One aspect of longitudinal data that is particularly valuable for the analysis of health insurance coverage is their ability to provide reliable measures of duration. As with other aspects of the use of longitudinal data, however, measuring spell duration requires a number of choices on the part of the analyst. These include defining the universe of spells to be included in the measure of duration, determining when a spell begins or ends, resolving how to handle the censoring of spells at either end, and electing how to treat multiple spells by the same individuals.
a. Choice of Universe of Spells
Over the lifetime of a panel survey there are spells of uninsurance that begin, spells that end, spells that begin and end, and spells that remain in progress without beginning or ending. The same can be said of any sub-period within the life of the panel--for example, a calendar year or fiscal year. Which spells the analyst chooses to include in a distribution of spell durations can have a profound effect on the average length and other features that are attributed to these spells. Essentially, it is difficult to restrict the universe of spells without selecting, indirectly, on their length.
Consider the following. A natural way to restrict the universe of spells is to limit the sample to spells that are active in a given month--that is, the spells of all children who are uninsured in that month. It turns out, however, that this restriction results in spells being represented in direct proportion to their completed duration. Spells of one-month duration are represented solely by spells that began in the selected month. Spells of two-months duration are represented solely by spells that began in either of two months: the selected month or the preceding month. Spells of three-months duration are represented by spells that began in any of three months, and so on. Thus spells of 12- months duration are represented by spells that began in any of 12 months while spells of 36-months duration are represented by spells that began in any of 36 months.(35)
As an alternative, consider the impact of restricting the universe to all spells that started in the same month. Selecting a subset of spells in this manner does not favor spells of any particular length except insofar as this particular month may differ from other months. The same can be said of a selection of spells that ended in the same month: no particular length is favored. This applies equally to spells that started or ended over a range of months--say, a particular year. Spells selected in any of these ways give an unbiased representation of all spells--again, barring any seasonal patterns or trends over time.
These observations on spell length do not imply that the distribution of durations among spells that were active in a given month or months does not provide useful information. It may be exactly the information that is required to address a specific policy question or research issue--for example, how many children would be eligible for CHIP coverage if there were a six month waiting period? But it is important to recognize that defining a subset of spells on the basis of when they were active as opposed to when they began or ended will yield a distribution with a longer average length than is true of the entire universe of spells. The shorter the period from which they are selected, the more prominent will be the bias. If the intent is to represent “all spells” in some sense, then spells should be sampled by their ending date or starting date rather than when they were active.
b. When Does a Spell Begin or End?
There are essentially two issues that an analyst must address in defining when spells of uninsurance begin or end. The first is whether spells are defined to end at the point that an individual leaves the population of children or whether they are followed past that point. A child turning 18 or 19, depending on the upper age limit of the child population, is no longer a child and therefore no longer an uninsured child, but the individual may still be uninsured. The analyst must determine what strategy for handling these situations is most consistent with the objectives of the analysis. The second issue is how to treat what appear to be brief interruptions of spells. For example, does a one- or two-month period of coverage constitute the end of a spell of uninsurance? Such interruptions may be nothing more than measurement error, but even if they are genuine there may be reasons to treat them as inconsequential and to regard the spell of uninsurance as continuing. In addition, when evaluating the accuracy of brief spells of coverage, it is important to take into consideration the survey design. SIPP, for example, utilizes a four-month reference period, and this creates the potential for erroneous reports to occur in groups of four months. In the SIPP an interruption that coincides exactly with a survey reference period should be viewed suspiciously. Ordinarily, evidence that the inconsistent information was provided by a proxy respondent would create a persuasive case for editing the reported spell of insurance to match the surrounding months.
Spells whose beginning or end lie outside the period of observation covered by the survey are described as “censored.” Spells whose starting point is observed but whose ending point is not observed are defined as “right-censored,” while spells whose ending points are observed but whose beginnings are not are defined as “left-censored.” Censored spells outnumber uncensored spells near the beginning and end of a panel, of course. For types of spells that commonly run to lengths of a year or more, even a two-year panel may yield few completed spells.
Observing spells from beginning to end is important for measuring the full distribution of spell duration, although there are analytic techniques for estimating distributions of duration for censored spells. Data on complete spells are even more important to understanding the dynamics of how children enter and leave uninsurance. Without seeing both ends of a spell, we cannot infer how the circumstances that precede uninsurance may compare with those that follow. For example, we learn from examining the beginnings and endings of spells that a disproportionate number of children enter uninsurance from Medicaid and leave uninsurance to enroll in Medicaid. But without seeing both ends of spells we cannot determine to what extent it is the same children leaving and re-entering Medicaid who account for the rates that we see or to what extent these exits and entries are independent.
While there are certain research questions that require observing both the beginnings and endings of spells to answer, there are other questions for which partial information may be sufficient. For example, how long do spells last? We can discern a lot about the distribution of spell lengths and the characteristics of children who experience spells of different lengths by following spells from their beginning through the end of 12 months. With a panel database covering 24 months we can identify all the spells that started in a 12-month period and follow them for at least 12 months. With this information we can discern what proportion of new spells last for 12 months or more and determine what differentiates the children who experience 12-month spells from those who experience very brief spells.
d. Multiple Spells
While some of what appear to be multiple spells are nothing more than long spells with erroneous reports of intermittent coverage, multiple spells remain a phenomenon of some interest. Analysis of SIPP data suggests that as many as one-third of new spells of uninsurance among children represent the second or third such spells within a year (Czajka 1999). The frequency of multiple spells makes it essential when counting spells to distinguish between spells and the children who experience them. Between October 1992 and September 1994 we found that children started 19 million new spells of uninsurance. But these 19 million new spells represented 12 million rather than 19 million children. Both numbers are staggering in terms of the needs that they reflect. But understanding how they are different is important to understanding how we can best address the social problem that these numbers present.