1
00:00:00,610 --> 00:00:09,040
Well, welcome today. I have Rafael PEREIRA with me, who the university lecturer in statistics at the Department of Primary Care Health Sciences.

2
00:00:09,370 --> 00:00:10,480
Good day to you. Good morning.

3
00:00:11,110 --> 00:00:20,919
So Rafael's expertise in statistics and runs the monitoring group here in Oxford and has been working in primary care health care statistics.

4
00:00:20,920 --> 00:00:23,950
And it's a good friend of mine for some 15 years now.

5
00:00:23,960 --> 00:00:29,230
So we're going to look today at three different papers while we have this discussion.

6
00:00:29,740 --> 00:00:34,660
The first of them is absence of evidence is not evidence of absence by Doug Altman.

7
00:00:35,170 --> 00:00:40,180
The second is a really interesting paper which does date quite a bit.

8
00:00:40,180 --> 00:00:49,120
1763 An Effort towards solving a problem problem in the Doctrine of Challenges by the late Reverend Mr. Bays.

9
00:00:50,290 --> 00:00:56,429
And final paper is actually generalised linear models.

10
00:00:56,430 --> 00:01:01,570
So where we're really going to see how we get on with that. So let me start.

11
00:01:02,650 --> 00:01:07,420
Let's say I'm a up and coming student.

12
00:01:07,420 --> 00:01:13,340
I'm doing a Ph.D. and I've come to see a statistician. What do you think are the best ways to prepare?

13
00:01:13,390 --> 00:01:17,440
What do you think people should really know? And statistics before they say come to you?

14
00:01:17,800 --> 00:01:23,440
They may be an epidemiologist and maybe a clinician, but what the sort of problems you see where you think,

15
00:01:23,440 --> 00:01:25,570
well, you could have actually solved that yourself?

16
00:01:26,200 --> 00:01:36,279
I think I think the main issue that we deal with day to day is that people believe that statistics is mainly about a series

17
00:01:36,280 --> 00:01:41,620
of techniques that you would employ once you have your data that will give you an answer or the answer that you want.

18
00:01:42,280 --> 00:01:47,950
And more and more fortunately people are beginning to realise that it's not about that.

19
00:01:47,950 --> 00:01:59,890
So statistics is really a way of thinking. It's more about trying to understand how the data is generated and in because of the same reason,

20
00:02:00,250 --> 00:02:03,340
what sort of data would be the most appropriate to answer a particular question.

21
00:02:04,180 --> 00:02:11,740
So really we want to be involved or people need to be thinking about statistics or if you want study, design, whatever you want to call it,

22
00:02:12,430 --> 00:02:19,840
from the very early phase of your study and you want to think about what are the reasons why you want to collect information,

23
00:02:20,050 --> 00:02:26,440
what's the best possible information you want you possibly can collect to answer the the the question that you have in mind.

24
00:02:27,370 --> 00:02:34,210
And once you have that, if you if you're thinking adequately early on, then the methods you're going to use could be very simple methods.

25
00:02:34,510 --> 00:02:38,470
Sometimes they have to be slightly more complex, sometimes they have to be slightly more technical.

26
00:02:38,710 --> 00:02:43,240
But generally, if you have your question set up, right, gathering data right,

27
00:02:43,600 --> 00:02:46,870
then the methods that you're going to employ will be relatively simple ones.

28
00:02:47,230 --> 00:02:51,040
So let me come on on that point because I think over the years I've seen this problem a lot.

29
00:02:51,520 --> 00:02:55,510
I'd say it's one of the major problems. People say, I have a bit of data.

30
00:02:55,540 --> 00:03:00,959
Yeah, can I see a statistician? Yeah. And actually the issue is you have some data.

31
00:03:00,960 --> 00:03:04,270
And most of the time, as we try to say, well, what question do you want to ask you this?

32
00:03:04,630 --> 00:03:07,990
That's correct. So the onus is it's almost reciprocal.

33
00:03:08,020 --> 00:03:11,440
So if you start early on thinking, okay, what are the data? What data?

34
00:03:11,440 --> 00:03:16,420
I'm going to be collecting too much the right question, then the methods you're going to be employing are going to be very simple.

35
00:03:16,660 --> 00:03:23,290
When it becomes really complex is when people suddenly around say, I've been collecting data for the last 20 years, this is my large dataset.

36
00:03:23,740 --> 00:03:27,910
I want to do something using, Well, what do you want to do?

37
00:03:27,910 --> 00:03:34,990
What are the questions that you want to address? And sometimes this was very, very good advice that I got from Patil.

38
00:03:35,440 --> 00:03:42,130
Who was it? The statistician. When I first arrived to this apartment, she said, Well, first things you need to ask is, what's your question?

39
00:03:43,450 --> 00:03:48,850
And very often you find that when people come in with data, they don't have a question.

40
00:03:49,000 --> 00:03:52,870
And that's that's crucial because I have a statistician, sometimes I have my own questions,

41
00:03:52,870 --> 00:03:59,020
but they may not necessarily match the questions that the clinician or epidemiologists would be wanting to answer.

42
00:03:59,560 --> 00:04:05,049
So I guess this is just relate this to the sort of old trials and making old trial data available.

43
00:04:05,050 --> 00:04:11,320
This is a real concern of people who say, well, if we make data available, people are just going to do what they call dredging.

44
00:04:11,500 --> 00:04:19,690
Yeah. Which I guess is what is the real concern when you have lots of data available and to to to people out there.

45
00:04:19,690 --> 00:04:30,700
What does that so I mean this term you see often bandied about for data dredging more so data dredging is mainly about and it's it's seen as a

46
00:04:30,700 --> 00:04:41,980
very pejorative term but I'll come back to why nowadays is not as bad or has been rebranded into something that is being called now data mining.

47
00:04:42,670 --> 00:04:50,410
But data dredging is mainly about exploring information and exploring data without a clear idea what you want to look at.

48
00:04:50,740 --> 00:04:54,370
It's mainly doing loads of different comparisons.

49
00:04:54,370 --> 00:04:59,650
Could be, for example, if you have different subgroups or just looking at any kind of structure that the data might be.

50
00:05:01,860 --> 00:05:06,089
What happened to have and then come up and say, this is an answer.

51
00:05:06,090 --> 00:05:13,240
This is the answer to a question. So it is almost really reverse engineering ending up with an answer and then going back and oh,

52
00:05:13,260 --> 00:05:16,440
what was the question that was going to be answered by that? Okay.

