variable is allowed for y in a linear regression analysis, but multiple variables can be used for x (as long as there are more equations than unknowns). For this study, I have grouped the x variables into seven classifications – General (G), Causes / Triggers (CA), Stressers (ST – those variables that can make BFS symptoms worse), Symptoms (S), Body Parts affected (B), Remedies (RE), and Various (V). I have used different color fonts to distinguish between these groups on the “Correlation Results” tab for convenience. For instance, the General (G) classification of variables consists of 7 parameters: age, sex, region, number of years with symptoms, years diagnosed, EMG, and MRI. The t-statistic is a good measure of correlation between corresponding x and y variables. The higher the absolute value of the t-statistic result, the better the correlation (lower standard error). A t-statistic value of greater than 2 means very strong correlation; a t-statistic 24 BFS Statistical Analysis value between 1.75 and 2 means moderate correlation; and a t- statistic value below 0.5 means the correlation is very weak. The sign or polarity (+ or -) of the t-statistic result is also important. A positive value means the x variable will tend to increase the value of the y variable, whereas a negative value means the x variable will tend to decrease the value of the y variable. For instance, a strong correlation between twitching (y variable) and muscle relaxants (x variable) can do one of two things: make the symptom better or worse (- or + respectively). In this case, a positive value can increase the twitching response (making it worse) whereas, a negative response (would lower the twitching value – remember, twitching was rated on a scale of 1 to 10 with 10 being the worse) would be beneficial and something for people to try (as long as the magnitude of the t-statistic showed strong correlation). In essence, the “Correlation Results” tab is a matrix of t-statistic results that is 57 long by 57 wide. T-statistic data was not obtained for x variables within the same classification. For instance, Age as a y variable was not modeled against other General (G) parameters such as sex, region, years with symptoms etc. These results are designated as “na” within the t-statistic matrix. Also, data in the matrix signified 25 BFS Statistical Analysis with ND (No Data) indicates the data was not linear dependent so no results were computed. T-statistic results with strong correlation and a positive polarity are in a bold green font. T-statistic results with strong correlation and an negative polarity are signified with a bold red font. T-statistic results with moderate correlation and a positive polarity are in a bold blue font. And finally, t-statistic results with moderate correlation and a negative polarity are signified with a bold orange font. One final note, I used the data on the “BFS” tab to model all results except for Remedies (RE). When Remedy parameters were the y variable I used the excel file tab “BFS No Zero” data to model the results. After all, it does not make much sense to find correlation to remedies that people have not tried (a “0” response means people did not try the remedy). Hence, the data within the “BFS No Zero” tab is the same as the data on the “BFS” tab except “0” responses to Remedy questions were omitted from the data. But, it is important to keep in mind, the model results of RE parameters using the “BFS No Zero” tab will result in fewer data points (smaller sample size, n) in the model. For this reason, the results from these models may prove to be less conclusive because the data size is in some cases significantly smaller. Hence, when evaluating the data models for RE 26 BFS Statistical Analysis correlation pay close attention to the sample size. When Remedies (RE) are grouped together as the x variables, I use the data on the “BFS” tab to run the models. Only a few people have tried all potential remedies, hence the sample size would only be a single digit number if the “BFS No Zero” tab data was used to model RE results as the x variable. Let’s examine the results of one y parameter, twitching. Six twitching models were run using twitching as the y variable and G, CA, ST, B, RE, and V