Longitudinal analysis of deciduous tooth emergence: II. Parametric survival analysis in Bangladeshi, Guatemalan, Japanese, and Javanese children

Abstract

We present a form of parametric survival analysis that incorporates exact, interval-censored, and right-censored times to deciduous tooth emergence. The method is an extension of common cross-sectional procedures such as logit and probit analysis, so that data arising from mixed longitudinal and cross-sectional studies can be properly combined. We extended the method to incorporate and estimate a proportion of agenic teeth. While we concentrate on deciduous tooth emergence, the method is relevant to studies of permanent tooth emergence and other developmental events. Deciduous tooth emergence data were analyzed from four longitudinal studies. The samples are 1,271 rural Guatemalan children examined every three months up to age two and every six months thereafter as part of the INCAP study; 397 rural Bangladeshi children examined monthly to age one and quarterly thereafter as part of the Meheran Growth and Development Study; 468 rural Indonesian children examined monthly as part of the Ngaglik study; and 114 urban Japanese children examined monthly in studies from 1910 and 1920. Although all four studies were longitudinal, many observations from the Guatemala and Bangladesh studies were effectively cross-sectionally observed. Three different parametric forms were used to model the eruption process: a normal distribution, a lognormal distribution, and a lognormal distribution with age shifted to shortly after conception. All three distributions produced reliable estimates of central tendencies, but the shifted lognormal distribution produced the best overall estimates of shape (variance) parameters. Estimates of emergence were compared to other studies that used similar methods. Japanese children showed relatively fast emergence times for all teeth. Bangladeshi and Javanese children showed emergence times that were slower than are found in most previous studies. Estimates of agenesis were not significantly different from zero for most teeth. One or two central incisors showed significant agenesis that ranged from 0.1 to 0.8% in three of the samples; even so, failure to model the agenic proportion did not seriously bias the estimates.

Longitudinal analysis of permanent tooth emergence in Japanese children

“…The distribution of tooth emergence was assumed to follow either a twoparameter normal or a log-normal distribution (Holman and Jones, 1998). The two-parameter log-normal probability density function (PDF) is given by .…”

“…Statistically, the presence of non-erupting teeth is a violation of underlying assumptions of standard survival-analytic methods. Holman and Jones (1998) statistically modeled an agenic fraction, under the assumption that all right-censored observations might potentially be agenic. For Kitamura's study of the permanent dentition, however, dental X-rays were taken for some children.…”

“…Kitamura's observations of tooth emergence can be classified as interval-censored or right-censored (see Holman and Jones, 1998, for a more detailed discussion of censoring in tooth emergence data). Briefly, interval-censored observations are those for which the child's age is known at some examination time prior to emergence and an examination time following emergence.…”

“…This would cover only the first half of the emergence of permanent teeth. Kitamura (1942a, b) and others (Yanagisono, 1960a, b;Ohta, 1966) published longitudinal studies of permanent tooth emergence in Japanese children, although both of these studies pre-date the advent of modern statistical methods to deal with the analytical difficulties such as right-censoring of the observations and agenesis that arise in longitudinal studies (Holman and Jones, 1998). Right-censoring occurs when a subject withdraws from the study prior to the emergence of a tooth, resulting in a missing observation of time to emergence.…”

“…Holman and Jones (1998) found a low prevalence of agenesis in deciduous teeth, and little bias by assuming that all teeth will eventually emerge. For the permanent teeth, however, controlling for agenesis is much more important, as many teeth exhibit significant levels of agenesis.…”