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<h1 class="title toc-ignore">Regression for Depression</h1>
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<pre class="r"><code>regression_df =
read_csv("data/nhis_data01.csv") %>%
janitor::clean_names() %>%
filter(year == 2020) %>%
select(worrx, deprx, age, sex, poverty, marst, cvddiag) %>%
mutate(
sex = recode_factor(sex,
"1" = "_Male",
"2" = "_Female"),
marital_status = recode_factor(marst,
"10" = "_Married", "11" = "_Married","12" = "_Married","13" = "_Married",
"20" = "_Widowed","30" = "_Divorced","40" = "_Separated",
"50" = "_Never married"),
poverty = recode_factor(poverty,
"11" = "_Less than 1.0", "12" = "_Less than 1.0",
"13" = "_Less than 1.0", "14" = "_Less than 1.0",
"21" = "_1.0-2.0", "22" = "_1.0-2.0",
"23" = "_1.0-2.0", "24" = "_1.0-2.0",
"25" = "_1.0-2.0",
"31" = "_2.0 and above","32" = "_2.0 and above",
"33" = "_2.0 and above","34" = "_2.0 and above",
"35" = "_2.0 and above","36" = "_2.0 and above",
"37" = "_2.0 and above","38" = "_2.0 and above"),
age = ifelse(age>=85, NA, age),
worrx = ifelse(worrx>=3, NA, worrx),
deprx = ifelse(deprx>=3, NA, deprx),
worrx = recode_factor(worrx,
'1' = 0,
'2' = 1),
deprx = recode_factor(deprx, '1' = 0, '2' = 1),
cvddiag = recode_factor(cvddiag,
"1" = "_Never had COVID-19",
"2" = "_Had COVID-19")
) %>%
drop_na(age, worrx, deprx, sex, poverty, marital_status, cvddiag)</code></pre>
<pre class="r"><code>mosi_regression_df =
read_csv("data/nhis_data01.csv") %>%
janitor::clean_names() %>%
filter(year == 2020) %>%
select(worrx, deprx, age, sex, poverty, marst, cvddiag) %>%
mutate(
sex = recode_factor(sex,
"1" = "Male",
"2" = "Female"),
marital_status = recode_factor(marst,
"10" = "Married", "11" = "Married","12" = "Married","13" = "Married",
"20" = "Widowed","30" = "Divorced","40" = "Separated",
"50" = "Never married"),
poverty = recode_factor(poverty,
"11" = "Less than 1.0", "12" = "Less than 1.0",
"13" = "Less than 1.0", "14" = "Less than 1.0",
"21" = "1.0-2.0", "22" = "1.0-2.0",
"23" = "1.0-2.0", "24" = "1.0-2.0",
"25" = "1.0-2.0",
"31" = "2.0 and above","32" = "2.0 and above",
"33" = "2.0 and above","34" = "2.0 and above",
"35" = "2.0 and above","36" = "2.0 and above",
"37" = "2.0 and above","38" = "2.0 and above"),
age = ifelse(age>=85, NA, age),
worrx = ifelse(worrx>=3, NA, worrx),
deprx = ifelse(deprx>=3, NA, deprx),
worrx = recode_factor(worrx,
'1' = 'No',
'2' = 'Yes'),
deprx = recode_factor(deprx, '1' = 'No', '2' = 'Yes'),
cvddiag = recode_factor(cvddiag,
"1" = "Never had COVID-19",
"2" = "Had COVID-19")
) %>%
drop_na(age, worrx, deprx, sex, poverty, marital_status, cvddiag)</code></pre>
<p>Whether taken medication for depression is associated with COVID-19
adjusting for age, sex, family income level and current marital
status.</p>
<div id="mosaic-plot" class="section level2">
<h2>Mosaic Plot</h2>
<p>The Mosaic Plot included four categorical variables and it was used
to visualize the proportional relationship between these variables and
the outcome (whether or not taken medication for depression) in the
population.</p>
<p>Based on the plot, we can observe that compared to the other three
variables (sex, family income level, and current marital status), there
was no obvious difference in the proportion of people who took
medication for depression when comparing those who had COVID-19 with
those who never had COVID-19. That is, having had COVID-19 or not had no
significant effect on whether or not taking medication for depression in
the population.</p>
<p>In truth, when comparing male with female, we can observe the largest
difference in the proportion of people who took medication for
depression. It means that among those four variables, the variable sex
has the largest difference in the proportion of people who took
medication for depression.</p>
<pre class="r"><code>sex_deprx =
mosi_regression_df %>%
ggplot() +
geom_mosaic(
aes(
x = product(deprx, sex),
fill = deprx
),
offset = 0.01,
show.legend = FALSE
)+
labs(
x="",
y=""
)+
theme(
axis.text.y = element_blank(),
axis.ticks.y=element_blank(),
axis.text.x = element_text(angle = 90, hjust = 1)
)
poverty_deprx =
mosi_regression_df %>%
ggplot() +
geom_mosaic(
aes(
x = product(deprx, poverty),
fill = deprx
),
offset = 0.01
)+
labs(
x="",
y="",
fill = "Whether taken medicine for depression")+
theme(
axis.text.y = element_blank(),
axis.ticks.y=element_blank(),