classification of parameters as x variables respectively (Figures 4 through Figure 9 respectively). The results listed below in Table III provide t-statistic data for each parameter versus twitching. Table III also contains a summary from the “Correlation” tab results to include those parameters with the best correlation versus the listed variable when it is modeled as the y variable: Variable; t-statistic v. twitching; list of parameters with the best correlation to the listed variable Green Font, (Red Font) General Group (G) Age; 1.17; cramps, acupuncture, (stress) Sex; 0.98; (sensitivity to temperature), (yoga) 27 BFS Statistical Analysis Region; -0.23; stress, prescription drugs, history Years Diagnosed (YD); -0.34; massage, altitude Years with Symptoms (YBFS); 0.78; benzodiazepine, remedies, (muscle pain) EMG; 1.37; exercise, back, arms, anti-convulsants, muscle relaxants, remedies, (stress1), (hip), (yoga) MRI; -2.33; (chemicals), (twitching), remedies n 120 (cases excluded: 5 due to missing values) 2 R 0.07 2 Adjusted R 0.01 SE 2.51 Term Coefficient 95% CI SE t statistic DF p Intercept 6.369 4.382 to 8.356 1.0028 6.35 112 <0 Age 0.02713 -0.01878 to 0.07303 0.023168 1.17 112 0 Sex 0.493 -0.499 to 1.485 0.5008 0.98 112 0 Region -0.04869 -0.46746 to 0.37009 0.211356 -0.23 112 0 Years Diagnosed (YD) -0.02415 -0.16649 to 0.11820 0.071840 -0.34 112 0 Years with BFS Symptoms (YBFS) 0.05059 -0.07735 to 0.17853 0.064572 0.78 112 0 EMG 0.751 -0.335 to 1.837 0.5481 1.37 112 0 MRI -1.196 -2.215 to -0.178 0.5142 -2.33 112 0 Figure 4: Linear Regression Model: Twitching V. General (G) There is strong negative correlation between twitching and a MRI. This suggests people are more apt to get an EMG than an MRI due to twitching symptoms. 28 BFS Statistical Analysis Cause / Trigger Group (CA) Flu Shot; -0.52; potassium channel Chemicals; 2; (MRI), twitching, (hip), missing Prescription Drugs (PD); 1.21; (region), vibration, (hands), anti- depressants, missing Spine or Neck Injury (SNI); 0.34; no correlation Sickness; -1.34; (years with symptoms), sickness1, (headaches), hands, diet Exercise; 0.31; exercise1 Stress / Anxiety (SA); -1.44; (EMG), (exercise1), stress1, itching, head, benzodiazepine, (time) History; 0.19; (region), years with symptoms Other; 0.83; (abdomen), anti-convulsants, (potassium channel), homeopathic, remedies n 120 (cases excluded: 5 due to missing values) 2 R 0.09 2 Adjusted R 0.02 SE 2.50 Term Coefficient 95% CI SE t statistic DF p Intercept 7.997 6.923 to 9.072 0.5422 14.75 110 <0.0001 Flu Shot (FS) -0.4126 -1.9880 to 1.1628 0.79496 -0.52 110 0.6048 Chemicals 2.218 0.019 to 4.417 1.1095 2.00 110 0.0481 Prescription Drugs (PD) 0.7057 -0.4523 to 1.8636 0.58430 1.21 110 0.2297 Spine or Neck Injury (SNI) 0.2437 -1.1709 to 1.6582 0.71379 0.34 110 0.7335 Sickness -0.6925 -1.7146 to 0.3296 0.51575 -1.34 110 0.1822 29 BFS Statistical Analysis Exercise 0.1821 -0.9658 to 1.3301 0.57925 0.31 110 0.7538 Stress / Anxiety (SA) -0.7645 -1.8178 to 0.2888 0.53151 -1.44 110 0.1532 History 0.1175 -1.0958 to 1.3308 0.61224 0.19 110 0.8482 Other 0.5219 -0.7309 to 1.7748 0.63219 0.83 110 0.4108 Figure 5: Linear Regression Model: Twitching V. Causes (CA) There is strong positive correlation between twitching and exposure to chemicals as a trigger for BFS. In other words, if exposure to chemicals were the cause or trigger of the BFS ailment, expect twitching to be a primary symptom. Stressers Group (ST) Stress Anxiety1 (SA1); -0.47; (EMG), prescription drugs, history, stress, head, (anti-convulsants), (potassium channel), homeopathic, benzodiazepine Exercise1; 0.58; exercise, sensitivity to temperatures, (acupuncture) Sickness1; 1.07; vibration, sleeping pills, muscle relaxants, (acupuncture), (benzodiazepine), missing n 120 (cases excluded: 5 due to missing values) 2 R 0.02 2 Adjusted R -0.01 SE 2.54 Term Coefficient 95% CI SE t statistic DF p Intercept 7.325 5.965 to 8.684 0.6864 10.67 116 <0.0001 Sickness1 0.08613 -0.07269 to 0.24495 0.080187 1.07 116 0.2850 Exercise1 0.04567 -0.10983 to 0.20116 0.078507 0.58 116 0.5619 30 BFS Statistical Analysis Stress / Anxiety 1 (SA1) -0.03896 -0.20454 to 0.12662 0.083602 -0.47 116 0.6421 Figure 6: Linear Regression Model: Twitching V. Stressers (ST) There is no moderate