53
00:05:16,710 --> 00:05:20,280
Yeah, you know, it's interesting. So but that's a really interesting start.

54
00:05:20,290 --> 00:05:24,989
Let's move on to some of these papers. Okay. What is it about tautology?

55
00:05:24,990 --> 00:05:29,370
The absence of evidence is not evidence of of absence.

56
00:05:30,890 --> 00:05:37,890
And this paper talks a little bit about throwing the term negative in the bin.

57
00:05:37,890 --> 00:05:43,380
And I'll say what is published in the BMJ by Doug Altman and Martin Bland,

58
00:05:43,560 --> 00:05:47,850
which many people will know in the Bland Open Box, which, if you have told me, might come back to that.

59
00:05:48,480 --> 00:05:57,240
So by convention a P-value greater than 5% P greater than 0.05 is called not significant randomised controlled clinical

60
00:05:57,240 --> 00:06:03,060
trial that do not show a significant difference between the treatments being compared are often called negative.

61
00:06:03,270 --> 00:06:13,490
Yeah. Yeah. You know you say I mean this artificial P of 0.05, where does that come from and why do we get in this body?

62
00:06:13,500 --> 00:06:16,530
Do see this? Well, it doesn't work or it's negative.

63
00:06:17,760 --> 00:06:25,440
The threshold, if we want to call it of p point nought five is remnant to when before we have computers.

64
00:06:25,920 --> 00:06:33,510
And before then what had happened is people had looked at specific what we call statistical distributions.

65
00:06:33,750 --> 00:06:40,680
People might know the normal distribution is the main one, which is a bell shaped distribution, but as many other types of distributions,

66
00:06:40,680 --> 00:06:48,450
not only that one, and calculated the specific value for that distribution at different probabilities.

67
00:06:49,080 --> 00:06:53,370
So it would be, for example, a probability of 1%. What would be the value of that distribution?

68
00:06:53,370 --> 00:06:57,210
A probability of 5%, 10%.

69
00:06:57,900 --> 00:07:05,580
And because they calculated these numbers, they became the thresholds that people could then use in the calculations.

70
00:07:05,730 --> 00:07:10,980
So there were just very specific values and the same thing applies for the normal distribution

71
00:07:10,980 --> 00:07:14,520
as to for other distributions are very commonly used in other statistical methods.

72
00:07:14,790 --> 00:07:23,640
For example, the F distribution of the TV screen and maybe what other people have heard of now with the arrival of a computer,

73
00:07:23,970 --> 00:07:30,840
it allows us to calculate the reverse. So for whatever value of X, for example, less than the normal distribution,

74
00:07:30,840 --> 00:07:39,600
what would be the probability that the would be, let's say that the the p value from that number onwards.

75
00:07:40,260 --> 00:07:47,490
And with that approach, it meant that a threshold of oh point nought five became a little bit outdated,

76
00:07:48,090 --> 00:07:53,250
which means that what it boils down to is if you have a certain amount of information,

77
00:07:53,670 --> 00:08:03,060
do your calculation end up with a P value of 0.051 that quantitatively and qualitatively is not different from 0.05.

78
00:08:03,250 --> 00:08:03,880
Hmm. Yeah.

79
00:08:03,900 --> 00:08:12,090
So having a predefined threshold point or five is really a line in the sand which says you'll get it wrong one in 20 times, roughly speaking.

80
00:08:12,660 --> 00:08:18,270
But people are moving away from that threshold and thinking more of what is the actual p value?

81
00:08:18,270 --> 00:08:25,110
Is it very, very small? Is it relatively large and making more if you want qualitative decisions based around that?

82
00:08:25,470 --> 00:08:32,129
Okay. So that's interesting. So one of the things that we often find and people are doing is and this paper is

83
00:08:32,130 --> 00:08:37,890
about is is more around the sort of sample size issues and it talks about here.

84
00:08:37,890 --> 00:08:46,440
Freeman himself found that only 30% of a sample of 71 trials published in the New England Journal of Medicine with a p greater than 0.1,

85
00:08:46,440 --> 00:08:54,150
were large enough to have a 90% chance of detecting even a 50% difference in the effectiveness of the treatment being compared.

86
00:08:54,270 --> 00:09:00,809
Yeah. So when we talk about that, this sort of terminology, alpha and beta isn't the sample size.

87
00:09:00,810 --> 00:09:08,000
So you see this is 80% power to detect a certain difference with an amount of confidence around

88
00:09:08,000 --> 00:09:13,780
that I could use so elaborate tried to explain in a drawing to explain I guess somebody said is it

89
00:09:13,860 --> 00:09:19,229
math with the letters which for us of clinicians is really difficult to understand and just trying

90
00:09:19,230 --> 00:09:24,360
to explain them terms a bit so people could understand how you arrive at sample size calculation.

91
00:09:24,390 --> 00:09:36,750
Okay. So let me give you a brief, some some brief terminology of what we use and set the scene of how we calculate these samples.

92
00:09:37,770 --> 00:09:43,050
Most of the calculations that we do or most of the comparisons that we do are based around medians.

93
00:09:43,230 --> 00:09:45,770
So it means so means of something very good.

94
00:09:45,990 --> 00:09:55,080
Could be, for example, the mean number of individuals, a proportion of individuals, that proportion can be thought of as a similar type of mean.

95
00:09:55,380 --> 00:10:00,020
So the proportion of individuals that recover in one group compared to proportion of.

96
00:10:00,060 --> 00:10:02,280
People that recover if you give them a different type of treatment.

97
00:10:02,310 --> 00:10:08,240
So the proportions can be thought of as a kind of mean if you want other types of means would be,

98
00:10:08,250 --> 00:10:10,960
for example, the mean blood pressure, one division in one group.

99
00:10:10,980 --> 00:10:14,700
So the mean blood pressure, if you don't give them treatment, this is the mean blood pressure.

100
00:10:14,700 --> 00:10:23,730
If you give them treatment. Most of these comparisons around means no means are a really interesting statistic because the more data you have,

101
00:10:24,000 --> 00:10:27,630
the more information you'll have about the overall mean of the population.

102
00:10:28,170 --> 00:10:31,650
And that translates into having more precise information around the mean.

