.bg-main4.column[.vmiddle.content[
.font1.amber[Aly Lamuri]  
.font1[Indonesia Medical Education and Research Institute]
]]

---

---

.bg-main1.column[.vmiddle.content[
- .amber[Variables: independent and dependent]
- Formulating a hypothesis
- Types of study design
- Assessing hypothesis in published papers
]]

---

<img src="https://i.pinimg.com/736x/16/47/a8/1647a81b28650ac3cf9c40a20819a3a4.jpg" width="80%">
]

---

# What are...?

- .font2[Cases]
  - Observable .amber[subjects]
  - Can be anything
--

- .font2[Variables]
  - .pink[Characteristics] in observed cases
  - Quantifiable

.amber[Ten schizophrenic patients] participated in a study on brain activity. 
--
They underwent computer-based tests on .pink[psychotic symptoms] and fMRI
examination to observe the .pink[functional connectivity].

A group of botanists observed .amber[different species of molds] under
conditioned environments. 
--
They set up different .pink[humidity levels] and
.pink[temperature] to observe .pink[cellular viability].

The Ministry of Finance investigated an urban population. They considered age
and ethnicity as a predictor of socioeconomic mobility.

---

- Unaffected by other variables
- In experiment: under your direct control
- Design-wise: A presumed .amber[cause]
]

- Affected by other variables
- In experiment: under your indirect control
- Design-wise: A presumed .amber[effect]
]

---

# Grouping the cases

.font2[
- Use categorical .amber[independent] variable
- Separate each observation
- Differentiate *within* and *between* subjects
]

## Within?

- Comparing the .amber[**same**] subject
- When we test the subject multiple times
- Temporal differences of `$t_0$` and `$t_1$`
- Using different measures

## Between?

- Comparing .amber[**different**] subjects
- When we use a test on multiple groups

---

# That's neat! 
--
But why?

# Any catch?

.font2[
- We need to control .amber[confounding variables]
- Reduce .amber[bias]
- Minimize .amber[random error]
]

---

# Confounding variable

.font2[
- Any variable: categoric or numeric
- Causal association with either in- / dependent variables
- .pink[**Reduces**] internal validity!
]

<div id="htmlwidget-64cdbed306c86dc3cd43" style="width:90%;height:30%;" class="grViz html-widget"></div>
<script type="application/json" data-for="htmlwidget-64cdbed306c86dc3cd43">{"x":{"diagram":"\n  digraph confounding {\n    graph [overlap = true, fontsize = 10, bgcolor = \"#ffffff00\"]\n    node [shape = box, fontname = Helvetica, color = lightseagreen, style = filled]\n    {rank = same; Independent; Dependent}\n    node [shape = circle, fontname = Helvetica, color = lightcoral, style = filled]\n    Confounding\n    # Set edges\n    Independent->Dependent [color = lightseagreen, style = bold]\n    edge [color = lightcoral, arrowhead = diamond, style = bold]\n    Confounding->{Independent; Dependent}\n  }\n","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>

---

.column[.vmiddle.content[
<img src="https://i.ytimg.com/vi/0xKklLplngs/maxresdefault.jpg" width="100%">
]]

???

Bias is a systematic error in research
- Selection bias: the proportion of selected subjects does not represent the population
  - Undercoverage
  - Overcoverage
- Information bias: the information does not represent the truth:
  - Recall bias
  - Interviewer bias
  - Response bias (vaguely interpreted questions)
  - Confirmation bias (only confirm what conforms)
- Detection bias: only detecting outcome in a group with certain characteristics
- Performance bias: a tendency to give different treatment to favour an outcome
- Attrition bias: due to drop out and lost to follow-up
- Reporting bias: only report significant findings and neglect insignificant ones

---

# Handling bias

.font2[
- Random sampling
- Random assignment
- Blinding:
  - Participant
  - Investigator
  - Mediating parties
]

---

# Systematic error

.font2[
- Both confounding variables and bias contribute to .pink[systematic errors]
- We have a hunch how they will affect our data
- So we can prevent them
- Often have a mathematical solution
- Example: offset and scale factor errors
]

---

# Random error

.font2[
- A.K.A: unsystematic error, .pink[system noise], random variation
- Unpredictable and unreplicable
- Thus, no mathematical solution
]

# Handling random error

---

.bg-main1.column[.vmiddle.content[
- Variables: independent and dependent
- .amber[Formulating a hypothesis]
- Types of study design
- Assessing hypothesis in published papers
]]

---

# Hypothesis: definition

.font2[
- Assumptions about the population parameter
- Stated as the *null* `$H_0$` and *alternative* `$H_a$` hypothesis
- Requires a formal procedure to reject `$H_0$`
]

