Linear spline (piecewise) models in Stata

I wrote a tutorial on how to construct linear spline (also known as piecewise) models using Stata, which has been uploaded to my RPubs site.

Previously, I have developed tutorial on using the linear spline method for interrupted time series analsyis with Stata. However, I did not properly go over the mkspline commands.

In this tutorial, I review the mkspline command and the marginal option to generate coefficients that could be interpreted as the slope within each segment or the change in slope between segments, respectively.

View fullsize

Mediation analysis using R

It’s not uncommon to see covariates in a regression model that should not be there. For example, measurements that occur after the treatment assignment are included into a regression model as baseline covariates. Rather, one should consider a mediation analysis.

I wrote a tutorial on how to perform mediation analysis using R on my RPubs site (link).

I know that I make this mistake at times. This tutorial helped me to carefully consider which covariates to include in a regression model and which ones to consider for mediation analysis.

View fullsize

Survival Analysis - Immortal Time Bias with Stata

I wrote a tutorial on how to handle immortal time bias with survival analysis using Stata. In the tutorial, I used a time-varying predictor for the grouping variable and assigned the period before exposure to the control group. This was inspired by the paper Redelmeier and Singh wrote on “Surival in Academy Award-Winner Actors and Actresses.” There was a lot of debate about the rigor of their analyses, and Sylvestre and colleagues re-analyzed the data with immortal time bias in mind. This tutorial uses data from Sylvestre and colleagues to re-create their results.

The tutorial is on my RPubs page. Data used for the tutorial is located on my GitHub page.

To load the data, you can use the Stata import command

import delimited "https://raw.githubusercontent.com/mbounthavong/Survival-analysis-and-immortal-time-bias/main/Data/data1.csv"

View fullsize

MEPS tutorial on interrupted time series analysis in R

I wrote a short tutorial on how to perform an interrupted time series analysis in R. I had a challenging time working on this because I wasn’t familiar with all the nuances of the ITSA. More importantly, I wasn’t able to leverage my Stata skills to do this in R. I’m used to the Stata margins command, which is great for creating constrasts. R has its own version of the margins command, but it lacks some of Stata’s features such as the pwcompare, which I use a lot in Stata. However, I found a workaround with linear splines, and I have uploaded this to my RPubs site (link). I hope you find this useful. I also saved my R Markdown code on my GitHub site (link).

View fullsize

Interrupted time series analysis (ITSA) with Stata

Interrupted time series analysis (ITSA) is a study design used to study the effects of an intervention across time. An important feature of the ITSA is the time when the intevention occurs. The time before and after the intervention are of interest because we want to visualize if the trends are similar or different. Additionally, we want to visualize the change immediately after the intervention is implemenated. I call this period the index date.

In this article, I’ll review the single-group ITSA and multiple groups ITSA. Then I’ll review how to perform an ITSA in Stata.

You can view the complete tutorial on my RPubs site.

Two-part models in R - Application with cost data

I created a tutorial on how to use two-part models in R for cost data. I used the healthcare expenditures from the Medical Expenditure Panel Survey in 2017 as a motivating example. Normally, I use Stata when I construct two-part models. But I wanted to learn how I could do this in R. Fortunately, R has a package called twopartm that was developed by Duan and colleagues. You can find their document for the twopartm package here.

The tutorial I created is located on my GitHub page and RPubs page.

View fullsize

Survival analysis in R

I wrote a tutorial on survival analysis using R, which is located on my RPubs page. The R Markdown code is located on my GitHub site.

I provide an introduction to survivor and hazard functions, Kaplan-Meier curves, and Cox proportional hazards model.

View fullsize

Visualizing linear regression models using R - Part 2

I continue my previous blog post on visualizing linear regression models using R (link). Part 2 focuses on using visualization to assess whether the model’s residuals were associated with the predicted values and whether they are normally distributed.

The R Markdown code that I wrote to create this tutorial is located on my GitHub site (link).

You can find the tutorials on my RPubs site:

• Part 1 - Visualizing linear regression model using R (link)

• Part 2 - Visualizing linear regression model using R (link)

(NOTE: on 30 January 2022, I updated these tutorials and they can be found in my RPubs page here. The R Markdown code is saved on my GitHub page here.)

View fullsize

Reproduction number—COVID-19

BACKGROUND

As the COVID-19 pandemic, which began in December 2019, continues into its second year, public health measures have been put into place to mitigate its spread. At the time of writing this article, there have been over 4.5 million deaths and over 216 million cases due to COVID-19.[1] Surveillance of COVID-19 remains an important public health measure of understanding the spread and impact. Daily reports such as the John Hopkins COVID-19 dashboard provide end users with visual and statistical information about the surges in cases and deaths associated with COVID-19. However, one measure that is of great interest is the reproduction number or R0.