103
00:10:32,280 --> 00:10:38,009
So if we think about that idea of precision as we extend the sample and we gather more precision,

104
00:10:38,010 --> 00:10:41,370
more information about where the actual mean of that group happens to be,

105
00:10:41,910 --> 00:10:48,150
what happens is when you compare two groups, if you have bigger numbers in each one of these groups with increased precision,

106
00:10:48,450 --> 00:10:51,450
you increase the certainty about a separation.

107
00:10:51,450 --> 00:10:56,370
If a separation exists between these two groups, and that's where the term sample size comes in.

108
00:10:57,870 --> 00:11:01,680
The separation that exists within these two groups is a hypothetical separation,

109
00:11:02,040 --> 00:11:06,900
because before we start the experiment, if you want, we don't know that separation exists.

110
00:11:07,440 --> 00:11:12,209
So it's down now to comparing two ideas of two hypotheses.

111
00:11:12,210 --> 00:11:16,560
You might be one idea. First, you usually call it the null hypothesis for the null idea.

112
00:11:16,580 --> 00:11:22,740
There's no difference between the two groups, in which case it doesn't matter how big a sample size is going to be, we're still going to get.

113
00:11:23,280 --> 00:11:25,290
In fact, the the bigger the sample it is,

114
00:11:25,290 --> 00:11:30,899
the more precise we precisely will know that there's no difference between these two things versus another hypothesis,

115
00:11:30,900 --> 00:11:33,030
another idea that there is some degree of separation.

116
00:11:33,450 --> 00:11:40,089
And it is this degree of separation that could be ten millimetres of mercury, for example, or 20 minutes of mercury.

117
00:11:40,090 --> 00:11:49,170
If we're talking about blood pressure, if we have a clear separation, if there's a very big separation, we need less data, smaller sample size.

118
00:11:49,380 --> 00:11:54,480
If there's a smaller separation between these two samples, we need more data because we need to increase the precision.

119
00:11:54,780 --> 00:11:59,130
And thus with this type of alpha, how if we reject,

120
00:11:59,400 --> 00:12:03,600
if we how much information we need to collect in order to decide whether one

121
00:12:03,600 --> 00:12:07,049
hypothesis is correct or we think we have evidence to reject one hypothesis,

122
00:12:07,050 --> 00:12:08,310
in fact or not.

123
00:12:08,760 --> 00:12:18,100
And beta, which is the capacity of us in a given experiment to identify or to collect data to say that this is actually happening is is the.

124
00:12:18,110 --> 00:12:24,450
Yeah, and so what are some people like here they go 90% power and some people say 80% power.

125
00:12:24,450 --> 00:12:28,559
And you put some grant applications in and people say increase the power.

126
00:12:28,560 --> 00:12:31,800
Why why do people do that before?

127
00:12:32,310 --> 00:12:36,650
If we if we think about it in sort of repetitions of the same experiment.

128
00:12:36,660 --> 00:12:41,910
So if you were doing this experiment lots of times because it's probably the easiest way to think about it theoretically,

129
00:12:42,270 --> 00:12:47,549
if you were to do the randomised controlled trial 100 times with these numbers,

130
00:12:47,550 --> 00:12:53,820
let's say you choose if you find that the sample size you need is 200 in each group with those numbers, 200 in each group,

131
00:12:54,300 --> 00:12:57,410
if you write a hundred times a power of 80% of a power,

132
00:12:57,430 --> 00:13:04,890
90% will tell you how many times 80 out of 100 for 90 to 100, you will find a significant again.

133
00:13:05,250 --> 00:13:08,370
Okay, that's how much that's made. That's simple even for me.

134
00:13:08,940 --> 00:13:16,469
An interesting one. Just finish this one point. I think about this paper which published in 1995 in the BMJ.

135
00:13:16,470 --> 00:13:21,810
So it's quite it's not an old paper book if it is, it is new compared to the other two.

136
00:13:21,930 --> 00:13:32,759
Yeah, I compared. And I guess there's something here about probably why systematic reviews came about talks about five fraud analytic treatments,

137
00:13:32,760 --> 00:13:40,169
mainly structure kinase in acute myocardial infarction and the overview of randomised controlled trials,

138
00:13:40,170 --> 00:13:48,990
which is what we now know is a systematic review, found a modest but clinically worthwhile and highly significant reduction in mortality of 22%.

139
00:13:49,500 --> 00:13:55,290
But only five of the 24 trials had shown a statistically significant effect with the p less than four whole point.

140
00:13:55,440 --> 00:14:03,729
Yeah. And I thought with some estimation, I just wonder is this an open source as wider research is on the power or is that still a problem?

141
00:14:03,730 --> 00:14:09,120
We see tonight today that actually many trials are still underpowered and we need to do more.

142
00:14:09,480 --> 00:14:13,200
Where are we actually moving into an age now? Where would you see much larger trials?

143
00:14:13,380 --> 00:14:25,620
I think there's a combination of things that so for one thing, probably nowadays people are more clear on the idea of power.

144
00:14:25,950 --> 00:14:34,890
And if you have a primary outcome, they normally funders would be adamant that you need enough information out there, enough patients,

145
00:14:35,160 --> 00:14:42,990
a large enough sample size to find it best if the if the primary outcome is going to to show significant finding or not.

146
00:14:43,230 --> 00:14:50,580
So the problem of powering on a primary outcome. It's I'm not saying it's solved, but it's not as big as it was maybe 20, 30 years ago.

147
00:14:51,120 --> 00:14:57,179
However, you have to think that each study will be looking at one particular primary outcome

148
00:14:57,180 --> 00:15:01,200
and there might be a whole host of other secondary outcomes that might be. Even more clinically relevant.

149
00:15:01,650 --> 00:15:04,709
But simply because they are less likely to have been reported.

150
00:15:04,710 --> 00:15:13,410
The event rate is smaller. That it means that you need much bigger sample sizes to identify an effect in those types of outcomes.

151
00:15:14,190 --> 00:15:18,780
Which means that a person doing the study may be focusing on a completely and a

152
00:15:18,780 --> 00:15:25,169
proxy which is not as clinically relevant as a secondary outcome by definition,

153
00:15:25,170 --> 00:15:28,830
than it means that that particular study would be underpowered for that secondary outcome.