## Null hypothesis

## Alternative hypothesis

---

# Hypothesis: example

---

```r
set.seed(1)
coin <- sample(c("H", "T"), 10, replace=TRUE, prob=rep(1/2, 2)) %T>% print()
```

```
##  [1] "T" "T" "H" "H" "T" "H" "H" "H" "H" "T"
```

.font2[
`$H_0:$` The probability of having the head is `$P = 0.5$`  
`$H_a:$` The probability of having the head is `$P \neq 0.5$`
]

---

```r
binom.test(x={sum(coin=="H")}, n=length(coin), p=0.5) %>%
	broom::tidy() %>% knitr::kable() %>% kable_minimal()
```

<table class=" lightable-minimal" style='font-family: "Trebuchet MS", verdana, sans-serif; margin-left: auto; margin-right: auto;'>
 <thead>
  <tr>
   <th style="text-align:right;"> estimate </th>
   <th style="text-align:right;"> statistic </th>
   <th style="text-align:right;"> p.value </th>
   <th style="text-align:right;"> parameter </th>
   <th style="text-align:right;"> conf.low </th>
   <th style="text-align:right;"> conf.high </th>
   <th style="text-align:left;"> method </th>
   <th style="text-align:left;"> alternative </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 0.6 </td>
   <td style="text-align:right;"> 6 </td>
   <td style="text-align:right;"> 0.754 </td>
   <td style="text-align:right;"> 10 </td>
   <td style="text-align:right;"> 0.262 </td>
   <td style="text-align:right;"> 0.878 </td>
   <td style="text-align:left;"> Exact binomial test </td>
   <td style="text-align:left;"> two.sided </td>
  </tr>
</tbody>
</table>

---

---

# Hypothesis: formal test

.font2[
- Does our data correspond to the `$H_0$`?
- Sample data are .amber[consistent] with `$H_0 \to$` do .pink[not reject] `$H_0$`
- Sample data are .amber[inconsistent] with `$H_0 \to$` .pink[reject] `$H_0$`
]

---

# Type of test

---

# Rejecting hypothesis

---

# Hypothesis: interpretation

.font2[
- We start from the assumption that `$H_0$` is true
- Collect evidence to show otherwise
- We then .amber[reject] or .amber[fail to reject] the `$H_0$` based on p-value
- When testing the hypothesis we may happen to see .pink[statistical errors]
]

# .pink[Statistical error]

.font2[
- Type I: False Reject Rate `$\alpha \to$` false positive
- Type II: False Accept Rate `$\beta \to$` false negative
]

---

---

---

# Hypothesis: p-value

.font2[
- Reflect the probability of making a type I error
- Lower p-value `$\to$` lower chance of `$H_0$` occurred by chance
- Lower p-value `$\to$` higher significance
- Common cut-off: .amber[0.05]
]

---

.bg-main1.column[.vmiddle.content[
- Variables: independent and dependent
- Formulating a hypothesis
- .amber[Types of study design]
- Assessing hypothesis in published papers
]]

---

# Study design

.font2[
- Cross-sectional
- Cohort
- Case-control
- Randomized controlled trial
- Systematic review
]

---

# Cross-sectional

.font2[
- A .amber[snapshot] of outcome and associated characteristics
- No intervention, inferencing .amber[existing differences]
- Relatively .amber[inexpensive and quick] to conduct
- .pink[Static,] reveal no temporal context
- .pink[Unable] to establish .pink[causality]
- Different time frame may lead to .pink[different result]
]

---

# Cohort

.font2[
- .amber[Longitudinal] study to see an effect overtime
- .amber[Prospective / retrospective:] observing the future or looking back in time
- Starting from a .amber[potential cause]
- Involving at least .amber[two groups] of interest
- Cannot completely control the .pink[confounding variables]
- No randomization `$\to$` lower .pink[external validity]
- .pink[Long] completion period
]

---

# Case-control

.font2[
- .amber[Longitudinal] study to see an effect overtime
- .amber[Retrospective] in nature
- Starting from an .amber[outcome of interest]
- Involving at least .amber[two groups]
- Usually employed to investigate .amber[rare conditions]
- Assessing multiple .amber[risk factors]
- Difficult to find a .pink[suitable] control group
- Inadequate to establish a .pink[diagnostic study]
- Should carefully address .pink[confounding variables]
]

---

# Randomized controlled trial

.font2[
- Randomization to control bias `$\to$` higher .amber[external validity]
- Akin to an experimental study, can effectively employ .amber[blinding methods]
- Statistically .amber[efficient]
- .amber[Clearly] identified population
- .pink[Expensive] to conduct
- Risk to have a .pink[volunteer bias]
- Loss to follow up `$\to$` .pink[attrition bias]
]