axis.text.x = element_text(angle = 90, hjust = 1)
)
marital_status_deprx =
mosi_regression_df %>%
ggplot() +
geom_mosaic(
aes(
x = product(deprx, marital_status),
fill = deprx
),
offset = 0.01,
show.legend = FALSE
)+
labs(
x="",
y=""
)+
theme(
axis.text.y = element_blank(),
axis.ticks.y=element_blank(),
axis.text.x = element_text(angle = 90, hjust = 1)
)
cvddiag_deprx =
mosi_regression_df %>%
ggplot() +
geom_mosaic(
aes(
x = product(deprx, cvddiag),
fill = deprx
),
offset = 0.01,
show.legend = FALSE
)+
labs(
x="",
y=""
)+
theme(
axis.text.y = element_blank(),
axis.ticks.y=element_blank(),
axis.text.x = element_text(angle = 90, hjust = 1),
)
sex_deprx = ggplotly(sex_deprx)
poverty_deprx =
ggplotly(poverty_deprx) %>%
layout(legend = list(orientation = "h"))
marital_status_deprx = ggplotly(marital_status_deprx)
cvddiag_deprx = ggplotly(cvddiag_deprx)
subplot(
style(sex_deprx, showlegend = F),
style(cvddiag_deprx, showlegend = F),
style(marital_status_deprx, showlegend = F),
poverty_deprx, nrows=1) %>%
layout(legend = list(x = 0, y = -0.4))</code></pre>
<div id="htmlwidget-5f89a4575a38c0a68f93" style="width:90%;height:576px;" class="plotly html-widget"></div>
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</div>
<div id="diagnostics" class="section level2">
<h2>Diagnostics</h2>
<p>We seek to validate our models and assess its goodness of fit. In our
motivating example, we have two models: (1) Crude model and (2) Adjusted
model.</p>
<ul>
<li>The crude model only has the outcome (Whether taking medication for
depression = Yes/No) and the predictor of interest (COVID-19
Status).</li>
<li>The adjusted model has the outcome and predictor of interest along
with other with four covariates (Sex, Age, Poverty(family income
level),and Current Marital Status).</li>
</ul>
<p>We can assess which of these two models fit the data better using the
likelihood ratio test.</p>
<pre class="r"><code>depre_crude_model =
glm(deprx ~ cvddiag,
family=binomial(link='logit'),
data = regression_df)</code></pre>
<pre class="r"><code>depre_adjusted_model =
glm(deprx ~ sex + poverty + age + marital_status + cvddiag,
family=binomial(link='logit'),
data = regression_df)</code></pre>
<pre class="r"><code>lrtest(depre_crude_model, depre_adjusted_model) %>%
kbl(caption = "Likelihood ratio test for crude model and adjusted model", col.names = c("Total df for each model", "LogLik", "difference in df", "Chisq-statistic", "p-value")) %>%
kable_paper("striped", full_width = F) %>%
column_spec(1, bold = T)</code></pre>
<table class=" lightable-paper lightable-striped" style="font-family: "Arial Narrow", arial, helvetica, sans-serif; width: auto !important; margin-left: auto; margin-right: auto;">
<caption>
Likelihood ratio test for crude model and adjusted model
</caption>
<thead>
<tr>
<th style="text-align:right;">
Total df for each model
</th>
<th style="text-align:right;">
LogLik
</th>
<th style="text-align:right;">
difference in df
</th>
<th style="text-align:right;">
Chisq-statistic
</th>
<th style="text-align:right;">
p-value
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:right;font-weight: bold;">
2
</td>
<td style="text-align:right;">
-6028.718
</td>
<td style="text-align:right;">
NA
</td>
<td style="text-align:right;">
NA
</td>
<td style="text-align:right;">
NA
</td>
</tr>
<tr>
<td style="text-align:right;font-weight: bold;">
10
</td>
<td style="text-align:right;">
-5790.814
</td>
<td style="text-align:right;">
8
</td>
<td style="text-align:right;">
475.8081
</td>
<td style="text-align:right;">
0
</td>
</tr>
</tbody>
</table>
<ul>
<li>Goodness of Fit</li>
<li>Likelihood ratio test The resulting p-value is so small it’s very
close to 0, so we can reject the null hypothesis. The p<0.00001
suggesting that the adjusted model with five covariates (Sex, Age,
Poverty(family income level), Current Marital Status and COVID-19
Status) fits the data significantly better than the crude model.</li>
</ul>
</div>
<div id="results" class="section level2">
<h2>Results</h2>
<p>Since four of these main effects were categorical variables, so we
need to create dummy variables that indicate which levels of the
predictors a given individual belonged. The outcome for this logistic
regression is binary (Whether taking medication for depression =
Yes/No).</p>
<ul>
<li>The variable <code>Sex</code> has one dummy variable and
<code>Sex_Male</code> is the reference group.</li>