154
00:15:29,370 --> 00:15:36,840
And that means that you would need still to use all these different studies that look at relatively same populations, have similar questions,

155
00:15:37,080 --> 00:15:42,990
combine them all in systematic reviews to find the real hopefully, if not the real answer,

156
00:15:43,650 --> 00:15:46,680
to gather enough evidence to say, well, we think this is the right answer.

157
00:15:47,490 --> 00:15:52,680
Yeah. Okay, good. And it's interesting. He finishes this. We'll just finish this paper with this sort of bold statement,

158
00:15:52,680 --> 00:15:59,280
which I think is probably were imprinted on your mind when we are told that there is no evidence of A causes B,

159
00:15:59,730 --> 00:16:04,320
we should first ask why the absence of evidence means simply that there is no information at all.

160
00:16:04,350 --> 00:16:12,400
Yes, if there are data, we should look for quantification of the association rather than just a p value quantity.

161
00:16:12,900 --> 00:16:16,290
What does that mean? So I can understand the first, but we haven't got the evidence.

162
00:16:16,290 --> 00:16:19,700
So you shouldn't say this is negative. You should just say, look, we don't know the answer.

163
00:16:19,710 --> 00:16:24,030
You don't know. But this quantification of the association rather than the p value.

164
00:16:24,720 --> 00:16:33,510
So. So that's, that's for example if you have information from randomised controlled trials and it's still uncertain as to what,

165
00:16:33,510 --> 00:16:39,300
what the real answer is because we don't have enough information. You might go back and look at observational studies.

166
00:16:40,020 --> 00:16:45,209
So the classic example might be of serious adverse events where from randomised

167
00:16:45,210 --> 00:16:48,150
controlled trials you might get some idea of what the serious adverse events are,

168
00:16:48,150 --> 00:16:52,070
but you don't have enough information because it's just not enough numbers.

169
00:16:52,080 --> 00:16:54,060
And then you see yourself and see, that's why very, very small.

170
00:16:54,630 --> 00:16:58,770
So you might want to revert back and look at what other sources of information might be

171
00:16:58,770 --> 00:17:06,120
providing you with more relevant data to explore whether there's an association or not.

172
00:17:06,120 --> 00:17:12,630
And that's what that's referring to. So you might want to use other forms of information to quantify if an association might be present.

173
00:17:12,840 --> 00:17:18,030
Okay. Well, that's good. Let's move back now just to 1763.

174
00:17:18,030 --> 00:17:24,460
I notice this small jump. I notice this an essay towards solving a problem in the doctrine of Genesis.

175
00:17:24,490 --> 00:17:29,820
Yes, I notice it was submitted on the 23rd of December three three just in time for Christmas.

176
00:17:30,960 --> 00:17:33,540
Now, this is interesting. I read this.

177
00:17:33,660 --> 00:17:38,670
I actually went over this again yesterday, some bits of a complex, but there's some very interesting bits in there.

178
00:17:39,420 --> 00:17:42,870
But let's I guess the Reverend Mr. Bayes.

179
00:17:42,870 --> 00:17:52,920
Yep. Is somebody who most people coming into statistics, epidemiology will have heard of the concept of Bayesian reasoning.

180
00:17:53,100 --> 00:17:55,800
That's correct. That's in a way the reason why I chose this paper.

181
00:17:55,830 --> 00:18:05,850
Okay, so give me the reason why I chose it and give me, in a sense, if possible, if possible at all, what is Mr. Bailey's issue in Bayesian reasoning?

182
00:18:06,060 --> 00:18:13,320
Well, actually, this paper is not about Bayesian reasoning, which is probably one thing that people might find or.

183
00:18:14,010 --> 00:18:19,200
It's it's not about the usual thing that people associate.

184
00:18:19,500 --> 00:18:23,820
Well, it is. And it isn't the main focus of this paper. It's not about Bayesian reasoning.

185
00:18:24,360 --> 00:18:31,950
It's about trying to solve a slightly different problem, which you can then regard as a basic problem or frequentist problem,

186
00:18:32,100 --> 00:18:41,579
which is the separation between two camps that was went on for many years and probably now it's converging

187
00:18:41,580 --> 00:18:48,330
because people don't necessarily new statisticians or probably not at least in the last decade or so,

188
00:18:48,930 --> 00:18:53,370
use Bayesian or frequentist methods, depending on what's more useful.

189
00:18:53,430 --> 00:18:56,579
Anyway, this paper is the focus of this paper.

190
00:18:56,580 --> 00:19:07,290
It's trying to understand coming up with a series of proofs of propositions to answer the following question a simple,

191
00:19:07,290 --> 00:19:18,209
relatively simple following question. If you have a series of experiments that are independent and you observe the series of experiments,

192
00:19:18,210 --> 00:19:23,610
one of the outcomes of these year's some experiments, let's say tossing a coin, you toss a coin, which is an unfair coin.

193
00:19:23,610 --> 00:19:27,780
So we don't know exactly the probability. If there's a third going, we would know it's 5050 chance.

194
00:19:28,320 --> 00:19:36,120
But it is an unfair coin. So we don't know what the probability of landing heads or tails is, but we observe a series of heads or a series of tails.

195
00:19:37,050 --> 00:19:44,640
And the question that we're trying to answer is if we knew what if we have observed all these outcomes of the experiments?

196
00:19:45,120 --> 00:19:56,310
Can we quantify what are the chances of this probability of heads, let's say, being between a number of another, let's say between 0.8 and .29?

197
00:19:57,750 --> 00:20:05,920
And that's in a way really. Missionary because although he doesn't think about it this way, it can be thought of it in a frequencies way.

198
00:20:06,130 --> 00:20:11,110
It switches around the problem of most of the time, we think.

199
00:20:11,710 --> 00:20:17,960
Given that we know this is a very common 5050 or given that we know that this coin is point three,

200
00:20:17,980 --> 00:20:23,920
the probability of point eight of being had some point of being tails one on one chance of winning eight times.

201
00:20:24,730 --> 00:20:29,230
And this is the other way around. So it switches it saying, okay, given that we observe all this evidence,

202
00:20:29,680 --> 00:20:37,000
what are how can we bound and calculate or determine the probability of heads or the probability of of tails?

203
00:20:37,810 --> 00:20:41,740
Now, within this paper, I think is Proposition four and five,

204
00:20:42,340 --> 00:20:52,930
you find the basis to of what is called Bayesian reasoning, which is all about in the way conditional probability.