---

# Systematic review

.font2[
- Concatenate findings from .amber[multiple studies]
- Critical appraisal .amber[removes redundancies] and .amber[addresses inconsistencies]
- Delineate where knowledge is lacking to .amber[guide] future research
- Does not establish .pink[novelty]
- .pink[Variation] among published articles is a challenge to overcome
- .pink[Potential bias] for including unreviewed articles
]

# Meta-analysis

.font2[
- Takes systematic review to another level :)
- Analyzing .amber[previous] analysis (thus the name: meta-analysis)
]

---

.bg-main1.column[.vmiddle.content[
- Variables: independent and dependent
- Formulating a hypothesis
- Types of study design
- .amber[Assessing hypothesis in published papers]
]]

---

Source: [10.1371/journal.pone.0165816](https://doi.org/10.1371/journal.pone.0165816)

---

# Reading scientific articles

.font2[
- Look for its underlying .amber[structure]
- Abstract
  - I: Introduction
  - M: Methods
  - R: Results
  - D: Discussion
- Introduction
  - .amber[S:] Situation
  - .amber[P:] Problem
  - .amber[Q:] Question
  - .pink[R: Resolution]
]

???

- By knowing the structure, you can extract information more efficiently
- When reading the abstract, focus on introduction and methods first
- Then shift into conclusions, since it contains the summary
- Finally, you may want to read the results and discussion as well
- Introduction usually elaborates the background and hypothesis
- You can look for the study design in methods
- Discussion part will help you understand current limitation and further suggestions

---

# Abstract - Introduction

.font2[
.pink[Current studies] of depression among people .amber[living with HIV] focus on
describing its .pink[point prevalence]. Given the .pink[fluctuating nature] of
depression and its profound impacts on clinical and quality-of-life outcomes,
this study .amber[**aimed**] to examine the .amber[**prevalence**], recurrence
and incidence of current depressive symptoms and its underlying
.amber[**catalysts** longitudinally] and systematically among these
individuals.
]

---

# Abstract - Methods

.font2[
We conducted a .amber[**prospective cohort**] study between October 1, 2007 and
December 31, 2012 using longitudinal linked data sources. Current depressive
symptoms was .amber[identified] using the Centre for Epidemiologic Studies
.pink[Depression Scale] or the Kessler Psychological .pink[Distress Scale],
first at .amber[**baseline**] and again during .amber[**follow-up**]
interviews. Multivariable regressions were used to characterize the three
outcomes.
]

---

# Abstract - Conclusion

.font2[
.amber[Depressive] symptoms are prevalent and .amber[**likely to recur**] among
people living with HIV. Our results support the direction of Ontario’s HIV/AIDS
Strategy to 2026, which addresses medical concerns associated with HIV (such as
depression) and the .pink[**social drivers**] of health in order to enhance the
overall well-being of people living with or at risk of HIV. Our findings
.pink[reinforce] the importance of providing effective .amber[mental health care]
and demonstrate the need for long-term .amber[support] and routine
management of depression, particularly for individuals at high risk.
]

---

# Abstract - Results

.font2[
Of the 3,816 HIV-positive participants, the .amber[point prevalence] of depressive
symptoms was estimated at .amber[28%]. Of the 957 participants who were identified with
depressive symptoms at baseline and who had at least two years of follow-up,
.amber[43% had a recurrent episode]. The .amber[cumulative incidence] among 1,745 previously
depressive symptoms free participants (at or prior to baseline) was .amber[14%]. During
the five-year follow-up, our multivariable models showed that participants with
greater risk of .pink[recurrent cases] were more likely to feel .amber[worried] about their
housing situation. Participants at .pink[risk of developing] incident cases were also
likely to be .amber[younger, gay or bisexual], and .amber[unable to afford] housing-related
expenses.
]

---

# Introduction - Situation

(par. 1)

.amber[Depression] affects up to half of people living with HIV, a prevalence that is
.amber[two to four times higher] than that found in the general population [1]. Over
50% of people living with HIV and depression do not receive treatment for their
depression [2–9], and this failure to treat contributes to significant .amber[negative]
clinical and quality-of-life .amber[outcomes] [10–14].

]

---

# Introduction - Situation

Growing evidence supports a bi-directional .amber[relationship] between .amber[HIV] and
.amber[depression] involving a number of .pink[biological, psychosocial and social] .amber[factors]
[1,14–16]. The persistent viral presence in the central nervous system may
release toxic viral proteins that induce depression-like symptoms [17,18];
people living with HIV may possess a negative self-image or experience stigma
[1,15,19–21]; and people living with HIV are more likely to struggle with
stressors such as financial insecurity and unstable housing [22–25]. Recent
reviews also suggest that people who suffer from severe mental illnesses
(including depression) and/or co-occurring substance use disorder are more
likely to engage in risky sexual behaviour, thereby elevating their risk of HIV
acquisition [26–34].