or strong correlation between twitching and stressers. Symptoms Group (S) Twitching – na; (MRI), chemicals, lower leg, arms, time, day Pins and Needles (PN) – na; time, feet, sickness1, Cramps – na; age, exercise, muscle relaxants, remedies, time Muscle Fatigue and Weakness (MFW) – na; back, (yoga), time Headaches – na; (exercise), (chest), head, (yoga) Itching – na; lower leg, head Numbness – na; anti-depressants Muscle Stiffness (MS) – na; sickness, head Vibration / Buzzing Sensation (VBS) – na; prescription drugs, sickness1, abdomen Muscle Pain / Soreness (MPS) – na; EMG, arms, time Sensitivity to Temperatures (STT) – na; exercise1, (day) Body Part Group (B) 31 BFS Statistical Analysis Feet; 1.47; (years diagnosed), twitching, pins and needles, sleeping pills Lower Leg (LL); 5.68; (years diagnosed), years with symptoms, twitching, cramps, diet, time Upper Leg (UL); -0.58; exercise1, muscle fatigue, (potassium channel), time Hip / Buttock (HBR); 0.78; prescription drugs Back; -0.53; muscle fatigue, altitude Abdomen; 0.23; (region), (age) Chest; -0.47; (potassium channel), muscle relaxants Neck / Head (NH); -0.63; headaches, (day) Hands; -1.1; (age), muscle relaxants Arms / Shoulders (AS); 2.12; (potassium channel), (sleeping pills), EMG n 113 (cases excluded: 12 due to missing values) 2 R 0.38 2 Adjusted R 0.32 SE 2.10 Term Coefficient 95% CI SE t statistic DF p Intercept 3.07 1.33 to 4.81 0.877 3.50 102 0.0007 Feet 0.1225 -0.0429 to 0.2879 0.08340 1.47 102 0.1449 Lower Leg (LL) 0.4831 0.3144 to 0.6517 0.08504 5.68 102 <0.0001 Upper Leg (UL) -0.06082 -0.26952 to 0.14788 0.105217 -0.58 102 0.5645 Hip / Buttock Region (HBR) 0.09856 -0.15053 to 0.34765 0.125580 0.78 102 0.4344 Back -0.06282 -0.29603 to 0.17039 0.117576 -0.53 102 0.5943 Abdomen 0.0423 -0.3158 to 0.4004 0.18056 0.23 102 0.8153 32 BFS Statistical Analysis Chest -0.0869 -0.4501 to 0.2763 0.18311 -0.47 102 0.6361 Neck / Head (NH) -0.06607 -0.27538 to 0.14323 0.105522 -0.63 102 0.5326 Hands -0.1052 -0.2954 to 0.0850 0.09590 -1.10 102 0.2753 Arms / Shoulder (AS) 0.2446 0.0160 to 0.4731 0.11524 2.12 102 0.0362 Figure 7: Linear Regression Model: Twitching V. Body Part (B) There is super strong positive correlation between twitching and the lower leg as well as the arms and shoulders. This should not come as much of surprise since the lower leg and the arms are two of the most affected body parts from BFS symptoms. The bottom line is that BFS sufferers will tend to have strong twitching symptoms in their lower legs and arms. Remedies Group (RE) Anti-Convulsants (AC); 0; EMG, sickness1, muscle pain, (chest) Anti-Depressants (AD); -1.11, numbness Potassium Channel Drugs (PCD); -0.95; (age), (head), (upper leg), (stress1), (exercise1), exercise Sleeping Pills (SP); 0.18; region, hip, (remedies) Muscle Relaxants (MR); -0.81; (chemicals), sickness, (muscle fatigue) Homeopathic Treatments (HT); 0.99; numbness Supplements; -0.83; exercise Diet; 1.2; sickness, vibration Acupuncture; -0.48; (sex); (time) 33 BFS Statistical Analysis Massage; 0.1; no correlation Yoga; 0.13; (sex); (EMG) Benzodiazepine Drugs (BD); 0.39; age, exercise, stress1, (headaches) n 116 (cases excluded: 9 due to missing values) 2 R 0.06 2 Adjusted R -0.05 SE 2.54 Term Coefficient 95% CI SE t statistic DF p Intercept 7.831 6.951 to 8.712 0.4439 17.64 103 <0.0 - Anti-Convulsants (AC) 0.0006226 0.2734014 to 0.2746467 0.13816823 0.00 103 0.9 Anti-Depressants (AD) -0.1761 -0.4897 to 0.1376 0.15814 -1.11 103 0.2 Potassium Channel Drugs (PCD) -0.6713 -2.0695 to 0.7270 0.70503 -0.95 103 0.3 Sleeping Pills (SP) 0.02569 -0.25187 to 0.30325 0.139951 0.18 103 0.8 Muscle Relaxants (MR) -0.1367 -0.4700 to 0.1967 0.16808 -0.81 103 0.4 Homeopathic Treatments (HT) 0.2113 -0.2121 to 0.6347 0.21347 0.99 103 0.3 Supplements -0.1376 -0.4673 to 0.1921 0.16623 -0.83 103 0.4 Diet 0.2273 -0.1493 to 0.6039 0.18989 1.20 103 0.2 Acupuncture -0.1221 -0.6235 to 0.3794 0.25282 -0.48 103 0.6 Massage 0.01742 -0.31329 to 0.34814 0.166753 0.10 103 0.9 Yoga 0.02319 -0.33952 to 0.38589 0.182884 0.13 103 0.8 Benzodiazepine Drugs (BD) 0.04001 -0.16197 to 0.24199 0.101842 0.39 103 0.6 Figure 8: Linear Regression Model: Twitching V. Remedies (RE) There is no moderate or strong correlation to suggest any remedies work