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Although many studies have found a kind of a relationship between an Epstein-Barr Virus (EBV) and the development of Multiple Sclerosis (MS), a fundamental aspect of this relationship remains uncertain. What is the cause of Multiple Sclerosis (MS)? In this study, we re-analysed the data as published by Wandinger et al. and were able to establish a new insight: without an Epstein-Barr Virus (EBV) infection no development of Multiple Sclerosis (MS). Furthermore, we determined a highly significant causal relationship between Epstein-Barr Virus (EBV) and multiple sclerosis. Altogether, Epstein-Barr Virus (EBV) is the cause of multiple sclerosis ( p-value 0.0004251570).

Multiple Sclerosis (MS) is an unpredictable disease of the central nervous system which disrupts the communication between the brain and other parts of the body. Multiple Sclerosis (MS) can range from relatively benign to somewhat disabling and devastating symptoms. Some of today approved drugs to treat multiple sclerosis include Novantrone (mitoxantrone), teriflunomide, dimethyl fumarate, copolymer I (Copaxone) and forms of beta interferon. Steroids are used to reduce the duration and severity of attacks in some patients suffering from multiple sclerosis. Exercise and physical therapy can help to preserve remaining function. Various aids such as foot braces, canes, and walkers are of use to help patients to remain independent and mobile. Thus far, there is as yet no cure for multiple sclerosis while millions of people are suffering from this many times deadly disease.

Epstein-Barr Virus (EBV), a herpes virus, is a primary cause of Infectious Mononucleosis (IM) and associated with several malignancies including such as Hodgkin lymphoma, non-Hodgkin lymphoma, Burkitt lymphoma and other. Epidemiological, molecular virology and other [

Definition. Bernoulli random variable

Let

Definition. The 2 × 2 table

Let A_{t} denote a Bernoulli/Binomial distributed random variable. Let _{t}. Let B_{t} denote a Bernoulli/Binomial distributed random variable. Let _{t}. Let _{t} and B_{t}. Let _{t} and_{t}. Let

Thus far, let

Definition. Risk ratio or relative risk

Various quantitative techniques are used in Biostatistics to the describe and evaluate relationships among biologic and medical phenomena. Relative risk, defined by Fischer [

In epidemiology and statistics, Relative Risk (RR) is the ratio of the probability of an event a occurring under conditions of being exposed to (a + b), the non-exposed to the probability of c occurring under conditions of being exposed to (c + d), the non-exposed group. The Relative Risk (RR) is a widely used measure of association in epidemiology. A risk ratio RR(A, B) < 1 suggest that an exposure can be considered as being associated with a reduction in risk. A risk ratio RR(A, B) > 1 suggest that an exposure can be considered as being associated with an increase in risk.

Conditions

The following relationships are taken with friendly permission by Ilija Barukčić [