]

---

# Introduction - Problem

(par. 3)

To date, most studies about the prevalence of depression among people living
with HIV have used cross-sectional designs [1,15]. Six studies have documented
the incidence [35–38] and persistence (or recurrence) [39,40] of depression
over time among people living with HIV. In Canada, information describing the
epidemiology of depression among people living with HIV is scarce. In Canada,
information describing the epidemiology of depression among people living with
HIV is scarce. There have been two small convenience sample studies describing
the prevalence of depression among people living with HIV. Williams et al.
(2005), employing a small convenience sample of 297 individuals, described the
prevalence of depressive symptoms at 54% among people living with HIV based on
a self-report screening instrument [41]. Logie, James, Tharao, and Loutfy
(2013), employing a sample of 173 Africa, Caribbean, and Black women, described
the prevalence of depressive symptoms as 64% [42]. .amber[Thus, the epidemiology of this condition is not yet well documented in Canada.]

---

# Introduction - Question

(par. 4)

Given the .amber[fluctuating nature of depression over the life span and its profound impacts on clinical and quality-of-life outcomes,] our study aimed to examine the prevalence, recurrence, and incidence of current depressive symptoms longitudinally and systematically among people living with HIV. We also characterized these three outcomes by HIV-positive participants’ socio-demographic characteristics, housing and neighbourhood conditions, substance-use behaviours and health status over a five-year follow-up period.  Understanding change in the burden of depressive symptoms and the underlying catalysts of the condition from a longitudinal perspective would be important to program planners, policy-makers, and health care providers when planning and implementing effective mental-health programs and interventions for people living with HIV.

---

# Introduction - Resolution

(par. 4)

Given the fluctuating nature of depression over the life span and its profound impacts on clinical and quality-of-life outcomes, our study .amber[aimed to examine the prevalence, recurrence, and incidence] of current depressive symptoms longitudinally and systematically among people living with HIV. We also .pink[characterized] these three .pink[outcomes] by HIV-positive participants’ .amber[socio-demographic characteristics, housing and neighbourhood conditions, substance-use behaviours and health status over a five-year follow-up period.] Understanding change in the burden of depressive symptoms and the underlying catalysts of the condition from a longitudinal perspective would be important to program planners, policy-makers, and health care providers when planning and implementing effective mental-health programs and interventions for people living with HIV.

---

# Extracted information

.font2[
- Case: people living with HIV
- Variables
  - .amber[Independent]: depressive symptoms prevalence, recurrence, incidence
  - .amber[Dependent]: younger, gay or bisexual, unable to afford expenses
  - Potential .amber[confounding]: worrying their household situation
- Study design: cohort prospective
- Hypothesis
  - `$H_0$`: Depressive symptoms are not likely to recur
  - `$H_a$`: Depressive symptoms are likely to recur
]

---

.amber.font5[Query?]

---

# Quick assignment

- Read two articles we briefly discussed in the first lecture
- Identify their underlying structures (abstract and introduction)
- Succintly describe the case, variables and study design
- Determine the hypotheses and formulate them as `$H_0$` and `$H_a$`
- Make a presentation on the abstract, introduction and extracted information
]

.font2[
Articles:
- [10.1371/journal.pone.0233137](https://doi.org/10.1371/journal.pone.0233137)
- [10.1097/acm.0000000000000134](https://doi.org/10.1097/acm.0000000000000134)
]

Notes for current slide

Notes for next slide

Hypothesis and Study Design

Aly Lamuri
Indonesia Medical Education and Research Institute

1 / 30

Overview

Variables: independent and dependent
Formulating a hypothesis
Types of study design
Assessing hypothesis in published papers

1 / 30

Research in a nutshell

1 / 30

What are...?CasesObservable subjects
Can be anything

1 / 30

What are...?CasesObservable subjects
Can be anything

VariablesCharacteristics in observed cases
Quantifiable

1 / 30

What are...?

Cases
- Observable subjects
- Can be anything
Variables
- Characteristics in observed cases
- Quantifiable

Example 1:

Ten schizophrenic patients participated in a study on brain activity.

1 / 30

What are...?

Cases
- Observable subjects
- Can be anything
Variables
- Characteristics in observed cases
- Quantifiable

Example 1:

Ten schizophrenic patients participated in a study on brain activity. They underwent computer-based tests on psychotic symptoms and fMRI examination to observe the functional connectivity.

1 / 30

What are...?

Cases
- Observable subjects
- Can be anything
Variables
- Characteristics in observed cases
- Quantifiable

Example 1:

Ten schizophrenic patients participated in a study on brain activity. They underwent computer-based tests on psychotic symptoms and fMRI examination to observe the functional connectivity.

