PAPP104 - S09: Parity progression and birth intervals

Period parity progression ratios (cont.)

Details of the calculations

Duration since 2nd birth ( t – t + x )	Number of 3rd births in 2000-04	Woman months of exposure to risk	Duration-specific fertility rate 6ft	Probability of progressing 6qt	Survivorship at start of segment lt2	Period parity progression ratio a'2(t)
0-8	0	15713	0.00000	0.0000	1	0.000
9-11	34.7	15238	0.00228	0.0136	1	0.000
12-17	127.4	14391	0.00885	0.0517	0.9864	0.014
18-23	187.2	13447	0.01392	0.0802	0.9354	0.065
24-29	226.1	11692	0.01934	0.1097	0.8604	0.140
30-35	186.3	10227	0.01822	0.1036	0.7660	0.234
36-41	166.2	8961	0.01855	0.1054	0.6866	0.313
42-47	156.5	7677	0.02039	0.1153	0.6143	0.386
48-53	106.5	6532	0.01630	0.0933	0.5435	0.457
54-59	98.9	5786	0.01709	0.0976	0.4928	0.507
60-65	94.1	4961	0.01897	0.1077	0.4447	0.555
66-71	69.2	4475	0.01546	0.0887	0.3968	0.603
72-77	56.0	3939	0.01422	0.0818	0.3616	0.638
78-83	44.9	3555	0.01263	0.0730	0.3320	0.668
84-89	44.6	3250	0.01372	0.0791	0.3078	0.692
90-95	29.3	2942	0.00996	0.0580	0.2835	0.717
96+					0.2670	0.733

The calculations are illustrated once again by measuring progression to the third birth using data from the 2011 Bangladesh Demographic and Health Survey. The counts of births in 2000–04 and of months exposed to the risk of having a 3^rd birth by interval duration are provided in the second and third columns of the table.

The duration-specific fertility rate in each interval t to t + x is calculated simply by dividing the births by the months spent exposed to risk. For example, at 24–29 months:

$${}_{6}f_{24}=\frac{226.1}{11692}=0.01934$$

(Note that, because these are monthly rates, not annual ones, they would have to be multiplied by 12 if one wished to compare them with conventional fertility rates).

Conversion of the rates to probabilities is done with the usual formula, substituting the order-specific fertility rates _xf_t for mortality rates, _xm_t:

$${}_{x}q_t=\frac{n{\cdot }_x{f}_t}{1+30.5\cdot x{\cdot }_x{f}_t}$$

Thus, at 24–29 months:

$${}_{6}q_{24}=\frac{6\times 0.01934}{1+3\times 0.01934}=0.1097$$

Once the _xq_t series has been calculated, l_t² and the period measures of a'_n(t) are calculated in exactly the same way as PPRs for real cohorts.