Randy Neil Biostats 02: Biostatistics Summary Step 1 - USMLE The Extra Stuff

NNT = 1 / ARR

ARR = control event rate − treatment event rate.

Positive LR = sensitivity / (1 − specificity)

Negative LR = (1 − sensitivity) / specificity

Attributable risk percent = (RR − 1) / RR

Find q² first, then take the square root to get q .

Answer: B) 4

ARR = 0.60 − 0.35 = 0.25. NNT = 1 / 0.25 = 4.

Answer: C) 7

Positive LR = sensitivity / (1 − specificity) = 0.70 / 0.10 = 7.

Answer: B) 0.40

Autosomal recessive disease frequency = q². If q² = 0.16, then q = 0.40.

Alright guys, this should be the second video and this will have some of the, you know, not as, you know, you always should, they were high yield. We'll instead want that first video pretty much recovery that stuff you're guaranteed to see. This stuff is kind of like the second tier, but for completeness, I think it makes it for a good job just, this should make you well prepared for step one definitely, even some items, step two and stuff like that. So, alright, so here we go. It says placebo versus new drug ex, blah, blah, blah, blah, blah, blah, a two by two table based on the physician assisted data, the number of patients who need to be treated, you need to be treated, which drug ex show improvement in one patient is which of the following. So what they're asking is a number needed to treat, okay, and you always see that the number needed to treat or number needed to harm. And for our purposes, just think of them as the same thing. So number needed to treat the formula and this is something you just got to memorize is one over the absolute risk reduction, okay? So what, the method you have to say was the absolute risk reduction. Well, the absolute risk reduction is like a separate formula that you really have to know. So the absolute risk reduction is the event rate of the controlled minus the event rate of treatment. So long story short, that's kind of what they are, but you got to know these formulas, okay? If you don't know the formulas, you're kind of dead in the water, but they like this question right here. They really like that number needed to treat one. So that's what this question says. Number needed to treat. So they don't give us the absolute risk reduction because they got they would say that they didn't have the question. What they do give us is placebo versus drug. Now placebo is like a control right? So the placebo is like the event rate of the

control and then the treatment would be actually the drug. So they say they based on a physician assisted data. So they have two types here. We got patient assisted, physician assisted. So they want this one. So don't fall on the trap. We don't care about that anymore because we want the physician assisted. So now we find the difference between the placebo or control and what the drug said. What's the difference between 60 and 35? That's actually what? 25, right? And we don't deal with percent in math. We deal with basically decimal. So 25, 25 percent is 0.25. And that's your absolute risk reduction. That's the difference between treatment and placebo. Your absolute risk reduction. They usually give you a chart to make you find this. So now you take that number here and then plug it back in to our formula for number needed to treat. And so 1 over 0.25. Now I can solve that. But if you don't know how, whatever basic math tips that you've kind of learned throughout the years, sometimes you say, well, oh, that was 25 percent. I know 25 percent is 25 out of 100. How do I get rid of a fractional bottom? I just do the inverse of it. So just flip it upside down. And so the bottom cancels out and on the top, I'm left with a hundred over 25. And again, that's just some basic math. If you can get to this stage, you're in shape and just solve them there. So what's 25 over 100 over 25 or 100 divided by 25? Answer is going to be 4. So in this question, they asked you what was the number needed to treat? You got another formula. And then you got to know this formula one extra step, because the absolute risk reduction is actually a formula with them itself. And then when you plug those numbers in, you're going to get answer choice A as in 4. Okay? Very good. Next one says, basically, let's go to the question. It says, which of the following is a positive likelihood ratio. And

