Advanced Research Methods Case 1 Corrector Therapy for infants with Malycosis & Case 2: Interpreting Study Results Using OLS Regression

Research case 1: Corrector therapy for infants with Malaria

Attentively read the case description:

Below is an altered version of a paper by researchers of a Dutch university. It was presented and discussed – using DAGs – during a conference. This discussion led to changes in the conclusions in the final paper. This exercise is based on the first version of the paper that was presented during the conference. For reasons of anonymity, the names of the condition and the remedy have been altered. Malcyclosis is not an existing condition, and the corrector is not an existing medical device. The actual analysis contained more variables, and the results were presented in more detail than in the description below.

Introduction

Mycosis is a cosmetic condition that affects 20% of infants in the first months of life. Parents of patients have a choice between two treatment options: a medical device called the corrector, which is applied for six months, or waiting for natural recovery. However, the use of the corrector is not undisputed. When infants grow older, most cases of Malaria improve without further treatment. At this moment, no randomised controlled trials (RCTs) have been performed to compare the effectiveness of corrector therapy compared to natural recovery.

To be able to engage, support and guide parents in decision-making, professionals need to understand the decision-making process in parents of infants with Malaria.

This study aims to assess which factors influence parental decision-making. It is hypothesised that parents of infants with more severe Malaria or who perceive the malaria as more severe, and who have high expectations of the effects of the corrector, are more likely to choose the corrector therapy.

Methods

Logistic regression was used to explore the association of the treatment decision (corrector or awaiting natural recovery) with several explanatory variables. The associations were calculated for each explanatory variable separately (unadjusted analysis) and for all variables together (which means that the estimate of the effect of the exposures was adjusted for other variables).

Explanatory Variables

• Severity of Malaria. At five months, objective measurement of Malaria was obtained by paediatric physical therapists. This measurement was expressed as a proportion of abnormality.
• Parental satisfaction with the infant’s appearance. Satisfaction with their infant’s appearance due to Malaria was rated.
• Expected treatment effect. For the expected treatment effect, parents were asked if they expected the corrective therapy would have more effect than natural recovery.

Results

The unadjusted and adjusted associations are presented in the table. A positive association means that a higher value of this variable was associated with a higher probability of choosing the correct treatment.

(Note: at this stage, you don't need to know exactly what logistic regression is. The previous sentences and the table below should provide sufficient information so you can understand what associations were found and what they mean.

If you do know that logistic regression means, you could replace the words ‘yes, positive’ with a coefficient greater than zero or an odds ratio greater than 1; the words ‘yes, negative’ with a coefficient smaller than zero or an odds ratio smaller than 1; the word ‘no’ by a coefficient close to zero or an odds ratio close to 1.)

Discussion

We (i.e., the researchers) found that parental decision-making for the management of Malaria is influenced by the expected additional treatment effect and parental satisfaction with their infant’s appearance. The actual severity of Malaria was also related to treatment decision, but only in univariate analyses. When combined in a multiple logistic regression analysis, the relationship of treatment decision and actual severity disappeared, while the association with parental satisfaction remained.

Hence, the subjective parental satisfaction score plays an important role in decision-making, in contrast to the actual severity.

Answers to be Prepared Before Work Group Session

• Does this study make a causal or purely associational claim? How can you tell?
• In general, what is the difference between an adjusted and an unadjusted analysis? In other words, how are they performed?
• Based on the description of the case and your own logical reasoning, draw the DAG that describes the parents’ decision process. Use the variables that are mentioned in the case: (in short) severity, parental satisfaction, expectations, and decision. (Forget the results in the table for now, imagine for a minute that the data have not been collected yet.) Identify all variables as exposure, outcome, confounder, intermediate variable, and/or collider.
• Compare the results of the adjusted and unadjusted analysis. Which results are different? 

For questions 5-8 below, consider that there are three exposures in this study (severity, parental satisfaction, and expected treatment effect).