Definition. Conditio sine qua non relationship

Let

The relationship before is expressed in the following 2 × 2 (

Conditioned B_{t} | ||||
---|---|---|---|---|

Yes | No | |||

Condition A_{t} | Yes | |||

No | ||||

1 |

Conditioned B | ||||
---|---|---|---|---|

Yes | No | |||

Condition A | Yes | a | b | |

No | c | d | ||

N |

Conditioned B | ||||
---|---|---|---|---|

Yes | No | |||

Condition A | Yes | a | b | |

No | c = 0 | d | ||

N |

Definition. Anti conditio sine qua non relationship

Let

The relationship before is expressed in the following 2 × 2 table (

Definition. Conditio per quam relationship

Let

The relationship before is expressed in the following 2 × 2 table (

Definition. Anti conditio per quam relationship

Let

The relationship before is expressed in the following 2 × 2 table (

Definition. Conjunction. A and B relationship

Let

Conditioned B | ||||
---|---|---|---|---|

Yes | No | |||

Condition A | Yes | a = 0 | b = 0 | |

No | c | d = 0 | ||

N |

Conditioned B | ||||
---|---|---|---|---|

Yes | No | |||

Condition A | Yes | a | b = 0 | |

No | c | d | ||

N |

Conditioned B | ||||
---|---|---|---|---|

Yes | No | |||

Condition A | Yes | a = 0 | b | |

No | c = 0 | d = 0 | ||

N |

The relationship before is expressed in the following 2 × 2 table (

Definition. Exclusion relationship

Let

or

The relationship before is expressed in the following 2 × 2 table (

Definition. Disjunction. A or B relationship

Let

or

The relationship before is expressed in the following 2 × 2 table (

Definition. Neither A nor B relationship

Let

The relationship before is expressed in the following 2 × 2 table (

Definition. Equivalence of A and B relationship

Let

The relationship before is expressed in the following 2 × 2 table (

Definition. Either A or B relationship

Let

The relationship before is expressed in the following 2 × 2 table (

Conditioned B | ||||
---|---|---|---|---|

Yes | No | |||

Condition A | Yes | a | b = 0 | |

No | c = 0 | d = 0 | ||

N |

Conditioned B | ||||
---|---|---|---|---|

Yes | No | |||

Condition A | Yes | a = 0 | b | |

No | c | d | ||

N |

Conditioned B | ||||
---|---|---|---|---|

Yes | No | |||

Condition A | Yes | a | b | |

No | c | d = 0 | ||

N |

Conditioned B | ||||
---|---|---|---|---|

Yes | No | |||

Condition A | Yes | a = 0 | b = 0 | |

No | c = 0 | d | ||

N |

Conditioned B | ||||
---|---|---|---|---|

Yes | No | |||

Condition A | Yes | a | b = 0 | |

No | c = 0 | d | ||

N |

Conditioned B | ||||
---|---|---|---|---|

Yes | No | |||

Condition A | Yes | a = 0 | b | |

No | c | d = 0 | ||

N |

Data and material for this re-analysis were published by Wandinger [

The data of the prevalence of IgG antibodies in serum samples from multiple sclerosis (MS) patients and healthy control subjects are viewed in the following 2 × 2 table (

The properties of the chi-squared distribution were first investigated by Karl Pearson [

In last consequence, the Chi Square with one degree of freedom is nothing but the distribution of a single normal deviate squared.

The statistical significance of deviations from a theoretically expected distribution of observations can be tested

Parameter | Multiple Sclerosis (MS) | Healthy control subjects |
---|---|---|

anti-EBNA-1 IgG | 108 | 147 |

Sample size | 108 | 163 |

Multiple sclerosis | ||||
---|---|---|---|---|

Yes | No | |||

EBV anti-EBNA-1 IgG | Yes | 108 | 147 | 255 |

No | 0 | 16 | 16 | |

108 | 163 | 271 |

Critical values of chi-square distribution | ||
---|---|---|

p-value | One sided X^{2} | Two sided X^{2} |

0.1000000000 | 1.642374415 | 2.705543454 |

0.0500000000 | 2.705543454 | 3.841458821 |

0.0400000000 | 3.06490172 | 4.217884588 |

0.0300000000 | 3.537384596 | 4.709292247 |

0.0200000000 | 4.217884588 | 5.411894431 |

0.0100000000 | 5.411894431 | 6.634896601 |

0.0010000000 | 9.549535706 | 10.82756617 |

0.0001000000 | 13.83108362 | 15.13670523 |

0.0000100000 | 18.18929348 | 19.51142096 |

0.0000010000 | 22.59504266 | 23.92812698 |

0.0000001000 | 27.03311129 | 28.37398736 |

0.0000000100 | 31.49455797 | 32.84125335 |

0.0000000010 | 35.97368894 | 37.32489311 |

0.0000000001 | 40.46665791 | 41.8214562 |

by a binomial test. For large samples, the binomial distribution is well approximated by convenient Pearson’s chi-squared test. The above relationships are grounded on the assumption, that the number of successes X out of a sample of n observations is equal to X = N. In general, let

Example.

Given a sample proportion p and sample size N we can test claims about the population proportion p_{0}. Different hypothesis tests and test methods (binomial test, one-sample z-test, the t statistic et cetera) can be used to determine whether a hypothesized population proportion p_{0} differs significantly from an observed sample proportionp. A hypothesis test requires that a null hypothesis and an alternative hypothesis are mutually exclusive. That is, if a null hypothesis is true, the alternative hypothesis must be false and vice versa. How can we conduct a hypothesis test of a proportion. Especially under conditions, where an observed sample proportion p is equal to 1, the F distribution [

In other words, we assume that the p in the population is greater or equal to 0.989006512. Furthermore, the one- sided lower confidence interval with confidence level 1 − alpha for the proportion of successes

A 100 ´ (1 − alpha)% confidence interval consists of all those values

The mathematical formula of the causal relationship k was used to determine the cause-effect relationship between Epstein-Barr Virus (EBV) infections and Multiple Sclerosis (MS). According to Barukčić [

The relationship before is expressed in the following 2 × 2 table (

Pearson’s chi-squared test X²

is used to evaluate how likely it is that the observed causal relationship k arose by chance. The 2 × 2 contingency table is dichotomous while the statistical X^{2} distribution is continuous. Thus far, Pearson’s chi-square test tends to make results larger than they should be and is biased upwards on this account. This upwards bias of Pearson’s chi-square test can be corrected by using Yates correction.

Scholium.

As a response to Yules association of two attributes Karl Pearson introduced the mean square contingency [

Effect B | ||||
---|---|---|---|---|

Yes | No | |||

Cause A | Yes | a | b | |

No | c | d | ||

N |

Still, Pearson failed to derive a mathematical formula of the causal relationship k and much more than this. Pearson himself exterminated any kind causation from statistics ultimately. Following Pearson, “We are now in a position, I think, to appreciate the scientific value of the word cause. Scientifically, cause… is meaningless…” [

Data were analyzed using Microsoft Excel version 14.0.7166.5000 (32-Bit) software (Microsoft GmbH, Munich, Germany). The mathematical formula of the causal relationship k [

Wandinger [

The viral status was classified by following serologic definitions. Wandinger [

A hypothesis test is used to distinguish between the null hypothesis and the alternative hypothesis.