you'll see this thing called likelihood ratios. And most of us don't know what those are. We always have to look these things up. But in step one, step two, and even step three, you're going to see a thing called likelihood ratio. And it's all fair game. It's all based on the formula. So likelihood ratio. You have a positive likelihood ratio and a negative likelihood ratio. And basically, likelihood ratio just says, it's looking at a test and saying, you know, really kind of how accurate is this test doing what we want it to do. But they don't really care that you know the definition. What they're going to do is they're going to give you this kind of stuff. And actually, say, can you figure out what the likelihood ratio is? So we got to know what the formula is. So likelihood ratio, think of like this, always say sensitivity over specificity. And this is for both of them. Sensitivity over specificity. Likely to ratio only has to do with that. It really has nothing to do with these guys. So there's one extra step. The positive likelihood ratio, you're going to put a one minus the specificity. And the negative likelihood ratio, you're going to put one minus the sensitivity. Okay. So as long as you know, it's sensitivity of a specificity. And then the positive one has the one minus on the bottom. And the negative likelihood ratio has one minus on top. The user of the formula is that you have to know, okay. That's why these questions aren't as much fun because it's all based on memorizing and using a silly formula. So from that, you know, from that, we go back to the problem. And all this is just kind of smoke and mirrors up top. If we know we're looking for this, all I need is sensitivity and specificity. So then we just plug a man. They asked for the positive likelihood ratio. So that I know that is actually sensitivity over one minus specificity. And so when I plug

those in, sensitivity is 70%, but we don't deal with percent speedy-lett decimals. And then the bottom is one minus specificity, which is 0.9. So if I take this out, little further, I have 0.7, 1 minus 0.9 is actually 0.1. And if I divide that out, I get 7. Okay. So pretty easy. Once we get down, once we realize what we're looking for, we know the formula and then we just kind of plug it in. You know, once you know the formula, this plug it in, I just kind of redo your basic math skills. But they do like this likelihood ratio formula. Know the positive and the negative. The only difference is where you put that one minus, okay. Alrighty. So we said this one says a perspective study was conducted to assess a relationship between elevated PSA and prostate cancer. Patients were selected at random. Result showed a 20 year relative risk, 4.0 for men with elevated PSA compared to the men with normal PSA. If the p-value was 0.03, 95% percent compensable, 1.55, then what percent of prostate cancer can be attributed to elevated PSA. So whenever you see a problem on step one, and it says, what percent, you know, any time they're dealing with percent, the only questions that I've really seen on step one, then when they talk about percent, and make you find this, is going to be the ab-attributable risk percent, okay. And so what is that? Well, the formula for that is just relative risk, one is one over relative risk, okay. Because it's the risk, or the triple risk percent, the triple risk percent. So all you know is a relative risk, okay. It's the relative risk, minus one over relative risk. So from that, all we need to do, so when I were S8%, I jumped on this formula right here, one that we have to memorize, and then I just plug in jug. So, relative risk is what? Relativist, that they told us in it, relative risk right here is four. So I go four minus one over four, four minus

one is three, but a bit four, and I get three out of four, or three coins out of a dollar, it's what 75% or 75% inch of choice F. So pretty basic problem. And the only thing that you're really doing is, again, it goes back to knowing the formulas. And again, we've done a slight memorizing things, but we want all the points to be one on step one. So we gotta do a good job. All right, now this one talks about the, obviously if I can kind of zoom in a little bit, if I have that's gonna be hard. So a research group, it talks about research group is studying a new biomarker for a disease in a random sample of asymptomatic patients, greater than 70 years of age. As a majority of this type of disease, it's slowly progressive, that's interesting, slowly progressive. The investigator's are concerned that the new test will be overestimated due to the detection of a disproportionate slowly progressive in nine cases. The investigators are concerned about what type of bias. So you have all the biases that are in the, you see them in the step one first aid book, all that kind of stuff. But the key with this one is, so the researchers are worried, but what they're worried about is the fact that they got all these, they're finding all these diseases that are slow the nine cases. So they're just detecting them and these people are living and living longer, but it's mainly because they're finding, it's more about the disease being more benign cases that they're adding in there. So whenever you see that, you know, whenever you see benign cases, if that says benign, you're gonna go with length time bias, the answer to choice E, okay? That's just a flat out just knowing, okay? Benign, slow growing, anything like that, that's adding to why people are living longer. It's an illusion of most of the living longer, length time bias. The one they want you to buy it on, of course, we always put

