Joshua A. Goode – Timing Is Everything?

Some Quick Notes

Slides are available on my website.
Please stop me with questions.

I’m Just a Padawan

Some materials have been adapted from Dr. Andrew Smith, who is a true Jedi Master. I am grateful and humbled by the opportunity to learn from him.

Personal Website

bit.ly/jagoode

Outline

Introduction to SLCMA
Common SLCMA Hypotheses
Manual Example
The slcma Package
- Example 1: Complete Case Analysis with Binary Exposures
- Example 2: Imputed Data Analysis with Continuous Exposures and Covariates
Important Issues to Keep in Mind

Part 6 · Time Permitting

Additional Topics

Additional Hypotheses
Extending SLCMA to New Analyses
Choosing Recency Weights

Part 1 Introduction to SLCMA

Moving Beyond “Ever Exposed”

Where We Are

Narrow focus in much of the research
- Current exposure
- Ever exposed

We can do so much more
- Several large panel studies
- Many years of data
- A plethora of data types
- Really interesting questions/theory

Enter life course hypotheses
- Often tested, but rarely in a careful, structured way

What We Need

A careful, structured way to test life course hypotheses
- Compares competing hypotheses head to head
- Guards against false-positive results
- Scales to many exposures or outcomes
- Easy to use

SLCMA can help!

What Is SLCMA?

Structured

Life

Course

Modeling

Approach

Which life course hypothesis best fits our data?

What Goes Into SLCMA?

SLCMA Steps

Fit a regression model for each single life course hypothesis of interest, as well as groups of compound hypotheses

Measure the goodness-of-fit of each model and select the best one

Calculate appropriate p-values for the selected model

Part 2 Common SLCMA Hypotheses

SLCMA Hypotheses

Big 3

Sensitive Periods
Accumulation
Recency

Others

Mobility
Change
Always Exposed
Ever Exposed

Sensitive Periods \(\left(\mathit{SP} \text{ at } t_j\right)\)

Idea: The developmental timing of an exposure has the strongest effect on the outcome at a specific time point due to heightened levels of plasticity or reprogramming
Construct: Just the exposure variable at each age
Exposure type: Binary or continuous

\[\mathit{SP}_j = x_j\]

Sensitive Periods \(\left(\mathit{SP} \text{ at } t_j\right)\)

Multiple time points can also be grouped into more meaningful sensitive periods.

Accumulation \(\left(\mathit{Acc}\right)\)

Idea: Every additional time point of exposure affects the outcome in a dose-response manner, independent of the exposure timing
Construct: Add up the exposure variable across time points
Exposure type: Binary or continuous

\[\mathit{Acc} = \sum_{j=1}^m{x_j}\]

Accumulation \(\left(\mathit{Acc}\right)\)

Example

ID	Exp₁	Exp₂	Exp₃	Acc
1	0	0	0	\(0 + 0 + 0 = 0\)
2	1	1	1	\(1 + 1 + 1 = 3\)
3	0	1	0	\(0 + 1 + 0 = 1\)
4	1	0	0	\(1 + 0 + 0 = 1\)
5	1	0	1	\(1 + 0 + 1 = 2\)

Recency \(\left(\mathit{Rec}\right)\)

Idea: More proximal exposures (closer in time to the measurement of the outcome) are more strongly linked to the outcome than are more distal exposures
Construct: Add up the products of each exposure variable multiplied by its age of observation
Exposure type: Binary or continuous

\[\mathit{Rec} = \sum_{j=1}^m{\left(x_jt_j\right)}\]

Recency \(\left(\mathit{Rec}\right)\)

Example

ID	Exp₁	Exp₂	Exp₃	Rec
1	0	0	0	\((0 \times 1) + (0 \times 2) + (0 \times 3) = 0\)
2	1	1	1	\((1 \times 1) + (1 \times 2) + (1 \times 3) = 6\)
3	0	1	0	\((0 \times 1) + (1 \times 2) + (0 \times 3) = 2\)
4	1	0	0	\((1 \times 1) + (0 \times 2) + (0 \times 3) = 1\)
5	1	0	1	\((1 \times 1) + (0 \times 2) + (1 \times 3) = 4\)

