Learning Medical Statistics at a Theme Park Chapter 1
A new series begins.
"Compared to conventional drugs..."
"The hazard ratio is..."
"The p-value is..."
"Using logistic regression analysis..."
???
Even when reading papers, many people find medical statistics difficult and are not good at it!
I think there are many such people.
Therefore,
▶︎Comparing medical statistics to familiar things
Example: Is there a difference in the male-to-female ratio between the Land group and the Sea group?
▶︎Making it fun to look at charts in papers starting tomorrow
I hope to be able to deliver articles like that.
Dr.and a statistics beginnerTaro-kunwhile reading the conversation between
let's learn about medical statistics together.
Dr. and Taro-kun
moved to a certain theme park.
Dr."Taro-kun, first of all, I want you to memorize the names of things."
Taro-kun"Huh? Memorization right away?"
Dr."Just three things for now. If you memorize these, statistics will become much easier to understand."
1️⃣ Let's memorize 3 statistical terms
Dr."Taro-kun, what is your gender? Are you an adult? Do you smoke?"
Taro-kun"I am a man and an adult. I don't smoke. What is this two-choice question?"
Dr."Things that can be answered with these two choices.
This is called【Categorical Variable】."
Categorical variable:
Things that can be answered with two choices, such as gender or smoking status
Dr."Then, what is your age? What was the price of the tea you bought earlier?"
Taro-kun"My age is 25. The tea earlier was 200 yen. Is it numbers this time?"
Dr."Yes. Things that can be answered with numerical values.
This is called【Continuous Variable】."
Continuous variable:
Things that can be expressed as numerical values, such as age, length of hospital stay, or waiting time
Dr."And finally, how much time is left until today's parade starts?"
Taro-kun"It's in 8 hours."
Dr."The time until an event occurs.
That is【Time Variable】."
Time variable:
Time until an event occurs, such as the time until a parade
DoctorThese three are the basics, so remember them. Now, let's finally start talking about statistics.
2️⃣ Is there a significant difference in the gender ratio between Land fans and Sea fans? What is a p-value?
TaroSignificant differences and p-values often appear in papers, but I don't fully understand them.
DoctorIt's difficult, isn't it? Significant differences and p-values can be called the basics of statistics. Let's get a firm grasp on them. Have you ever seen a chart like this in a paper?
TaroI see it often. I often see it in charts of patient backgrounds in papers.
DoctorSince we are at a theme park, let's think of Treatment Group A as Land fans and Treatment Group B as Sea fans.
Are you a Land fan or a Sea fan, Taro?
TaroI'm a Sea fan! I like the stylish feel.
DoctorI see. Let's ask everyone else too.
We surveyed 200 park visitors on whether they were Land fans or Sea fans, and analyzed the gender differences and ages of those who answered Land fan versus Sea fan
DoctorLand fans are 40% male, while Sea fans are 60%. The average age is 27 for Land fans and 35 for Sea fans.
TaroIt seems there are more men among Sea fans. And the Land fans seem to be in a younger age group! Indeed, Sea has a more mature image than Land, so maybe it's more popular with men?
DoctorBut looking at this table, we cannot say for sure that there is a significant difference. This is because the 200 people who answered the survey this time might have just happened to have this gender ratio by chance.
TaroThat's true... If we asked 200 other people, it might be different!
DoctorThat is where [Statistical testing]
and the [p-value] calculated from it come in.
TaroIt's about to get difficult, isn't it...
DoctorRelax, Taro. I won't talk about anything that difficult.
First, in statistical testing, we make this assumption.
"There is no difference in the gender ratio between the Land group and the Sea group."
If we assume that, we calculate: what is the probability that a difference like this one, or even greater, would occur by chance?
The probability obtained from that calculation is the p-value.
If we calculate the p-value from the table earlier, it looks like this.
Dr."When I calculated it, the p-value for the gender ratio was 0.005.