205
00:20:53,230 --> 00:21:01,000
So given that one experiment that if you have two events that that only if both events happen,

206
00:21:01,000 --> 00:21:06,520
you will receive a prize and say and you observe either one event and not the other one.

207
00:21:06,730 --> 00:21:11,770
How do you update your probability or calculate the probability on the first event and all

208
00:21:11,770 --> 00:21:17,259
these conditional probability if we then revert that into parameters like for example,

209
00:21:17,260 --> 00:21:23,770
this probability of has or probability of tails gets us back to base and reason directly to Bayesian reason.

210
00:21:24,640 --> 00:21:27,610
So it's interesting. Yeah, I mean, you look at it so it says here,

211
00:21:28,210 --> 00:21:35,830
find out a method by which we might judge concerning the probability that an event has to happen in given circumstances and upon

212
00:21:35,830 --> 00:21:42,790
supposition that we know nothing concerning that under the same circumstances that has happened a certain number of times.

213
00:21:43,040 --> 00:21:45,130
About a certain of the number of times. That's right.

214
00:21:45,550 --> 00:21:54,459
But I guess it goes back to the large pie, because there's a bit here on on page 47 two that the larger the number of experiments,

215
00:21:54,460 --> 00:21:57,940
we have to support a conclusion so much more.

216
00:21:57,940 --> 00:22:02,409
The reason we have to take it for granted. Yes.

217
00:22:02,410 --> 00:22:06,100
And this is at the heart of statistics, if you want.

218
00:22:06,310 --> 00:22:11,320
We can't with statistics, we can't prove anything.

219
00:22:11,710 --> 00:22:17,680
And that's that's the major thing that needs to be ingrained on everyone that

220
00:22:17,710 --> 00:22:22,810
the use of statistics for works in statistics should we can't prove anything.

221
00:22:23,080 --> 00:22:29,190
And it's also sort of part of the scientific method. Science allows for uncertainty,

222
00:22:29,200 --> 00:22:37,170
shoot up and since we think we know but we should always be ready to readjust if the information

223
00:22:37,180 --> 00:22:43,360
that the evidence now that suddenly switches or changes or changed our ideas behind it.

224
00:22:43,840 --> 00:22:50,590
So what here what he's saying is the more information we have, the most certain we should be, which makes sense.

225
00:22:50,920 --> 00:22:54,940
But it doesn't say we should be certain, which is, I think, a clear distinction.

226
00:22:55,870 --> 00:23:00,370
So that's interesting because I'm just looking here through I noted yesterday when I was reading that

227
00:23:00,370 --> 00:23:07,509
there's a particular here on 409 when he talked about when you born and it talks about a second

228
00:23:07,510 --> 00:23:13,899
appearance or one of the return of the sun and an expectation would we might be raised the name of

229
00:23:13,900 --> 00:23:18,250
a second return and he might know that there was another 3 to 1 with some probability of that.

230
00:23:18,270 --> 00:23:25,450
So talked about the fact the sun's going to come up tomorrow and it would increase, but it would never be 100%.

231
00:23:25,450 --> 00:23:30,280
That's correct. Yes. So basically, statisticians can never be certain of anything.

232
00:23:31,780 --> 00:23:36,410
Yes, that's correct. We can never be certain. We can attach a probability to an answer.

233
00:23:37,420 --> 00:23:42,360
I'm 90% sure. Okay. So I think this bit was really interesting to me.

234
00:23:42,380 --> 00:23:43,090
It is lower than this.

235
00:23:43,090 --> 00:23:49,690
Some of this is a bit complicated for me, but this seems to be low even like around normal distributions and everything in here.

236
00:23:49,690 --> 00:23:55,570
And another important thing to highlight of this paper is how much the writing in statistics had changed.

237
00:23:55,960 --> 00:24:02,800
So, I mean, I also have to be honest, I also had trouble following some of his proofs and some of his arguments.

238
00:24:03,460 --> 00:24:08,770
And this is mainly because, although it's using logical argument to present what his proposition for,

239
00:24:08,770 --> 00:24:14,350
his justification for the different propositions that he's he's making in the paper,

240
00:24:14,800 --> 00:24:20,920
it doesn't produce what we now would be the main tool that we now use, which is algebra.

241
00:24:21,550 --> 00:24:30,340
So with algebraic terms, things, people that have studied maths particularly things become a lot more simple to follow.

242
00:24:30,550 --> 00:24:36,520
And the second paper about my now that uses very complex algebra but still

243
00:24:36,520 --> 00:24:43,419
relatively easy to follow compared to the 50 pages or so the Reverend Bias uses.

244
00:24:43,420 --> 00:24:49,420
Well, let's try this out. Well, some of this is on the last page full on a okay Australia.

245
00:24:49,840 --> 00:24:51,430
He says since this was written,

246
00:24:51,430 --> 00:24:59,740
I found a method of considerably improving the approximation in the 2D and 3D rules by demonstrating that the expression and I have.

247
00:24:59,850 --> 00:25:01,830
No chance of seeing that expression.

248
00:25:02,880 --> 00:25:14,860
So I want to test your ability to communicate this equation to our audience today without taking any breath or pauses in between you.

249
00:25:14,910 --> 00:25:17,460
That's that's going to be quite tricky. But let me let me have a go.

250
00:25:17,850 --> 00:25:23,270
So the equation says something like it's a ratio and it's two sigma divided by one plus to

251
00:25:23,910 --> 00:25:31,860
expectation of A to the P to the to the power of p b to the power of Q plus 2e8 to the power of P.

252
00:25:31,860 --> 00:25:36,240
Beat the power of Q the violent. And it sounds it looks very complex.

253
00:25:36,360 --> 00:25:40,419
And the main thing is we use these approximations.

254
00:25:40,420 --> 00:25:46,280
So we use these values many times they come from fairly large calculations,

255
00:25:46,290 --> 00:25:55,829
very large sums that are then simplified with assumptions and arguments that would say, for example, well, is this particular value?

256
00:25:55,830 --> 00:25:59,850
We think it's very, very small so we can get rid of it. Well, this particular way cancels with another thing.

257
00:25:59,850 --> 00:26:04,380
So let's get rid of it and end up with something that will be relatively simple to compute.

258
00:26:04,530 --> 00:26:07,200
Usually at this time it was the 17th,

259
00:26:07,200 --> 00:26:14,010
18th century by hand that would then allow them to use to create an approximation to the calculation that they wanted to obtain.