it in the answer to choice A, that's how they do things is lead time bias. Remember, lead time bias is just when you're detecting the disease earlier, okay? It's like in prostate cancer instead of detecting people, it's say 60 years older, you're detecting them at 50. So when this gives us illusion, oh, oh, if we're gonna get 50 and they're living to 80, people are living longer and you're like, no, no, no, no, no, that's not the case. The case is actually just finding these people a little bit earlier, that's lead time bias. Laint time, more benign, slow growing cases. So you really have to know these two. They like to test between those. Hawthorne, obviously, it was people who know that they're being watched, they changed their behaviors. Sanctal bias is something like where you're doing a test and you, and the test was on like, say a Hispanic population, and you're trying to say, well, does that really apply to everybody that I'm, everybody else in the world? Can I, can I adapt those results? So, but I just want you to know a length time lead time for that right now. This one says, a drug ABC versus Santa Therapy and for vending UTIs was recently published, a study, I'm sorry, a study of the drug. The absolute risk reduction, okay, absolute risk reduction for drug ABC versus Santa Therapy is 6% so I'm gonna say 6% or 0.6 because we deal in decimals. If the incidence of UTIs with Santa Therapy is 8% and there are 29 UTI patients in the drug ABC group, how many total subjects are in the drug ABC group? All right, so when you look at this, you say, I know clue where to start. What do I know? Well, I know absolute risk reduction to gaming. I know the formula for absolute risk reduction is the event rate of the control minus the event rate of treatment. So let's just start there and see if we can figure this out. They told me the absolute risk reduction is 0.06. I can

put that right there. And then it says, the, if the incidence of UTIs with Santa Therapy, okay, remember, standard therapy is like your control. That's your baseline, that's your gold standard. So it's team therapy is 8%. So that's the event rate of the control is 8% or 0.08. And there are 29 UTI patients in drug in the drug group. So here's the drug group, this is a treatment. And usually there's some percent, but all they're giving us is the number of people that actually tested positive for it. So there's 29 people out of some number, and actually that's the question that they're asking us is a total number of subjects in there. So here's our formula. So if you can get to this point right here, you know, you get the battle half one. So absolute risk reduction is event rate control, minus event rate treatment. So now let's solve for X, and I think we got this thing. So let's, you know, to get X by itself, we've got to move everything to the other side. So 0.06 minus 0.08. Well, technically that's like a negative number. And that's okay for right now. So that goes away. And all I did there was some basic math, 0.08, I'm sorry. I'm gonna get negative two. Now in this side, I got negative 29, X, or minus one, and X. So I can get rid of the minus sign, just say I multiply both sides by negative one. I can do that. If you want something to one side, do it to the other, it goes away. Basic math. And then I'm left with 0.02, over equals 29 over X. So again, solving for X, like most level, sides, 0.02, and X equals 29, and I can divide by X. Oh, what am I doing? The same thing. I'm divided by 0.02, I'm sorry. So X equals 29 divided by 0.02. So then I take this, I say, well, can I divide 29 divided by 0.02? And I say, well, I can go one two. Desk one, if I don't see this at the end, one two. So now I got two, they go into this. So two goes into two once, carry down nine,