Reproduction number (R0) and effective reproduction number (Rt)

The reproduction number is the number of new cases that is directly caused by exposure to a single case.[2,3] Figure 1 provides a visual explanation of the basic reproduction number. However, the underlying assumption with R0 is that everyone in the population is susceptible to infection. With the introduction of vaccines, the R0 isn’t a good measure of the reproductive capabilities of COVID-19. Instead, the effective reproduction number (Rt) is used to provide a more realistic reproduction number based on the population being infected, recovered, or vaccinated. The Rt changes over time as the population susceptible to infection changes.

Figure 1. Basic reproduction number.

View fullsize

I wanted to create a figure that would highlight the changes associated with the Rt for each state in the United States. To do this, I downloaded the Rt data from the by Xihong Lin's Group in the Department of Biostatistics at the Harvard T.H. Chan School of Public Health. They have an amazing COVID-19 tracker dashboard that captures the changing patterns of Rt for each state. Then I created a Cleveland plot to show where the Rt was near the beginning of the pandemic and where it is currently (August 2021). (Note: I wrote a tutorial on creating Cleveland plots that you can review here.) Here is the final figure (because of the length of the figure, I cropped it to show the first 30 states or territories):

Figure 2. Effective reproduction number (Rt) for U.S. states and territories, April 17, 2020 (past) to August 14, 2021 (recent).

View fullsize

The blue dots denote the most recent effective reproduction number (14 August 2021) and the past dots denote the earliest effective reproduction number (17 April 2020).

It seems that some states have gotten worse in terms of increase effective reproduction number since the beginning of the pandemic. This could be due to lack of good data in the early phases of the pandemic. However, what is of concern is the high effective reproduction numbers in some states (Rt > 2), which indicates that the pandemic is still spreading at an alarming rate.

There were some missing data which are identified by a single dot (blue or red) or an empty field in the recent or past effective reproduction number. Rather than fill these in, I left them empty. There may be data in between the two time periods that I could have used, but I left those out.

One thing to mention is that this Cleveland plot only tells us one dimension of the effective reproduction number story (the difference between the most recent Rt and the earliest Rt). It doesn’t tell us much about how the effective reproduction number changes across time. For that, I direct your attention to the Lin’s Laboratory Group at Harvard, they have a great figure that shows the fluctuation of the effective reproduction number for the U.S. and its states/territories (see example):

View fullsize

Source: Lin’s Laboratory Group at Harvard (link). [last accessed on 30 August 2021].

CONCLUSIONS

The effective reproduction number provides us with some interesting patterns in spread of COVID-19 by states/territories. It seems to have worsened over time, but this could be due to poor data early in the pandemic. There are some issues with the us of effective reproduction number for policy decisions. Reporting delays can impact the estimates for the effective reproduction number. A technique called “nowcasting” is used to estimate the reproduction number.[3] But when I explored some of the work in this area, there appears to be a variety of methods for performing this technique. Despite this limitation, the effective reproduction number may be useful to evaluate public health policy decisions to reduce the spread of the COVID-19 pandemic.[4,5]

DATA SOURCE

I provided the link to the COVID-19 Spread Tracker from the Lin Lab at Harvard. You can also download a curated version of the data for this article from my Dropbox folder. The data are current as of 17 August 2021. If you’re interested in recreating this Cleveland plot, I recommend downloading the most recent data to see how much the effective reproduction number has changed.

REFERENCES

1. Worldometeres.info. COVID Live Update: 217,770,381 Cases and 4,521,936 Deaths from the Coronavirus - Worldometer. Accessed August 30, 2021. https://www.worldometers.info/coronavirus/

2. Lim J-S, Cho S-I, Ryu S, Pak S-I. Interpretation of the Basic and Effective Reproduction Number. J Prev Med Pub Health. 2020;53(6):405-408. doi:10.3961/jpmph.20.288

3. Adam D. A guide to R — the pandemic’s misunderstood metric. Nature. 2020;583(7816):346-348. doi:10.1038/d41586-020-02009-w

4. Inglesby TV. Public Health Measures and the Reproduction Number of SARS-CoV-2. JAMA. 2020;323(21):2186-2187. doi:10.1001/jama.2020.7878

5. Pan A, Liu L, Wang C, et al. Association of Public Health Interventions With the Epidemiology of the COVID-19 Outbreak in Wuhan, China. JAMA. 2020;323(19):1915-1923. doi:10.1001/jama.2020.6130

Formulating a good research question

On April 16, 2020, I gave a presentation to students from the International Society for Pharmacoeconomics and Outcomes Research (ISPOR) Student Chapter at the University of Washington’s Comparative Health Outcomes, Policy, & Economics (CHOICE) Institute. I reviewed some of the ways to think about a research topic, how to narrow the scope of the topic, and how to formulate a specific and testable research question. The presentation was meant to help students develop their own process for developing a good research question for their thesis.

I discussed the FINER criteria for formulating a research question

I also discussed the PICOT format of a research question.

The presentation is available on the CHOICE Institute’s blog: https://choiceblog.org/2020/04/27/best-practices-in-developing-research-questions/