Anyone with statistic knowledge, please provide me feedback. My statistic knowledge may have regressed over the years since my retirement so I may be a little rusty. So please correct me if my assumptions/conclusions are wrong or if you have a better way to explain these results. And if you have any suggestions for some future model results from our survey please let me know. In the past, my goal when building a linear regression model was to predict an outcome, so I was more interested in the R² value of the model and not so much for correlation – so I welcome some insight I may be overlooking. My hope here is to try to show what type of information can be generated to get more people involved in the survey. Remember, the sample size is too small to jump to any conclusions. And this is not an official scientific study, but it may shed light on what to study in the future or what we can try to do to alleviate symptoms. Once again, the data columns is not aligned properly when I compied over the results. If someone wants me to send them these excel files so they can be viewed easier, please provide me your email address. My email is
[email protected].
Below are a couple of linear regression models based on the data we have to date (31 participants, so n = 31). However, in the models below participant data was eliminated if they answered 0 (have not tried) certain remedies. The first model solves for Benzo drugs to see if there is correlation between symptoms and body part affected by the symptoms. We only have data for 14 people (n=14) that have tried the Benzo drug, this is a very small sample size. First, I ran the model using all symptoms and body parts and by trial and error kept eliminating those parameters that did not correlate. The Benzo model is fairly weak. It has about 41% (Adjusted R²) correlation to the symptoms Pins and Needles, Cramps, Muscle Stiffness, Vibration / Buzzing, and Arms and Shoulders. Another statistic of importance is “t statisticâ€. Those parameters that have a high absolute value of t statistic have the highest correlation. A t statistic above 2 is best. In this case Cramps (-2.44), Vibration / Buzzing (2.18), and Pins and Needles (2.06) have the best correlation. Hence, a person that tries a Benzo drug has a chance to see some change in the symptoms: Cramps, Vibration / Buzzing, and Pins and Needles; and the body part that may see a change are the arms and shoulders (although that correlation is fairly weak, t-statistic -1.42). The higher the value of F Statistic the better the model, which equates to a lower value of p. A higher t statistic also means a lower value of p. SE is the standard error of the model. In this case, the standard error is 1.99. If for example a person answered that Benzo helped them by a factor of 2 (out of 10 in the survey), it is possible their value in the model may be 2+1.99 or 2-1.99 (3.99 or .01). This is the worst case scenario. This can be shown by the residual error plot that I did not include below. The coefficients are the solution to the model:
Benzo = 3.095 + .5338x(Pins and Needles) - .8296x(cramps) + .5226 (Muscles Stiffness) + .6073x(Vibration / Buzzing) - .6986x (Arms/shoulders)
Hence, if you have tried Benzo, then if we fill your questionnaire results into the above equation for Pins and Needles, cramps, muscle stiffness, vibration/buzzing sensation, and arms shoulders the result should equal your questionnaire response for Benzo within the standard error of 1.99. Those positive coefficients will drive the Benzo value up and those negative coefficients drive the Benzo value down. My assumption is that most people may have had fairly low survey answers to the above parameters for pins and needles, cramps, muscle stiffness, vibration / buzzing, and arms and shoulders.
n 14 (cases excluded: 17 due to missing values)
R2 0.64
Adjusted R2 0.41
SE 1.99
Term Coefficient 95% CI SE t statistic DF p
Intercept 3.095 -0.850 to 7.040 1.7108 1.81 8 0.1080
Pins and Needles 0.5338 -0.0634 to 1.1309 0.25897 2.06 8 0.0732
Cramps -0.8296 -1.6122 to -0.0471 0.33936 -2.44 8 0.0403
Muscle Stiffness 0.5226 -0.1686 to 1.2139 0.29977 1.74 8 0.1194
Vibration / Buzzing Sensation 0.6073 -0.0341 to 1.2486 0.27812 2.18 8 0.0605
Arms / Shoulder -0.6986 -1.8336 to 0.4365 0.49220 -1.42 8 0.1936
Source of variation Sum squares DF Mean square F statistic p
Model 55.29 5 11.06 2.80 0.0947
Residual 31.63 8 3.95
Total 86.92 13
The next model below is for muscle relaxants. This is the strongest model. People taking a muscle relaxant may see a 77% chance of seeing some change on a variety of symptoms over several body parts. Once again, the sample size is very small, only 15 participants have tried muscle relaxants.