very well to alleviate the twitching symptom. Various Group (V) Remedies; -0.4; EMG, sickness1, cramps, back, massage Day; 2.27; twitching, (sensitivity to temperatures), (head) 34 BFS Statistical Analysis Time; 4.86; (stress), exercise1, twitching, cramps, lower leg Missing; 1.91; prescription drugs, history, sickness1, back, anti- convulsants Altitude; 0.05; years diagnosed n 120 (cases excluded: 5 due to missing values) 2 R 0.22 2 Adjusted R 0.18 SE 2.28 Term Coefficient 95% CI SE t statistic DF p Intercept 3.753 2.169 to 5.337 0.7996 4.69 114 <0.0001 Remedies -0.2534 -1.5071 to 1.0004 0.63289 -0.40 114 0.6897 Time 0.5327 0.3154 to 0.7500 0.10972 4.86 114 <0.0001 Day 0.5712 0.0724 to 1.0701 0.25182 2.27 114 0.0252 Missing 1.379 -0.053 to 2.811 0.7228 1.91 114 0.0590 Altitude 0.04856 -1.77122 to 1.86835 0.918623 0.05 114 0.9579 Figure 9: Linear Regression Model: Twitching V. Various (V) There is super strong positive correlation between twitching and how it affects us during the day and over time. Once again, this should come as no surprise since BFS sufferers feel twitching 76.4% of the time. Oddly, there is also moderate correlation between missing remedies from the survey and making twitching symptoms worse. I cannot explain this result. 35 BFS Statistical Analysis Data Naming Convention: Since it is impossible to input all the statistical data and graphs (Figure 2 and Figure 3) as well as all the modeling data (Figures 4 through Figure 9) into this paper for all parameters (there are nearly 400 data summaries and models), the information can be obtained from my BFS website. I will keep the survey open and update the information periodically. The data responses for each parameter (similar to Figure 2 and Figure 3) and linear regression models (similar to Figures 4 through 9) can be found at: http://patrickbohan.home.bresnan.net/BFS.htm and click on the link “BFS Data Summary” and “BFS Correlation Summary” respectively. Each tab on these excel files has a unique name and represents the statistical data summary of one variable or one model simulation. The tab naming convention used on the “BFS Data Summary” link is the parameter name and the extension DA (short for Data). Hence, the tab name Age-DA will contain a statistical data summary of the Age parameter. In some cases, the name is abbreviated such as YD-DA is short for Years Diagnosed or YBFS-DA is short for years with BFS Symptoms. For Remedy (RE) parameters I used the “BFS No Zero” tab to compute the data summary results (to eliminate “0” responses where people never tried the remedy). The naming convention on the 36 BFS Statistical Analysis excel file tabs is, for example, Diet-NZDA (NZDA stands for No Zero Data). If the –DA and –NZDA results do not equal the results on the “Data Summary” tab of the “Survey Data” excel file, it is because the information on the “Survey Data” is updated immediately when the data is downloaded. The –DA and –NZDA data pages are not updated as often. The tab naming convention for the “BFS Correlation Summary” link is: y parameter–x parameter group. For this study, the x variables are grouped into seven classifications – General (G), Causes / Triggers (CA), Stressers (ST – those variables that can make BFS symptoms worse), Symptoms (S), Body (B), Remedies (RE), and Various (V). For instance, the General (G) variables consist of 7 parameters: age, sex, region, number of years with symptoms (YBFS), years diagnosed (YD), EMG, and MRI. Hence, the tab names for Age models (when Age is the y variable) are Age-CA, Age-ST, Age-S, Age- B, Age-RE, and Age-V. In some cases I abbreviated the y variable names such as YD-CA, YD-ST, YD-S, YD-B, YD-RE, and YD-V (YD is for Years Diagnosed). Data Results: Do the data results make sense? This is a difficult question to answer, but it is one that scientists, engineers, and mathematicians must try to address. An eyeball test of some results entered by participants does 37 BFS Statistical Analysis not make sense to me. For instance, some people scored their symptoms and body parts affected by BFS very high (well above average), but at the same time they claimed that certain remedies were very helpful. People that scored remedies usefulness for example, an 8, on a scale of 10, I would