Abstract: Dichotomization of the outcome by a single cut-off point is an important part of various medical studies. Usually the relationship between the resulted dichotomized dependent variable and explanatory variables is analyzed with linear regression, probit regression or logistic regression. However, in many real-life situations, a certain cut-off point dividing the outcome into two groups is unknown and can be specified only approximately, i.e. surrounded by some (small) uncertainty. It means that in order to have any practical meaning the regression model must be robust to this uncertainty. In this paper, we show that neither the beta in the linear regression model, nor its significance level is robust to the small variations in the dichotomization cut-off point. As an alternative robust approach to the problem of uncertain medical categories, we propose to use the linear regression model with the fuzzy membership function as a dependent variable. This fuzzy membership function denotes to what degree the value of the underlying (continuous) outcome falls below or above the dichotomization cut-off point. In the paper, we demonstrate that the linear regression model of the fuzzy dependent variable can be insensitive against the uncertainty in the cut-off point location. In the paper we present the modeling results from the real study of low hemoglobin levels in infants. We systematically test the robustness of the binomial regression model and the linear regression model with the fuzzy dependent variable by changing the boundary for the category Anemia and show that the behavior of the latter model persists over a quite wide interval.
Abstract: Dengue fever has become a major concern for health
authorities all over the world particularly in the tropical countries.
These countries, in particular are experiencing the most worrying
outbreak of dengue fever (DF) and dengue haemorrhagic fever
(DHF). The DF and DHF epidemics, thus, have become the main
causes of hospital admissions and deaths in Malaysia. This paper,
therefore, attempts to examine the environmental factors that may
influence the recent dengue outbreak. The aim of this study is twofold,
firstly is to establish a statistical model to describe the
relationship between the number of dengue cases and a range of
explanatory variables and secondly, to identify the lag operator for
explanatory variables which affect the dengue incidence the most.
The explanatory variables involved include the level of cloud cover,
percentage of relative humidity, amount of rainfall, maximum
temperature, minimum temperature and wind speed. The Poisson and
Negative Binomial regression analyses were used in this study. The
results of the analyses on the 915 observations (daily data taken from
July 2006 to Dec 2008), reveal that the climatic factors comprising of
daily temperature and wind speed were found to significantly
influence the incidence of dengue fever after 2 and 3 weeks of their
occurrences. The effect of humidity, on the other hand, appears to be
significant only after 2 weeks.