260
00:26:14,520 --> 00:26:19,290
Nowadays, with computers, we end up with really, really large equations.

261
00:26:19,290 --> 00:26:28,229
So this they talk about an expression that is an approximation. Nowadays we have expressions of many several lines long, which we can then,

262
00:26:28,230 --> 00:26:35,070
including a computer that would get a much more accurate and a value that is much more

263
00:26:35,070 --> 00:26:38,910
closer to the real value that we want to calculate is usually still an approximation,

264
00:26:38,910 --> 00:26:45,959
but it's much closer to what we want. While there's no chance I could say that, so if you can say that without coming up for breath,

265
00:26:45,960 --> 00:26:49,340
that means you're pretty qualified in sophistication and about to be an example.

266
00:26:49,820 --> 00:26:57,900
Let's say just page 376. There's some issues here which I think are definitions which he says are fundamental to probability.

267
00:26:58,620 --> 00:27:02,819
And I guess probability is is a fundamental principle in health care.

268
00:27:02,820 --> 00:27:09,260
And we're always trying to estimate what's the risk of A causing B, but just point one's untreated.

269
00:27:09,600 --> 00:27:12,870
Several events are inconsistent when if one of them happens,

270
00:27:12,870 --> 00:27:21,570
none of the rest can and then point to two events are contrary when one or other of them most and both together cannot happen.

271
00:27:21,690 --> 00:27:25,560
Yes. And I and I, we touched on it in I mentioned it before with these terms.

272
00:27:26,220 --> 00:27:33,570
They're sort of the terms of independent. Independent of in the same way you just explain them because they seem to be important concepts.

273
00:27:34,170 --> 00:27:47,730
Yeah. So, so you have things like but if you have an independent, well this first two terms are mainly about what we call sometimes disjoint events.

274
00:27:48,060 --> 00:27:52,410
So there is a series of events that one of them might happen or not happen.

275
00:27:52,890 --> 00:27:58,920
And in those cases, we, we say that these events are not independent because if one happens, the other will not happen,

276
00:27:58,920 --> 00:28:05,340
for example, and they are particularly useful for defining what are the totality of events that might happen.

277
00:28:05,850 --> 00:28:09,239
And that also defines everything that might might happen if you want.

278
00:28:09,240 --> 00:28:13,770
So that's that's that's a really crucial aspect of probability because then you say, well,

279
00:28:14,250 --> 00:28:22,470
if you have only one type of event death, let's say the country of that would be surviving.

280
00:28:22,650 --> 00:28:32,700
And if you are not dead, your life and that some of those two things as of 2 to 1 now the other the flip side of that is when you have

281
00:28:32,700 --> 00:28:39,810
events that are independent of each other and that normally means that the chance if one of those events occur,

282
00:28:40,320 --> 00:28:48,090
it does not affect the other event. And this is a little more difficult to come up with examples of what these might be.

283
00:28:48,090 --> 00:28:54,150
Let's think about is, for example, whether it's going to be sunny or rainy today,

284
00:28:54,400 --> 00:28:57,990
that there might be one event, let's say it's sunny today for a change here in Oxford.

285
00:28:58,500 --> 00:29:07,220
And then the type of breakfast I'm going to have, I normally have toast, I might have eggs and I haven't seen weather, weather, the weather reported.

286
00:29:07,380 --> 00:29:10,770
And it might be that if it's it might be exactly the same temperature.

287
00:29:10,770 --> 00:29:15,690
So it might not necessarily affect my decision of what I'm going to have for breakfast.

288
00:29:15,930 --> 00:29:20,490
So the probability of me having eggs or having a piece of toast and the probability of it being

289
00:29:20,700 --> 00:29:26,310
sunny or raining or the events are thought to be independent because one will not affect the other.

290
00:29:27,120 --> 00:29:36,480
What tends to happen is that these type of probabilities are not very or independent between two events are not very easy to show in,

291
00:29:37,140 --> 00:29:39,360
particularly in medical terminology,

292
00:29:39,360 --> 00:29:46,350
because that is because many things are associated and the concept of association and correlation then becomes very, very important to use.

293
00:29:47,020 --> 00:29:50,309
Yeah, okay, great. I mean, that's a real education.

294
00:29:50,310 --> 00:29:54,510
This program that we could have probably stayed here for about an hour going over this paper and

295
00:29:54,510 --> 00:29:59,690
there are a whole about ten problems to look out many things in the but let's move on now with.

296
00:29:59,810 --> 00:30:03,610
We're into a paper in the Journal of the Royal Statistical Society,

297
00:30:03,620 --> 00:30:08,450
which you are a member of the Statistical Society with join in if you're interested.

298
00:30:08,780 --> 00:30:13,400
Definitely. Definitely. There's lots of different chapters, medical statistics, primary care.

299
00:30:14,930 --> 00:30:19,190
And I think that's that's there's several that people are interested.

300
00:30:19,490 --> 00:30:23,810
Welcome to join not only statisticians but also people who are interested in statistics, of course.

301
00:30:24,200 --> 00:30:33,980
And then we've got this paper by Jane, Nelda and our W.M. Wedderburn and it's about generalised linear model from 1972.

302
00:30:34,190 --> 00:30:41,550
Yep. So I guess the first thing is to say, well, what's the generalisability in your model?

303
00:30:42,360 --> 00:30:42,620
Mm hmm.

304
00:30:44,900 --> 00:30:59,690
This paper I chose, because it really is, is presenting a series of method that underpins most of the modelling we use or we do in medical statistics.

305
00:30:59,690 --> 00:31:10,370
Not all of it, but most of it. If we think of a model being a way of saying what will happen to, let's say, my health,

306
00:31:10,970 --> 00:31:19,720
given the one of my chances and say of survival of of not having or let's say, of having a cardiovascular event,

307
00:31:19,730 --> 00:31:29,959
heart attack, given that I am a smoker and I'm overweight, I'm an adult 55 that I am in touch with within the next year,

308
00:31:29,960 --> 00:31:32,100
one of my probabilities of having a heart attack in the next year.

309
00:31:32,960 --> 00:31:38,000
That association of the different factors of the individual and something else is a model.

310
00:31:39,590 --> 00:31:42,829
And what these papers are describing is a series,

311
00:31:42,830 --> 00:31:50,930
a type of models that links up pretty much any kind of modelling or most kind of modelling that we do in in medical, medical statistics.