n 15 (cases excluded: 16 due to missing values)
R2 0.92
Adjusted R2 0.77
SE 1.1
Term Coefficient 95% CI SE t statistic DF p
Intercept 6.234 2.075 to 10.393 1.6178 3.85 5 0.0120
Muscle Fatigue and Weakness -1.201 -2.126 to -0.276 0.3598 -3.34 5 0.0206
Headaches 0.6397 0.0355 to 1.2438 0.23502 2.72 5 0.0417
Itching 0.9998 -0.1660 to 2.1656 0.45352 2.20 5 0.0786
Muscle Stiffness 0.558 -0.385 to 1.501 0.3668 1.52 5 0.1887
Sensitivity to Temperatures -1.437 -2.459 to -0.415 0.3977 -3.61 5 0.0153
Feet -0.477 -0.759 to -0.196 0.1095 -4.36 5 0.0073
Neck / Head 1.133 0.407 to 1.859 0.2823 4.01 5 0.0102
Hands 0.2661 -0.0567 to 0.5889 0.12556 2.12 5 0.0876
Arms / Shoulder -0.6067 -1.3740 to 0.1607 0.29850 -2.03 5 0.0978
Source of variation Sum squares DF Mean square F statistic p
Model 72.1 9 8.0 6.31 0.0282
Residual 6.3 5 1.3
Total 78.4 14
The final model is for anti convulsant drugs. This model is also fairly strong based on 16 inputs. Itching, Numbness, Feet, and Arms and Shoulders are the symptoms and body parts with the highest correlation.
n 16 (cases excluded: 15 due to missing values)
R2 0.87
Adjusted R2 0.73
SE 1.20
Term Coefficient 95% CI SE t statistic DF p
Intercept -1.188 -4.656 to 2.280 1.4666 -0.81 7 0.4447
Itching -1.149 -2.400 to 0.102 0.5289 -2.17 7 0.0664
Numbness -0.7151 -1.3615 to -0.0687 0.27335 -2.62 7 0.0346
Vibration / Buzzing Sensation 0.3033 -0.1620 to 0.7685 0.19677 1.54 7 0.1672
Muscle Pain / Soreness 0.2795 -0.2622 to 0.8213 0.22910 1.22 7 0.2619
Sensitivity to Temperatures 0.3696 -0.4083 to 1.1475 0.32898 1.12 7 0.2983
Feet 0.3711 -0.0276 to 0.7698 0.16862 2.20 7 0.0636
Upper Leg -0.3152 -0.9837 to 0.3533 0.28270 -1.11 7 0.3017
Arms / Shoulder 0.6515 0.1719 to 1.1310 0.20280 3.21 7 0.0148
Source of variation Sum squares DF Mean square F statistic p
Model 69.82 8 8.73 6.04 0.0142
Residual 10.12 7 1.45
Total 79.94 15
FYI, although the muscle relaxant model had the best correlation, it has the 2nd lowest average of improvement when compared to anti convulsants and benzo drugs. On average, people that have tried these drugs say that benzo helps about 3.6 (out of 10), muscle relaxants 3.4, and anti-convulsants 3.2. And there are a significant amount of respondents that saw no improvement using these drugs. And finally, we do not know what particular drug and dosage levels that people are taking. This could be a follow up study if we can get a sample size of 100 participants or more. There also could be outliers in the results (people’s whose responses fall outside the typical response of the survey population), which could be eliminated from the model results.