two goes into nine, four times. Okay, one, bring down a zero, two goes into ten, five times, and that makes it nice and bring down a zero, and then zero. So this gives me X. In X actually, you went right there. So that's the number of people. So X equals 14, 50, and X actually, just to be this guy right here, should be, I choice D, but it should be 14, 50, because two, yet one, two, four, yeah, should be 14, 50. But the moral of this problem is, when you see something like this, don't get confused, don't get upset, just ask yourself what do I know. Well, I know a couple formulas. They told me I started out absolute rest reduction. I know that guy. And then all I did was read the problem, plug in some numbers, and then just gotta know your basic math, how to solve for that X, and then you got it. But I want you to know this guy's, know your formulas, and know how to plug things in. Don't get frustrated, ask yourself what do I know. All right, this one says, you're asked to assess the efficacy of a new psych drug which is being hailed as a new blogbuster. The result of a randomize control style at eight years is given table below. Okay, treat me to drug, placebo psychosis, and psychosis is 2 by 2 table. What is the number needed to treat? Okay, so it's one of those number needed to treat ones. It always talk about this second before. Number needed to treat equals 1 over the absolute rest reduction. But what's the absolute rest reduction? alltså rest reduction is event rate, control minus event rate is treatment. So, let's figure this out. Event rate controlled. The control would be placebo. So, that's going to be this guy. So, it's 30 people had psychosis and 9 and 7 he didn't. So, 30 people did out of 1,000. And all ideas was add these guys up. And then minus the event rate of the treatment. Well, the treatment is a new drug. And there's 15 people that had psychosis

out of, well, there's out of the whole bunch. There was 1,000 people. So, that's going to be my absolute risk reduction. So, what's different between those is 30 minus 15, 15 over 1,000, just a basic math. So, that's actually my absolute risk reduction. And I plug that in just like before. I have 1 over 15 over 1,000. It's nice. It's an infraction form. Makes my life a little easier. So, then you get rid of this fractional bottom. I just got a multiplied by the inverse. So, flip it upside down. And whatever I do to the bottom, I got to do to the top. Bottom cancels out. And I'm left with 1,000 over 15 or 1,000 divided by 15. Now, I can 15 go into 1. Note, can 15 go into 10. No, can 15 go into 100. Yep, how many times? 6. That's 90. I'm left with 10. I bring down my 0. Can 15 go into 100? 6. And that's 90. And you see the pattern there. And I could put a decimal. And I keep running into this whole 6. So, my number needed to treat is actually going to be 66.6. But if we're dealing in people, we got to read the round-up round-down. And we're going to round-up. So, 66 is actually going to equal 67, which is going to be answer choice E. So, in this one again, what are they asking? Number needed to treat? You got to know your formula. And you got to take that and expand it all the way down to this. And from there, you just find the difference. It should be a reverse production. Absolutely a reverse production. It's just a difference between something. It's just a difference between them. You do that, put it over 1, put it under 1, and then just solve some basic math. So, if we don't real quickly. All right. Now, we got how do you winberg stuff? All right. So, the key with how do you hardy winberg. And let me just kind of jump ahead, because this is something kind of popular. No, they like it. There's two formulas that you had to hardy winberg. Whenever you do a hardy

winberg stuff, they basically hardy winberg said, look, let's just figure out the chances of seeing stuff in a population that has no excuse and stuff like that. So, there's two formulas. First one is this p squared plus 2 p cubed plus q squared equals 1. This other one's p plus q cubed equals 1. So, this formula here is just the alleles and the genes. So, if they, you know, they talk about, like if you know, if you have a gene for a certain thing, they're talking about this p plus q. Now, p, you always have to know as a sociosuit to dominate. Q is going to be the recessive. And these are just alleles. And if I had to dominate plus recessive in society, it should equal 1. Got to know it. Now, when they start talking phenotype, this is just what phenotype is like, how things are expressed. So, this goes to end of p squared plus 2 p cubed plus q is 1. So, again, p is a dominant. So, p squared represents the dominant expression of someone carrying both dominant alleles. And then the 2 p cubed is actually going to be expressed what? It's going to actually express as a dominant, right? Because it has both dominant and recessive, the dominant, obviously, is dominant, so it's going to be expressed. So, that's going to be someone that's called what heterozygous, right? Homosigous had both the same heterogyous, I guess got one of each. And then it's q squared. This is super duper important, right there? The q squared is going to be the recessive, uh, missing. Rescessive expression, okay? Now, this is kind of how they test, okay? They're going to give you something and they, in pretty much, they always do it this way. They give you q squared. Somewhere in the problem, they give you q squared and then from this, you can work backwards and you can find out any one of these. Because I can take q squared and do what with it. I can technically take q squared, take the square root,