312
00:31:51,320 --> 00:32:02,049
The reason we call linear is because we show each one of these factors would have a linear life if you want to some shape of,

313
00:32:02,050 --> 00:32:08,930
let's say in this case, a transformation of the probability. You might be a lot easier to explain in terms of, let's say, weight and height.

314
00:32:09,350 --> 00:32:15,000
So we want to explain height in relation to weight we can fit aimed at the height.

315
00:32:15,110 --> 00:32:20,240
The taller you are, you're playing along a lot. So y in excess of height against weight.

316
00:32:20,300 --> 00:32:22,880
But what these models do is extend that line,

317
00:32:23,030 --> 00:32:32,030
which would be only in certain circumstances would be useful only when you have a very transformation of X and Y to other types of approaches,

318
00:32:32,030 --> 00:32:38,210
like for example, probability, like for example, risk, like for example, one of the other ones.

319
00:32:39,020 --> 00:32:42,860
So he talks about a plus on distribution and he talks about, well, let me comment on that.

320
00:32:42,860 --> 00:32:46,429
Let me come in on the introduction. And this is the thing for us.

321
00:32:46,430 --> 00:32:53,600
I said simple clinical clinician in the first almost two sentences.

322
00:32:53,600 --> 00:32:59,870
Yeah, let's just listen to these two linear models customarily embody both systematic and

323
00:32:59,870 --> 00:33:04,510
random error component where the errors usually seem to have normal distribution.

324
00:33:04,940 --> 00:33:08,120
The associated analytic technique is least squares.

325
00:33:08,120 --> 00:33:09,050
Very. Yeah.

326
00:33:09,170 --> 00:33:18,950
Now, well, I've got one, two, three systematic random error I need to know about normal distributions to and then I've got these square theory now.

327
00:33:19,130 --> 00:33:23,720
No wonder I'm in trouble. Yes. So then how to give that?

328
00:33:24,320 --> 00:33:29,230
How would you go about sort of thinking this thing through and how would a students then think,

329
00:33:29,240 --> 00:33:32,680
well, you've got to understand these concepts before you can then move on to.

330
00:33:32,700 --> 00:33:42,140
Yeah, these. I think the best way to approach these type of thoughts in this type of paper is to think in terms of,

331
00:33:42,350 --> 00:33:45,560
first of all, this, this what we call the simple linear regression.

332
00:33:46,550 --> 00:33:53,660
So in simple in regression, which is a specialised case and by specialised case we call it a simple case

333
00:33:53,660 --> 00:33:58,520
of this type of models that this paper is presented in superior aggression.

334
00:33:58,520 --> 00:34:05,840
What we have is one viable outcome, whatever you want to call it, that we call it a dependent outcome.

335
00:34:06,200 --> 00:34:13,310
So something that we want to say something about and something that is an independent variable,

336
00:34:13,430 --> 00:34:16,970
that is something that we either have control of or that we know.

337
00:34:18,440 --> 00:34:27,020
So in the in, again, probably the best way to think about it, let's say BMI and blood pressure.

338
00:34:27,230 --> 00:34:30,590
So BMI goes up and see a weight is an it. Yeah,

339
00:34:30,950 --> 00:34:36,019
as a weight go so maybe your blood pressure is also is also going going up and we might want then

340
00:34:36,020 --> 00:34:44,960
to fit align to if we think of available in a graphical shape like a scatterplot as your BMI.

341
00:34:45,620 --> 00:34:49,640
If you plot a BMI individuals with a particular BMI, a particular blood pressure,

342
00:34:49,970 --> 00:34:56,900
you would start seeing a pattern that might follow a line as your BMI goes up, your blood pressure goes down.

343
00:34:58,340 --> 00:35:03,850
And this linear regression is why they. Two is you can just see the line, say, okay, we draw a line on those points.

344
00:35:04,420 --> 00:35:11,290
But because there's going to be small variation in this comes to the idea of either thing you call it

345
00:35:12,460 --> 00:35:19,600
random viability or systematic viability because there's going to be viability between individuals.

346
00:35:19,600 --> 00:35:23,259
And that viability might be because some individuals naturally have lower blood pressure.

347
00:35:23,260 --> 00:35:27,930
So high blood pressure, but they also might be because of the measurement error.

348
00:35:27,940 --> 00:35:32,110
As you take the blood pressure, you might be some error. There's some merit in the measurements.

349
00:35:32,350 --> 00:35:35,080
There's going to be scatter around that particular line.

350
00:35:36,460 --> 00:35:47,200
So we use here where this weighted least squares comes in, we use different methods to come up with the best possible line.

351
00:35:47,920 --> 00:35:54,430
And that best possible line in the case of a simple linear regression is one that minimises the difference.

352
00:35:54,740 --> 00:36:01,070
We'll go from each point to the line, and that's what the least squares comes in an end with this.

353
00:36:01,090 --> 00:36:08,950
And then the coach, I'm trying to understand these folks so we've got weight and say blood pressure going up in a line,

354
00:36:09,130 --> 00:36:11,740
but some people will vary from that line. Right.

355
00:36:12,010 --> 00:36:18,010
And the difference in their variation, you'll use the least squares method to come up with the best possible line.

356
00:36:18,010 --> 00:36:22,120
And there are two sources of variability, the random variability that occurs in blood pressure.

357
00:36:22,120 --> 00:36:26,800
But there may be some systematic variability because the blood pressure curves not working, for example.

358
00:36:27,640 --> 00:36:31,240
And then look, this is if I can get this, I'll be happy.

359
00:36:31,420 --> 00:36:37,059
Then obtain the approximation to the weights isn't there will be to the reward.

360
00:36:37,060 --> 00:36:44,290
So what? So you see the what if we can just get that that would not be the panacea if that light.

361
00:36:44,290 --> 00:36:52,120
So you have an A the A line which is almost a regression line and then you talk about either the beaches or the weights of each component.

362
00:36:52,390 --> 00:36:58,510
There's like two things. So the weights, the weights that they talk about in terms of of weight, at least squares,

363
00:36:58,840 --> 00:37:02,110
is in relation to how much weight you're going to give to each one of these points.

364
00:37:02,890 --> 00:37:08,770
And if you are talking of simple linear regression, you give equal weights to each one of the points.

