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Hereditary is one of the key risk factors of the Parkinson’s disease (PD) and children of individuals with the Parkinson’s carry a two-fold risk for the disease. In this article, chance of developing the Parkinson’s disease is estimated for an individual in five types of families. That is, families with negative history of the PD (I), families with positive history where n either one of the parents (II), one of the parents (III-IV), or both parents (V) are diagnosed with the disease. After a sophisticated modeling, Maximum Likelihood and Bayesian Approach are used to estimate the chance of developing the Parkinson’s in the five mentioned family types. It is extremely important knowing such probabilities as the individual can take precautionary measures to defy the odds. While many physicians have provided medical opinions on chance of developing the PD, our study is one of the first to provide statistical modeling and analysis with real data to support the conclusions.

Parkinson’s disease (PD) is a chronic and progressive movement disorder, meaning that symptoms continue and worsen over time. Nearly one million Americans are living with Parkinson’s disease and approximately 60,000 are diagnosed with PD each year. This number does not reflect thousands of cases that remain undetected. The cause for the PD is unknown, and although there is presently no cure, there are available treatments such as medication and surgery to manage its symptoms [

The diagnosis of PD depends upon the presence of one or more of the four most common motor symptoms of the disease. That is, tremor, bradykinesia, rigidity, and postural instability. In addition, there are other secondary and non-motor symptoms that affect many people and are increasingly recognized by doctors as important to diagnosing Parkinson’s. These symptoms contribute to severe disability and impaired quality of life in advanced Parkinson’s cases. Symptoms include anxiety, depression, cognitive mood swings, dementia, constipation, pain, genitourinary problems, sudden drop in blood pressure upon standing, excessive sweating, sleep disturbances, sense of smell, vision, memory, weight loss, psychosis, hallucinations and loss of energy, among others [

There are several research centers and foundations that study Parkinson’s disease with the aim of providing education to the society about Parkinson’s, providing facilities for people with Parkinson’s, better understanding of the Parkinson’s disease, reducing its effect in patients, and potentially finding a cure for the Parkinson’s. Among them are National Parkinson Foundation, Parkinson’s Disease Foundation, American Parkinson Disease Association, Davis Phinney Foundation, and Michael J. Fox Foundation for Parkinson’s Research.

Through contact with The Michael J. Fox Foundation for Parkinson’s Research, we were granted access to the vast database of Parkinson’s Progression Markers Initiative (PPMI) [

The approach shown in

case i, (F_{i}, M_{i}) = (0, 0) when neither one of the parents carried Parkinson’s, (F_{i}, M_{i}) = (0, 1) when father was healthy, and mother was diagnosed with Parkinson’s, etc. In this approach, the number of cases with Parkinson’s in each one of the five categories follows a Binomial distribution with two parameters: total number of siblings in the family including the person himself/herself (n_{i}), and probability of developing Parkinson’s (θ). Generally, for case i, one can write

X i ( j , k , l ) | ( H i = j , F i = k , M i = l ) ~ Bin ( n i ( j , k , l ) , θ j k l ) , j , k , l = 0 , 1 , (1)

where H_{i} = j with j = 0, 1 shows the negative/positive heredity group, F_{i} = k, M_{i} = l with k, l = 0, 1 shows the Healthy/PD status of the parents, n i ( j , k , l ) shows the total number of siblings in the family, and 0 ≤ θ j k l ≤ 1 represents the probability of developing the PD. The likelihood function can then be written as

L ( θ j k l | X ( j , k , l ) ) = ∏ i = 1 k j k l ( n i ( j , k , l ) x i ( j , k , l ) ) θ j k l x i ( j , k , l ) ( 1 − θ j k l ) n i ( j , k , l ) − x i ( j , k , l ) , (2)

where k j k l is the number of cases in each of the five family types represented by H_{i} = j, F_{i} = k, M_{i} = l. Furthermore, it is easy to arrive at the following maximum likelihood estimator

θ ^ j k l = ∑ i X i ( j , k , l ) ∑ i n i ( j , k , l ) (3)

In deriving estimations of

The combined information suggests that the chance of developing the PD in families with positive PD history when neither one of the parents had the PD is five times more than that of with no history of the disease. It is about four times

