Authors: Melissa Ferriter, Kristy Pan, Cole Diloreto, Paul Radu, Aidan O’Connor

The Salk Polio trials conducted in 1954 were used to test the efficacy of the polio vaccine devloped by Jonas Salk. The National Foundation for Infantile Paralysis (NFIP) performed two clinical trials corresponding to two statistical designs, a randomized control and an observed control experiment.

Polio, also known as Poliomyelitis, is a potentially deadly infectious disease caused by the poliovirus. Symptoms include muscle weakness, respiratory infection, fever, abdominal pain, and paralysis. Depending on immune system strength, polio can be a minor illness that does not affect the central nervous system, or it can develop into a major illness involving the central nervous, which may be paralytic or non-paralytic.

Project Objective: Using the data from the 1954 polio trials, we want to explore if the polio vaccine was effective at preventing paralytic and non-paralytic polio.

The dataset below describes two experiments used to test the efficacy of the polio vaccine. The original observed control design, used second-grade children given the vaccine as the treatment group, and non vaccinated first and third graders as the control group. In the second design, the randomized control experiment, a sample of school children was randomly divided into the vaccinated treatment group and a control group given a placebo. This second expirment utilized the double-blind method, meaning that neither the child nor the doctors knew which group the child belonged to. The not-inoculated category refers to children who did not participate in the study, and the incomplete vaccination category refers to children who did not complete all three doses of the vaccine.

Experiment Group Population Paralytic NonParalytic FalseReports
ObservedControl Vaccinated 221998 38 18 20
ObservedControl Control 725173 330 61 48
ObservedControl NotInoculated 123605 43 11 12
ObservedControl IncompleteVaccinations 9904 4 0 0
RandomizedControl Vaccinated 200745 33 24 25
RandomizedControl Placebo 201229 115 27 20
RandomizedControl NotInoculated 338778 121 36 25
RandomizedControl IncompleteVaccinations 8484 1 1 0

Quantitative

  • Population

  • Incidence of paralytic polio

  • Incidence of non-paralytic polio

  • Number of false reports

Categorical

  • Type of experiment (randomized vs. observed)

  • Group (vaccinated, control, not innoculated, incomplete vaccination)

    Experiment Group Polio No_Polio
    ObservedControl Vaccinated 56 221942
    ObservedControl Control 391 724782
    ObservedControl NotInoculated 54 123551
    ObservedControl Incomplete 4 9900
    RandomizedControl Vaccinated 57 200688
    RandomizedControl Placebo 142 201087
    RandomizedControl NotInoculated 157 338621
    RandomizedControl Incomplete 2 8482

We transformed the data to visualize more clearly the test subjects who contracted polio vs. the subjects who were healthy at the end of the study. We did this by adding the “Paralytic” and “NonParalytic” Columns from the original dataset to get the total number of subjects who got polio. We then subtracted this number from the “Population” column to get the number of subjects who did not have polio. These columns became “Polio” and “No_Polio” respectively in the new data table. Both data tables are used throughout the analysis. Due to the nature of our data (count rather than continuous), we were severely limited on what kind of analyses we could perform. Consequently, we chose questions that could be answered with chi-square tests, and visualized our data with bar graphs.




Questions we can explore with our data:

  1. Is there a difference in incidence of polio in the vaccinated and placebo groups for the randomized control experiment? (chi-square test for homogeneity)
  2. Is the proportion of polio infection for the vaccinated and control groups the same for the first observed control study, as it was for the second randomized control, double-blind study? (chi-square test for homogeneity)
  3. In the randomized control experiment, is vaccination associated with a decrease in the serverity of polio contracted? (chi-square test for homogeneity)
  4. Is there a detectable placebo effect in the randomized control experiment? (chi-square test for homogeneity)
  5. Are you equally likely to get polio as you are to not get polio in the randomized control experiment? (chi-square goodness-of-fit test)

Question 1: Is there a difference in incidence of polio in the vaccinated and placebo groups for the randomized control experiment?

            Polio No Polio
Vaccinated     57   200688
Placebo       142   201087

    Pearson's Chi-squared test

data:  qone
X-squared = 36.12, df = 1, p-value = 1.855e-09

H0: The proportion of vaccinated subjects who get polio = The proportion of placebo subjects who get polio
H0: The proportion of vaccinated subjects who don’t get polio = The proportion of placebo subjects who don’t get polio
Ha: The proportion of vaccinated subjects who get polio ≠ The proportion of placebo subjects who get polio or The proportion of vaccinated subjects who don’t get polio ≠ The proportion of placebo subjects who don’t get polio

At alpha = .05 we reject the null hypotheses and conclude that there is sufficient evidence to say that the proportion of polio infection is different among vaccinated and placebo patients in the randomized placebo experiment. Along with this test of homogeneity, a visual inspection of the data also indicates that vaccine is effective at preventing polio infection. The bar graph shows the counts of patients who have polio and those who don’t for each of the treatment groups. Although subtle, the difference between the vaccinated and placebo groups can be seen in these counts, and is statistically significant.