have expected that their symptom average to be no higher than 2. In other words, I would expect these two categories to be inversely proportional, but that was not necessarily the case for all respondents. That is the problem with a subjective questionnaire; each person has its own interpretation of the questions. After all, there are no right or wrong answers, but some of these responses were omitted as outliers. There were a few models where one would expect to find strong correlation between certain x and y parameters. For instance, people who felt the cause / trigger of their BFS symptoms were stress, exercise, or sickness, I would therefore naturally hypothesize stress, exercise, and sickness would make their symptoms worse once they were stricken with the BFS disorder. So, let’s examine the correlation models between Causes (CA) and Stressers (ST) to see if this hypothesis is true. To do so, there are six models we need to evaluate: Exercise-ST, SA-ST, Sickness-ST, Exercise1-CA, SA1-CA, and Sickness1-CA (SA is short for Stress / Anxiety). The ST model results 38 BFS Statistical Analysis are what one would suspect. Exercise-ST showed strong correlation between people who felt their illness was caused / triggered by exercise and therefore, exercise makes their BFS symptoms worse. Conversely, SA-ST and Sickness-ST showed strong correlation between people who felt their BFS illness was caused / triggered by stress and or a sickness did indeed show that stress and or a sickness made their symptoms worse, respectively. The SA1-CA and Exercise1- CA models were also predictable. They showed very strong correlation between stress making their symptoms worse and stress and exercise causing / triggering the onset of their BFS illness respectively. However, the Sickness1-CA model only showed moderate correlation between sickness making their symptoms worse and sickness causing / triggering the onset of their illness (but the sickness variable had the strongest correlation of all cause (CA) variables. It is also important to note that the model results for people where stress makes their symptoms worse also indicates that exercise could help relieve their symptoms. Here are a few other correlation model results that make some sense: only women have primarily used yoga as a remedy; cramping tends to get worse the older we become; older people primarily have tried 39 BFS Statistical Analysis acupuncture; pins and needles primarily occur in our feet; and people with strong BFS symptoms in their head tend to have headaches. The analysis of the above 6 models does, for the most part, illustrate that data responses for these questions does in fact make sense. Other model categories would be much harder to deduce if the data makes sense. However, if the results for some questions make sense then one can be fairly confident that other model category results are most likely, fairly accurate. At least we can hope they are. Future Studies: It is possible to expand this study in the future. For instance, it was learned that supplements were a good treatment for BFS sufferers whose symptoms are caused by exercise. However, we do not know what supplements that people used so this result can be vague and misleading. However, a future study can pin point what supplements people used (for example, magnesium, potassium, vitamin D, and quinine are all common supplements tried by BFS sufferers). Acknowledgments: I would like to thank my fellow BFS suffers for taking part in this survey and study. Without their cooperation we would have failed to 40 BFS Statistical Analysis obtain a decent sample size to conduct this study and subsequently bring forth pertinent statistical information about the BFS ailment. Conclusions: The best way to characterize a person with BFS is as follows (those parameters with an average above 65% on Table I): A North American male about 39 years old who has had symptoms for about 3.5 years and has been diagnosed with BFS for about 2.25 years. They had a MRI to prove they do not have MS. This person believes that stress caused or triggered the symptoms and stress will most likely make symptoms worse. The primary symptom is twitching in the lower leg and most remedies and drugs do very little to