Example 2:

A group of botanists observed different species of molds under conditioned environments.

1 / 30

What are...?

Cases
- Observable subjects
- Can be anything
Variables
- Characteristics in observed cases
- Quantifiable

Example 1:

Ten schizophrenic patients participated in a study on brain activity. They underwent computer-based tests on psychotic symptoms and fMRI examination to observe the functional connectivity.

Example 2:

A group of botanists observed different species of molds under conditioned environments. They set up different humidity levels and temperature to observe cellular viability.

1 / 30

What are...?

Cases
- Observable subjects
- Can be anything
Variables
- Characteristics in observed cases
- Quantifiable

Example 1:

Ten schizophrenic patients participated in a study on brain activity. They underwent computer-based tests on psychotic symptoms and fMRI examination to observe the functional connectivity.

Example 2:

A group of botanists observed different species of molds under conditioned environments. They set up different humidity levels and temperature to observe cellular viability.

Example 3:

The Ministry of Finance investigated an urban population. They considered age and ethnicity as a predictor of socioeconomic mobility.

1 / 30

Independent variable
Unaffected by other variables
In experiment: under your direct control
Design-wise: A presumed cause

2 / 30

Independent variable
Unaffected by other variables
In experiment: under your direct control
Design-wise: A presumed cause

Dependent variable
Affected by other variables
In experiment: under your indirect control
Design-wise: A presumed effect

2 / 30

Grouping the casesUse categorical independent variable
Separate each observation
Differentiate within and between subjects

3 / 30

Grouping the casesUse categorical independent variable
Separate each observation
Differentiate within and between subjects

Within?Comparing the same subject
When we test the subject multiple times
Temporal differences of t0t0 and t1t1
Using different measures
3 / 30

Grouping the casesUse categorical independent variable
Separate each observation
Differentiate within and between subjects

Within?Comparing the same subject
When we test the subject multiple times
Temporal differences of t0t0 and t1t1
Using different measures
Between?Comparing different subjects
When we use a test on multiple groups
3 / 30

That's neat!3 / 30

That's neat! But why?3 / 30

That's neat! But why?Enables inferential statistics
Describes an association
Significance?

3 / 30

That's neat! But why?Enables inferential statistics
Describes an association
Significance?

Any catch?We need to control confounding variables
Reduce bias
Minimize random error

3 / 30

Confounding variableAny variable: categoric or numeric
Causal association with either in- / dependent variables
Reduces internal validity!

3 / 30

Confounding variableAny variable: categoric or numeric
Causal association with either in- / dependent variables
Reduces internal validity!

confounding

Independent

Independent

Dependent

Dependent

Independent->Dependent

Confounding

Confounding

Confounding->Independent

Confounding->Dependent

3 / 30

Cognitive bias $\to$ partiality

Selection
Information
Detection
Performance
Attrition
Reporting

Reduces internal validity!

4 / 30

Bias is a systematic error in research

Selection bias: the proportion of selected subjects does not represent the population
- Undercoverage
- Overcoverage
Information bias: the information does not represent the truth:
- Recall bias
- Interviewer bias
- Response bias (vaguely interpreted questions)
- Confirmation bias (only confirm what conforms)
Detection bias: only detecting outcome in a group with certain characteristics
Performance bias: a tendency to give different treatment to favour an outcome
Attrition bias: due to drop out and lost to follow-up
Reporting bias: only report significant findings and neglect insignificant ones

Handling biasRandom sampling
Random assignment
Blinding:Participant
Investigator
Mediating parties


4 / 30

Systematic errorBoth confounding variables and bias contribute to systematic errors
We have a hunch how they will affect our data
So we can prevent them
Often have a mathematical solution
Example: offset and scale factor errors

5 / 30

Systematic error

Both confounding variables and bias contribute to systematic errors
We have a hunch how they will affect our data
So we can prevent them
Often have a mathematical solution
Example: offset and scale factor errors

Is there any error we cannot completely handle?

5 / 30

Systematic error

Both confounding variables and bias contribute to systematic errors
We have a hunch how they will affect our data
So we can prevent them
Often have a mathematical solution
Example: offset and scale factor errors

Is there any error we cannot completely handle?

Yes.