Question 2: Is the proportion of polio infection for the vaccinated and control groups the same for the first observed control study, as it was for the second randomized control, double-blind study?

                     Vaccinated      Control
Randomized Control 0.0002839423 0.0007061620
Observed Control   0.0002522545 0.0005391817

    Pearson's Chi-squared test

data:  qtwo
X-squared = 2.1341e-06, df = 1, p-value = 0.9988

H0: The proportion of vaccinated subjects who get polio in the randomized control experiment = The proportion of vaccinated subjects who get polio in the observed control experiment
H0: The proportion of control subjects who get polio in the randomized control experiment = The proportion of control subjects who get polio in the observed control experiment.
Ha: The proportion of vaccinated subjects who got polio in the randomized control experiment ≠ The proportion of vaccinated subjects who got polio in the observed control experiment or The proportion of control subjects who got polio in the randomized control experiment ≠ The proportion of control subjects who got polio in the observed control experiment.

The purpose of this test was to see if the studies were coming to different results since the utilized different experimental designs. At alpha = .05 we fail to reject the null hypotheses and conclude that there is insufficient evidence to say that the proportion of polio infection in the vaccinated and control populations is different among the two experiments. After getting and insignificant p-value and inspecting the distirbution of proportions on a bar graph, we conclude the experiments yielded similar distributions. Note that in the observed control experiment the control group gets no treatment, but in the randomized control experiment the control group gets a placebo.




Question 3: In the randomized control experiment, is vaccination associated with a decrease in the serverity of polio contracted?

           Paralytic NonParalytic
Vaccinated        33           24
Placebo          115           27

    Pearson's Chi-squared test

data:  qthree
X-squared = 11.378, df = 1, p-value = 0.0007431

H0: The proportion of vaccinated subjects who get paralytic polio = The proportion of placebo subjects who get paralytic polio
H0: The proportion of vaccinated subjects who get non-paralytic polio = The proportion of placebo subjects who get non-paralytic polio
Ha: The proportion of vaccinated subjects who get paralytic polio ≠ The proportion of placebo subjects who get paralytic polio or The proportion of vaccinated subjects who get non-paralytic polio ≠ The proportion of placebo subjects who get non-paralytic polio

Although earlier tests suggested that the vaccine was effective at preventing polio, we also wanted to see if the vaccine was effective at preventing the more severe, paralytic form of polio. At alpha = .05 we reject the null hypotheses and conclude that there is sufficient evidence to say that the proportion of paralytic and non-paralytic polio infection is different among vaccinated and placebol patients in the randomized placebo experiment. Along with the significant p-value, the proportional bar graph also suggests vaccinated subjects have a lower proportion of paralytic polio.








Question 4: Is there a detectable placebo effect in the randomized control experiment?

               Polio No Polio
Placebo          142   201087
NotInoculated    157   338621

    Pearson's Chi-squared test

data:  qfour
X-squared = 13.386, df = 1, p-value = 0.0002535

H0: The proportion of placebo subjects who get polio = The proportion of not inoculated subjects who get polio
H0: The proportion of placebo subjects who don’t get polio = The proportion of not inoculated subjects who don’t get polio
Ha: The proportion of placebo subjects who get polio ≠ The proportion of not inoculated subjects who get polio or The proportion of placebo subjects who don’t get polio ≠ The proportion of not inoculated subjects who don’t get polio

At alpha = .05 we fail to reject the null hypotheses and conclude that there is insufficient evidence to say that the proportion of polio infection is different among placebo and not inoculated patients in the observed control experiment. The not inoculated group consists of subjects who received no treatment, while the placebo group received an unspecified placebo. This chi-square test was used to see if the placebo group had significantly different distributions of infection than the not inoculated group. If there was no placebo effect, we would expect proportions to be the same, which is what the test of homogeneity showed us.









Question 5: Are you equally likely to get polio as you are to not get polio in the randomized control experiment?


    Chi-squared test for given probabilities

data:  qfive
X-squared = 338150, df = 1, p-value < 2.2e-16

H0: The data are consistent with an even distribution
Ha: The data are not consistent with an even distribution

At alpha = .05, we reject the null hypothesis and conclude that people do not have an equal probability of getting polio as they do not getting polio. The purpose of this test was to establish that polio infection does not have an even (50/50) distribution in the general population.














Conclusions

After performing chi-square tests for goodness-of-fit and homogeneity, and visualizing the data with multiple bar graphs, we concluded that the polio vaccination was effective at preventing polio infection. We also saw that there was no significant difference between the outcomes of the two different experimental designs, which further suggests that the vaccination is effective. Interestingly, we identified that vaccination was also associated with a decrease in the severity of polio contracted (paralytic vs. non-paralytic), although this is not something the original researchers focused on. Finally, we determined that there was no detectable placebo effect, which further legitimizes the polio vaccine’s efficacy. Although designing our study around limited count data was difficult, we believe we were able to effectively explore this groundbreaking medical research that led to the eradication of the polio virus.