In this exercise, we showed that two different methods led to basically the same conclusions with respect to fertility stalls and to equivalent slopes and confidence intervals. This is reassuring, since cumulative period fertility can be considered as a synthetic cohort or as the sum of age-specific fertility rates. This finding also indicates that basic assumptions underlying both methods are likely to be fulfilled, namely the equivalence of period and cohort and the constant age pattern of fertility during the process of fertility changes. What the preferable method of testing is can be discussed endlessly. The logistic regression method tends to provide lower p-values, which suggests that it is more sensitive. However, the linear regression method might be more specific and seems to provide a higher p-value when the case is borderline, therefore ignoring false positives (as seen for Mozambique over the period 1995 to 2003). Therefore, it may be more realistic. In any case, both methods led to the same conclusions in most instances.

Data quality is usually not an issue in DHS. Completed family size (or TFR) values tend to be very consistent for the same cohorts (or periods) in the same country, and comparisons with more precise data from demographic surveillance systems did not reveal errors that could not be explained by random fluctuations due to sample size and to cluster sampling [25]. Minor errors often found in DHS, such as the dating of birth around five years before the survey, are unlikely to affect levels or trends over longer periods of time; they will simply increase the variations in yearly estimates (i.e., data errors) and therefore reduce the power of statistical tests.

Other authors have used Poisson regression, or negative-binomial regression, to do similar testing of slopes. There is no obvious comparative advantage to using Poisson or negative-binomial regressions when calculating yearly fertility rates, since most women will have only one delivery at most over a 12-month period (the case would be different when using five-year periods or longer). Therefore, a simple outcome of 0/1 as used in the logistic regression method seems to be more appropriate. We did some basic comparisons of Poisson regression versus logistic regression and found similar results in the case of Kenya displayed in Table 1. Further testing could be done to investigate whether Poisson or negative-binomial regressions have any comparative advantage in this type of situation.

Other options are available for further testing fertility trends. For instance, one could use an age pattern of fertility in each situation in order to make the testing more precise. However, this is likely to be difficult. A Coale-Trussell function could be tried, but is likely to miss premarital fertility, which accounts for 20% to 40% of total fertility in some southern African countries [26]. Simpler functions such as polynomials could be tried, but probably with little advantage when compared with the straightforward empirical pattern presented by dummy variables associated with each age group.

Sophisticated statistical models have been developed in the past 20 years for testing changing slopes of a response variable in a variety of situations. Some of these models, such as "switching regression" or "change point regression" could also be tried to estimate fertility trends from DHS [27–29].

Using retrospective data leads necessarily to some minor mortality biases, compared with full-scale vital registration or prospective data. However, these biases are likely to be small, since mortality between age 12 and 40 is usually very low. In Africa, the high prevalence of HIV/AIDS and high mortality among young women could lead to larger biases. This would lead to overestimating fertility levels in recent years, since the fertility of HIV-infected women tends to be lower than that of others. In theory, this could produce some apparent fertility stalls in retrospective surveys, but in our studies we did not find any obvious correlation with HIV prevalence nor with HIV mortality. This point could be further investigated when more data become available.

Fertility stalls appear uncommon in African countries. Of the 31 countries investigated in our earlier studies, only eight exhibited some kind of fertility stall, of which five were restricted to either urban areas (Ghana and Senegal) or to rural areas (Nigeria, Tanzania, Zambia), while the other three cases affected both urban and rural areas (Kenya, Madagascar, and Rwanda). Most of these stalls were of short duration (< 10 years) or had been occurring for less than 10 years before the last survey. These stalls of short duration do not compare with formal stalls such as that of Argentina, which lasted for about 30 years (over an entire generation) at a much lower level of TFR (about three children per women). Fertility stalls in Africa appear so far to be minor accidents in the course of the fertility transition. However, if they last longer, they could have serious consequences for long-term demographic dynamics, especially when they occur at relatively high levels of fertility. Furthermore, African countries are still in the middle of the fertility transition, and anything could happen in the future. A recent study in the Pacific Islands showed that new forms of fertility stalls or of fertility reversals could happen as a result of deliberate reproductive strategies of couples. Because couples might have an economic advantage to produce children who will be sent later in migration and who could remit money to the family, they may choose to have more children [30].

Some of the fertility stalls proposed by other authors appeared undocumented in our analysis. This is due to the differences in case definition and in statistical testing. Using only two successive surveys with wide confidence intervals and point estimates based on a period of three years before a survey could be misleading when compared with a detailed analysis of fertility trends using all data available based on longer periods of 10 years or more. The case is even more delicate when comparisons are made on smaller sample sizes or when stalls are studied at the regional level or according to socioeconomic characteristics.

More research could be conducted on the rationale for these well documented stalls. In an earlier study, we showed that country situations were highly diverse, and one could use a variety of factors to explain them without any consistent pattern [23].

More research could also be conducted on the provision of family planning services, both in terms of quantity and in quality. Some authors have suggested that reduced financing for family planning services could explain the fertility stalls [31]. This could be further analyzed, case by case, while separating urban and rural areas whenever this is feasible.