5 / 30

Random errorA.K.A: unsystematic error, system noise, random variation
Unpredictable and unreplicable
Thus, no mathematical solution

5 / 30

Random errorA.K.A: unsystematic error, system noise, random variation
Unpredictable and unreplicable
Thus, no mathematical solution

Handling random errorTake the average measurement value
Increase sample size

5 / 30

Overview

Variables: independent and dependent
Formulating a hypothesis
Types of study design
Assessing hypothesis in published papers

5 / 30

Hypothesis: definitionAssumptions about the population parameter
Stated as the null H0H0 and alternative HaHa hypothesis
Requires a formal procedure to reject H0H0

6 / 30

Hypothesis: definition

Assumptions about the population parameter
Stated as the null $H_{0}$ and alternative $H_{a}$ hypothesis
Requires a formal procedure to reject $H_{0}$

Null hypothesis

Observed results happened purely from chance

6 / 30

Hypothesis: definition

Assumptions about the population parameter
Stated as the null $H_{0}$ and alternative $H_{a}$ hypothesis
Requires a formal procedure to reject $H_{0}$

Null hypothesis

Observed results happened purely from chance

Alternative hypothesis

Observed results happened due to some non-random causes

6 / 30

Hypothesis: example

Remember when we flipped the coin last times?

set.seed(1)
coin <- sample(c("H", "T"), 10, replace=TRUE, prob=rep(1/2, 2)) %T>% print()

##  [1] "T" "T" "H" "H" "T" "H" "H" "H" "H" "T"

7 / 30

Hypothesis: example

Remember when we flipped the coin last times?

set.seed(1)
coin <- sample(c("H", "T"), 10, replace=TRUE, prob=rep(1/2, 2)) %T>% print()

##  [1] "T" "T" "H" "H" "T" "H" "H" "H" "H" "T"

Let's state a hypothesis on our coin flip!

$H_{0} :$ The probability of having the head is $P = 0.5$
$H_{a} :$ The probability of having the head is $P \neq 0.5$

7 / 30

Hypothesis: example

Remember when we flipped the coin last times?

set.seed(1)
coin <- sample(c("H", "T"), 10, replace=TRUE, prob=rep(1/2, 2)) %T>% print()

##  [1] "T" "T" "H" "H" "T" "H" "H" "H" "H" "T"

Let's state a hypothesis on our coin flip!

$H_{0} :$ The probability of having the head is $P = 0.5$
$H_{a} :$ The probability of having the head is $P \neq 0.5$

coineeing the proportion being 0.6, can we reject the $H_{0}$ ?

7 / 30

Hypothesis: example

Not quite! ;) We need a formal process to reject $H_{0}$

7 / 30

Hypothesis: example

Not quite! ;) We need a formal process to reject $H_{0}$

binom.test(x={sum(coin=="H")}, n=length(coin), p=0.5) %>%
    broom::tidy() %>% knitr::kable() %>% kable_minimal()

estimate	statistic	p.value	parameter	conf.low	conf.high	method	alternative
0.6	6	0.754	10	0.262	0.878	Exact binomial test	two.sided

7 / 30

Hypothesis: example

Not quite! ;) We need a formal process to reject $H_{0}$

binom.test(x={sum(coin=="H")}, n=length(coin), p=0.5) %>%
    broom::tidy() %>% knitr::kable() %>% kable_minimal()

estimate	statistic	p.value	parameter	conf.low	conf.high	method	alternative
0.6	6	0.754	10	0.262	0.878	Exact binomial test	two.sided

Seeing the p-value > 0.05, we can formally state the failure on rejecting $H_{0}$

7 / 30

Hypothesis: formal testDoes our data correspond to the H0H0?
Sample data are consistent with H0→H0→ do not reject H0H0
Sample data are inconsistent with H0→H0→ reject H0H0

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Hypothesis: formal testDoes our data correspond to the H0H0?
Sample data are consistent with H0→H0→ do not reject H0H0
Sample data are inconsistent with H0→H0→ reject H0H0

Type of testTwo-tailed: H0≠HaH0≠Ha
Right-tailed: H0>HaH0>Ha
Left-tailed: H0<HaH0<Ha

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Hypothesis: formal testDoes our data correspond to the H0H0?
Sample data are consistent with H0→H0→ do not reject H0H0
Sample data are inconsistent with H0→H0→ reject H0H0

Rejecting hypothesisRegion of acceptance with critical value (older)
P-value (newer)

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Hypothesis: interpretationWe start from the assumption that H0H0 is true
Collect evidence to show otherwise
We then reject or fail to reject the H0H0 based on p-value
When testing the hypothesis we may happen to see statistical errors

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Hypothesis: interpretationWe start from the assumption that H0H0 is true
Collect evidence to show otherwise
We then reject or fail to reject the H0H0 based on p-value
When testing the hypothesis we may happen to see statistical errors

Statistical errorType I: False Reject Rate α→α→ false positive
Type II: False Accept Rate β→β→ false negative

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Hypothesis: p-valueReflect the probability of making a type I error
Lower p-value →→ lower chance of H0H0 occurred by chance
Lower p-value →→ higher significance
Common cut-off: 0.05

