Change point testing in logistic regression models with interaction term

Abstract

A threshold effect takes place in situations where the relationship between an outcome variable and a predictor variable changes as the predictor value crosses a certain threshold/change point. Threshold effects are often plausible in a complex biological system, especially in defining immune responses that are protective against infections such as HIV-1, which motivates the current work. We study two hypothesis testing problems in change point models. We first compare three different approaches to obtaining a p-value for the maximum of scores test in a logistic regression model with change point variable as a main effect. Next, we study the testing problem in a logistic regression model with the change point variable both as a main effect and as part of an interaction term. We propose a test based on the maximum of likelihood ratios test statistic and obtain its reference distribution through a Monte Carlo method. We also propose a maximum of weighted scores test that can be more powerful than the maximum of likelihood ratios test when we know the direction of the interaction effect. In simulation studies, we show that the proposed tests have correct type I error and higher power than several existing methods. We illustrate the application of change point model-based testing methods in a recent study of immune responses that are associated with the risk of mother to child transmission (MTCT) of HIV-1.

Maternal HIV-1 envelope–specific antibody responses and reduced risk of perinatal transmission

“…Table 1 and Figure 1, A-D). A single-predictor, change point logistic model (15) indicated that a threshold at the tenth percentile of the IgG V3 binding score was associated with transmission (P = 0.04). The transmission rate of mothers with IgG V3 binding responses below this threshold was 56% (14 of 25) compared with 31% (69 of 223) for mothers with responses above the threshold.…”

“…Combined immune variable scores (such as IgG V3 binding score) were defined as a weighted combination of immune response variables against related antigens or viruses. Change-point models explored the threshold of identified immune correlates and transmission status (15). In secondary analyses, individual humoral immune responses were analyzed by logistic regression.…”

Gender Differences in Psychosocial Factors Associated with HIV Viral Suppression Among African–American Injection Drug Users

“…Religious activity was assessed by, “How often do you go to religious services?” Responses were on a 6-point Likert scale, from “Never” to “More than once a week”. Categories trichotomized at the tertiles, such that 0 = low attendance, 1 = moderate attendance, 2 = frequent attendance [56]. Health-related support refers to support that Indexes have which assists them in engagement in health-related behaviors.…”

“…Physical functioning was assessed by a nine-item scale based on the Medical Outcomes Study Physical Functioning Measure [58]. These items included “How much does your health affect your ability to bend, lift, or squat down?”, and “How much does your health affect your ability to eat, dress, or bathe?” Responses were trichotomized at the tertiles, where 0 = low physical functioning, 1 = moderate physical functioning, and 2 = high physical functioning [56]. Educational attainment was assessed by a single item, “What is the highest level of education you've had?” Responses were collapsed into categories, where 0 = 8th grade or less, 1 = some high school, 2 = high school diploma or GED, and 3 = some college or above.…”

Basis and Statistical Design of the Passive HIV-1 Antibody Mediated Prevention (AMP) Test-of-Concept Efficacy Trials

“…In our illustration we take “0” and “2” to be a VRC01 serum concentration ≤ 10 mcg/mL and > 50 mcg/mL, respectively, and “1” an intermediate concentration. The actual data analysis would vary the thresholds used in dichotomous and trichotomous markers and explore how the PE curve depends on the different thresholds (Fong, Di, and Permar 2015). …”