θ 000 ( k 000 ) | θ 100 ( k 100 ) | θ 101 ( k 101 ) | θ 110 ( k 110 ) | θ 111 ( k 111 ) |
---|---|---|---|---|

584 2729 = 0.214 (825) | 189 584 = 0.324 (165) | 104 380 = 0.274 (125) | 113 385 = 0.294 (124) | 12 29 = 0.414 (9) |

θ 000 ( k ′ 000 ) | θ 100 ( k ′ 100 ) | θ 101 / 110 ( k ′ 101 / 110 ) | θ 111 ( k ′ 111 ) |
---|---|---|---|

732 11728 = 0.062 (2993) | 376 1196 = 0.314 (280) | 239 887 = 0.269 (253) | 19 72 = 0.264 (20) |

more when one or both parents carry the disease. Surprisingly, the chances for developing the PD when neither one of the parents were diagnosed with the PD are significantly higher than the case where one or both parents are diagnosed with the disease (p-value = 0.00014 for Binomial test). This could suggest a dormant gene effect for the Parkinson’s.

The chance of passing the PD to next generations depends on many factors and could vary from one family to another. This random nature justifies using Bayesian approach for estimations. Moreover, one can use sets of hierarchical information as prior-likelihood and update prior information anytime new observations are added to the dataset.

To conduct a Bayesian approach, data in

To select a prior for θ 100 , cases with positive family history of PD were selected (decided based on the status of grandparents, aunts, and uncles) whose neither one of the paternal grandparents had PD (H = 1, F = 0, M = 0). Then, in each of such families, the chance of developing the Parkinson’s disease is estimated by counting the number of cases with the PD divided by the total number of siblings. This estimator can be written as follows:

Father ’ sstatus + # ofpaternalaunts / uncleswithPD 1 + total# ofpaternalaunts / uncles . (4)

Following the same procedure in the maternal family yields estimate of the chance of developing the PD using maternal family

Mother ’ sstatus + # ofpaternalaunts / uncleswithPD 1 + total# ofmaternalaunts / uncles . (5)

These two separate estimations when computed for each case provide a frequency distribution that can be used as a priori information in estimating θ 100 . Likewise, one can gather prior information for θ 110 by frequency of disease in the paternal and maternal families with positive history where the grandfather did, and grandmother did not have the PD. However, the only information available in the grandparents’ families is the sum of the PD status of grandmother/grandfather. In that case, the number of the PD diagnosed cases is counted but the prior for θ 101 and θ 110 is set to be the same. Prior information for θ 111 can be derived using the same technique but in different families with respect to grandparents’ status. The same approach is used to derive prior for θ 000 .