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Overview

Variables: independent and dependent
Formulating a hypothesis
Types of study design
Assessing hypothesis in published papers

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Study designCross-sectional
Cohort
Case-control
Randomized controlled trial
Systematic review

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Cross-sectionalA snapshot of outcome and associated characteristics
No intervention, inferencing existing differences
Relatively inexpensive and quick to conduct
Static, reveal no temporal context
Unable to establish causality
Different time frame may lead to different result

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CohortLongitudinal study to see an effect overtime
Prospective / retrospective: observing the future or looking back in time
Starting from a potential cause
Involving at least two groups of interest
Cannot completely control the confounding variables
No randomization →→ lower external validity
Long completion period

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Case-controlLongitudinal study to see an effect overtime
Retrospective in nature
Starting from an outcome of interest
Involving at least two groups
Usually employed to investigate rare conditions
Assessing multiple risk factors
Difficult to find a suitable control group
Inadequate to establish a diagnostic study
Should carefully address confounding variables

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Randomized controlled trialRandomization to control bias →→ higher external validity
Akin to an experimental study, can effectively employ blinding methods
Statistically efficient
Clearly identified population
Expensive to conduct
Risk to have a volunteer bias
Loss to follow up →→ attrition bias

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Systematic reviewConcatenate findings from multiple studies
Critical appraisal removes redundancies and addresses inconsistencies
Delineate where knowledge is lacking to guide future research
Does not establish novelty
Variation among published articles is a challenge to overcome
Potential bias for including unreviewed articles

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Systematic reviewConcatenate findings from multiple studies
Critical appraisal removes redundancies and addresses inconsistencies
Delineate where knowledge is lacking to guide future research
Does not establish novelty
Variation among published articles is a challenge to overcome
Potential bias for including unreviewed articles

Meta-analysisTakes systematic review to another level :)
Analyzing previous analysis (thus the name: meta-analysis)

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Overview

Variables: independent and dependent
Formulating a hypothesis
Types of study design
Assessing hypothesis in published papers

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Source: 10.1371/journal.pone.0165816

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Reading scientific articlesLook for its underlying structure
AbstractI: Introduction
M: Methods
R: Results
D: Discussion

IntroductionS: Situation
P: Problem
Q: Question
R: Resolution


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By knowing the structure, you can extract information more efficiently
When reading the abstract, focus on introduction and methods first
Then shift into conclusions, since it contains the summary
Finally, you may want to read the results and discussion as well
Introduction usually elaborates the background and hypothesis
You can look for the study design in methods
Discussion part will help you understand current limitation and further suggestions

Abstract - Introduction

Current studies of depression among people living with HIV focus on describing its point prevalence. Given the fluctuating nature of depression and its profound impacts on clinical and quality-of-life outcomes, this study aimed to examine the prevalence, recurrence and incidence of current depressive symptoms and its underlying catalysts longitudinally and systematically among these individuals.

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Abstract - Methods

We conducted a prospective cohort study between October 1, 2007 and December 31, 2012 using longitudinal linked data sources. Current depressive symptoms was identified using the Centre for Epidemiologic Studies Depression Scale or the Kessler Psychological Distress Scale, first at baseline and again during follow-up interviews. Multivariable regressions were used to characterize the three outcomes.

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Abstract - Conclusion

Depressive symptoms are prevalent and likely to recur among people living with HIV. Our results support the direction of Ontario’s HIV/AIDS Strategy to 2026, which addresses medical concerns associated with HIV (such as depression) and the social drivers of health in order to enhance the overall well-being of people living with or at risk of HIV. Our findings reinforce the importance of providing effective mental health care and demonstrate the need for long-term support and routine management of depression, particularly for individuals at high risk.

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Abstract - Results

Of the 3,816 HIV-positive participants, the point prevalence of depressive symptoms was estimated at 28%. Of the 957 participants who were identified with depressive symptoms at baseline and who had at least two years of follow-up, 43% had a recurrent episode. The cumulative incidence among 1,745 previously depressive symptoms free participants (at or prior to baseline) was 14%. During the five-year follow-up, our multivariable models showed that participants with greater risk of recurrent cases were more likely to feel worried about their housing situation. Participants at risk of developing incident cases were also likely to be younger, gay or bisexual, and unable to afford housing-related expenses.

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Introduction - Situation

(par. 1)

Depression affects up to half of people living with HIV, a prevalence that is two to four times higher than that found in the general population [1]. Over 50% of people living with HIV and depression do not receive treatment for their depression [2–9], and this failure to treat contributes to significant negative clinical and quality-of-life outcomes [10–14].