• Which causal paths do you see in the DAG?
• Which paths remain open when the adjusted analysis is applied?
• What does the paper conclude on the causal effects of each exposure variable on the decision?
• Combining the DAG and the results table, do you agree with the conclusions?
• How would you analyse the data if you were interested in the effect of objective severity on treatment decisions? What adjustments would be necessary or harmful?
• Imagine that you are a policymaker in a publicly financed healthcare system and that you have to decide whether or not to include the corrector in the basic benefits package of the mandatory health insurance. What would be your decision and why?

Research case 2: Interpreting study results using OLS regression

Attentively read the case Description:

In 2001, a group of health scientists and health economists from several Californian institutions published a paper on willingness-to-pay (WTP). This is a concept from health economics that can be used to estimate the value of a good, often in the absence of a market where the value of a good can be determined through supply and demand.
The group wanted to find out what women from different ethnic backgrounds would be willing to pay for a mammography cancer screening. In practice, health insurance covered the costs for most people, which made the procedure free at the point of consumption. This also made it impossible for the researchers to observe what people would pay in reality. For this reason, they asked their respondents what they would be willing to pay for screening. These WTP data were then analysed in a linear regression model (ordinary least squares, OLS).

The study was published in a peer-reviewed scientific journal called Health Policy:

NOTE: The tables in the paper contain two editing mistakes, which may lead to confusion. In Table 1, first column, “Proportion of life in US: mean” should be “Proportion of life spent in US”. In Table 2, “Education: mean (S.D.) should be “Education (years)”.

Answers to be Prepared Before Work Group Session

• Most scientific papers in the field of health sciences explicitly state their research question or objective near the end of the Introduction section. Find this statement in the paper by Wagner et al. and write it down. Also read the final paragraphs of the Introduction and Conclusions sections. Would you say that Wagner et al. are looking for the causal effect of ethnicity on WTP, or merely for statistical associations?
• What was the dependent variable? How was this variable obtained from each respondent?
• Where can you find the explanatory variables that Wagner et al. used in their analysis? In this list, how are ethnicity and ‘state of change’ used in the regression?
• Write down the regression equation. Either use the coefficients from the table or represent them as β1, β2, etc.
• Calculate the expected WTP for screening of a woman with the following characteristics: white (non-hispanic), spent all of her life in the US, 50 years old in 1999, 15 years of education, household income $40,000 per year, no health insurance, no relatives with breast cancer, married, in full-time employment, has had screenings and is scheduled for a future screening. Use the regression equation.
• Draw a DAG that explains the causal effect of ethnicity on WTP. For simplicity, include only the following elements: ethnicity, WTP, income, education, and stage of change. Identify exposure, outcome, confounders, intermediate variables, and colliders.
• Given your DAG, which regression coefficients represent estimates of full causal effects and which represent partial causal effects?
  Note: for this question, we must consider all variables, except WTP, to be exposures. Otherwise, it makes no sense to ask whether their coefficients represent causal effects.
• If your DAG is correct, is the analysis of Wagner et al. consistent with the stated aim of their study?
• Calculate the 95%-confidence interval for the coefficient for income. Interpret the coefficient and the associated uncertainty. Does this coefficient represent a full or partial effect of income on WTP?
• How do you interpret the p-value for income?
• All in all, what do you think about the estimated effect of income on WTP?
• What is the estimated (mean) difference in WTP for screening between non-Hispanic white and Chinese-American women if everything else were equal? Can you read this directly from a table in the paper?
• And what is the estimated (mean) difference in WTP for screening between Filipino and Latino women?
• (Extra question, discuss only when sufficient time). Imagine that you are a policymaker or manager in healthcare and want to install a co-payment for mammography cancer screening. Would you install the same co-payment for all women, or would you install different co-payments for women, depending on their ethnic background (in other words: copayments that vary depending on their WTP)? Why?