alleviate the symptoms. There was a pattern on the “Data Summary” tab for parameters whose responses were between 1 and 10. Generally speaking, parameters with high averages (7 or higher) or parameters with low averages (3 or lower) tended to have lower standard deviations, variances, and standard errors than parameters with medium averages (4 through 6). This tells us that parameters with medium averages had mixed results (some people answered 10 while others answered 1). This means these parameters are less predictable and do not necessarily define BFS symptoms. For instance, the results for Symptom (S) variables 41 BFS Statistical Analysis illustrates that Twitching (high average) and Itching (low average) had lower variances (tighter distribution – more predictable) than medium average symptoms such as Muscle Stiffness (MS), Muscle Pain and Soreness (MPS), Vibration/Buzzing Sensation (VBS), and Muscle Fatigue and Weakness (MFW). Hence, BFS can be better defined by saying sufferers are most likely to exhibit muscle twitching symptoms, but no itching symptoms, whereas MS, MPS, VBS, and MFW may be a symptom in some sufferers but not in others – less predictable. The summary of the strong correlation results in Table III can tell us a lot about the BFS disorder. One thing that sticks out is that 5 of the 11 symptoms showed strong positive correlation to the variable time indicating the symptoms are becoming worse over time. In fact, BFS symptoms can get worse over time unless the disorder was triggered by stress and made worse by stress. Stress is the one thing we can control to minimize symptoms even though no remedy seems to work to alleviate stress. In fact, of the nine potential causes only exercise (benzodiazepines and supplements) and sickness (diet and muscle relaxants) show some success with remedies (but remember the amount of relief from these remedies is usually very small – low statistical averages). We may also be able to draw some other conclusions from Table III: prescription drugs causing or triggering 42 BFS Statistical Analysis BFS leads to the vibration / buzzing symptom; anti-depressants may be the best remedy to treat the symptom numbness; the itching symptom primarily occurs on the head; muscle fatigue primarily occurs on the back; sensitivity to temperatures is primarily caused and triggered by exercise; exercise may help alleviate headaches; and so forth. I am not a doctor, but I am an expert on BFS because I am inflicted with the disorder. I am not a PhD, but I have worked extensively on data analysis and modeling over my 22 year career as an engineer. I would offer my services to collect and analyze data for any disorder free of charge (contact me at pbohan1@gmail.com), as long as someone will generate the questionnaire or survey. The goal of this paper is to not only better define and understand BFS, but to give it the exposure it deserves. At a minimum, if the information in this study can provide some sense of comfort to the people inflicted with BFS, then it accomplishes its goal. Remember, stress is a big trigger and can inflate symptoms – and having BFS creates unneeded stress – People with BFS are always asking themselves morbid questions: Do I have MS? Do I have ALS? Am I going to die? If we can alleviate these fears by showing others are going through the same situation, then we accomplished one major goal in this writing. 43 BFS Statistical Analysis i Boslaugh, Sarah, Watter, Andrew Paul, Statistics in a Nutshell, (O’Reilly Media Corp, 2008), page 56 ii Boslaugh, Watter, Statistics in a Nutshell, page 57 iii Boslaugh, Watter, Statistics in a Nutshell, page 58 iv Boslaugh, Watter, Statistics in a Nutshell, page 60 v Boslaugh, Watter, Statistics in a Nutshell, page 64 vi Boslaugh, Watter, Statistics in a Nutshell, page 174 vii Boslaugh, Watter, Statistics in a Nutshell, page 162 viii Boslaugh, Watter, Statistics in a Nutshell, page 368 ix Boslaugh, Watter, Statistics in a Nutshell, page 370 x Boslaugh, Watter, Statistics in a Nutshell, page 59 xi Boslaugh, Watter, Statistics in a Nutshell, page 62 xii Boslaugh, Watter, Statistics in a Nutshell, page 58 xiii Boslaugh, Watter, Statistics in a Nutshell, page 179 xiv Boslaugh, Watter, Statistics in a Nutshell, page 182 44