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Introduction - Situation

(par. 2)

Growing evidence supports a bi-directional relationship between HIV and depression involving a number of biological, psychosocial and social factors [1,14–16]. The persistent viral presence in the central nervous system may release toxic viral proteins that induce depression-like symptoms [17,18]; people living with HIV may possess a negative self-image or experience stigma [1,15,19–21]; and people living with HIV are more likely to struggle with stressors such as financial insecurity and unstable housing [22–25]. Recent reviews also suggest that people who suffer from severe mental illnesses (including depression) and/or co-occurring substance use disorder are more likely to engage in risky sexual behaviour, thereby elevating their risk of HIV acquisition [26–34].

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Introduction - Problem

(par. 3)

To date, most studies about the prevalence of depression among people living with HIV have used cross-sectional designs [1,15]. Six studies have documented the incidence [35–38] and persistence (or recurrence) [39,40] of depression over time among people living with HIV. In Canada, information describing the epidemiology of depression among people living with HIV is scarce. In Canada, information describing the epidemiology of depression among people living with HIV is scarce. There have been two small convenience sample studies describing the prevalence of depression among people living with HIV. Williams et al. (2005), employing a small convenience sample of 297 individuals, described the prevalence of depressive symptoms at 54% among people living with HIV based on a self-report screening instrument [41]. Logie, James, Tharao, and Loutfy (2013), employing a sample of 173 Africa, Caribbean, and Black women, described the prevalence of depressive symptoms as 64% [42]. Thus, the epidemiology of this condition is not yet well documented in Canada.

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Introduction - Question

(par. 4)

Given the fluctuating nature of depression over the life span and its profound impacts on clinical and quality-of-life outcomes, our study aimed to examine the prevalence, recurrence, and incidence of current depressive symptoms longitudinally and systematically among people living with HIV. We also characterized these three outcomes by HIV-positive participants’ socio-demographic characteristics, housing and neighbourhood conditions, substance-use behaviours and health status over a five-year follow-up period. Understanding change in the burden of depressive symptoms and the underlying catalysts of the condition from a longitudinal perspective would be important to program planners, policy-makers, and health care providers when planning and implementing effective mental-health programs and interventions for people living with HIV.

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Introduction - Resolution

(par. 4)

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Extracted informationCase: people living with HIV
VariablesIndependent: depressive symptoms prevalence, recurrence, incidence
Dependent: younger, gay or bisexual, unable to afford expenses
Potential confounding: worrying their household situation

Study design: cohort prospective
HypothesisH0H0: Depressive symptoms are not likely to recur
HaHa: Depressive symptoms are likely to recur


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Query?

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Quick assignment

In completing this assignment, you will:

Read two articles we briefly discussed in the first lecture
Identify their underlying structures (abstract and introduction)
Succintly describe the case, variables and study design
Determine the hypotheses and formulate them as $H_{0}$ and $H_{a}$
Make a presentation on the abstract, introduction and extracted information

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Quick assignment

In completing this assignment, you will:

Read two articles we briefly discussed in the first lecture
Identify their underlying structures (abstract and introduction)
Succintly describe the case, variables and study design
Determine the hypotheses and formulate them as $H_{0}$ and $H_{a}$
Make a presentation on the abstract, introduction and extracted information

Articles:

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Overview

Variables: independent and dependent
Formulating a hypothesis
Types of study design
Assessing hypothesis in published papers

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Research in a nutshell

What are...?

What are...?

What are...?

What are...?

What are...?

What are...?

What are...?

Independent variable

Independent variable

Dependent variable

Grouping the cases

Grouping the cases

Within?

Grouping the cases

Within?

Between?

That's neat!

That's neat! But why?

That's neat! But why?

That's neat! But why?

Any catch?

Confounding variable

Confounding variable

Cognitive bias →→ partiality

Handling bias

Systematic error

Systematic error

Systematic error

Random error

Random error

Handling random error

Hypothesis: definition

Hypothesis: definition

Null hypothesis

Hypothesis: definition

Null hypothesis

Alternative hypothesis

Hypothesis: example

Hypothesis: example

Hypothesis: example

Hypothesis: example

Hypothesis: example

Hypothesis: example

Hypothesis: formal test

Hypothesis: formal test

Type of test

Hypothesis: formal test

Rejecting hypothesis

Hypothesis: interpretation

Hypothesis: interpretation

Statistical error

Hypothesis: p-value

Study design

Cross-sectional

Cohort

Case-control

Randomized controlled trial

Systematic review

Systematic review

Meta-analysis

Reading scientific articles

Abstract - Introduction

Abstract - Methods

Abstract - Conclusion

Abstract - Results

Introduction - Situation

Introduction - Situation

Introduction - Problem

Introduction - Question

Introduction - Resolution

Extracted information

Quick assignment

Quick assignment

Help

Cognitive bias $\to$ partiality