Support | Frequency | Percent |
---|---|---|

0.000 | 2021 | 93.18% |

0.091 | 2 | 0.09% |

0.111 | 4 | 0.18% |

0.125 | 3 | 0.14% |

0.143 | 9 | 0.41% |

0.167 | 7 | 0.32% |

0.200 | 15 | 0.69% |

0.250 | 20 | 0.92% |

0.333 | 35 | 1.61% |

0.500 | 31 | 1.43% |

1.000 | 22 | 1.01% |

Total | 2169 | 100% |

Support | Frequency | Percent |
---|---|---|

0.000 | 54 | 42.19% |

0.111 | 2 | 1.56% |

0.125 | 2 | 1.56% |

0.167 | 1 | 0.78% |

0.200 | 2 | 1.56% |

0.250 | 6 | 4.69% |

0.333 | 13 | 10.16% |

0.400 | 2 | 1.56% |

0.429 | 1 | 0.78% |

0.500 | 19 | 14.84% |

0.571 | 1 | 0.78% |

0.667 | 7 | 5.47% |

0.750 | 4 | 3.13% |

0.875 | 1 | 0.78% |

1.000 | 13 | 10.16% |

Total | 128 | 100% |

Support | Frequency | Percent |
---|---|---|

0.091 | 2 | 1.74% |

0.100 | 2 | 1.74% |

0.111 | 2 | 1.74% |

0.125 | 5 | 4.35% |

0.143 | 10 | 8.70% |

0.167 | 11 | 9.57% |

0.182 | 1 | 0.87% |

0.200 | 6 | 5.22% |

0.250 | 10 | 8.70% |

0.286 | 5 | 4.35% |

0.333 | 21 | 18.26% |

0.400 | 6 | 5.22% |

0.500 | 16 | 13.91% |

0.600 | 3 | 2.61% |

0.667 | 6 | 5.22% |

0.750 | 4 | 3.48% |

0.833 | 2 | 1.74% |

1.000 | 3 | 2.61% |

Total | 115 | 100% |

Support | Frequency | Percent |
---|---|---|

0.000 | 7 | 63.64% |

0.167 | 1 | 9.09% |

0.250 | 1 | 9.09% |

0.500 | 1 | 9.09% |

1.000 | 1 | 9.09% |

Total | 11 | 100% |

To use these information as discrete priors, the set of {0.000, 0.001, 0.002, ..., 0.999, 1} with 101 values has been used as the distribution’s support and a weight equal to frequencies in

This approach does not change the mean of the priors significantly and provides a nonzero probability for other values in the support when mixed with likelihood. The prior then could be written as:

P ( θ j k l = m 100 ) = p m j k l m = 0 , 1 , … , 100 , j , k , l = 0 , 1 , (6)

where p m j k l is derived from

P ( θ j k l = m 100 ) = p m j k l m ∑ i = 1 k j k l x i ( j , k , l ) ( 100 − m ) ∑ i = 1 k j k l n i ( j , k , l ) − ∑ i = 1 k j k l x i ( j , k , l ) ∑ m = 0 100 p m j k l m ∑ i = 1 k j k l x i ( j , k , l ) ( 100 − m ) ∑ i = 1 k j k l n i ( j , k , l ) − ∑ i = 1 k j k l x i ( j , k , l ) . (7)

PD to families with negative heredity is 0.32801 0.20012 = 1.64 % . The estimation for

θ 101 and θ 110 are 0.2649 and 0.3148 respectively both with 99% credible set of [0.25, 0.33]. The chance of developing the PD increases to 0.4422 when both parents had PD which is 1.35% higher than the families where neither one of the parents were diagnosed with the PD. These estimations are close to the maximum likelihood estimations in

In this section, the available data from grandparents’ family is considered as Binomial counts and is mixed with the data from the individual’s family in the form of likelihood to derive Bayesian estimations by using non-informative uniform priors. In this case, the posterior distribution could be written as

f ( θ j k l ) = θ j k l ∑ i = 1 k ′ j k l x i ( j , k , l ) ( 1 − θ j k l ) ∑ i = 1 k ′ j k l n i ( j , k , l ) − ∑ i = 1 k ′ j k l x i ( j , k , l ) ∫ 0 1 θ j k l ∑ i = 1 k ′ j k l x i ( j , k , l ) ( 1 − θ j k l ) ∑ i = 1 k ′ j k l n i ( j , k , l ) − ∑ i = 1 k ′ j k l x i ( j , k , l ) d θ j k l , (8)

where k ′ j k l accounts for the new sample cases in families when H_{i} = j, F_{i} = k, M = l for fixed j, k, l. Since no information regarding the gender of the grandparents with the Parkinson’s was available, the information from this link has been copied for both θ 101 and θ 110 . When combined with the primary likelihood, this provides distinct estimations for θ 101 and θ 110 .

The Bayesian computations in this section have been carried out using WinBUGS. Monte Carlo Simulations with three simultaneous chains have been utilized to arrive at stable estimations. A burn in of 110,000 with threads of 150,000 long has been used for this part of the analysis.

The model parameter θ 000 is estimated to be 0.0625 with 95% credible interval of (0.0582, 0.0669). For positive heredity group, θ_{100} through θ_{111} were estimated to be 0.3147, 0.2700, 0.2785, and 0.2702, respectively. As expected, all estimations are close to their respective maximum likelihood estimations provided in _{100}/θ_{000} =5.042, the chance of developing the Parkinson’s for an offspring in positive heredity family when neither one of the parents had the