and now I got q. Well, I know of q plus p equals 1, then I can find p. And then if I know about p and q, I can solve any of these guys. So, long story short, when you see Hardy Weinberg problems, and these start talking all this kind of stuff, you know, the, the, the, the, the, the recessive expression, as an population, just know that you're looking for q squared, take the square root of that work backwards, and you'll solve all these problems. So, here's our problem. Hardy Weinberg. It says 16% of the population is unable to smell a chemical bubble gas. These non-smellers are recessive for the smelling gene. What percentage individuals in the population are smellers? All right, so this first one is just basically, you know, with 16%, 16% of people are non-smellers, how many are smellers? Well, it's everybody else, right? So, what's 100 minus 16, and you actually get 84%. So, first one's not even like a Hardy Weinberg thing, it's just some basic stuff, okay? Basic common sense. It's 16% of the people can't do it. Well, the remaining people can. So, that would be a single unit minus that. Now, it says, what's a frequency of the dominant and recessive allele? Well, it's, what's key is they said, the 16% of people are recessive for that smelling gene. They're recessive. So, what does that mean? That's recessive expression. It's not necessarily a gene that's a recessive. They're saying they can't smell and smell and it's like it is some type of expression of that. So, the 16% actually represents q squared, okay? So, that's q squared equals 16%. So, remember what we said? They're going to give you the recessive. Now you just work backwards, okay? I can take the square root of that and come up with q. What's the square root of 0.16? What's the square root of 0.16? Just ask yourself, what times itself can you give me 0.16? And if you didn't know, you can just kind of write

these out so you get it correct. And the answer is going to be 0.4. Now, you'll be sorry, if I had 4 times 4 or 16, 2 decimal spots, 0.16. So, it's 0.4. Now, again, if q is 0.4, I know that p plus q equals 1. So, q is 0.4. So, I know p has to equal what? What plus 0.4 equals n? It's 0.6. So, there we go. What's the frequency of the dominant allele? 0.6. What is it about the recessive allele? Well, recessive is going to be 0.4 because I work backwards. So, that answers that 1.6 of the way 4. And then it says, what percentage of the population are heterozygous for the tray? Okay, so heterozygous. Remember, heterozygous? That's 2 p q. Heterozygous meaning they have 1 of each. Homeless, I guess, means they have both of the same. So, then I just take what I know 2 times p plus q. And then you can kind of solve that out. You know, it's a, you see, 0.6 times 2. 1.2 times 0.4, say 0.48, 0.48 or 48%. Okay, it's a basic map. But again, the key with Hardy-Wine Burgers are going to give you the recessive expression, which is basically q squared. And then from there, you take the square root of it, work backwards, fine q, then you find p, and then you can solve anything that's in these equations. But you must know the equations, right? You must know the equations. All right. And we are going to talk about that one. All right. So, looking at this, this is just another Hardy-Wine Burg problem. You know, healthy 25-year-old, she comes in. She has a kid. She does ours have another kid, but her actual husband has a little problem, so he can't do it. So, she went out and, you know, had a sperm donor, whatever, but then she comes out and then her kid has some rare autosomal recessive disease. Okay. So, in this disease, there's known to be effect 190,000 people. What is the probability of the patient who would have a second child effect with the new healthy sperm donor? So, kind of a