Part 3 Manual Example

Manual Example Simulate Example Data

# set seed
set.seed(1234)

# simulate exposure & outcome data
n <- c(141, 20, 88, 80, 40, 35, 317, 367)
y <- c(28.7, 27.5, 29.1, 27.8, 28.3, 27.1, 27.6, 26.0)
se <- c(0.5, 1.1, 0.7, 0.7, 0.8, 0.9, 0.3, 0.2)
sp04 <- rep(c(0, 1, 0, 0, 1, 1, 0, 1), times = n)
sp26 <- rep(c(0, 0, 1, 0, 1, 0, 1, 1), times = n)
sp43 <- rep(c(0, 0, 0, 1, 0, 1, 1, 1), times = n)
e <- lm(rnorm(sum(n)) ~ sp04 * sp26 * sp43)$residuals
y <- rep(y, n) + rep(se * sqrt(n), n) * e / sd(e)

# create data frame
dats_bin <- data.frame(cbind(y, sp04, sp26, sp43))

# clean up
rm(n, y, se, sp04, sp26, sp43, e)

Manual Example Step 1: Fit Models

Which single hypothesis best fits our data?

model_sp04 <- lm(y ~ sp04, data = dats_bin)
summary(model_sp04)


Call:
lm(formula = y ~ sp04, data = dats_bin)

Residuals:
     Min       1Q   Median       3Q      Max 
-21.6360  -3.3888  -0.1199   3.0812  20.1639 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  28.0842     0.2092 134.219  < 2e-16 ***
sp04         -1.7368     0.3211  -5.409  7.8e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.235 on 1086 degrees of freedom
Multiple R-squared:  0.02623,   Adjusted R-squared:  0.02534 
F-statistic: 29.26 on 1 and 1086 DF,  p-value: 7.8e-08

Manual Example Step 1: Fit Models

Which single hypothesis best fits our data?

model_sp26 <- lm(y ~ sp26, data = dats_bin)
summary(model_sp26)


Call:
lm(formula = y ~ sp26, data = dats_bin)

Residuals:
     Min       1Q   Median       3Q      Max 
-20.6257  -3.4331  -0.3213   3.2145  21.1742 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  28.1493     0.3181  88.494  < 2e-16 ***
sp26         -1.0754     0.3682  -2.921  0.00357 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.285 on 1086 degrees of freedom
Multiple R-squared:  0.007793,  Adjusted R-squared:  0.00688 
F-statistic:  8.53 on 1 and 1086 DF,  p-value: 0.003566

Manual Example Step 1: Fit Models

Which single hypothesis best fits our data?

model_sp43 <- lm(y ~ sp43, data = dats_bin)
summary(model_sp43)


Call:
lm(formula = y ~ sp43, data = dats_bin)

Residuals:
     Min       1Q   Median       3Q      Max 
-22.2352  -3.3593  -0.3219   3.1224  19.5647 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  28.6834     0.3085  92.987   <2e-16 ***
sp43         -1.8202     0.3600  -5.057    5e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.244 on 1086 degrees of freedom
Multiple R-squared:  0.023, Adjusted R-squared:  0.0221 
F-statistic: 25.57 on 1 and 1086 DF,  p-value: 5.004e-07

Manual Example Step 1: Fit Models

Which single hypothesis best fits our data?

dats_bin <- dats_bin |>
  dplyr::mutate(acc = sp04 + sp26 + sp43)
model_acc <- lm(y ~ acc, data = dats_bin)
summary(model_acc)


Call:
lm(formula = y ~ acc, data = dats_bin)

Residuals:
    Min      1Q  Median      3Q     Max 
-21.771  -3.318  -0.039   3.160  20.029 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  29.1837     0.3376  86.433  < 2e-16 ***
acc          -0.9642     0.1566  -6.158 1.04e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.215 on 1086 degrees of freedom
Multiple R-squared:  0.03373,   Adjusted R-squared:  0.03285 
F-statistic: 37.92 on 1 and 1086 DF,  p-value: 1.039e-09

Manual Example Step 1: Fit Models

Which single hypothesis best fits our data?

dats_bin <- dats_bin |>
  dplyr::mutate(rec = (sp04 * 4) + (sp26 * 26) + (sp43 * 43))
model_rec <- lm(y ~ rec, data = dats_bin)
summary(model_rec)


Call:
lm(formula = y ~ rec, data = dats_bin)

Residuals:
     Min       1Q   Median       3Q      Max 
-21.7415  -3.3916  -0.2966   3.1105  20.0584 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 29.011119   0.352959   82.19  < 2e-16 ***
rec         -0.031594   0.005983   -5.28 1.56e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.238 on 1086 degrees of freedom
Multiple R-squared:  0.02503,   Adjusted R-squared:  0.02413 
F-statistic: 27.88 on 1 and 1086 DF,  p-value: 1.557e-07