365
00:37:09,430 --> 00:37:15,759
If, for example, you're talking about something slightly more complex where you think some points have more information than others,

366
00:37:15,760 --> 00:37:21,330
you give more value to those points. Similar to what happens in meta analysis, where you might give more weight to studies are bigger.

367
00:37:21,790 --> 00:37:24,309
That's one area the betas are you talking about.

368
00:37:24,310 --> 00:37:33,730
It's more of the quantification of how much things change by a change of one unit in your independent variable.

369
00:37:33,760 --> 00:37:44,170
Let me be clear when we're talking about this line, if you think of a line, the line would have a which is completely defined by an intercept.

370
00:37:44,380 --> 00:37:50,170
That is the point where if you had zero BMI, this is completely theoretical,

371
00:37:50,170 --> 00:37:54,970
but if you had a similar BMI, what would be your blood pressure say might be 20.

372
00:37:55,240 --> 00:38:01,480
Let's a hypothetical. So that's that's that in a way uncross your line tells you where you start.

373
00:38:02,230 --> 00:38:06,430
And then the other bit that completely defines your line is the slope.

374
00:38:07,360 --> 00:38:12,880
So by a change of one unit and BMI, how much your blood pressure is going to change.

375
00:38:13,120 --> 00:38:20,409
And it might be that when you move from 20 for a BMI of 25 to a BMI of 26 to blood pressure increases by two millimetres millimetres

376
00:38:20,410 --> 00:38:28,690
of make it so that to the change in one unit in one unit of BMI is an increase of two units of systolic blood pressure.

377
00:38:29,110 --> 00:38:37,090
That two is exactly your slope. Okay, now the slope and the betas are exactly the same thing.

378
00:38:37,120 --> 00:38:42,630
Okay. So when you want to do with a combination of lean squares or whatever you want to call it, you know,

379
00:38:42,710 --> 00:38:48,580
to determine your betas is basically to determine the slope or the increase in the

380
00:38:48,580 --> 00:38:52,570
dependent variable that you obtain by increasing your independent by one unit.

381
00:38:52,720 --> 00:39:00,790
So that so basically you, like we said, you may have blood pressure, may be affected by weight, you may add another factor in like age.

382
00:39:00,790 --> 00:39:06,100
Yeah. Which would come into your model. That's right. And that would increase the slope or decrease it.

383
00:39:06,550 --> 00:39:09,970
What happens is that each one of these characteristics have their own slopes.

384
00:39:09,970 --> 00:39:18,640
Yeah. So BMI might have a slope of two, but once you bring age, your slope of the of BMI might decrease, as you were saying to one or 1.2.

385
00:39:18,850 --> 00:39:22,810
And there is another slope of three or 1.2 as well.

386
00:39:23,140 --> 00:39:31,150
And so then the only other factor, if we get these folks, we're running out of time is this this sort of idea in models is how much can be

387
00:39:31,150 --> 00:39:36,250
explained by the model and how much count what that value and how to test for that.

388
00:39:36,550 --> 00:39:39,040
So we're talking about the scatter that you obtain. Yes.

389
00:39:39,070 --> 00:39:44,050
And because there's going to be scatter, I mean, it could be natural variability or whatever it is,

390
00:39:44,290 --> 00:39:48,370
that scatter is precisely that you can't explain through your model.

391
00:39:48,380 --> 00:39:51,420
Yeah. So your line is brilliant if you only have two dots.

392
00:39:51,430 --> 00:39:53,379
Yeah. So you can explain everything.

393
00:39:53,380 --> 00:39:59,260
If you have that's once you have three dots or more, three individuals or more, there's going to be some variability you won't be able to explain.

394
00:39:59,970 --> 00:40:03,810
And that very belief that you won't be able to explain tells you how good your model is.

395
00:40:03,840 --> 00:40:04,200
Okay.

396
00:40:04,560 --> 00:40:11,280
And there's different ways of quantifying how good your model is in terms of how much of the total variability of the data you manage to explain.

397
00:40:11,850 --> 00:40:12,320
Okay.

398
00:40:12,330 --> 00:40:19,740
And that could be in terms of, for example, just looking at the differences from design to each one of these dots or other types of measurements.

399
00:40:20,160 --> 00:40:23,370
Gosh. So that's been an amazing, very quick journey.

400
00:40:23,400 --> 00:40:27,870
40 minutes on probability sample five linear models.

401
00:40:28,170 --> 00:40:32,710
Now let's just finish with, let's say, a bit of advice.

402
00:40:32,730 --> 00:40:38,440
What would you say the best advice if you're embarking on a course epidemiology statistics?

403
00:40:38,460 --> 00:40:46,080
What sort of resource for what would be the best way to just keep improving your statistical knowledge, improving existing knowledge?

404
00:40:46,110 --> 00:40:50,310
I think what has worked for me is getting your hands dirty.

405
00:40:50,430 --> 00:40:51,690
So doing the things,

406
00:40:52,410 --> 00:41:01,320
having some idea of what you want to achieve or what you can possibly achieve through either lectures or through going to courses.

407
00:41:01,770 --> 00:41:04,649
But more than anything is the in applying these things.

408
00:41:04,650 --> 00:41:12,240
So if, for example, you have data and you want to use a particular model that has a linear model of these claims, then go ahead and do it.

409
00:41:13,020 --> 00:41:17,639
Ask for advice. Many times there's advice either in the statistical packages,

410
00:41:17,640 --> 00:41:25,170
also in the in the in the text and also in in the individuals in your own own organisation or elsewhere.

411
00:41:25,380 --> 00:41:29,670
And the earlier you go for advice, the better that will be. The other thing that I would I would say.

412
00:41:29,940 --> 00:41:32,940
Okay. Well, on that note, let me just let me just finish here.

413
00:41:33,480 --> 00:41:37,800
You go. And you got to answer one of the two. Okay. Mean all the median?

414
00:41:42,260 --> 00:41:45,440
Medium. The like a true statistician has to think about it.

415
00:41:45,740 --> 00:41:49,700
Stator or are are all the time.

416
00:41:49,890 --> 00:41:55,820
Okay. There you go. I going with speed. You know, while on that now I'd like to say thank you very much to Rafael Perera for what's

417
00:41:55,820 --> 00:42:00,950
been a very interesting discussion on statistics and many issues around that.

418
00:42:00,980 --> 00:42:03,110
Thank you. You're welcome. Thanks. You're welcome.