complicated problem, but we knew about it. They started talking rare autosomal recessive disease, and they gave us some ratio of the frequency of this rare autosomal disease. So, I know they're talking highly wineburg. So, what are my two formulas? Okay. P squared plus 2 pq plus q squared equals 1, and then p plus q equals 1. This is the phenotype expression. So, it's the alleles. Okay. And they always gave me this guy, which they did. They said that's 1 in 90,000, and that's q squared. Okay. That's the expression out there in public. All right. So, how do I work this? I could say, well, basically, what's the question? It says, what does the probability that the patient would have a second child effect with the new sperm donor? So, this gets into a little bit of genetics, but we know the mom, you know, she has this gene. Okay. So, chances are, you know, if we're drawing one of those, you know, the planet squared deals, you know, mom has this, and then she's got the gene down here. So, chances are she might give this as to her offspring, it's going to be one half. Okay. One half. Now, the chances of her finding another person, you know, with a new healthy sperm donor, well, this healthy sperm donor is drawn from the public. And that's what Harvey Weinberg says. He's just giving ratios in the public. So, we're looking to see what is the gene frequency, the allele frequency, of someone random in public. So, now we're dealing with this guy over here. So, we're not really looking for, you know, the cue, because that's the expression, we want another gene. So, we take the square root of that, and then a cue equals one. And what time to self gives me 90,000? And that's going to be 300. So, you know, a guy off the street, per se, his would be one in 300. So, if we combine the guy off the street with a one in 300, which is basically cue, with the chances of it coming from on,

well, we already know she's got it. So, it's a one in two. So, her plus this guy is going to give me, we multiply cross the word, one times one is one, two times, there's a hundred, it's six hundred. So, what is a probability? One in six hundred. This is a Harvey Weinberg problem that was taken one extra step. You know, they gave us a autosum recessive, and they could have asked, they could have asked us any of these things. They could have asked us any of them. But they went ahead and just started talking about, you know, when the woman had something with the man, what's the ratio, but if you can set this problem up and know the Harvey Weinberg asked this, and you'd start taking the square root and working backwards, you can basically solve anything. So, this is an interesting problem. Because it took, it made you a one extra step. Most people fall in the trap into stopping right here and one in 300, but the actual answer would be one in 600, because we're talking her genes plus his genes, what's the frequency? What's the frequency? Okay. Let me see. This is that one. I'm not going to worry about too much this. So, the video would be way too long. So, basically, here's a formula. When you walk into step one, you're going to get a lame and age sheet. And that lame and age sheet, you can do anything with it. So, use before the test starts, I just write down some basic formulas and stuff. You know, if you, and basically it's only in biased statistics. You know, this is just one area where we need to kind of really dominate, and it's really not that bad of an area. So, here's just some formulas and probably what I would do. When I first get in that test, I would probably go in there. And if I didn't have these memorized, I'd say, Oh, well, I remember, I mean, see, this is reality on top, the test goes on the side, sensitivity went this way, specificity, positive value,

negative value. And so, those are all my formulas. And watch that first day to understand that. I'd also kind of redirect myself to say, remember, this is that null hypothesis, a table. And again, reality, test, alpha, beta. This is type 1, error, this is a type 2 error. And then one minus beta is power. And you know, this is the null hypothesis, and there's no associations when it says there is an association. And remember, they like to test you on this box here, and then where you might have to actually, and they put this into words. Okay, we have to know what, we have to write, we have to write, write down, there's case control, and there's cohort studies. So there are two big ones, case controls associated with odds ratio, which is one number over, one number. And then we have cohort, remember, these things look the same. So it's associated with relative risk, which is one number over two. Okay, so I'd easily just quickly write that down. And then I'd probably come in there and say, oh, my number needed to treat or harm, think of that way as one over the absolute risk reduction. Absolute risk reduction is event rate. Control minus event rate treatment. I probably have that one on there. And then obviously, the likelihood ratios, positive and negative likelihood ratios. And you can remember it's sensitivity over specificity, sensitivity over specificity, and it's all where you put the one. And when the positive likelihood ratio is one minus specificity, negative likelihood ratio, one minus the sensitivity. And so that's pretty much it. So I immediately kind of go in there and, and what else we do? We do attribute risk per cent. Anytime you see a percent, you think this formula, relative risk minus one over relative risk. If you go in there with these formulas, guys, you should pretty much dominate the biostatistic portion of the USML. You always hear about people

maybe not pass them. I want to point, don't make it on this topic. So kind of look at these and hopefully you'll do well in the test, guys. Good luck.