This means that
if there really is no difference in the gender ratio between the Land group and the Sea group, there is only a 0.5% chance that a difference like this would be found by accident."
Taro"That's a very low probability. It seems like the initial assumption that 'there is no difference in gender ratio' is likely wrong."
Dr."Exactly. It's hard to believe that such a difference just appeared by chance.
In other words, the initial hypothesis that 'there is no difference in gender ratio between the Land group and the Sea group' is rejected, and
'there is a difference in gender ratio between the Land group and the Sea group' is judged to be the case.
And then, we say there is a statistically significant difference."
Taro"The same applies to age, right? If we assume there is no difference in average age, the probability of finding a difference like this by chance is less than 0.01%. If so, the initial assumption is rejected, and there is a significant difference in average age!"
Dr."That's right! Generally, if the p-value is less than 0.05, we consider it
'difficult to explain by chance alone,' and judge that there is a statistically significant difference."
Column
Dr."Let me talk a little bit about the tests we calculate here.
Gender is a categorical variable classified as 'male/female.'
Categorical variables are often compared using the chi-squared test.
However, when the number of people is small, Fisher's exact test is sometimes used."
On the other hand, things that can be expressed as numbers, like age, are continuous variables.
Continuous variables are often compared using a t-test. However, if the data is not normally distributed, the Mann–Whitney U test is sometimes used."
Taro“Do I really have to memorize... statistical tests?”
Doctor“It is necessary knowledge when you perform your own analysis, and I think it will help you lose your fear of the names of tests you see in papers.
I will explain the details after we delve deeper into statistics, so you can just let it slide for now.”
3️⃣ Let's learn about 95% confidence intervals
Doctor“Now, you understand p-values, right? And we found that there is a significant difference in age and gender in this survey.
But do you think the ratio of men in the C-group will be 60% every time we ask another 200 people?”
Taro“I don't think so. It might turn out to be a completely different number.”
Doctor“That's right. Every time we redo the survey, the results could change. That's why in statistics, we think in terms of a
‘range where the true proportion is likely to be’as arange.”
Taro“Could it be that thing I often see in papers called the[95% confidence interval]?”
Doctor“That's exactly it.”
“For example, let's assume these were the results. In this case, it was 60% in this survey, but it means that thetrue proportion of the Land-group is likely to be around 53–67%
.”
Taro“So a 95% confidence interval is a
[range where the true value is likely to exist]!”
Doctor“That's right. To be precise, it is
an interval created by a method that includes the true value in 95% of cases when the same survey is repeated many times—but your understanding is fine for now.”
Taro“I understand. Now I've got it perfectly!”
Doctor“Wait, wait. There is one more important thing.”
Taro“What is it?”
Doctor“What do you think would happen if we surveyed2,000 people instead of 200?”
Taro“Since there are more people, the results would likely be more accurate.”
Doctor“Exactly! For example, it would look like this.”
Taro“Even though it's the same 60%, the confidence interval keeps getting narrower as the number of people increases!”
Dr. "That's right. The narrower the 95% confidence interval, the higher the precision of the results."
Taro "In other words, the 95% confidence interval is an indicator to see how accurate the results are."
Dr. "Exactly. You understand it well. Wonderful!"
Taro "Statistics is becoming more and more interesting."
Dr. "That's nice to hear. It gets even more interesting from here."
In Chapter 1, I explained the "p-value" and the "95% confidence interval." But the really interesting part is yet to come.
Q. How much higher is the probability of riding a popular attraction if you use a FastPass?
→ Odds Ratio
Q. If you use a FastPass, "how much faster" can you ride a popular attraction? → Hazard Ratio
Q. Even considering age and entry time, is it really the effect of the FastPass?
→ Regression Analysis
From next time, let's tour the theme park with the Doctor and Taro, and conquer the popular attractions of medical statistics one by one!
Thank you for reading this article so far. Look forward to the next one!