<li>The variable <code>poverty</code> has two dummy variables and
<code>poverty_less than 1.0</code> is the reference group.</li>
<li>The variable <code>marital_status</code> has four dummy variables
and <code>marital_status_Married</code> is the reference group.</li>
<li>The variable <code>cvddiag(COVID-19 status)</code>has one dummy
variable and <code>cvddiag_Had COVID-19</code> is the reference
group.</li>
</ul>
<pre class="r"><code>depre_adjusted_model %>%
broom::tidy() %>%
mutate(OR = exp(estimate),
Lower_CI = exp(estimate -1.96*std.error),
Upper_CI = exp(estimate +1.96*std.error)) %>%
select(term, OR, Lower_CI, Upper_CI, statistic, p.value) %>%
kbl(caption = "Effect of Selected Predictors on whether taking medication for depression"
, col.names = c("Predictors", "OR", "Lower bound of 95% CI","Upper bound of 95% CI", "t-statistic", "p-value"),
digits= 2) %>%
kable_paper("striped", full_width = F) %>%
column_spec(1, bold = T)</code></pre>
<table class=" lightable-paper lightable-striped" style="font-family: "Arial Narrow", arial, helvetica, sans-serif; width: auto !important; margin-left: auto; margin-right: auto;">
<caption>
Effect of Selected Predictors on whether taking medication for
depression
</caption>
<thead>
<tr>
<th style="text-align:left;">
Predictors
</th>
<th style="text-align:right;">
OR
</th>
<th style="text-align:right;">
Lower bound of 95% CI
</th>
<th style="text-align:right;">
Upper bound of 95% CI
</th>
<th style="text-align:right;">
t-statistic
</th>
<th style="text-align:right;">
p-value
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;font-weight: bold;">
(Intercept)
</td>
<td style="text-align:right;">
0.07
</td>
<td style="text-align:right;">
0.06
</td>
<td style="text-align:right;">
0.10
</td>
<td style="text-align:right;">
-20.43
</td>
<td style="text-align:right;">
0.00
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
sex_Female
</td>
<td style="text-align:right;">
2.49
</td>
<td style="text-align:right;">
2.24
</td>
<td style="text-align:right;">
2.76
</td>
<td style="text-align:right;">
16.86
</td>
<td style="text-align:right;">
0.00
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
poverty_1.0-2.0
</td>
<td style="text-align:right;">
0.76
</td>
<td style="text-align:right;">
0.64
</td>
<td style="text-align:right;">
0.90
</td>
<td style="text-align:right;">
-3.13
</td>
<td style="text-align:right;">
0.00
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
poverty_2.0 and above
</td>
<td style="text-align:right;">
0.59
</td>
<td style="text-align:right;">
0.51
</td>
<td style="text-align:right;">
0.69
</td>
<td style="text-align:right;">
-6.91
</td>
<td style="text-align:right;">
0.00
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
age
</td>
<td style="text-align:right;">
1.01
</td>
<td style="text-align:right;">
1.00
</td>
<td style="text-align:right;">
1.01
</td>
<td style="text-align:right;">
3.79
</td>
<td style="text-align:right;">
0.00
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
marital_status_Widowed
</td>
<td style="text-align:right;">
1.13
</td>
<td style="text-align:right;">
0.95
</td>
<td style="text-align:right;">
1.35
</td>
<td style="text-align:right;">
1.41
</td>
<td style="text-align:right;">
0.16
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
marital_status_Divorced
</td>
<td style="text-align:right;">
1.45
</td>
<td style="text-align:right;">
1.28
</td>
<td style="text-align:right;">
1.66
</td>
<td style="text-align:right;">
5.64
</td>
<td style="text-align:right;">
0.00
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
marital_status_Separated
</td>
<td style="text-align:right;">
1.31
</td>
<td style="text-align:right;">
0.92
</td>
<td style="text-align:right;">
1.87
</td>
<td style="text-align:right;">
1.47
</td>
<td style="text-align:right;">
0.14
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
marital_status_Never married
</td>
<td style="text-align:right;">
1.19
</td>
<td style="text-align:right;">
1.04
</td>
<td style="text-align:right;">
1.36
</td>
<td style="text-align:right;">
2.54
</td>
<td style="text-align:right;">
0.01
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
cvddiag_Had COVID-19
</td>
<td style="text-align:right;">
1.13
</td>
<td style="text-align:right;">
0.89
</td>
<td style="text-align:right;">
1.45
</td>
<td style="text-align:right;">
1.02
</td>
<td style="text-align:right;">
0.31
</td>
</tr>
</tbody>
</table>