Parameter | Mean | S.D. | % Coverage | Credible Set |
---|---|---|---|---|

θ_{000} | 0.20012 | 0.001657 | 99.353 | {0.20} |

θ_{100} | 0.32801 | 0.008845 | 94.451 | {0.33} |

θ_{101} | 0.26487 | 0.031059 | 98.649 | [0.25, 0.33] |

θ_{110} | 0.31477 | 0.031213 | 98.779 | [0.25, 0.33] |

θ_{111} | 0.44222 | 0.100040 | 90.687 | [0.17, 0.50] |

Parameter | Mean | S.D. | % Coverage | Credible Set |
---|---|---|---|---|

θ_{000} | 0.0625 | 0.00223 | 95 | [0.0582, 0.0669] |

θ_{100} | 0.3147 | 0.01341 | 95 | [0.2887, 0.3414] |

θ_{101} | 0.2700 | 0.01490 | 95 | [0.2411, 0.2996] |

θ_{110} | 0.2785 | 0.01500 | 95 | [0.2495, 0.3085] |

θ_{111} | 0.2702 | 0.05119 | 95 | [0.1758, 0.3756] |

PD is about five times higher than an offspring in a family with negative heredity. Interestingly, children were less likely to have the PD when both parents had the PD than the condition where neither one of the parents were diagnosed with the PD. This might suggest the effect of dormant genes or lack of adequate data for case of positive PD status of both parents. This estimation is in accordance with some research studies [

The chance of developing the PD in families with negative heredity and in four family types with positive heredity has been estimated using four different approaches, two Maximum Likelihood and two Bayesian.

The information for grandparents and their families date respectively to two and one generation back thus might not be as reliable as it should be. There were registered cases having 18 and 21 aunts/uncles which might be due to registration error or might represent extreme cases that could affect the analysis to some degree. For this reason, the first and second-generation information of 47 cases that had more than 11 aunts/uncles has been excluded from the present study. It is more reasonable to use former less reliable information as prior knowledge and let the more recent and authentic information shape it to more reliable estimations. Thus, we opt to report the Bayesian estimations with discrete prior as the most reliable.

ML | Bayes | ||||
---|---|---|---|---|---|

Parameter | Primary using 1^{st} link | Secondary using 2^{nd} links | Discrete Prior | Uniform Prior | |

θ_{000} (SD) | 0.214 (0.0079) | 0.016 (0.0022) | 0.20012 (0.0017) | 0.0625 (0.0022) | |

θ_{100} (SD) | 0.324 (0.0194) | 0.314 (0.0134) | 0.32801 (0.0088) | 0.3147 (0.0134) | |

θ_{101} (SD) | 0.274 (0.0229) | 0.269 (0.0149) | 0.26487 (0.0311) | 0.2700 (0.0149) | |

θ_{110} (SD) | 0.294 (0.0232) | 0.269 (0.0149) | 0.31477 (0.0312) | 0.2785 (0.0150) | |

θ_{111} (SD) | 0.414 (0.0915) | 0.264 (0.0519) | 0.44222 (0.1000) | 0.2702 (0.0514) | |

For negative heredity group, estimations of θ_{000} vary from 0.016 to 0.214, both extreme estimations are ML estimations based on sample sizes of 2169 and 824. Increasing sample size should increase the consistency and efficiency of the ML estimations but one must consider the authenticity of information as well. This difference could also point out the change in prevalence of the Parkinson’s through generations. The Bayesian method with discrete prior provides an estimation of 0.20012 meaning that a child in this family has a 20% chance of developing the Parkinson’s disease.

Estimations for θ_{100} are less volatile among four different methods. In this case, Bayesian method with discrete prior estimates a chance of 33% for developing the Parkinson’s for the children. When compared to θ_{000}, a relative risk of 1.59 is derived suggesting 1.59 times more chance of developing the PD if there is a positive Parkinson history in the family although neither one of the parents had the disease. This estimation is in accordance with findings of a community-based study in 1996 [

The chance of developing the PD in a family whose mother is diagnosed with the disease is estimated to be 0.26487 in comparison to 0.31477 when father had the Parkinson’s; suggesting that the chance of passing the Parkinson’s from father to children is slightly higher than passing it from mother to children [

Although a primary cause for Parkinson’s disease is yet to be identified [

The authors declare no conflicts of interest regarding the publication of this paper.

Saghafi, A., Tsokos, C.P. and Wooten, R.D. (2018) On Heredity Factors of Parkinson’s Disease: A Parametric and Bayesian Analysis. Advances in Parkinson’s Disease, 7, 31-42. https://doi.org/10.4236/apd.2018.73004