Theorem 1.

Null hypothesis: EBV is a conditio sine qua non of multiple sclerosis (MS) (p_{0} ≥ p).

Alternative hypothesis: EBV is not a conditio sine qua non of multiple sclerosis (MS) (p_{0} < p).

Significance level (Alpha) below which the null hypothesis will be rejected: 0.05.

Proof by a statistical hypothesis test.

The data of the prevalence of IgG antibodies in serum samples from Multiple Sclerosis (MS) patients and healthy control subjects are viewed in the following 2 × 2 table (

The proportion of successes

The critical value p_{lower} is calculated approximately as

The critical value p_{lower} = 0.989006512 and is less than the proportion of successes

Conclusio.

We cannot reject the null hypothesis in favor of the alternative hypotheses. The sample data do support the Null hypothesis that Epstein Barr Virus (EBV) is a conditio sine qua non of Multiple Sclerosis (MS).

In other words, without an infection with Epstein Barr Virus (EBV) no development of multiple sclerosis (MS).

Quod erat demonstrandum.

Theorem 2.

Conditions.

Alpha level = 5%.

The two tailed critical Chi square value (degrees of freedom = 1) for alpha level 5% is 3.841458821.

Claims.

Null hypothesis (H_{0}): k = 0 (No causal relationship).

There is no causal relationship between Epstein Barr virus (EBV) and multiple sclerosis (MS).

Alternative hypothesis (H_{A}): k ¹ 0 (Causal relationship).

There is a significant causal relationship between Epstein Barr virus (EBV) and multiple sclerosis (MS).

Proof by two sided hypothesis test.

Based on the data (_{Obtained} (our test statistic) as

Following Barukčić, the test statistics obtained is equivalent with a X^{2} value of

A two tailed Chi square of 11.2664020209 is equivalent to a p-value of 0.0004251570.

Multiple sclerosis | ||||
---|---|---|---|---|

Yes | No | |||

EBV anti-EBNA-1 IgG | Yes | 108 | 147 | 255 |

No | 0 | 16 | 16 | |

108 | 108 | 271 |

Multiple sclerosis | ||||
---|---|---|---|---|

Yes | No | |||

EBV anti-EBNA-1 IgG | Yes | 108 | 147 | 255 |

No | 0 | 16 | 16 | |

108 | 163 | 271 |

Conclusio.

The value of the test statistic (k obtained or Chi square calculated) is 11.2664020209 and exceeds the critical Chi square value of 3.841458821. Consequently, we reject the null hypothesis (H_{0}) and accept the alternative hypothesis (H_{A}).

There is a highly significant causal relationship between Epstein Barr virus (EBV) and multiple sclerosis (k = +0.2038956576, p-value 0.0004251570).

Quod erat demonstrandum.

Today, the etiology of Multiple Sclerosis (MS) is largely unknown but Multiple Sclerosis (MS) is rare among individuals without serum EBV antibodies. Thus far, there is an accumulating literature for a role of Epstein- Barr Virus (EBV) infections in the pathogenesis of Multiple Sclerosis (MS). Especially, several epidemiological studies suggested an association between infection with Epstein-Barr Virus (EBV) and the occurrence of Multiple Sclerosis (MS) disease. In particular, a recent large prospective epidemiological study showed a relationship between an increase of serum antibody titres against EBV before onset of MS. Acherio et al. [

We conducted a re-analysis of the study of Wandinger [

In addition, our study confirms a conditio sine qua non relationship between EBV infection and Multiple Sclerosis (MS). In other words, without an infection with Epstein-Barr Virus (EBV) no development of Multiple Sclerosis (MS) (significance level alpha = 0.05). We observed a highly significant causal relationship between Epstein-Barr Virus (EBV) and multiple sclerosis (k = +0.203895658, p value = 0.000425157). A particular aspect of our study is the identification of Epstein-Barr Virus (EBV) as the cause of multiple sclerosis. Since without an infection by Epstein-Barr Virus (EBV) no multiple sclerosis develops and due to the fact that there is a highly significant causal relationship between Epstein-Barr Virus (EBV) and multiple sclerosis, we are allowed to deduce that Epstein-Barr Virus (EBV) is not only a cause but the cause of Multiple Sclerosis (MS).

A particular aspect of our study is the identification of Epstein-Barr Virus (EBV) as the cause of Multiple Sclerosis (MS). Finally, the cause of multiple sclerosis is identified. Consequently, it is more than necessary to develop a low-cost and highly effective vaccine against Epstein-Barr Virus (EBV).

Katarina Barukčić,Ilija Barukčić, (2016) Epstein Barr Virus—The Cause of Multiple Sclerosis. Journal of Applied Mathematics and Physics,04,1042-1053. doi: 10.4236/jamp.2016.46109